## References

1. Kidd C, Hayden BY. The psychology and neuroscience of curiosity. Neuron. 2015;88:449–60.

2. Oudeyer PY, Kaplan F. What is intrinsic motivation? A typology of computational approaches. Front Neurorobot. 2007;1:6.

3. Olsen CM, Winder DG. Stimulus dynamics increase the self-administration of compound visual and auditory stimuli. Neurosci Lett. 2012;511:8–11.

## P32

### Using statistical sampling to balance error function contributions to optimization of conductance-based models

Timothy Rumbell¹, Julia Ramsey², Amy Reyes², Danel Draguljić², Patrick R. Hof³, Jennifer Luebke⁴, Christina M. Weaver²

¹Computational Biology Center, IBM Research, Thomas J. Watson Research Center, Yorktown Heights, NY 10598; ²Department of Mathematics, Franklin and Marshall College, Lancaster, PA 17604; ³Fishberg Department of Neuroscience and Friedman Brain Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029; ⁴Department of Anatomy and Neurobiology, Boston University School of Medicine, Boston, MA 02118

**Correspondence:** Christina M. Weaver - christina.weaver@fandm.edu

BMC Neuroscience 2016, 17(Suppl 1):P32

Recently we developed a three-stage optimization method for fitting conductance-based models to data [1]. The method makes novel use of Latin hypercube sampling (LHS), a statistical space-filling design, to determine appropriate weights automatically for various error functions that quantify the difference between empirical target and model output. The method uses differential evolution to fit parameters active in the subthreshold and suprathreshold regimes (below and above action potential threshold). We have applied the method to spatially extended models of layer 3 pyramidal neurons from the prefrontal cortex of adult rhesus monkeys, in which in vitro action potential firing rates are significantly higher in aged versus young animals [2]. Here we validate our optimization method by testing its ability to recover parameters used to generate synthetic target data. Results from the validation fit the voltage traces of the synthetic target data almost exactly (Fig. 22A–C), whether fitting a model with 4 ion channels (10 parameters), or 8 ion channels (23 parameters). The optimized parameter values are either identical to, or nearby, the original target values (Fig. 22D–F), except for a few parameters that were not well constrained by the simulated protocols. Further, our LHS-based scheme for weighting error functions is significantly more efficient at recovering target parameter values than by weighting all error functions equally, or by choosing weights manually. We are now using the method to fit models to data from several young, middle-aged, and

aged monkeys. Adding new conductances to the model, and allowing altered channel kinetics in the axon initial segment versus the soma, improves the quality of the model fits to data. We use published results from empirical studies of layer 3 neocortical pyramidal neurons to determine whether the optimized parameter sets are biologically plausible.

## References

1. Rumbell T, Draguljić D, Luebke J, Hof P, Weaver CM. Prediction of ion channel parameter differences between groups of young and aged pyramidal neurons using multi-stage compartmental model optimization. BMC Neurosci. 2015;16(Suppl. 1):P282.

2. Chang YM, Rosene DL, Killiany RJ, Mangiamele LA, Luebke JI. Increased action potential firing rates of layer 2/3 pyramidal cells in the prefrontal cortex are significantly related to cognitive performance in aged monkeys. Cereb Cortex. 2005;15(4):409–18.

## P33

### Exploration and implementation of a self-growing and self-organizing neuron network building algorithm

Hu He¹, Xu Yang², Hailin Ma¹, Zhiheng Xu¹, Yuzhe Wang¹

¹Institute of Microelectronics, Tsinghua University, Beijing, 100081, China;

²School of Software, Beijing Institute of Technology, Beijing, 100083, China

**Correspondence:** Xu Yang - yangxu@tsinghua.edu.cn

BMC Neuroscience 2016, 17(Suppl 1):P33

In this work, an algorithm to build self-growing and self-organizing neuron network according to external signals is presented, in attempt to build neuron network with high intelligence. This algorithm takes a bionic way to build complex neuron network. We begin with very simple external signals to provoke neurons.

In order to propagate the signals, neurons will seek to connect to each other, thus building neuron networks. Those generated networks will be verified and optimized, and be treated as seeds to build more complex networks. Then we repeat this process, use more complex external signals, and build more complex neuron networks. A parallel processing method is presented, to enhance the computation efficiency of the presented algorithm, and to help build large scale of neuron network with reasonable time. The result shows that, neuron network built by our algorithm can self-grow and self-organize as the complexity of the input external signals increase. And with the screening mechanism, neuron network that can identify different input external signals is built successfully (Fig. 23).

**Acknowledgements:** This work is supported by the Core Electronic Devices, High-End General Purpose Processor, and Fundamental System Software of China under Grant No. 2012ZX01034-001-002, the National Natural Science Foundation of China under Grant No. 61502032, Tsinghua National Laboratory for Information Science and Technology (TNList), and Samsung Tsinghua Joint Laboratory.

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>
P34

**Disrupted resting state brain network in obese subjects: a
data-driven graph theory analysis**

Kwangyeol Baek¹,², Laurel S. Morris¹, Prantik Kundu³, Valerie Voon¹

¹Department of Psychiatry, University of Cambridge, Cambridge, CB2 0QQ, United Kingdom; ²Department of Biomedical Engineering, Ulsan National Institute of Science and Technology, Ulsan, South Korea; ³Departments of Radiology and Psychiatry, Icahn School of Medicine at Mount Sinai, New York City, 10029, USA

**Correspondence:** Kwangyeol Baek - kb567@cam.ac.uk

BMC Neuroscience 2016, **17**(Suppl 1):P34

The efficient organization and communication of brain networks underlies cognitive processing, and disruption in resting state brain network has been implicated in various neuropsychiatric conditions including addiction disorder. However, few studies have focused on whole-brain networks in the maladaptive consumption of natural rewards in obesity and binge-eating disorder (BED). Here we use a novel multi-echo resting state functional MRI (rsfMRI) technique along with a data-driven graph theory approach to assess global and regional network characteristics in obesity and BED.

We collected multi-echo rsfMRI scans from 40 obese subjects (including 20 BED patients) and 40 healthy controls, and used multi-echo independent component analysis (ME-ICA) to remove non-BOLD noise. We estimated the normalized correlation across mean rsfMRI

signals in 90 brain regions of the Automated Anatomical Labeling atlas, and computed global and regional network metrics in the binned connectivity matrix with density threshold of 5–25 %. In addition, we confirmed the observed alterations in network metrics using the Harvard-Oxford atlas which was parcellated into 470 even-sized regions.

Obese subjects exhibited significantly reduced global and local efficiency as well as decreased modularity in the whole-brain network compared to healthy controls (Fig. 24). Both BED patients and the obese subjects without BED exhibited the same alteration of network metrics compared with healthy controls, but two obese groups did not differ from each other. In regional network metrics, bilateral putamen, thalamus and right pallidum exhibited profoundly decreased nodal degree and efficiency in obese subjects, and left superior frontal gyrus showed decreased nodal betweenness in obese subjects (all p < 0.05, Bonferroni correction). Network-based statistics revealed a cortico- striatal/cortico-thalamic network with significantly decreased functional connectivity which consisted of bilateral putamen, pallidum, thalamus, primary motor cortex, primary somatosensory cortex, supplementary motor area, paracentral lobule, superior parietal lobule, superior temporal cortex and left amygdala. Interestingly, when examining the same network properties but using only single-echo rsfMRI data analysis without ME-ICA, we find no significant differences between groups.

Therefore, using data-driven graph theory analysis of multi-echo rsfMRI data, we highlight more subtle impairments in cortico- striatal/ cortico-thalamic networks in obesity that have previously been associated with substance addictions. We emphasize global impairments in network efficiency in obesity with disrupted local network organization closer to random networks. Mathematically capturing brain network alterations in obesity provides novel insights into potential biomarkers and therapeutic targets.

P35

**Dynamics of cooperative excitatory and inhibitory plasticity**

Everton J. Agnes¹, Tim P. Vogels¹

¹Centre for Neural Circuits and Behaviour, University of Oxford, Oxford, OX1 3SR, UK

**Correspondence:** Everton J. Agnes - everton.agnes@cncb.ox.ac.uk

BMC Neuroscience 2016, **17**(Suppl 1):P35

Neurons receive balanced excitatory and inhibitory inputs, a phenomenon thought to be essential for a variety of computations [1–3]. Inhibitory synaptic plasticity is an obvious candidate for imposing this balanced input regime [2,4], leaving excitatory synapses available to learn patterns and memories. Recent experimental work seems to agree with that notion of collaborative excitatory and inhibitory plasticity [4], but recent models do not take direct interactions into consideration. Instead, learning rules are usually tuned to indirectly but constructively interact via the firing-rates they elicit [3,5]. Without proper parameter tuning, this can be problematic because excitatory and inhibitory synaptic plasticity models may have different homeostatic set points, making synaptic weights fluctuate wildly (Fig. 25A, B; green lines). Here we present a hybrid model of inhibitory synaptic plasticity that combines the simplicity of spike-based models with the addition of a excitatory/inhibitory input dependence. It captures recent experimental findings showing that changes at inhibitory synapses are strongly correlated with the balance between excitation and inhibition and that inhibitory synapses do not change when excitatory input is blocked [4]. Essentially, our model is a symmetric spike-timing-dependent plasticity (STDP) rule in which the learning-rate is controlled by excitatory and inhibitory activities—a spike-timing- and current-dependent plasticity (STCDP) model. Balance is maintained, but the learning rule does not impose fixed-point attractor dynamics to post-synaptic neurons, because there is no change in inhibitory synapses once the total input is balanced. Inhibitory synapses change depending on excitatory synapses, which means that plasticity depends on at least three synaptic participants (trisynaptic) instead of only two (bisynaptic). We show that when combined with an excitatory synaptic plasticity model, both excitatory and inhibitory weights converge to stable values, as the firing-rate reaches the fixed-point

<figure><img src="image_25.png" /></figure>
<figure><img src="image_26.png" /></figure>

imposed by the excitatory learning rule (Fig. 25B; *yellow lines*). More importantly, the learning rule allows efficient and stable learning of new weights when the balance is disrupted, opening the door for effective and stable learning of arbitrary synaptic patterns.

**Acknowledgements:** This work was partially funded by the Brazilian agency CNPq (Grant Agreement Number 235144/2014-2) and the Sir Henry Dale Fellowship (Grant Agreement WT100000).

### References

1. Denève S, Machens CK. Efficient codes and balanced networks. Nat Neurosci. 2016;19:375-85.

2. Vogels TP, Froemke RC, Doyon N, Gilson M, Haas JS, Liu R, Maffei A, Miller P, Wierenga CJ, Woodin MA, et al. Inhibitory synaptic plasticity: spike timing-dependence and putative network function. Front Neural Circuits. 2013;7:119.

3. Zenke F, Agnes EJ, Gerstner W. Diverse synaptic plasticity mechanisms orchestrated to form and retrieve memories in spiking neural networks. Nat Commun. 2015;6:6922.

4. D'amour JA, Froemke RC. Inhibitory and excitatory spike-timing-dependent plasticity in the auditory cortex. Neuron. 2015;86:514-28.

5. Sprekeler H, Clopath C, Vogels TP. Interactions of excitatory and inhibitory synaptic plasticity. Front Comp.

## P36

### Frequency-dependent oscillatory signal gating in feed-forward networks of integrate-and-fire neurons

William F. Podlaski¹, Tim P Vogels¹

¹Centre for Neural Circuits and Behaviour, University of Oxford, Oxford, UK

**Correspondence:** William F. Podlaski - william.podlaski@cncb.ox.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P36

Neural oscillations—the periodic synchronisation of neuronal spiking—is a common feature of brain activity, with several hypothesised functions relating to information flow, attention and brain state [1]. Previous experimental work has shown that oscillatory activity correlates with moments of heightened attention, and that communication between different brain areas is often marked by an increase in oscillatory coherence between the regions [2]. Theoretical and modelling work has helped to explore the mechanisms behind neuronal oscillations, and some of their effects on neural coding and signal propagation [3]. Recently, theoretical studies have explored how resonance

might affect signal processing [4, 5] and how information can be propagated along different pathways according to oscillatory phase and frequency [6].

We expand this work here by studying how resonance at the single neuron level might be used for frequency-dependent gating of information flow in neuronal networks. We show that in feed-forward spiking network simulations background oscillations can synchronise or desynchronise the spikes of a propagated signal, changing its content and emphasis from rate code to synfire code or vice versa. Such a mechanism can modulate information flow without rewiring the signal pathways themselves, allowing to select for specific downstream readout targets. Building on this idea, we can create entire pathways that can be selectively (in-)activated by different background oscillatory frequencies without changing the connectivity of the network. We hypothesise that neuronal resonance, combined with resonance in synapses and network motifs, can allow for precise oscillatory gating of information in cortex. Building on previous studies of resonance and oscillatory signal propagation [4,5,6] we propose a plausible mechanism for how fast and precise frequency-dependent gating might be achieved in the brain.

**Acknowledgements:** Research was supported by a Sir Henry Dale Royal Society and Wellcome Trust Research Fellowship (WT100000).

### References

1. Bussáki G. Rhythms of the brain. Oxford: Oxford University Press; 2011.

2. Engel AK, Fries P, Singer W. Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci. 2001;2(10):704-16.

3. Wang XJ. Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev. 2010;90:1195-1268.

4. Richardson MJE, Brunel N, Hakim V. From subthreshold to firing-rate resonance. J Neurophysiol. 2003;89:2538-54.

5. Hahn G, Bujan AF, Frégnac Y, Aertsen A, Kumar A. Communication through resonance in spiking neuronal networks. PLoS Comput Biol. 2014;10(8):e1003811.

6. Akam T, Kullmann DM. Oscillatory multiplexing of population codes for selective communication in the mammalian brain. Nat Rev Neurosci. 2014;15(2):111-22.

## P37

### Phenomenological neural model for adaptation of neurons in area IT

Martin Giese¹, Pradeep Kuravi², Rufin Vogels²

¹Section Computational Sensomotorics, CIN & HIH, Department of Cognitive Neurology, University Clinic Tübingen, Germany; ²Lab. Neuro en Psychofysiolgie, Dept. Neuroscience, KU Leuven, Belgium

**Correspondence:** Martin Giese - martin.giese@uni-tuebingen.de

BMC Neuroscience 2016, 17(Suppl 1):P37

For repeated stimulation neurons in higher-level visual cortex show adaptation effects. Such effects likely influence repetition suppression paradigms in fMRI studies and the formation of high-level after-effects, e.g. for faces [1]. A variety of theoretical explanations has been discussed, which are difficult to distinguish without detailed electrophysiological data [2]. Meanwhile, detailed physiological experiments on the adaptation of shape-selective neurons in inferotemporal cortex (area IT) have provided constraints that help to narrow down possible neural processes. We propose a neurodynamical model that reproduces a number of these experimental observations by biophysically plausible neural circuits. Our model uses the mean-field limit and consists of a neural field of shape-selective dynamic linear-threshold neurons that are augmented several adaptation processes: (i) spike-rate adaptation; (ii) an input fatigue adaptation process, modeling adaptation in earlier hierarchy levels and of afferent synapses; (iii) a firing-rate fatigue adaptation process that models adaptation dependent on the output firing rates of the neurons. The model with a common parameter set is compared to results from several studies about adaptation in area IT. The model reproduces the following experimentally observed effects: (i) shape of the typical PSTHs of IT neurons; (ii) temporal decay for repeated stimulation of the same neurons with many repetitions of the same stimulus [3] (Fig. 26A); (iii) dependence of adaptation on efficient and ineffective adaptor stimuli, which stimulate the
<figure><img src="image_27.png" /><figcaption>**Fig. 26** Simulation results. **A** Decay of neural activity for multiple repetitions of the same stimulus. **B** Experiment adapting with effective and ineffective stimuli. **C** Dependence of the PSTH on adaptor duration and unadapted response (black)</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>**Fig. 27** **A** Visualizations available on the web-resource [2] for model browsing. **B** Schematic of upload and evaluation. Both experimental current traces and mod files can be uploaded to our servers, where they are scored and compared to all models currently in the database. **C** Exemplary result of automated comparison: Current traces (recorded from "Ramp" and "Activation" voltage clamp protocols) of the uploaded model (red) together with mean (1st, 2nd, 3rd, 4th) and individual (gray) traces of the four most similar clusters of channel models in the database</figcaption></figure>

neuron strongly or only moderately [4] (Fig. 26B); (iv) dependence of the strength of the adaptation effect on the duration of the adaptor (Fig. 26C). A mean field model with several additional adaptive processes can account for the observed experimental effects, where all introduced processes were necessary to account for the results. Especially the observed dependence on the effectiveness of the adaptor cannot be reproduced without an appropriate mixture if an input fatigue and a firing-rate fatigue mechanism. This suggests that adaptation in IT neurons is significantly influenced by several biophysical processes with different spatial and temporal scales.

**Acknowledgements:** Supported by EC Fp7-PEOPLE-2011-ITN PITN-GA-011-290011 (ABC), FP7-ICT-2013-FET-F/604102 (HBP), FP7-ICT-2013-10/611909 (Koroibot), BMBF, FKZ: 01GQ1002A, DFG GI 305/4-1 + KA 1258/15-1.

## References

1. Leopold DA, O'Toole AJ, Vetter T, Blanz V: Prototype-referenced shape encoding revealed by high-level aftereffects. Nat Neurosci. 2001;4(1):89-94.

2. Grill-Spector K, Henson R, Martin A. Repetition and the brain: neural models of stimulus-specific effects. Trends Cogn Sci. 2006;10(1):14-23.

3. Sawamura H, Orban GA, Vogels R. Selectivity of neuronal adaptation does not match response selectivity: a single-cell study of the FMRI adaptation paradigm. Neuron. 2006;49(2):307-18.

4. De Baene W, Vogels R. Effects of adaptation on the stimulus selectivity of macaque inferior temporal spiking activity and local field potentials. Cereb Cortex. 2010;20(9):2145-65.

# P38
## ICGenealogy: towards a common topology of neuronal ion channel function and genealogy in model and experiment

Alexander Seeholzer<fnref n="1" />,<fnref n="1" />, William Podlaski<fnref n="2" />,†, Rajnish Ranjan³, Tim Vogels<fnref n="2" />

**Correspondence:** Alexander Seeholzer - alex.seeholzer@epfl.ch

BMC Neuroscience 2016, 17(Suppl 1):P38

Ion channels are fundamental constituents determining the function of single neurons and neuronal circuits. To understand their complex interactions, the field of computational modeling has proven essential: since its emergence, thousands of ion channel models have been created and published as part of detailed neuronal simulations [1]. Faced with this large variety of models, it is difficult to determine how particular models relate to each other, to the interpretability of simulations and, importantly, to experimental data.

Here, we present a framework within which we analyzed a pilot set of 2378 voltage- or calcium-dependent published ion channel models for the NEURON simulator [1]. We extracted annotated metadata from

all associated publications, helping identify their use in simulations (e.g. the animal type, neuron type or area of compartmental models) and the provenance of ion channel models as they were derived from other published work. This categorical and relational metadata is combined with quantitative evaluations of all channel models: individual channels are characterized by their responses to voltage clamp protocols. With subsequent cluster analysis, we extract topologies of ion channel similarity and genealogy, identifying redundancy and groups of common channel kinetics.

The result of this large-scale assay of published work is freely accessible through interactive visualizations (see Fig. 27A) on the Ion Channel Genealogy (ICG) web-resource [2], providing a tool for model discovery and comparison. Bridging the gap between model and experiment, our resource allows classifying new channel models and experimental current traces within the topology of all models currently in the database (see Fig. 27B, C). The ICG framework thus allows for quantitative comparison of ion channel kinetics, experimental and model alike, aimed to facilitate field-wide standardization of experimentally-constrained modeling.

**Acknowledgements:** Research was supported by a Sir Henry Dale Royal Society & Wellcome Trust Research Fellowship (WT100000). A.S. was supported by the Swiss National Science Foundation (200020_147200). R.R. was supported by the EPFL Blue Brain Project Fund and the ETH Board funding to the Blue Brain Project.

## References

1. Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM. ModelDB. A database to support computational neuroscience. J Comput Neurosci. 2004;17:7-11.

2. ICGenealogy Project Website. http://icg.neurotheory.ox.ac.uk.

# P39
## Temporal input discrimination from the interaction between dynamic synapses and neural subthreshold oscillations

Joaquin J. Torres<fnref n="1" />, Fabiano Baroni<fnref n="2" />, Roberto Latorre³, Pablo Varona³

**Correspondence:** Pablo Varona - pablo.varona@uam.es

BMC Neuroscience 2016, 17(Suppl 1):P39

Neuronal subthreshold oscillations underlie key mechanisms of information discrimination in single cells while dynamic synapses provide channel-specific input modulation. Previous studies have shown that intrinsic neuronal properties, in particular subthreshold oscillations, constitute a biophysical mechanism for the emergence of non-trivial single-cell input/output preferences (e.g., preference towards

<footnote n="1">¹Laboratory of Computational Neuroscience, EPF Lausanne, Switzerland;</footnote>

<footnote n="2">²Centre for Neural Circuits and Behaviour, University of Oxford, UK; ³The Blue Brain Project, EPF Lausanne, Switzerland</footnote>

<footnote>† These authors contributed equally to this work.</footnote>

<footnote n="1">¹Departamento de Electromagnetismo y Física de la Materia, and Institute "Carlos I" for Theoretical and Computational Physics, University of Granada, Granada, Spain; ²School of Psychological Sciences, Faculty of Biomedical and Psychological Sciences, Monash University, Australia; ³Grupo de Neurocomputación Biológica, Dpto. de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, Spain</footnote>
decelerating vs. accelerating input trains of the same average rate) [1, 2]. It has also been shown that short-term synaptic dynamics, in the form of short-term depression and/or short-term facilitation, can provide a channel-specific mechanism for the enhancement of the post-synaptic effects of temporally specific input sequences [3, 4]. While intrinsic oscillations and synaptic dynamics are typically studied independently, it is reasonable to hypothesize that their interplay can lead to more selective and complex temporal input processing.

Here, we extend and refine our previous computational study on the interaction between subthreshold oscillations and synaptic depression [5]. In particular, we investigated whether, and under which conditions, the combination of intrinsic subthreshold oscillations and short-term synaptic dynamics can act synergistically to enable the emergence of robust and channel-specific selectivity in neuronal input-output transformations. We calculated analytically the voltage trajectories and spike output of generalized integrate-and-fire (GIF) model neurons in response to temporally distinct trains of input EPSPs. In particular, we considered triplets of input EPSPs in a range that covers intrinsic and synaptic time scales, and analyzed the model output as intrinsic and synaptic parameters were varied.

Our results show that intrinsic and synaptic dynamics interact in a complex manner for the emergence of specific input-output transformations. In particular, precise non-trivial preferences emerge from synergistic intrinsic and synaptic preferences, while broader selectivity is observed for mismatched intrinsic and synaptic dynamics. We discuss the conditions for robustness of the observed input/output relationships.

We conclude that the interaction of intrinsic and synaptic properties can enable the biophysical implementation of complex and channel-specific mechanisms for the emergence of selective neuronal responses. We further interpret our results in the light of experimental evidence describing distinct short-term synaptic dynamics in different afferents converging onto the same neuron, as in the case of parallel and climbing fiber inputs to cerebellar Purkinje cells, and advance specific hypotheses that link heterogeneous synaptic dynamics of distinct pathways onto the same post-synaptic target to their distinct computational function. We also discuss the impact of single-channel/single-neuron temporal input discrimination in the context of information processing based on heterogeneous elements.

**Acknowledgements:** We acknowledge support from MINECO FIS2013-43201-P, DPI2015-65833-P, TIN-2012-30883 and ONRG Grant N62909-14-1-N279.

## References

1. Baroni F, Varona P. Subthreshold oscillations and neuronal input-output relationships. Neurocomputing. 2007;70:1611-14.

2. Baroni F, Torres JJ, Varona P. History-dependent excitability as a single-cell substrate of transient memory for information discrimination. PLoS One. 2010;5:e15023.

3. O'Donnell C, Nolan MF. Tuning of synaptic responses: An organizing principle for optimization of neural circuits. Trends Neurosci. 2011;34:51-60.

4. Torres JJ, Kappen HJ. Emerging phenomena in neural networks with dynamic synapses and their computational implications. Front Comp Neurosci. 2013;7.

5. Latorre R, Torres JJ, Varona P. Interplay between subthreshold oscillations and depressing synapses in single neurons. PLoS One. 2016;11:e0145830.

## P40

### Different roles for transient and sustained activity during active visual processing

Bart Gips¹,†, Eric Lowet¹,²,†, Mark J Roberts¹,², Peter de Weerd², Ole Jensen¹, Jan van der Eerden¹

¹Radboud University, Donders Institute for Brain, Cognition and Behaviour, 6525 EN Nijmegen, The Netherlands; ²Faculty of Psychology and Neuroscience, Maastricht University, 6200 MD Maastricht, the Netherlands

**Correspondence:** Bart Gips - bart.gips@donders.ru.nl

† Authors have made equal contribution

BMC Neuroscience 2016, 17(Suppl 1):P40

Neural activity in awake primate early visual cortex exhibits transients with intervals of 250-300 ms. Experimental work by us and others has shown that these transients are related to microsaccadic eye movements [1, 2]. These short transients are followed by periods of steady activity that last until the next microsaccade (Fig. 28A).

We found that computational models of excitatory-inhibitory spiking networks organized in a structure of columns and hypercolumns, are able to represent relevant stimulus information when subjected to 3-4 Hz saccade-like transients. The simulated networks expressed evoked responses with power in the alpha-beta band (~8-25 Hz) as well as gamma rhythmic activity (~25-80 Hz) similar to in vivo local field recordings in monkey V1 (Fig. 28A, B).

We show that in phase I, the model produces large-scale spatial synchrony and pronounced alpha-beta power. In phase II the model exhibits narrow-band gamma oscillations with spatially local synchrony. The activity in the model network (rate and timing coding) in phase I mainly reflects feedforward input (Fig. 28C, D), whereas, the network activity in phase II was dominated by recurrent connections (Fig. 28C, E).

The model network activity closely matches that found in experiments. The simulation results suggest that transient phase (phase I) allows for resetting the network and rapid feedforward processing of novel information, whereas detailed processing and contextualization by recurrent activity take place in the period of steady gamma activity (phase II). Therefore we arrived at hypotheses on the functional interpretation of phases I and II that can be possibly tested in

A Primate V1 data

<figure><img src="image_29.png" /></figure>

Time from MS onset (s)

B Model Network

<figure><img src="image_30.png" /></figure>

Time from MS onset (s)

C

<figure><img src="image_31.png" /></figure>

D

<figure><img src="image_32.png" /></figure>

input-output relation

Phase I Phase II

E

<figure><img src="image_33.png" /></figure>

recurrent-output relation

Phase I Phase II

**Fig. 28** A Time-frequency representation of local field potential (LFP) locked to a microsaccade (MS) recorded in primate V1. B Time-frequency representation of simulated LFP. C Schematic representation of the model network illustrating input (injection current), recurrent connection pattern and output (spike trains). D The input to the neurons is best reflected in the simulated spike trains (output) during phase I, quantified by mutual information (MI). E Recurrent connection pattern is best reflected in the output during phase II
an experimental setup. First, because of the reset of network activity by a microsaccade, phase I is the optimal time window to switch information flow among competing networks through a top-down signal. This indicates that signals related to visual attention are most likely to occur just after a saccade. Second, the increased efficacy of recurrent connections during phase II indicate that contextualization operations such as figure-ground segregation [3] and contour completion occur in the steady phase ~100 ms after the onset of a (micro)saccade.

## References

1. Lowet E, Roberts MJ, Bosman CA, Fries P, de Weerd P. Areas V1 and V2 show microsaccade-related 3-4 Hz covariation in gamma power and frequency. Eur J Neurosci. 2015.

2. Martinez-Conde S, Otero-Millan J, Macknik SL. The impact of microsaccades on vision: towards a unified theory of saccadic function. Nat Rev Neurosci. 2013;14:83-96.

3. Self MW, van Kerkoerle T, Supèr H, Roelfsema PR. Distinct roles of the cortical layers of area V1 in figure-ground segregation. Curr Biol. 2013;1:9.

# P41
## Scale-free functional networks of 2D Ising model are highly robust against structural defects: neuroscience implications

Abdorreza Goodarzinick¹, Mohammad D. Niry¹,², Alireza Valizadeh¹,³

¹Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran; ²Center for Research in Climate Change and Global Warming (CRCC), Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran; ³School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran - Iran

**Correspondence:** Abdorreza Goodarzinick - a.goodarzinick@iasbs.ac.ir

BMC Neuroscience 2016, 17(Suppl 1):P41

In recent years, several experimental observations have confirmed the emergence of self-organized criticality (SOC) in the brain at different scales [1]. At large scale, functional brain networks obtained from fMRI data have shown that node-degree distributions and probability of finding a link versus distance are indicative of scale-free and small-world networks regardless of the tasks in which the subjects were involved [2]. At small scale, the study of neuronal avalanches in networks of living neurons revealed power-law behavior in both spatial and temporal scales [3]. It is also shown that functional networks of the brain are strikingly similar to those derived from the 2D Ising model at critical temperature [4] and the 2D abelian sandpile model [5].

The importance to see whether brain network's scaling properties associated with healthy conditions are altered under various pathologies and how structural defects of a system at criticality can affect its functional connectivity motivated us to study robustness of functional networks of 2D Ising model at critical point against elimination of structural sites. The results showed that the statistics of the functional network indicative of criticality (evident in healthy brain controls), such as power-law behavior and small-worldness remained robust against random elimination of structural sites up to percolation limit (see Fig. 29). The resulting functional network maintained its key properties orders of magnitude higher than those of the same system poised in a super-critical or sub-critical state. These results can show that self-organized critical behavior, besides having unique

advantages like fascilitation of alteration of functional patterns, optimization of information transfer and maximization of correlation length, shows striking robustness against structural deficits. Taking into account brain's long-range anatomical connections and compensatory mechanisms like neuroplasticity, if the results of this study are generalizable to the brain, they may help to explain the delay in clinical diagnosis of multiple neurodegenerative diseases in which possible deficit in functional connectivity among brain regions contribute to the cognitive dysfunctions.

## References

1. Chialvo DR. Emergent complex neural dynamics. Nat Phys. 2010;6:744-50.

2. Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Phys Rev Lett. 2005;94:018102.

3. Beggs J, Plenz D. Neuronal avalanches in neocortical circuits. J Neurosci. 2003;23:11167-77.

4. Fraiman D, Balenzuela P, Foss J, Chialvo D. Ising-like dynamics in large-scale functional brain networks. Phys Rev E. 2009;79:061922.

5. Zarepour M, Niry MD, Valizadeh A. Functional scale-free networks in the two-dimensional Abelian sandpile model. Phys Rev E. 2015;92:012822.

# P42
## High frequency neuron can facilitate propagation of signal in neural networks

Aref Pariz¹, Shervin S Parsi¹, Alireza Valizadeh¹,²

¹Department of Physics, Institute for advanced studies in basic sciences, Zanjan, Iran; ²School of Cognitive Sciences, Institute for Studies in Theoretical Physics and Mathematics, Niavaran, Tehran, Iran

**Correspondence:** Aref Pariz - a.pariz@iasbs.ac.ir

BMC Neuroscience 2016, 17(Suppl 1):P42

Signal transmission is of interest from both fundamental and clinical perspective and has been well studied in nonlinear science and complex networks [1, 2]. In particular, in nervous systems, cognitive processing involves signal propagation through multiple brain regions and the activation of large numbers of specific neurons [3-6]. In information propagation through brain regions, each part, known as generator, activated locally as information comes to it from neighboring generators. Although the problem is well studied in the context of complex networks, our focus here is on the effect of the intrinsic dynamical properties of the reciprocal generators on the propagation of signal.

In this study we explored the propagation of information in a chain of neurons and networks. As signal propagate through the chain of networks, the firing rate of networks show a fluctuation as host network (the network which receive signal). Here the response is the amplitude of fast Fourier transform of firing rates of each network. If the host network has sufficiently higher intrinsic firing rate than others, signal can transfer with higher amplitude, otherwise, other networks will not get affected. As a result of propagation of signal, for the former case, all networks will show a peak in frequency domain at exactly the same frequency as input signal (Fig. 30A), but with different amplitude which show the efficacy of transmitted information. Also the same result can obtain by a chain of single LIF neurons (Fig. 30B). As phase response curve of the chain and it response to signal show, if the host neuron has higher firing rate (call it leader neuron), the propagation

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>
of information will be enhanced. But this higher firing rate has a limit
which after that the whole chain will act asynchronously and results
the loss of information was aimed to propagate.

References

1. Liang X, Liu Z, Li B. Weak signal transmission in complex networks and its application in detecting connectivity. Phys Rev E. 2010;80:046102.

2. Perc M. Stochastic resonance on weakly paced scale-free networks. Phys Rev E. 2008;78:036105.

3. Abeles M. Corticonics: neural circuits of the cerebral cortex. Cambridge: Cambridge UP; 1991.

4. Aertsen A, Diesmann M, Gewaltig MO. Propagation of synchronous spiking activity in feedforward neural networks. J Physiol. 1996;90:243-247.

5. van Rossum MC, Turrigiano GG, Nelson SB. Fast propagation of firing rates through layered networks of noisy neurons. J Neurosci. 2002;22:1956-66.

6. Vogels TP, Abbott LF. Signal propagation and logic gating in networks of integrate-and-fire neurons. J Neurosci. 2005;25(46):10786-95.

P43

Investigating the effect of Alzheimer's disease related amyloidopathy on gamma oscillations in the CA1 region of the hippocampus

Julia M. Warburton¹, Lucia Marucci², Francesco Tamagnini³,⁴, Jon Brown³,⁴, Krasimira Tsaneva-Atanasova⁵

¹Bristol Centre for Complexity Sciences, University of Bristol, Bristol, BS8 1TR, UK; ²Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1UB, UK; ³School of Physiology and Pharmacology, University of Bristol, Bristol, BS8 1TD, UK; ⁴Medical School, University of Exeter, Exeter, EX4 4PE, UK; ⁵Department of Mathematics, University of Exeter, Exeter, EX4 4QF, UK

**Correspondence:** Julia M. Warburton - julia.warburton@bristol.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P43

Alzheimer's disease (AD) is the main form of dementia and is characterised clinically by cognitive decline and impairments to memory function. One of the key histopathological features of AD thought to cause this neurodegeneration is the abnormal aggregation of the protein amyloid-β (Aβ) [1]. Transgenic mouse models that overexpress Aβ are used to investigate the potential functional consequences of this amyloidopathy in AD. In this study we use in vitro electrophysiology data recorded from PDAPP transgenic mice (a mouse model of amyloidopathy) and their wild-type littermates to parameterise a hippocampal network model [2]. The aim of the study is to investigate how amyloidopathy alters gamma frequency oscillations within the hippocampus, which is one of the regions first affected in AD.

We use a synaptically connected network of excitatory pyramidal neurons and inhibitory interneurons to simulate the gamma frequency activity [3]. Each cell is described by a single-compartment Hodgkin-Huxley type equation, with the properties of the voltage-gated channels fit to the intrinsic properties measured experimentally, which included stimulated firing frequency data and the associated action potentials from CA1 pyramidal neurons and three-types of CA1 interneuron. Network activity is either driven deterministically via a direct stimulus, such as a step pulse or a theta wave, or via a stochastic input. We perform power spectral density analysis to analyse the oscillatory activity.

Our model focuses on gamma frequency oscillations, which lie in the
30-100 Hz range, because of the associations with attention, sen-
sory processing and potentially of most relevance to AD, with learn-
ing and memory. It has been shown that within the hippocampus
gamma oscillations enable cross-talk between distributed cell assem-
blies, with low frequency gamma associated with coupling between
the CA1 and the CA3 region and fast frequency gamma associated
with coupling between the CA1 and the medial entorhinal cortex [4].
EEG measurements from AD mouse models have identified network
hypersynchrony alongside decreased gamma activity, with the role
of interneurons in this process highlighted. [5]. By incorporating the
pyramidal neuron and interneuron data in our model we aim to learn
more about which parameters are most significant in these effects and

to further understanding of the effects of amyloidopathy on oscilla-
tory activity.

**Acknowledgements:** This work was supported by funding from the EPSRC.

References

1. Hardy J, Selkoe DJ. The amyloid hypothesis of Alzheimer's disease: progress and problems on the road to therapeutics. Science. 2002;297:353-6.

2. Kerrigan TL, Brown JT, Randall TL. Characterization of altered intrinsic excitability in hippocampal CA1 pyramidal cells of the Aβ-overproducing PDAPP mouse. Neuropharmacology. 2014;79:515-24.

3. Kopell NJ, Borgers C, Pervouchine D, Maerba P, Tort A. Gamma and theta rhythms in biophysical models of hippocampal circuits. In: Hippocampal microcircuits: a computational modeler's resource book, chap 15; p. 423-57.

4. Colgin LL, Denninger T, Fyhn M, Hafting T, Bonnevie T, Jensen O, Moser M-B, Moser El. Frequency of gamma oscillations routes flow of information in the hippocampus. Nature. 2009;462:353-7.

5. Verret L, et al. Inhibitory interneuron deficit links altered network activity and cognitive dysfunction in Alzheimer model. Cell. 2012;149:708-21.

P44

Long-tailed distributions of inhibitory and excitatory weights in a balanced network with eSTDP and iSTDP

Florence I. Kleberg¹, Jochen Triesch¹

¹Frankfurt Institute for Advanced Studies, Frankfurt am Main, Hessen, Germany, 60438

**Correspondence:** Florence I. Kleberg - kleberg@fias.uni-frankfurt.de

BMC Neuroscience 2016, 17(Suppl 1):P44

The strengths of excitatory synapses in cortex and hippocampus have been shown to follow a rightward-skewed or long-tailed distribution [1,2]. Such distributions can be achieved in recurrent balanced networks [3, 4], after synaptic modification by spike-timing dependent plasticity (STDP) [5] and synaptic scaling [6]. Recently, long-tailed distributions have also been observed for inhibitory synapses in cultured cortical neurons [7], confirming early findings in hippocampal slices [8]. However, the conditions and plasticity mechanisms necessary for achieving long-tailed distributions of inhibitory synapses are unknown. Furthermore, different forms of inhibitory STDP have been reported, but their effect on the distribution of inhibitory synaptic efficiencies are largely unknown [9-11].

Here we investigate how plasticity in the inhibitory synapses in a self-
organised recurrent neural network (SORN [12]) with leaky integrate-
and-fire neurons can lead to long-tailed distributions of synaptic
weights. We examine different inhibitory STDP (iSTDP) rules and char-
acterize the conditions under which right-skewed shapes of inhibitory
synaptic weight distributions are obtained while a balance between
excitation and inhibition is maintained. While the ratio of long-term
potentiation to long-term depression in iSTDP affects the shape
of the distribution, a variety of window shapes for iSTDP can each
achieve long-tailed distributions of inhibitory weights. We find that
a precise balance of excitation and inhibition can be achieved with a
strongly right-skewed distribution of inhibitory weights. Our results
suggest that long-tailed distributions of inhibitory weights could be
a ubiquitous feature of neural circuits that employ different plasticity
mechanism.

References

1. Bekkers, JM, Stevens, CF. NMDA and non-NMDA receptors are co-localized at individual excitatory synapses in cultured rat hippocampus. Nature. 1989;341:230-3.

2. Loewenstein Y, Kuras A, Rumpel S. Multiplicative dynamics underlie the emergence of the log-normal distribution of spine sizes in the neocortex in vivo. J Neurosci. 2011;31(26):9481-8.

3. Effenberger F, Jost J, Levina A. Self-organization in balanced state networks by STDP and homeostatic plasticity. PLoS Comput Biol. 2015;11(9):e1004420.
4. Miner D, Triesch J. Plasticity-driven self-organization under topological constraints accounts for non-random features of cortical synaptic wiring. PLoS Comput Biol. 2016;12(2):e1004759.

5. Bi G, Poo M. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci. 1998;18(24):10464–72.

6. Turrigiano GG, Leslie KR, Desai NS, Rutherford LC, Nelson SB. Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature. 1998;391(6670):892–6.

7. Rubinski A, Ziv NE. Remodeling and tenacity of inhibitory synapses: relationships with network activity and neighboring excitatory synapses. PLoS Comput Biol. 2015;11(11):e1004632.

8. Miles R. Variation in strength of inhibitory synapses in the CA3 region of guinea-pig hippocampus in vitro. J Physiol. 1990;431:659–76.

9. Woodin MA, Ganguly K, Poo M. Coincident pre-and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl⁻ transporter activity. Neuron. 2003;39(5):807–20.

10. Haas JS, Nowotny T, Abarbanel HDI. Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. J Neurophysiol. 2006;96(6):3305–13.

11. D'Amour JA, Froemke RC. Inhibitory and excitatory spike-timing-dependent plasticity in the auditory cortex. Neuron. 2015;86(2):514–28.

12. Lazar A, Pipa G, Triesch J. SORN: a self-organizing recurrent neural network. Front Comp Neurosci. 2009;3:23.

## P45
### Simulation of EMG recording from hand muscle due to TMS of motor cortex

Bahar Moezzi¹, Nicolangelo Iannella¹,⁴, Natalie Schaworonkow², Lukas Plogmacher², Mitchell R. Goldsworthy³, Brenton Hordacre³, Mark D. McDonnell¹, Michael C. Ridding³, Jochen Triesch²

¹Computational and Theoretical Neuroscience Laboratory, School of Information Technology and Mathematical Sciences, University of South Australia, Australia; ²Frankfurt Institute for Advanced Studies, Goethe-Universität, Germany; ³Robinson Research Institute, School of Medicine, University of Adelaide, Australia; ⁴School of Mathematical Sciences, University of Nottingham, UK

**Correspondence:** Bahar Moezzi - bahar.moezzi@unisa.edu.au

BMC Neuroscience 2016, 17(Suppl 1):P45

Single pulse transcranial magnetic stimulation (TMS) is a technique which (at moderate intensities) activates corticomotor neuronal output cells transynaptically and evokes a complex descending volley in the corticospinal tract. Rusu et al. developed a computational model of TMS induced I-waves that reproduced observed epidural recordings in conscious humans [1]. In humans, epidural responses can be recorded in anaesthetized subjects during surgery or conscious subjects with electrodes implanted for the treatment of chronic pain. Such opportunities are uncommon and invasive. The effects of TMS can be non-invasively studied using surface electromyography (EMG) recordings from the hand first dorsal interosseous (FDI) muscle.

We simulated the surface EMG signal due to TMS of motor cortex in the hand FDI muscle. Our model comprises a population of cortical layer 2/3 cells, which drive layer 5 cortico-motoneuronal cells with excitatory and inhibitory synaptic inputs as in [1]. The layer 5 cells in turn project to a pool of motoneurons, which are modeled as an inhomogeneous population of integrate-and-fire neurons to simulate motor unit recruitment and rate coding. The input to motoneurons from cortical layer 5 consists of TMS-induced spikes and baseline firing. We modeled baseline firing with a Poisson drive to layer 2/3 cells. Hermite-Rodriguez functions were used to simulate motor unit action potential shape. The EMG signal was obtained from the summation of motor unit action potentials of active motor units. Parameters were tuned to simulate recordings from the FDI muscle.

Our simulated EMG signals match experimental surface EMG recordings due to TMS of motor cortex in the hand FDI muscle in shape, size and time scale both at rest and during voluntary contraction (see

<figure><img src="image_36.png" /><figcaption>**Fig. 31** Comparison of simulated and experimental EMG during A rest, B 10 % maximum voluntary contraction</figcaption></figure>

Fig. 31). The simulated EMG traces exhibit cortical silent periods (CSP) that lie within the biological range.

### Reference

1. Rusu CV, Murakami M, Ziemann U, Triesch J. A model of TMS-induced I-waves in motor cortex. Brain Stimul. 2014;7(3):401–14.

## P46
### Structure and dynamics of axon network formed in primary cell culture

Martin Zapotocky¹,², Daniel Smit¹,²,³, Coralie Fouquet³, Alain Trembleau³

¹Institute of Physiology of the Czech Academy of Sciences, Prague, Czech Republic; ²Institute of Biophysics and Informatics, First Faculty of Medicine, Charles University in Prague, Czech Republic; ³IBPS, Neuroscience Paris Seine, CNRS UMR8246, Inserm U1130, UPMC UM 119, Université Pierre et Marie Curie, Paris, France

**Correspondence:** Martin Zapotocky - zapotocky@biomed.cas.cz

BMC Neuroscience 2016, 17(Suppl 1):P46

Axons growing in vivo or in culture may adhere to each other and form a connected network, which subsequently guides the paths of newly arriving axons. We investigated the development of such a network formed by growing axons in primary cell culture.

Olfactory epithelium explants from mouse embryos (day 13–14) were cultured on laminin substrate for 2 days and then recorded using DIC or phase contrast videomicroscopy for up to 24 h. The growing axons established a dense network within which large fascicles of axons were progressively formed. Within the recorded time period, the network remained stable, with limited further growth of the axons but with ongoing rearrangement in the network structure. Based on segmentation of the recorded images, we determined the principal network characteristics (including the total length, the total number of vertices, and the network anisotropy) and their evolution in time.

This quantitative characterization permitted an analysis of the mechanisms of the observed network coarsening. We relate the network dynamics to the elementary processes of zippering, during which two axons or axon fascicles progressively adhere to each other [1]. We compare the structural features of the network (such as the distribution of vertex angles) with those reported in an electron microscopy investigation of a plexus of sensory neurites in Xenopus embryo [2]. We show that both our ex vivo study and the in vivo study of Ref. [2] support a similar underlying mechanism of the formation of the axon network.

**Acknowledgements:** Work supported by GAČR 14-16755S, GAUK 396213, MŠMT 7AMB12FR002, NIH 1RO1DCO12441 and ANR 2010-BLAN-1401-01.

### References

1. Smit D, Fouquet C, Pincet F, Trembleau A, Zapotocky M. Axon zippering in neuronal cell culture and its biophysical modeling. BMC Neurosci. 2015;16(Suppl 1):P298.
2. Roberts A, Taylor JSH. A scanning electron microscope study of the development of a peripheral sensory neurite network. J Embryol Exp Morph. 1982;69:237–50.

P47
**Efficient signal processing and sampling in random networks that generate variability**

Sakyasingha Dasgupta<sup>1,2</sup>, Isao Nishikawa<sup>3</sup>, Kazuyuki Aihara<sup>3</sup>, Taro
Toyoizumi<sup>2</sup>

<sup>1</sup>IBM Research - Tokyo, Tokyo, Japan; <sup>2</sup>RIKEN Brain Science Institute, Tokyo, Japan; <sup>3</sup>The University of Tokyo, Tokyo, Japan

**Correspondence:** Sakyasingha Dasgupta - sdasgup@jp.ibm.com

BMC Neuroscience 2016, 17(Suppl 1):P47

The source of cortical variability and its influence on signal processing remain an open question. We address the latter, by studying two types of randomly connected networks of quadratic integrate-and-fire neurons with balanced excitation-inhibition that produce irregular spontaneous activity patterns (Fig. 32A): (a) a deterministic network with strong synaptic interactions that actively generates variability by chaotic dynamics (internal noise) and (b) a stochastic network that has weak synaptic interactions but receives noisy input (external noise), e.g. by stochastic vesicle releases. These networks of spiking neurons are analytically tractable in the limit of a large network-size and slow synaptic-time-constant. Despite the difference in their sources of variability, spontaneous (baseline) activity patterns of these two models are indistinguishable unless majority of neurons are simultaneously recorded. We characterize the network behavior with dynamic mean field analysis and reveal a single-parameter family that allows interpolation between the two networks, sharing nearly identical spontaneous activity (Fig. 32B). Despite the close similarity in the spontaneous activity, the two networks exhibit remarkably different sensitivity to external stimuli. Input to the former network reverberates internally and can be successfully read out over long time. Contrarily, input to the latter network rapidly decays and can be read out only for short time. This is also observed in the significant changes in the spiking probability of evoked responses across this family (Fig. 32C). The difference between

the two networks is further enhanced if input synapses undergo activity-
dependent plasticity, producing significant difference in the ability to
decode external input from neural activity. We show that, this difference
naturally leads to distinct performance of the two networks to integrate
spatio-temporally distinct signals from multiple sources. Unlike its sto-
chastic counterpart, the deterministic chaotic network activity can serve
as a reservoir to perform near optimal Bayesian integration and Monte-
Carlo sampling from the posterior distribution. We describe implications
of the differences between deterministic and stochastic neural computa-
tion on population coding and neural plasticity.

P48
Modeling the effect of riluzole on bursting in respiratory neural networks

Daniel T. Robb¹, Nick Mellen², and Natalia Toporikova³

<sup>1</sup>Department of Mathematics, Computer Science and Physics, Roanoke College, Salem, VA 24153, USA; <sup>2</sup>Department of Pediatrics, University of Louisville, Louisville, KY 40208, USA; <sup>3</sup>Department of Biology, Washington and Lee University, Lexington, VA 24450, USA

**Correspondence:** Daniel T. Robb - robb@roanoke.edu

BMC Neuroscience 2016, 17(Suppl 1):P48

To accommodate constantly changing environmental and metabolic demands, breathing should be able to vary flexibly within a range of frequencies. The respiratory neural network in the pre-Botzinger complex of the ventrolateral medulla controls and flexibly maintains the breathing rhythm, coordinating network-wide bursting to signal the inspiratory phase of the breath. The frequency of this rhythmic activity is controlled by a number of neuromodulators, the majority of which are excitatory. Therefore, the central pattern generator for rhythmic respiratory activity should possess two seemingly contradictory properties: it has to be able to change frequency in response to excitatory input, but it also has to preserve stable rhythmic activity under a wide range of conditions. A persistent sodium current (I<sub>NaP</sub>) been identified as one of the key currents for generation of inspiratory activity [1]. It has been shown that some of the neurons in Pre-BotC possess an intrinsic bursting mechanism, which relies on inactivation of this current. Higher expression of I<sub>NaP</sub> correlates with higher burst frequency of a single pacemaker neuron [2]. However, the I<sub>NaP</sub> pacemaker mechanism can only function within very narrow ranges of external excitation—NaP dependent pacemaker tends to switch to tonic firing after a small increase in depolarizing current [3].

In this combined experimental and computational study, we tested the effect of the persistent sodium blocker Riluzole (RIL) in several different levels of continuous depolarization, simulated by application of K+. Whereas increased potassium increases the bursting frequency of the control network, in the presence of RIL the increased potassium does not alter the bursting frequency (Fig. 33). These findings indicate

<figure><img src="image_37.png" /><figcaption>**Fig. 32** A Schematic illustrations of the two balanced QIF networks models considered in the present study. The left network consists of strongly coupled neurons without noise, while the right network consists of weak coupling among neurons with noisy input. B Nearly identical rate autocorrelation functions in the two networks. The red line ($C_0$) represents the value of the autocorrelation at time 0 and cyan line ($C_\infty$) is the value of auto-correlation function in the limit of large $t$. C Change in spiking probability for different network connectivity strengths ($\tilde{g}$), after being stimulated by a brief input at time $t = 0$</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>**Fig. 33** Summary of experiment on the effect of riluzole on the dependence of burst frequency on potassium concentration. Without riluzole (left), the frequency increases steadily with increasing potassium concentration. With riluzole present (right), the frequency remains essentially constant with increasing potassium concentration</figcaption></figure>
that *I*<sub>NaP</sub> is responsible for flexible modulation of respiratory rhythm,
but there is another mechanism, which can sustain rhythmic activity in
its absence. We developed a computational model which incorporates
a Calcium sensitive Non-specific cationic current (*I*<sub>CaN</sub>) in addition to
*I*<sub>NaP</sub>. Our simulations indicate that *I*<sub>CaN</sub> and *I*<sub>NaP</sub> can maintain the rhythm
in respiratory neurons in the presence of RIL, and are capable of pro-
viding stable oscillations in the presence of tonic excitation by K+.

References

1. Butera RJ Jr, Rinzel J, Smith JC. Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. J Neurophysiol. 1999;82:382-97.

2. Purvis LK, Smith JC, Koizumi H, Butera RJ. Intrinsic bursters increase the robustness of rhythm generation in an excitatory network. J Neurophysiol. 2007;97:1515-26.

3. Del Negro CA, Morgado-Valle C, Hayes JA, Mackay DD, Pace RW, Crowder EA, Feldman JL. Sodium and calcium current-mediated pacemaker neurons and respiratory rhythm generation. J Neurosci Off J Soc Neurosci. 2005;25:446-53.

P49

Mapping relaxation training using effective connectivity analysis

Rongxiang Tang¹, Yi-Yuan Tang²

¹Department of Psychology, Washington University in St. Louis, St. Louis, MO 63130, USA; ²Department of Psychological Sciences, Texas Tech University, TX 79409, USA

Correspondence: Yi-Yuan Tang - yiyuan.tang@ttu.edu

BMC Neuroscience 2016, 17(Suppl 1):P49

Relaxation training (RT) is a behavioral therapy that has been applied in stress management, muscle relaxation and other health benefit. However, compared to short-term meditation training, previous studies did not show the significant differences in brain changes following same amount of RT [1,2]. One possible reason might derive from the insensitive correlation based routine functional connectivity method that could not reveal training-related changes in effective connectivity (directed information flow) among these distributed brain regions. Here, we applied a novel spectral dynamic causal modeling (spDCM) to resting state fMRI to characterize changes in effective connectivity. Twenty-three healthy college students were recruited through campus advertisements and received 4 weeks of RT (10 h in total), previously reported in our randomized studies [1, 2]. All neuroimaging data were collected using an Allegra 3-Telsa Siemens scanner and processed using the Data Processing Assistant for Resting-State fMRI, which is based on SPM and Resting-State fMRI Data Analysis Toolkit [3]. For each participant, the subsequent standard procedures included slice timing, motion correction, regression of WM/CSF signals, and spatial normalization [3]. Based on previous literature, we specified four regions of interest within default mode network (DMN)—medial prefrontal cortex (mPFC), posterior cingulate cortex (PCC), and bilateral inferior parietal lobule (left IPL and right IPL), same coordinates as in previous spDCM studies [4]. A standard DCM analysis involves a specification of plausible models, which are then allows the model parameters to be estimated following Bayesian model selection. In both pre- and post-RT conditions, the procedure selected the fully connected model as the best model with a posterior probability of almost 1. The fully connected model had 24 parameters describing the extrinsic connections between nodes, the intrinsic (self-connections) within nodes and neuronal parameters describing the neuronal fluctuations within each node. We used Bayesian Parametric Average to quantify the differences between pre- and post-RT, and a classical multivariate test—canonical variate analysis to test for any significances in these differences [4]. Our results showed no significant differences in causal relationships among the above nodes following RT (all P > 0.05).

**Conclusions** Four weeks of RT could not induce significant changes in effective connectivity among DMN nodes. Long-term RT effect on brain changes warrants further investigation.

**Acknowledgements:** This work was supported by the Office of Naval Research.

References

1. Tang YY, Holzel BK, Posner MI. The neuroscience of mindfulness meditation. *Nat Rev Neurosci.* 2015;16:213–25.

2. Tang YY, Lu Q, Geng X, Stein EA, Yang Y, Posner MI. Short-term meditation induces white matter changes in the anterior cingulate. Proc Natl Acad Sci USA. 2010;107:15649–52.

3. Tang YY, Tang R, Posner MI. Brief meditation training induces smoking reduction. Proc Natl Acad Sci USA. 2013;110:13971–75.

4. Razi A, Kahan J, Rees G, Friston KJ. Construct validation of a DCM for resting state fMRI. Neuroimage. 2015;106:1–14.

P50

Modeling neuron oscillation of implicit sequence learning

Guangsheng Liang¹, Seth A. Kiser²,³, James H. Howard, Jr.³, Yi-Yuan Tang¹
¹Department of Psychological Sciences, Texas Tech University, TX 79409, USA; ²The Department of Veteran Affairs, District of Columbia VA Medical Center, Washington, DC 20420, USA; ³Department of Psychology, The Catholic University of America, Washington, DC 20064, USA

Correspondence: Yi-Yuan Tang - yiyuan.tang@ttu.edu

BMC Neuroscience 2016, 17(Suppl 1):P50

Implicit learning (IL) occurs without goal-directed intent or conscious
awareness but has important influences on our everyday function-
ing and overall health such as environmental adaptation, developing
habits and aversions. Most of IL studies used event-related poten-
tials (ERPs) to study brain response by taking the grand average of all
event-related brain signals. How neuron oscillation (EEG frequency
band) involves in IL remains unknown. Moreover, ERP analysis requires
brain signals that are not only time locked, but also phase locked to
the event, therefore the information with phase locked signals are
missed and not presented in potentials. To address this issue, we
applied time-frequency analysis and cluster-based permutation test
in this study.

Fifteen healthy participants were recruited to perform three ses-
sions of triplets learning task (TLT), an IL task commonly used in the
field [1]. Three successive cues were presented and participants were
asked to observe the first two cues and only respond to the third cue
(target) by pressing corresponding keys. During the task, EEG signals
were recorded. Cluster based permutation on alpha and theta band
is used to deal with family-wise error rate and in the same time, help
to find out difference occurred in specific time range along with spa-
tial information among different triplet types.

Base on the behavioral result, overall learning occurs in session1, while triplet-specific learning takes place in session2. We find significant difference in both alpha (8–13 Hz) and theta (4–8 Hz) frequency band. For alpha band, power modulation shows significant difference between high versus low frequency triplet group in session2 in the frontal cortex. For theta band, theta power shows significant difference between session1 and session3 in the frontal cortex. It started from as early as target onset until the end of the trial in high frequency triplet group. However, in the low frequency triplet group, the power differential occurs later, from around 1000 ms till the end of the next trial.

**Conclusions** Behavioral result showed that the brain learned the regularity of sequence implicitly. Alpha power modulation indicated that the brain allocated resource in attention among two different triplet types. Theta power modulation showed the difference of memory processing and retrieval among two different triplet types. Our results indicated that participants did not find the regularity of the triplet types till the end of the study, but the brain in fact reacts to these two different triplet types differently.

**Acknowledgements:** This work was supported by the Office of Naval Research.

Reference

1. Howard JH, Howard DV, Dennis N, Kelly AJ. Implicit learning of predictive relationships in three-element visual sequences by young and old adults. J Exp Psychol Learn Mem Cogn. 2008, 34: 1139-57.
P51

**The role of cerebellar short-term synaptic plasticity in the pathology and medication of downbeat nystagmus**

Julia Goncharenko¹, Neil Davey¹, Maria Schilstra¹, Volker Steuber¹
¹Centre for Computer Science and Informatics Research, University of Hertfordshire, Hatfield, AL10 9EJ, UK

**Correspondence:** Julia Goncharenko - i.goncharenko@herts.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P51

Downbeat nystagmus (DBN) is a common eye fixation disorder that is linked to cerebellar pathology. DBN patients are treated with 4-aminopyridine (4-AP), a K channel blocker, but the underlying mechanism is unclear. DBN is associated with an increased activity of floccular target neurons (FTNs) in the vestibular nuclei. It was previously believed that the reason for the increased activity of FTNs in DBN is a pathological decrease in the spike rate of their inhibitory Purkinje cell inputs, and that the effect of 4-AP in treating DBN could be mediated by an increased Purkinje cell activity, which would restore the inhibition of FTNs and bring their activity back to normal [1]. This assumption, however, has been questioned by in vitro recordings of Purkinje cells from tottering (tg/tg) mice, a mouse model of DBN. It was shown that therapeutic concentrations of 4-AP did not increase the spike rate of the Purkinje cells, but that they restored the regularity of their spiking, which is impaired in tg/tg mice [2].

Prompted by these experiments, Glasauer and colleagues performed computer simulations to investigate the effect of the regularity of Purkinje cell spiking on the activity of FTNs [3]. Using a conductance based FTN model, they found that changes in the regularity of the Purkinje cell input only affected the FTN spike rate when the input was synchronized. In this case, increasing the regularity of the Purkinje cell spiking resulted in larger gaps in the inhibitory input to the FTN and an increased FTN spike rate. These results predict that the increased irregularity in the Purkinje cell activity in DBN should lead to a decreased activity of the FTNs, rather than the increased activity that is found in experiments, and they are therefore unable to explain the therapeutic effect of 4-AP.

However, the model by Glasauer and colleagues does not take short-term depression (STD) at the Purkinje cell—FTN synapses into account. We hypothesized that this absence of STD could explain the apparent contradiction between the experimental [2] and computational [3] results. To study the role of STD in the pathology and 4-AP treatment of DBN, we used a morphologically realistic conductance based model of a cerebellar nucleus (CN) neuron [4, 5] as an FTN model to simulate the effect of irregular versus regular Purkinje cell input. The coefficients of variation of the irregular and regular Purkinje cell spike trains during DBN and after 4-AP treatment, respectively, were taken from recordings from wild-type and tg/tg mice [6], which served as a model system for DBN. We presented the FTN model with synchronized and unsynchronized input and found that, for both conditions, irregular (DBN) input trains resulted in higher FTN spike rates than regular (4-AP) ones. In the presence of unsynchronized Purkinje cell input, the acceleration of the FTN spike output during simulated DBN and the deceleration during simulated 4-AP treatment depended on STD at the Purkinje cell synapses. Our results provide a potential explanation for the pathology and 4-AP treatment of pathological nystagmus.

**References**

1. Glasauer S, Kalla R, Buttner U, Strupp M, Brandt T. 4-aminopyridine restores visual ocular motor function in upbeat nystagmus. J Neurol Neurosurg Psychiatry. 2005;76:451–3.

2. Alvina K, Khodakhah K. The therapeutic mode of action of 4-aminopyridine in cerebellar ataxia. J Neurosci. 2010;30:7258–68.

3. Glasauer S, Rössert C, Strupp M. The role of regularity and synchrony of cerebellar Purkinje cells for pathological nystagmus. Ann NY Acad Sci. 2011;1233:162–7.

4. Steuber V, Schultheis NV, Silver RA, de Schutter E, Jaeger D. Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells. J Comp Neurosci. 2011;30:633–58.

5. Luthman J, Hoebeek FE, Maex R, Davey N, Adams R, de Zeeuw CI, Steuber V. STD-dependent and independent encoding of input irregularity as spike rate in a computational model of a cerebellar nucleus neuron. Cerebellum. 2011;10:667–82.

6. Hoebeek FE, Stahl JS, van Alphen AM, Schonewille M, Luo C, Rutteman M, van den Maagdenberg AM, Molenaar PC, Goossens HH, Frens MA, et al. Increased noise level of Purkinje cell activities minimizes impact of their modulation during sensorimotor control. Neuron 2005, 45(6):953–965.

P52

**Nonlinear response of noisy neurons**

Sergej O. Voronenko¹,², Benjamin Lindner¹,²

¹Department of Physics, Humboldt University, Berlin, 10099, Germany;

²Bernstein Center for Computational Neuroscience, Berlin, 10115, Germany

**Correspondence:** Sergej O. Voronenko - sergej@physik.hu-berlin.de

BMC Neuroscience 2016, 17(Suppl 1):P52

In many neuronal systems that exhibit high trial-to-trial variability the time-dependent firing rate is thought to be the main information channel for time-dependent signals. However, for nerve cells with low intrinsic noise and highly oscillatory activity synchronization, mode locking and frequency locking seem to be of major importance. Here, we present an extension to the linear response theory [1, 2] for the leaky integrate-and-fire neuron model to second order and demonstrate how the time-dependent firing rate can exhibit features that are reminiscent of mode-locking and frequency-locking. Although our theory allows to predict the response to general weak time-dependent signals, the second-order effects are best demonstrated using cosine signals as in Fig. 34A. We consider a leaky integrate-and-fire model for which the subthreshold voltage, Fig. 34B, is subject to the signal and to Gaussian white noise. Whenever the voltage hits the threshold, it is reset to zero and a spike time is recorded in the raster plot, Fig. 34C. The firing rate can be obtained numerically by averaging over the spike trains or via a perturbation approach similar to the weakly nonlinear analysis in [3]. We find that the firing rate can exhibit pronounced nonlinear behavior as can be seen from the excitation of a harmonic oscillation in Fig. 34D. Further effects that are not shown in Fig. 34 but are revealed by our analysis are a signal-dependent change of the mean firing rate and a pronounced nonlinear response to the sum of two cosine signals.

**Summary and conclusions** Here we demonstrate that the time-dependent firing rate (equivalent to the instantaneous population rate for neurons driven by a common stimulus) can exhibit pronounced

<figure><img src="image_39.png" /><figcaption>**Fig. 34** Nonlinear modulation of the firing rate by a cosine signal. **A** Signal, **B** subthreshold voltage, **C** rasterplot, **D** The time-dependent firing rate (red, noisy trace) is significantly different from the linear theory (dashed line) but is accurately described by the second-order response (solid line)</figcaption></figure>
nonlinearities even for weak signal amplitudes. The linear theory does not only give quantitatively wrong predictions but also fails to capture the timing of the modulation peaks. Hence, our theory has not only implications for sinusoidal stimulation that is commonly used to study dynamic properties of nerve cells but also demonstrates the relevance of the nonlinear response for the encoding of complex time-dependent signals.

**Acknowledgements:** This work was supported by the BMBF (FKZ: 01GQ1001A) and the DFG (research training group GRK1589/2).

## References

1. Brunel N, Chance FS, Fourcaud N, Abbott LF. Effects of synaptic noise and filtering on the frequency response of spiking neurons. PRL. 2001;86(10):2186-9.

2. Lindner B, Schimansky-Geier L. Transmission of noise coded versus additive signals through a neuronal ensemble. PRL. 2001;86(14):2934-7.

3. Brunel N, Hakim V. Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput. 1999;11(7):1621-71.

## P53

### Behavioral embedding suggests multiple chaotic dimensions underlie *C. elegans* locomotion

Tosif Ahamed¹, Greg Stephens¹,²

¹Biological Physics Theory Unit, Okinawa Institute of Science and Technology, Okinawa 904-0495, Japan; ²Department of Physics and Astronomy, Vrije Universiteit Amsterdam

**Correspondence:** Tosif Ahamed - tosif.ahamed@oist.jp

BMC Neuroscience 2016, 17(Suppl 1):P53

Behavior is the primary output of an organism; genetic and neural circuits, no matter how complex, seek to optimize this output. A

quantitative understanding of behavior is therefore crucial to our understanding of biological processes. A key characteristic of natural behavior is variability; even the most stereotyped movements such as reaching to a target, which are similar in aggregate, can vary substantially from trial to trial. In motor control such variability is often ascribed to noise in the sensorimotor control circuit. On the other hand, deterministic dynamical systems can generate variability intrinsically when operating in a chaotic regime. Differentiating between the two is important as they generate separate mechanistic predictions about how variability is generated in the brain. Here, we use tools from nonlinear dynamics to understand behavioral variability in the movement of *C. elegans*. We reconstruct a 6-dimensional phase space by developing a novel extension of multivariate singular systems analysis [1] and applying it to a low-dimensional but complete representation of worm postures obtained from videos of freely foraging worms [2]. At a coarse level, the reconstructed phase space naturally separates into three stereotyped behaviors: forward locomotion, reversals and turns (Fig. 35A, B). However, there is also substantial variability at finer scales, which is reflected in positive maximal Lyapunov exponents (MLE) [3] within trajectories corresponding to each individual behavior (Fig. 35C). The MLEs calculated this way differ significantly from MLEs calculated from a random shuffle of the data that preserves its linear structure (or power spectrum). This implies that the positive MLEs, which indicate sensitive dependence to initial conditions in *C. elegans* behavior are a result of nonlinear structure present in the dynamics. These results are strengthened by the fact that we observe little inter-animal variability in the estimated values of MLE, additionally the values also agree well with the estimated time scales of the three behaviors. Based on these observations we propose that *C. elegans* behavior might be driven by the activity of multiple coupled chaotic attractors. We expect our analysis will also be relevant in understanding global neural dynamics, recently imaged in freely-moving worms [4].

## References

1. Read PL. Phase portrait reconstruction using multivariate singular systems analysis. Phys D. 1993;69(3):353-65.

2. Stephens GJ, Johnson-Kerner, B, Bialek W, Ryu WS. Dimensionality and dynamics in the behavior of *C. elegans*. PLoS Comput Biol. 2008;4(4):e1000028.

3. Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A. 1994;185(1):77-87.

4. Nguyen JP, Shipley FB, Linder AN, Plummer GS, Liu M, Setru SU, Shaevitz JW, Leifer AM. Whole-brain calcium imaging with cellular resolution in freely behaving *Caenorhabditis elegans*. PNAS. 2015;120507110.

## P54

### Fast and scalable spike sorting for large and dense multi-electrodes recordings

Pierre Yger¹, Baptiste Lefebvre¹, Giulia Lia Beatrice Sampinato¹, Elric Esposito, Marcel Stimberg et Olivier Marre¹

¹Institut de la Vision, INSERM UMRS 968, CNRS UMR 7210, Paris

**Correspondence:** Pierre Yger - pierre.yger@inserm.com

BMC Neuroscience 2016, 17(Suppl 1):P54

Understanding how assemblies of neurons encode information requires recording of large populations of cells in the brain. In recent years, multi-electrode arrays and large silicon probes have been developed to record simultaneously from thousands of electrodes packed with a high density. However, these new devices challenge the classical way to do spike sorting. First, the large number of electrodes preclude approaches based on manual clustering. Even automatic approaches need to be fast enough to handle the amount of extracellular data. Second, the density of the electrodes is high enough so that a single spike will be detected on many electrodes. So the different channels must be processed simultaneously. Third, within a large and dense array of electrodes, overlapping spikes are rather the rule than the exception, and it is known that classical clustering methods cannot easily capture the synchronous occurrence of two spikes from two different cells [1].

<figure><img src="image_40.png" /><figcaption>**Fig. 35** Phase space portrait and divergence of nearby trajectories. **A** The top panel shows the orthogonal relationship between the forward and reversal behaviors, while the bottom panel shows the transition from reversal to an omega turn in the phase space. To aid visualization color coding is done by radial distance from the origin. **B** Escape response visualized in the phase planes. When the worm is hit with a laser impulse, it makes a reversal, followed by an omega turn and then resumes forward crawling. **Color map** encodes time in frames. **C** Divergence curves for the three different attractors. **Y-axis** shows the exponential of the divergence between neighboring trajectories plotted on a semilog scale on the y axis, each curve corresponds to a single worm ($n = 12$). $\lambda_L$ is estimated by calculating the slope of the linear region. **Boxplots** show the range of $\lambda_L$ obtained from different animals</figcaption></figure>
Here we developed a new software to solve all these aforementioned issues, based on a highly automated algorithm to extract spikes from extracellular data, and show that this algorithm reached near optimal performance both in vitro and in vivo. The algorithm is composed of two main steps: (1) a "template-finding" phase to extract the cell templates, i.e. the pattern of activity evoked over many electrodes when one neuron fires an action potential; (2) a "template-matching" phase where the templates are matched onto the raw data to find the location of the spikes. The manual intervention by the user is reduced to the minimal, and the time spent on manual curation did not scale with the number of electrodes. For the template-finding phase, we start by detecting all the possible times in the raw data that could contain a spike. Spikes are then clustered into groups using a density-based clustering derived from [1], and we then extract the template corresponding to each group. In the fitting phase, we match the templates onto the raw data with a method that allows amplitude variation for each template [2]. The algorithm is written in Python and is entirely parallelized such that it can handle large amount of data. It also provides a graphical user interface so that the output of the algorithm can be checked, and to refine the sorting.

We tested our algorithm with large-scale data from in vitro and in vivo recordings, from 32 and up to 4225 electrodes. In all cases, we estimated its performance on data with ground truth, i.e. cases where the solution to the sorting problem is at least partially known. The performance was always close to the maximal expected performance. Therefore, our method appears as a general solution to sort spikes from large-scale extracellular recordings.

## References

1. Einевolt GT, et al. Towards reliable spike-train recordings from thousands of neurons with multielectrodes. Curr Opin Neurobiol. 2012;22:11–17.

2. Rodriguez A, et al. Clustering by fast search and find of density peaks. Science. 2014;344(6191):1492–96.

## P55

### Sufficient sampling rates for fast hand motion tracking

Hansol Choi¹, Min-Ho Song²

¹Bernstein Center Freiburg, Institute of Biology III, University of Freiburg, Germany, 79100; ²fourMs group, Dept. Musicology, University of Oslo, Norway, 0371

**Correspondence:** Min-Ho Song - minho.song@imv.uio.no

BMC Neuroscience 2016, 17(Suppl 1):P55

When tracking fine motor behaviors in human body parts, passive marker-based tracking is one of the best-suited methods not only because of its high spatial precision and temporal resolution, but also allowing high degrees-of-freedom [1]. However, the passive marker approach suffers from identity confusion problem (Fig. 36A) between

the markers. As the speed of motion increases, sufficient sampling rate is required to avoid the problem. In a recent study [2], we reported that the problem still occurs even with the sampling rate significantly higher than the Nyquist sampling rate. The study suggested a sampling rate criterion to avoid identity problem for the worst-case condition. In this poster, the confusion problem is tested in more realistic human motor control behavior. Grids of 3 × 3 markers with different distances (1, 1.5 and 2 cm) were attached to a skilled piano player's right hand (Fig. 36B). The experimental task was repeated right-hand alternative keystrokes between D#5 and D#7 (two octave) with a tempo of 176 bpm for 10 s. This is an excerpt from Liszt's *La Campanella*, which requires fast horizontal jump of the right-hand. These motions were recorded with 7 optical motion capture cameras (Qualisys Ltd. Oqus 400) changing the sampling rates from 50 to 200 Hz. The maximum frequency components of these hand movements were lower than 8 Hz. The probability of successful tracking is measured by counting the number of successful repetition of the center marker (Fig. 36C). Estimated required sampling rates for successful tracking (where the probabilities reach 100 %) were 101, 137z, and 181 Hz (fitted to piece-wise linear functions by expectation maximization). The theoretically predicted values are 176, 235, and 353 Hz [2].

We found that the required sampling rates are lower than the theoretical criterion. This is because the theoretical prediction was developed to avoid the worst case where marker trajectories overlap from perfect periodic motion; not realistic for human movement, which has variability. Our results show that in practical situations involving human movements, the sampling criterion can be weakened considerably. But, it should be noted that a motion slower than 10 Hz still requires more than 100 Hz, which far exceeds the Nyquist sampling rate.

## References

1. Guerra-Filho G. Optical motion capture: theory and implementation. J Theor Appl Inf. 2005;12(2):61–8.9

2. Song M-H, Godøy RI. How fast is your body motion? Determining a sufficient frame rate for an optical motion tracking system using passive markers. PLoS One (in press).

## P56

### Linear readout of object manifolds

SueYeon Chung¹, Dan D. Lee², Haim Sompolinsky¹,³

¹Center for Brain Science, Harvard University, Cambridge, MA 02138, USA; ²Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA; ³Edmond and Lily Safra Center for Brain Sciences, Hebrew University, Jerusalem 91904, Israel

**Correspondence:** SueYeon Chung - schung@fas.harvard.edu

BMC Neuroscience 2016, 17(Suppl 1):P56

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity [1]. It has been hypothesized that object identity can be decoded from high level representations, by simple downstream readout networks. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We generalize Gardner's statistical mechanical analysis of points [2, 3] and establish a replica theory of linear classification of manifolds synthesizing statistical and geometric properties of high dimensional signals. We show how changes in the dimensionality, size, and shape of the object manifolds affect the capacity and the distribution of configurations in downstream perceptors (Fig. 37).

Our analysis shows how linear separability of the manifolds depends intimately upon the dimensionality, size and shape of the manifolds. These properties are expected to differ at different stages in the sensory hierarchy. Thus, the present work enables systematic analysis of the degree to which this reformatting enhances the capacity for object classification in different sensory processing stages. The present work lays the groundwork for a computational theory of neuronal processing of objects in the presence of variability, providing quantitative measures for assessing the properties of representations in biological and artificial neural networks.

<figure><img src="image_41.png" /></figure>
<figure><img src="image_42.png" /></figure>

## References

1. DiCarlo JJ, Cox DD. Untangling invariant object recognition. Trends Cogn Sci. 2007;11(8):333-41.

2. Gardner E. Maximum storage capacity in neural networks. EPL (Europhys Lett). 1987;4(4):481.

3. Abbott LF, Kepler TB. Universality in the space of interactions for network models. J Phys A Math Gen. 1989;22(12):2031.

## P57

### Differentiating models of intrinsic bursting and rhythm generation of the respiratory pre-Bötzinger complex using phase response curves

Ryan S. Phillips¹,², Jeffrey Smith¹

¹NINDS, NIH, Bethesda, MD 20892, USA; ²Department of Physics, University of New Hampshire, Durham, NH, 03824, USA

**Correspondence:** Ryan S. Phillips - Ryan.Phillips@nih.gov

BMC Neuroscience 2016, 17(Suppl 1):P57

The pre-Bötzinger complex (PBC) is an essential rhythmogenic brain-stem nucleus located in the ventrolateral medulla. Rhythmic output from the PBC is relayed through premotor and motor neurons to the diaphragm and intercostal muscles to drive the active inspiratory phase of respiration. The specific biophysical mechanisms responsible for generating rhythmic bursting and network synchronization are not well understood and remain a highly controversial topic within the field. A wide variety of biophysical mechanisms have been proposed to explain the origins of intrinsic bursting and rhythmogenesis including persistent sodium currents [1, 2], calcium-activated nonspecific cation channels [2, 3], inositol trisphosphate (IP3) signaling [2], and synaptic mechanisms [4]. Computational simulations of these models produce similar patterns of bursting and network synchronization compared to each other and experimental recordings despite having different underlying mechanisms. In this theoretical study we demonstrate a method to differentiate between biophysically distinct models using phase response curves (PRCs). PRCs characterize the change in phase of an oscillator as a function of the timing of a perturbation to the system. Depolarizing and hyperpolarizing perturbations were generated by incorporating the light sensitive channels, Channelrhodopsin-2

and Archaerhodopsin, respectively, into our conductance based PBC models. A library of model PBC neurons was generated by varying the conductance of each ion channel over equally spaced intervals. PRCs were then calculated for each neuron capable of producing rhythmic bursting. Preliminary results found that in general depolarizing perturbations produced qualitatively similar PRCs and could both advance or delay the next cycle. Conversely, hyperpolarizing perturbations produced qualitatively distinct PRCs depending on the combination of conductance magnitudes. In conclusion, these PRCs provide a method for differentiating models of intrinsic bursting and rhythm generation based on underlying biophysical mechanisms and provide a means for interpreting experimentally derived PRCs from the PBC.

## References

1. Butera RJ, Rinzel J, Smith JC. Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. J Neurophysiol. 1999;82:382-97.

2. Jasinski PE, Molkov YI, Shevtsova NA, Smith JC, Rybak IA. Sodium and calcium mechanisms of rhythmic bursting in excitatory neural networks of the pre-Bötzinger complex: a computational modelling study. Eur J Neurosci. 2013;37:212-30.

3. Rubin JE, Hayes JA, Mendenhall JL, Del Negro CA. Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations. Proc Natl Acad Sci USA. 2009;106:2939-44.

4. Guerrier C, Hayes JA, Fortin G, Holcman D. Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics. Proc Natl Acad Sci. 2015;120:4219-27.

## P58

### The effect of inhibitory cell network interactions during theta rhythms on extracellular field potentials in CA1 hippocampus

Alexandra Pierri Chatzikalymniou¹,², Katie Ferguson¹,³, Frances K. Skinner¹,²,⁴

¹Krembil Research Institute, University Health Network, Toronto, ON, Canada; ²Department of Physiology, University of Toronto, Toronto ON, Canada; ³Department of Neuroscience, Yale School of Medicine, New Haven, CT, 06520, USA; ⁴Department of Medicine (Neurology), University of Toronto, Toronto ON, Canada

**Correspondence:** Alexandra Pierri Chatzikalymniou - alexandra.chatzikalymniou@mail.utoronto.ca

BMC Neuroscience 2016, 17(Suppl 1):P58

Oscillatory local field potentials (LFPs) are extracellularly recorded potentials with frequencies of up to ~500 Hz. They are associated with a number of physiological functions in health and disease and complement the information obtained by analysis of spikes. Because multiple neuronal processes contribute to the LFP, the signal is inherently ambiguous and more difficult to interpret than spikes [1]. However, the biophysical origin of LFPs is well understood in the framework of volume conductor theory [4]. Using "LFPy" [3], a python package that implements this framework, we construct a pyramidal cell model in CA1 hippocampus which generates extracellular potentials. Our pyramidal cell model receives inhibitory synaptic input from four different types of CA1 interneuron populations. These interneuron models are taken from a previous, experimentally constrained inhibitory network model developed to understand spontaneous theta (4-12 Hz) rhythms as expressed in an intact hippocampus preparation [2]. We investigate the contribution of the different inhibitory cell type interactions to the extracellular potential. In our current model we placed a virtual electrode probe along the vertical axis of the pyramidal cell to record its output in a layer dependent manner. We identified distinct regimes where specific interneuron cell type interactions distinctively affect the polarity, amplitude and frequency of the LFP signal (Fig. 38). We also distinguish between regimes where synaptic connection strengths preserve the extracellular potential frequency versus those that lead to lag or abolishment of the extracellular rhythm. In this way, our model helps us understand the cellular contributions to extracellular field patterns that arise in experimental recordings as a function of biologically relevant network states when the efficacy of inhibitory connections dynamically varies.
<figure><img src="image_43.png" /><figcaption>**Fig. 38** Example of the spatial attenuation of the extracellular potential signal for a particular set of inhibitory connections. The temporal traces at two electrode locations are represented with blue and green dots accordingly. Average over the absolute maximum extracellular potential amplitudes is shown in 2D space. According to the schematic the rate of the extracellular signal spatial attenuation generated by the pyramidal cell is approximately 400 µ</figcaption></figure>

**Acknowledgements:** Supported by NSERC Canada, U. of T. Fellowship P.S.L., and the SciNet HPC Consortium.

## References

1. Buzsáki G, Anastassiou CA, Koch C. The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nat Rev Neurosci. 2012;13:407–20.

2. Ferguson KA, Huh CYL, Amilhon B, Williams S, Skinner FK. Network models provide insight into how oriens-lacunosum-moleculare (OLM) and bistratified cell (BSC) interactions influence local CA1 theta rhythms. Front Syst Neurosci. 2015;9:110

3. Lindén H, Hagen E, Leski S, Norheim ES, Pettersen KH, Einevoll GT. LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front Neuroinform. 2014;7:41.

4. Rall W, Shepherd GM. Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. J Neurophysiol. 1968;31:884–915.

## P59

### Expansion recoding through sparse sampling in the cerebellar input layer speeds learning

N. Alex Cayco Gajic¹, Claudia Clopath², R. Angus Silver¹

¹Department of Neuroscience, Physiology and Pharmacology, University College London, London, UK; ²Department of Bioengineering, Imperial College London, London, UK

**Correspondence:** N. Alex Cayco Gajic - natasha.gajic@ucl.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P59

Feed-forward networks often have many more output neurons than input neurons. This is thought to enable them to project neuronal activity patterns into a higher dimensional space. When such expansion recoding is combined with sparse representations it provides a powerful way to increase the separation between activity patterns [1–4]. In the input layer of the cerebellar cortex, granule cells (GCs) integrate sensorimotor input from the less numerous mossy fibre afferents (MFs), with each GC sampling from only 2 to 7 local MFs. Recent work has revealed that this sparse sampling of input by GCs provides an optimal tradeoff between information transmission and sparsification over a range of activity levels [4]. Moreover, theories of cerebellar function have linked expansion recoding under sparse regimes to pattern separation and associative learning [5, 6]. However, the relationship between the feedforward excitatory synaptic connectivity and the learning performance is poorly understood.

To investigate how the number of MF inputs per GC affects the performance we simulated a model of an 80µ ball of the MF-GC feedforward layer with either random or clustered MF activation. The connectivity

profile of the network was constrained with recent anatomical data [4]. MF stimulation was modeled as random binary patterns with varying levels of population activity and correlation, and GCs as high-thresholded rectified linear units. We then measured the speed at which granule cell population activity can be used to classify random patterns via backpropagation learning as the number of synaptic inputs was varied. We found that the largest speedup of learning in the GC activity (compared to learning based on the MF inputs) occurred when each GC received only a few synaptic inputs. We probed this result by analyzing the eigenvalues of the covariance matrix of the population-level activity, finding that sparse sampling of MF inputs allows GCs to both expand and decorrelate MF activity patterns. Interestingly, this feature is robustly preserved even in the presence of clustered inputs. In summary, we find that sparse sampling combined with sparsification of activity allows GCs to optimize both pattern expansion and pattern decorrelation.

**Acknowledgement:** This research is funded by the Wellcome Trust.

## References

1. Laurent G. Olfactory network dynamics and the coding of multidimensional signals. Nat Rev Neurosci. 2001;3:884–95.

2. Olshausen BA, Field DJ. Sparse coding of sensory inputs. Curr Opin Neurobiol. 2004;14:481–7.

3. Billings G, Piasini E, Lorincz A, Nusser Z, Silver A. Network structure within the cerebellar input layer enables lossless sparse encoding. Neuron. 2014;83:960–74.

4. Babadi B, Sompolinsky H. Sparseness and expansion in sensory representations. Neuron. 2014;83:1–14.

5. Marr D. A theory of cerebellar cortex. J Physiol. 1969;202:437–70.

6. Tyrell T, Wilshaw D. Cerebellar cortex: its simulation and the relevance of Marr's theory. Philos Trans R Soc B. 1992;336:239–57.

## P60

### A set of curated cortical models at multiple scales on Open Source Brain

Padraig Gleeson¹, Boris Marin¹, Sadra Sadeh¹, Adrian Quintana¹, Matteo Cantarelli², Salvador Dura-Bernal³, William W. Lytton³, Andrew Davison⁴, R. Angus Silver¹

¹Department of Neuroscience, Physiology and Pharmacology, University College London, London, UK; ²Metacell LLC, San Diego, CA, USA; ³State University of New York Downstate Medical Center, Brooklyn, NY, USA;

⁴Neuroinformatics group Unité de Neurosciences, Information et Complexité, CNRS, Gif sur Yvette, France

**Correspondence:** Padraig Gleeson - p.gleeson@ucl.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P60

Computational models of spiking cortical networks are implemented using a variety of approaches from large scale models with simplified point neurons and anatomically inspired connectivity, to networks on smaller scales with morphologically and biophysically detailed neurons. In between these scales many published models have used intermediate representations of neurons (e.g. conductance based with one compartment or abstract morphologies). These studies, and the associated modelling scripts, provide many potential starting points for experimental and theoretical neuroscientists wishing to use biologically constrained cortical models in their investigations. In addition, there are an increasing number of public neuroinformatics resources which are providing structured experimental data on the electrophysiology, connectivity and morphology of cortical neurons. While these modelling and experimental resources should lead to a proliferation in well constrained cortical models there remain a number of practical and technical barriers to more widespread development and use of such models among researchers.

The Open Source Brain (OSB) initiative (http://www.opensourcebrain.org) is a resource for collaborative development of models in computational neuroscience. Sharing of models in standardised representations such as NeuroML 2 [1] and PyNN is encouraged and actively supported on the site. Conversion of cell and network models to NeuroML allows them to be visualised and analysed in 3D in a standard web browser through the OSB website. We have recently added
a feature to allow simulations to be executed on our servers (e.g. by conversion to NEURON) and the results displayed within the browser. We have been actively converting published cortical models to NeuroML format and making these available on OSB. These range from point neuron models [2, 3], to abstract [4] and detailed [5] multicompartmental models. We are working to develop these and others into a curated set of cortical models in a common format which can be used as the basis for new models. We have also developed frameworks for importing resources from neuroinformatics datasets such as the Allen Institute Cell Types database (http://celltypes.brain-map.org) and NeuroMorpho.org (http://neuromorpho.org). We have greatly improved compatibility between PyNN and NeuroML, allowing the modeller freedom to choose between procedural (Python) and declarative (XML) model specification. We have also extended a model optimization framework (https://github.com/NeuralEnsemble/NeuroTune) facilitating generation of new NeuroML models from electrophysiological data. All of this work is aimed at making existing cortical models easier to access, visualise and simulate, simplifying development of new models based on these prototypes, and ensuring the latest experimental datasets can be used to constrain and validate complex models of cortical function.

**Acknowledgements:** This work has been primarily funded by the Wellcome Trust (101445/095667).

## References

1. Cannon RC, Gleeson P, Crook S, Ganapathy G., Marin B, Piasini E, Silver RA. LEMS: a language for expressing complex biological models in concise and hierarchical form and its use in underpinning NeuroML2. Front Neuroinform. 2014;8:79.

2. Izhikevich E. Simple model of spiking neurons. IEEE Trans Neural Netw. 2003;14(6):1569-72.

3. Brunel N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci. 2000;8(3):183-208.

4. Traub RD, Contreras D, Cunningham MO, et al. Single-column thalamo-cortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. J Neurophysiol. 2005;93(4):2194-2232.

5. Markram H, Muller E, Ramaswamy S, et al. Reconstruction and simulation of neocortical microcircuitry. Cell. 2015;163(2):456-92.

## P61

### A synaptic story of dynamical information encoding in neural adaptation

Luozheng Li<fnref n="1" />, Wenhao Zhang<fnref n="1" />, Yuanyuan Mi<fnref n="1" />, Dahui Wang<fnref n="1" />,<fnref n="2" />, Si Wu<fnref n="1" />

¹State Key Laboratory of Cognitive Neuroscience & Learning, IDG/ McGovern Institute for Brain Research, Beijing Normal University, Beijing 100875, China; ²School of System Science, Beijing Normal University, Beijing 100875, China

**Correspondence:** Si Wu - wusi@bnu.edu.cn

BMC Neuroscience 2016, 17(Suppl 1):P61

Adaptation refers to the general phenomenon that a neural system dynamically adjusts its response property according to the statistics of external inputs [1]. In response to a prolonged constant stimulation, neuronal firing rates always first increase dramatically at the onset of the stimulation; and afterwards, they decrease rapidly to a low level close to background activity (see Fig. 39A). This attenuation of neural activity seems to be contradictory to our experience that we can still sense the stimulus after the neural system is adapted [2]. Thus, it prompts a question: where is the stimulus information encoded during the adaptation? Here, we investigate a computational model in which the neural system employs a dynamical encoding strategy during the neural adaptation: at the early stage of the adaptation, the stimulus information is mainly encoded in the strong independent firings; and as time goes on, the information is shifted into the weak but concerted responses of neurons (see Fig. 39B). We find that short-term plasticity [3], a general feature of synapses, provides a natural mechanism to achieve this goal. Furthermore, we demonstrate that with balanced excitatory and inhibitory inputs, this correlation-based information can be read out efficiently. The implications of this study on our understanding of neural information encoding are discussed.

<figure><img src="image_44.png" /><figcaption>**Fig. 39** Firing rates, synaptic efficacy and cross-correlation change during the adaptation. **A** The time course of firing rates and the averaged synaptic efficacy of the network during the adaptation. (ux) is temporally enhanced during the adaptation due to the STF, but in the long term, strong STD drives the synaptic efficacy to background level. Stimulation is during 0-1500 ms. **B** The enhancement of cross-correlation between neurons during the adaptation</figcaption></figure>

**Conclusions** We have explored a dynamical encoding strategy in neural adaptation. By constructing a computational model, we show that this can be achieved through varying the information encoder during the adaptation, that is, at the early stage of the adaptation, the stimulus information is mainly encoded in the strong and independent firings of neurons; and as time goes on, the stimulus information is shifted into the weak but concerted responses of neurons. This shift of information encoder can be naturally implemented via STP, a general feature of synapses.

## References

1. Wark B, Lundstrom B N, Fairhall A. Sensory adaptation. Curr Opin Neurobiol. 2007;17(4):423-9.

2. Christopher deCharms R, Merzenich MM. Primary cortical representation of sounds by the coordination of action-potential timing. Nature. 1996;381:13.

3. Markram H, Wang Y, Tsodyks M. Differential signaling via the same axon of neocortical pyramidal neurons. Proc Natl Acad Sci. 1998;95(9):5323-28.

## P62

### Physical modeling of rule-observant rodent behavior

Youngjo Song<fnref n="1" />, Sol Park<fnref n="1" />,<fnref n="2" />, Ilhwan Choi<fnref n="2" />, Jaeseung Jeong<fnref n="1" />, Hee-sup Shin<fnref n="2" />

**Correspondence:** Jaeseung Jeong - jsjeong@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P62

There is training room for a mouse. In the room, there are two lights which is used as a cue for reward, and there are two reward zone. If a mouse goes left reward zone when the left light cue turns on, the mouse gets reward, and if a mouse go right reward zone when the right light cue turns on, the mouse gets reward. The reward is given by brain stimulation from the electrode implanted in MFB. A pair of mice trained individually in the room in order to make them understand the meaning of two light cues. After individual training, the two mice released in the same training room at the same time. In this experiment, 15 out of 19 pairs showed tendency to separate their own reward zone.

In order to explain the rodent behavior, we made a computational rodent model. This model is based on Rescorla-Wagner Model. We defined a success rate as probability that a mouse is in the correct reward zone when any cue is given. In each trial, the model mouse learns the left success rate and the right success rate by reinforcement learning. In this model, we assume that success rates for the left cue and right cue are independent and we eliminate social interaction between two model mice.

**Results** The simulation result is given in below figures. Figure 40A is a graph of success rate of a pair of model mice which shows rule between them. You can see the right que success rate of mouse1 and the left que success rate of mouse2 converge to 1, but the left que success rate of mouse1 and the right que success rate of mouse2 converge below 0.4. It means that mouse1 tends to move only when the right cue is given,

<footnote n="1">¹Bio and Brain Engineering, KAIST, Daejeon, 34141, Republic of Korea;</footnote>

<footnote n="2">²Center for Cognition and Sociality, IBS, Daejeon, 34047, Republic of Korea</footnote>
<figure><img src="image_45.png" /></figure>

and mouse2 tends to move only when the left cue is given. Our model mice, however, shows this rule with less probability than actual behavior result. Figure 40B, C 43% of model mice showed rule, but 79% of actual mice showed rule in behavior experiment.

**Conclusion** If we assume the mouse as a simple independent creature which doesn't have social element, they show rules with lower probability than the actual mouse in behavior experiment. It means that we can't regard the mouse as a non-social creature. Therefore, we have to add the social factors such as empathy or cooperation to simulate actual rodent behavior.

**Reference**

1. Glimcher PW, Fehr E. Neuroeconomics, 2nd ed. Academic Press.

P64

**Predictive coding in area V4 and prefrontal cortex explains dynamic discrimination of partially occluded shapes**

Hannah Choi¹,²,³, Anitha Pasupathy²,³, Eric Shea-Brown¹,³

¹Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA; ²Department of Biological Structure, University of Washington, Seattle, WA 98195, USA; ³UW Institute

for Neuroengineering, University of Washington, Seattle, WA 98195, USA

**Correspondence:** Hannah Choi - hannahch@uw.edu

BMC Neuroscience 2016, 17(Suppl 1):P64

The visual system recognizes objects in natural scenes without difficulty, even when most objects are partially occluded. The neural basis of this capacity is unknown. Recent results from primate area V4, an intermediate stage in the shape processing pathway, suggest that feedback from higher cortices may be important for the emergence of V4 shape selective signals [1] when animals are engaged in discriminating partially occluded shapes. Here we implement predictive coding, which has been previously applied to explain responses in early visual areas [2], to investigate possible mechanisms underlying robust discrimination of partially occluded shapes in V4. We propose that higher cortical areas such as prefrontal cortex (PFC) make predictions about V4 activities; when these PFC signals are relayed via feedback to V4, they can reproduce the delayed peak of V4 responses observed in experiments. With a model (Fig. 41A) composed of PFC and V4 units that are selective for different input features, we capture response characteristics of V4 and PFC measured in experiments, by combining feed-forward sensory inputs and feedback predictions to maximize the posterior probability of the responses. We found that inclusion of the feedback predictions results in stronger shape-selective responses across a range of occlusion levels (Fig. 41B), thus maintaining robust discrimination of partially occluded shapes (Fig. 41C).

<figure><img src="image_46.png" /></figure>

**Acknowledgements:** This research was supported by the Washington Research Foundation Innovation Postdoctoral Fellowship in Neuroengineering (HC), National Science Foundation CRCNS Grant IIS1309725 (AP), and NEI Grant R01EY018839 (AP).

**References**

1. Kosai Y, El-Shamayleh Y, Fyll AM, Pasupathy A. The role of visual area V4 in the discrimination of partially occluded shapes. J Neurosci. 2014;34:8570–84.

2. Rao RPN, Ballard DH. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature Neurosci. 1999;2:79–87.

P65

**Stability of FORCE learning on spiking and rate-based networks**

Dongsung Huh¹, Terrence J. Sejnowski¹,²

¹The Salk Institute for Biological Studies, La Jolla, CA 92037 USA; ²Division of Biological Sciences, University of California at San Diego, La Jolla, CA 92095 USA

**Correspondence:** Dongsung Huh - huh@salk.edu

BMC Neuroscience 2016, 17(Suppl 1):P65

Neurons in the brain often exhibit complex activity patterns, with fluctuations on time scales of several seconds. The generation of complex patterns is critical for directing movements, and is likely to be involved in processing time-varying input (such as speech). However, it is not yet understood how networks of spiking neurons, with time constants of only a few milliseconds, could exhibit such slow dynamics. This should be contrasted with rate-based neural networks, which can be easily trained to generate arbitrary complex activity patterns in a reservoir-based manner [1] by an iterative training method (FORCE learning [2]). So far, however, FORCE learning has not led to successful training of spiking neural networks.

Here, we analyze the stability of the networks that result from such learning schemes. For linear rate-based networks, we can analytically predict the full dynamic property of the networks. As the network's recurrent connectivity reaches the "edge of chaos", the neuronal activity exhibits a broad distribution of phase, providing appropriate basis for generating the fluctuations. For weaker recurrent connectivity, however, the phase distribution becomes much narrower. In this case, the trained network exhibits highly non-normal structure, which becomes unstable even under small perturbations. Our analysis also illuminates the source of instability in training spiking networks, which is mainly due to the rectified nature of the neuronal output. In numerical simulations, rectified-linear rate networks exhibit narrow phase distribution, even with strong recurrent connectivity near the edge of chaos. Moreover, introducing spiking-dynamics further
reduces the width of the distribution, leading to highly unstable network dynamics. Our result reveals the limitation of the reservoir-based approaches, and may lead to more stable, alternative training methods.

**Acknowledgements:** Supported by HHMI.

## References

1. Jaeger H, Haas H. Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science. 2004;304:78–80.

2. Sussillo D, Abbott LF. Generating coherent patterns of activity from chaotic neural networks. Neuron. 2009;63(4):544–57.

## P66

### Stabilising STDP in striatal neurons for reliable fast state recognition in noisy environments

Simon M. Vogt¹, Arvind Kumar²,³, Robert Schmidt¹,²

¹BrainLinks-BrainTools, Cluster of Excellence, University of Freiburg, Germany; ²Faculty of Biology and Bernstein Center Freiburg, University of Freiburg, Germany; ³Department of Computational Biology, Royal Institute of Technology Stockholm, Sweden

**Correspondence:** Simon M. Vogt - simonsunimail@gmail.com

BMC Neuroscience 2016, 17(Suppl 1):P66

The brain must be able to quickly identify environmental states based on sensory inputs and select appropriate actions. To obtain neurons that respond selectively to states with short response latencies, a neural plasticity rule is required. Spike timing dependent plasticity (STDP) is known to find the earliest predictors of spatiotemporal spike patterns without supervision. While this feature of STDP is often seen as a hindrance when aiming to reproduce an exact target output spike train, we exploit it to generate short-latency, reliable pattern recognition.

There are, however, some difficulties in using STDP in real-world continuous scenarios. In models, presynaptic firing rates are often assumed to be stationary or have constant correlation for simplification, and STDP rule parameters must be closely fitted to form a stable fixed point in the postsynaptic firing rate and normalise postsynaptic activity. Any deviation from these requirements can cause the postsynaptic neuron to become quiet before it is able to form strong selectivity, or exhibit a runaway effect that makes the neuron responsive to a large set of inputs. Soft-bound STDP with a weight-dependent attractor has been suggested as a means for stabilising postsynaptic activity, but this actively hinders separation of spatiotemporal patterns from background noise: as during learning the synaptic weight moves away from the attractor, noisy input becomes more likely to undo these weight changes. Furthermore, activity-dependent scaling also aims to keep the postsynaptic neuron active indefinitely, so neurons may lose any learned selectivity when enduring long periods of background noise. Interpolations between different types of STDP have been suggested, but a problem of balance between premature selectivity and longtime noise robustness remains.

We solve this dilemma by including a slow continuous potentiation in our model, which depends on metabolic cost of maintaining strong synapses and slowly vanishes as neurons become selective. It is independent of pre- or postsynaptic activity and can recover silent neurons if a metabolic cost function allows it to. Together with negative-integral STDP as taken from experimental data, it stabilises the activity of untrained neurons for a much wider range of rule parameters and heterogeneous input activity. Our model maintains a unimodal weight distribution while the postsynaptic neuron has not yet become selective, but does not impair the formation of selectivity to spatiotemporal patterns. Selectivity is quickly achieved as soon as patterns are present, even after enduring long periods of noise. Connections that only present noise, represent only other patterns, or present only late parts of a trained pattern become ineffective as the neuron becomes selective, and may be pruned. Any selectivity is hence ensured to represent actual spatiotemporal spike patterns

that were at some point present in the postsynaptic neuron's inputs. This makes the process of training neurons to detect environmental states encoded as spatiotemporal patterns more robust to variations in input statistics and rule parameters, thus easing application in larger-scale networks.

Our model of fast pattern detection may apply specifically to the striatum of the basal ganglia where fast reliable decisions need to be made within milliseconds. Unsupervised learning should coexist with rare dopaminergic reinforcement to continuously form new representations of environmental events and decide which of these events are behaviourally important and which can safely be ignored.

**Acknowledgements:** Cluster of Excellence BrainLinks-BrainTools funded by German Research Foundation (DFG, Grant Number EXC 1086).

## P67

### Electrodiffusion in one- and two-compartment neuron models for characterizing cellular effects of electrical stimulation

Stephen Van Wert¹, Steven J. Schiff¹,²

¹Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA; ²Departments of Neurosurgery and Physics, The Pennsylvania State University, University Park, PA 16802, USA

**Correspondence:** Stephen Van Wert - szv124@psu.edu

BMC Neuroscience 2016, 17(Suppl 1):P67

Standard approaches for modeling the neuronal effects of electrical fields and currents (such as [1, 2]) apply transmembrane current to Hodgkin-Huxley membrane patches without regard to ion fluxes and conservation of ions inside and outside the cell. We propose cellular models that reflect polarization and preserve the biophysics of the spaces the neurons are embedded within. By including ion fluxes and maintaining conservation of mass and charge, the gradients of ionic concentrations both within and outside of the neuron can be accounted for. This requires characterizing the ionic fluxes with electrodiffusion, such that ionic charge gradients as well as ionic concentration gradients drive flux. This electrodiffusion mechanism, derived from Nernst-Planck flux equation, not only allows for more accurate modeling of physiological and pathophysiological conditions with substantial ionic and volume changes, but it also provides a means to model application of electrical stimulation. The model being developed here builds on recent one-compartment model development in [3] that extends the Hodgkin-Huxley formalism in several distinct ways, most notably in using conservation to track all ion fluxes and volume changes to determine the extra- and intra-cellular concentrations. The proposed model also extends the model in [3] to a two compartment model which allows for simulation of neuronal polarization with control applied in the direction of a soma-dendritic axis.

We first characterize the resultant model dynamics in the absence of any control stimulus and compare these to the dynamics seen with standard diffusion. In particular, the dynamics are characterized through trajectories of dynamically evolving variables, with a focus on bifurcation structure at points where the dynamics transition from different states such as normal firing, seizure, or spreading depression. We then simulate the effects of applying excitatory or inhibitory control on these dynamics and optimize the dynamics of the neuron to be consistent with experimental evidence. Such a model gives very different results from the customary approach to modeling the effects of electrical stimulation, where the stimulation is applied internally or externally to a neuron without taking the nature of the charge carriers present into account. There are a variety of effects of excitatory and inhibitory stimulation observed now that could not be possible before, and we can describe the trajectories of the effects of such stimulation in ways that shed light on multiple experimental scenarios.

This type of model development offers the ability to understand a wide variety of previously unexplained experimental observations for both excitatory and inhibitory stimulation. Doing so offers a platform
for us to study electrical feedback control of neuronal systems and to
offer model-based control strategies for pathological dynamics such
as seizures and spreading depression.

References

1. Park E-H, Barreto E, Gluckman BJ, Schiff SJ, So P. A model of the effects of applied electric fields on neuronal synchronization. J Comput Neurosci. 2005;19: 53–70.

2. Berzhanskaya J, Chernyy N, Gluckman BJ, Schiff SJ, Ascoli GA. Modulation of hippocampal rhythms by subthreshold electric fields and network topology. J Comput Neurosci. 2013;34(3):369–89.

3. Wei Y, Ullah G, Schiff SJ. Unification of neuronal spikes, seizures, and spreading depression. J Neurosci. 2014;34(35):11733–43.

P68

STDP improves speech recognition capabilities in spiking
recurrent circuits parameterized via differential evolution Markov
chain Monte Carlo

Richard Veale¹, Matthias Scheutz²

¹National Institute for Physiological Sciences, Okazaki, Aichi, Japan;

²Department of Computer Science, Tufts University, Medford, MA, USA

**Correspondence:** Richard Veale - richard@nips.ac.jp

BMC Neuroscience 2016, 17(Suppl 1):P68

A major issue in using spiking neural circuits for pragmatic tasks such as speech recognition is how to parameterize them. Here, we apply a hybrid Differential Evolution/Markov Chain Monte Carlo (DE/MCMC) [1, 2] approach to estimate optimal parameters for a spiking neural circuit that is used for real time speech recognition [3] from raw auditory input using PSWEEP2 (rveale.com/software.php). To avoid the expensive training step, we use a surrogate measure of word recognition performance. Specifically, we maximize average within-word similarity in the neural circuit's state space trajectory, while simultaneously minimizing between-word similarity. We executed the algorithm for 7000 generations (48 h of runtime) using 2016 cores of the super computer Big Red II at Indiana university. The average fitness increases significantly with successive generations. Panel a is a visualization of the first 3 principle components of the state space for the exemplars of each different word category (shown as different colors). The different categories move to take more distant trajectories through the state space with successive generations. We verify that the state-space separation is a good surrogate measure of word recognition performance by taking the set of circuits with the highest fitness from the first, middle, and last 100 generations and training readout neurons for the 7-word corpus. Word recognition performance increases from 19 to 71 to 85 % (Fig. 42).

Finally, we evaluated the performance benefit of adaptation to sen-
sory stimuli via synaptic plasticity mechanisms, to make pragmatic
use of our previous work investigating auditory habituation [4]. We
take the most performant parameter points that were found during
the parameter sweep, and test their fitness before and after expo-
sure to 100 presentations of the word stimuli while a nearest-neigh-
bor temporally asymmetric Hebbian plasticity model of spike timing
dependent plasticity (STDP) is implemented in all excitatory synapses.
Although sensitive to STDP model parameters, Panel B shows that
word recognition performance can be improved by as much as 8 % by
familiarizing a neural circuit to the type of sensory stimulus that it will
be used to compute. This follows previous findings by Triesch et al. [5],
who reported similar effects in non-spiking neural networks.

<figure><img src="image_47.png" /></figure>

References

1. Veale R, Isa T, Yoshida M. Applying differential evolution MCMC to parameterize large-scale spiking neural simulations. In: IEEE conference on evolutionary computation (CEC). IEEE, p. 1620–27.

2. Laloy E, Vrugt JA. High-dimensional posterior exploration of hydrologic models using multiple-try dream (zs) and high-performance computing, Water Resour Res. 2012;48(1)

3. Veale R, Scheutz M. Neural circuits for any-time phrase recognition. In: Proceedings of the 34th annual conference of the Cognitive Science Society; 2012. p. 1072–7.

4. Veale R, Scheutz M. Auditory habituation via spike-timing dependent. In: Proceedings of the international conference on development and learning and epigenetic robotics (ICDL), San Diego, CA; 2012.

5. Lazar A, Pipa G, Triesch J. Fading memory and time series prediction in recurrent networks with different forms of plasticity. Neural Netw. 2007;20(3):312–22.

P69

Bidirectional transformation between dominant cortical neural
activities and phase difference distributions

Sang Wan Lee¹‚²‚³

¹Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea; ²Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea; ³KAIST Institute for Health Science and Technology, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea

Correspondence: Sang Wan Lee - sangwan@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P69

The brain is a complex nonlinear dynamic system comprising multiple different types of subsystems. Each subsystem encodes different types of information, and its states are context-dependent. Unlike sensory or motor processing occurring at relatively early or terminal stages of functional hierarchy, cognitive processes, including learning, inference, and top-down attention, require interactions between brain's multiple subsystems. The associated neural dynamics inevitably leave an imprint on neural activity patterns over a wide areas of cortex. Considerable progress has been made toward understanding such functional network dynamics. This includes the causal connectivity [1], its extension to distinguish causality from correlation within nonseparable weakly connected dynamic systems [2], and the integrated information theory to quantify the effect of a neuronal network connectivity on the increase in the amount of information above and beyond the capability of a single locally connected network [3, 4]. However, none of these methods is applicable to real-time analyses when the network size is large.

Here I develop a simple and efficient computational framework for
analyzing cortical dynamics both in time and space, arising from
complex interactions between brain's multiple subsystems. Accom-
modating the fact that both a covariance and a gram matrix can be
computed by using a combination of a certain idempotent matrix with
a data matrix, I derive a set of matrix operators F, with which one set
of eigenvectors associated with a covariance matrix of data and of
mean-corrected data can be transposed to another set of eigenvec-
tors associated with a gram matrix, and vice versa (see Fig. 43). For
example, suppose that a *d*-by-*n* data matrix is a set of time-series data
recorded from multiple locations of cortices where *d* and *n* refers to
the number of electrodes and time points, respectively, and *d* ≪ *n*.
One can then perform a singular value decomposition (SVD) for the
*d*-by-*d* covariance or gram matrix to obtain an associated eigenvector
set, followed by applying matrix operator *F'* to the eigenvector set to
convert it to the eigenvector set of their counterparts. There is no need
to perform SVD for *n*-by-*n* matrix whose computational load is high. If
*n* ≪ *d*, then one could simply start with performing the SVD for the
*n*-by-*n* matrix, followed by applying the matrix operator *F* to its eigen-
vector set. It is noted that the acquired *d*-by-*1k* eigenvectors and *n*-by-
*1k* eigenvectors correspond to dominant cortical neural activities and
phase difference distributions, respectively.

**Conclusion** An efficient computational framework for analyzing cortical dynamics both in time and space is proposed, taking into account the relationship between a covariance and a gram matrix. For analyzing
<figure><img src="image_48.png" /><figcaption>**Fig. 43** Computational framework for analyzing space–time cortical dynamics. *T* is an idempotent projection matrix</figcaption></figure>

neural data acquired from multiple locations of cortices, the framework replaces the SVD with a simple matrix operator *F* so as to reduce a heavy computational load of performing SVD on large-size data matrices. In doing so, it allows efficient bidirectional transformation between dominant neural activities and phase difference distributions.

**Acknowledgements:** I thank Barclay Lee and Dae-Hyun Kim for their assistance. This work was supported by the research fund of the KAIST (Korea Advanced Institute of Science and Technology) (Grant code: G04150045).

## References

1. Seth AK. Causal connectivity of evolved neural networks during behavior. Network. 2005;16:35–54.

2. Sugihara G, May R, Ye H, Hsieh C, Deyle E, Fogarty M, Munch S. Detecting causality in complex ecosystems. Science. 2012;338(6106):496–500.

3. Balduzzi D, Tononi G. Qualia: the geometry of integrated information. PLoS Comput Biol. 2009;5(8):e1000462.

4. Edlund JA, Chaumont N, Hintze A, Koch C, Tononi G, Adami C. Integrated information increases with fitness in the evolution of animats. PLoS Comput Biol. 2011;7(10):e1002236.

## P70

### Maturation of sensory networks through homeostatic structural plasticity

Júlia Gallinaro¹, Stefan Rotter¹

¹Bernstein Center Freiburg and Faculty of Biology, University of Freiburg, Freiburg, Baden-Württemberg, 79194, Germany

**Correspondence:** Simon M. Vogt - julia.gallinaro@bcf.uni-freiburg.de

BMC Neuroscience 2016, 17(Suppl 1):P70

Neurons in the adult visual cortex of mice prefer to make synapses with neurons responding to similar visual features. As such a bias in connectivity is not observed at the time of eye opening, it has been proposed that the functional subnetworks are formed through rewiring of recurrent synaptic connections, induced by visual experience [1]. However, it is not clear according to which rules this structure develops. The emergence of feature specific wiring was recently demonstrated in a balanced network model with appropriate rules of functional synaptic plasticity [2]. In this model, however, connectivity was evaluated based on the strength of already existing synapses, and the structure of the network remained unchanged throughout the simulation.

Referring to recent findings of homeostatic regulation of cortical activity in rodent visual cortex in vivo [3], we employ here a structural plasticity rule based on firing rate homeostasis described previously [4] for simulating network restructuring during sensory stimulation. We show that, next to other biologically meaningful properties, feature specific connectivity also emerges in a balanced network of changing structure (see Fig. 44), using a plasticity rule that does not depend on spike timing.

<figure><img src="image_49.png" /><figcaption>**Fig. 44** Network connectivity before and after sensory stimulation. **A, B.** Connectivity matrix, pre- and post-synaptic neurons are sorted according to their preferred orientation (PO) and subdivided into groups. **C, D.** Mean output connectivity plotted against the difference between pre and post PO</figcaption></figure>

**Acknowledgements:** Supported by the Erasmus Mundus Joint Doctoral program EuroSPIN, the German Federal Ministry of Education and Research, grant 01GQ0830, and the state of Baden-Württemberg through bwHPC.

## References

1. Ko H, Cossell L, Baragli C, Antolik J, Clopath C, Hofer SB, Mrsic-Flogel TD: The emergence of functional microcircuits in visual cortex. Nature. 2013;496:96–100.

2. Sadeh S, Clopath C, Rotter S. Emergence of functionalspecificity in balanced networks with synapticplasticity. PLoS Comput Biol. 2015;11:e1004307.

3. Bishop HI, Zito K. The downs and ups of sensorydeprivation: evidence for firing rate homeostasis in vivo. Neuron. 2013;80:247–9.

4. van Ooyen A: Using theoreticalmodels to analyseneuraldevelopment. Nat Rev Neurosci. 2011;12:311–26.

## P71

### Corticothalamic dynamics: structure, number of solutions and stability of steady-state solutions in the space of synaptic couplings

Paula Sanz-Leon¹,², Peter A Robinson¹,²

¹School of Physics, University of Sydney, New South Wales, Australia;

²Center for Integrative Brain Function, University of Sydney, New South Wales, Australia

**Correspondence:** Paula Sanz-Leon - paula.sanz-leon@sydney.edu.au

BMC Neuroscience 2016, 17(Suppl 1):P71

The interconnections of a model of the corticothalamic system [1] define an 8-dimensional parameter space where specific combinations of dimensions correspond to one of the three loops of the system (e.g., intracortical, corticothalamic and intrathalamic). The form of the steady-state equation of the corticothalamic system imposes an odd number of solutions, which in terms of dynamics correspond to fixed points of the system. Here, the structure of regions with different number of solutions is systematically investigated within physiologically valid ranges of synaptic couplings representing different brain states [2, 3]. For instance, Fig. 45A, Bdisplay the regions where the
<figure><img src="image_50.png" /><figcaption>**Fig. 45** Three dimensional subsets of the 8D corticothalamic coupling space. **A, B** Regions with 1, 3 or 5 roots are enclosed by surfaces (blue, violet and yellow respectively). The sharp transition between zones of 1–3 roots along the $v_{ee}$ axis (excitatory intracortical feedback) indicates the plane at which the total intracortical feedback ($v_{ee} + v_{ei}$) changes sign. The difference between **A, B** is the value of $v_{ei}$ (inhibitory intracortical feedback). In **a** the probability of having multiple roots is lower than in **B**</figcaption></figure>

steady state equation has one, three or five solutions for two 3-dimensional subsets of the full space. These results show how small changes in the connectivity can cause additional roots of the steady state equation to appear or vanish. More importantly, they illustrate the effect of intracortical feedback: for more than one solution to exist the total intracortical feedback needs to be negative (inhibitory). The occurrence of multiple roots happens for parameter values that characterize normal arousal states [3], indicating that the approach presented here has a potential to (i) quantify and predict the existence of additional (abnormal) arousal states and (ii) categorize subtle differences in states such as anesthesia, coma [4].

## References

1. Robinson PA, Rennie CJ, Wright JJ, Bourke PD. Steady states and global dynamics of electrical activity in the cerebral cortex. Phys Rev E. 1998;58:3557–71.

2. Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL. Prediction of electroencephalographic spectra from neurophysiology. Phys Rev E. 2001; 63:021903.

3. Abeysuriya RG, Rennie CJ, Robinson PA. Physiologically based arousal state estimation and dynamics. J Neurosci Methods. 2015;253:55–69.

4. Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilcocks LC. Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. I. A thermodynamics analogy. Phys Rev E. 2001;64:942–53.

# P72
## Optogenetic versus electrical stimulation of the parkinsonian basal ganglia. Computational study

Leonid L. Rubchinsky¹,², Chung Ching Cheung¹, Shivakeshavan Ratnadurai-Giridharan¹

¹Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA; ²Stark Neurosciences Research Institute, Indiana University School of Medicine, Indianapolis, IN, USA

**Correspondence:** Leonid L. Rubchinsky - Irubchin@iupui.edu

BMC Neuroscience 2016, 17(Suppl 1):P72

Deep brain stimulation (DBS) is used as a therapeutic procedure to treat symptoms of several neurological and neuropsychiatric disorders. In particular it is used to treat motor symptoms of Parkinson's disease (PD) by delivering high-frequency regular stimulation to subcortical targets. Hypokinetic symptoms of PD are associated with excessive oscillatory synchronized activity in the beta frequency band, and effective DBS is believed to suppress it. An alternative way to stimulate neural circuits is an emerging technology of optogenetics. It is an experimental technique and it is not clear if it eventually will be possible to implement it in clinical practice. However it is used as an experimental tool, and maybe, in time, it will be developed into safe therapeutic technique.

The goal of his study is to explore how effective an optogenetic stimulation in comparison with electrical stimulation in their network effects on elevated synchronized oscillatory activity. We use a model for the basal ganglia activity [1], which was developed to reproduce experimentally observed beta-band activity patterns [2]. We introduce electrical stimulation as well as optogenetic stimulation of two types: excitatory via channelrhodopsin and inhibitory via halorodopsin. We explore the effect of different stimulation types on oscillatory synchronized dynamics and consider the efficacy of stimulation for different kind of network's dynamics.

All three modes of stimulation can decrease beta synchrony that is commonly associated with hypokinetic symptoms of Parkinson's disease. Generally speaking, growing intensity of stimulation leads to larger suppression of the beta-band synchronized oscillatory activity. But the actions of different stimulation types on the beta activity may differ from each other. Electrical DBS and optogenetic excitation have somewhat similar effects on the network. Both of these stimulation types cause desynchronization and suppression of the beta-band bursting. As intensity of stimulation is growing, they synchronize the network at higher (non-beta) frequencies in a close to tonic spiking dynamics. Optogenetic inhibition effectively reduces spiking and bursting activity of the targeted neurons.

We compare the stimulation modes in terms of the minimal effective current delivered to basal ganglia neurons in order to suppress beta activity below a threshold: the less stimulation current is needed to suppress the activity, the more efficacious stimulation is. We found that optogenetic inhibition usually requires less effective current than electrical DBS to achieve beta suppression. Optogenetic excitation, while as not efficacious as optogenetic inhibition, still usually requires less effective current than electrical DBS to suppress beta activity.

Thus our results suggest that optogenetic stimulation may introduce less of effective currents to a neuron than conventional electrical DBS, but still achieve sufficient beta activity suppression. Optogenetics is presently not used in humans. However, it was implemented in the basal ganglia of non-human primates [3]. So we suppose our results may motivate further research into applicability of optogenetic technologies in humans. Optogenetic stimulation is also used as a research tool. Our results suggest that it may be more effective than electrical stimulation in control of synchronized oscillatory activity, because it does its job with less current injected into the neurons.

**Acknowledgements:** The study was supported by ICTSI and the Indiana University Health – Indiana University School of Medicine Strategic Research Initiative.

## References

1. Park C, Worth RM, Rubchinsky LL. Neural activity in Parkinsonian brain: the boundary between synchronized and nonsynchronized dynamics. Phys Rev E. 2011;83:042901.

2. Park C, Worth RM, Rubchinsky LL. Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson's disease. J Neurophysiol. 2010;103:2707–16.

3. Galvan A, Hu X, Smith Y, Wichmann T. In vivo optogenetic control of striatal and thalamic neurons in non-human primates. PLoS One. 2012;7(11):e50808.

# P73
## Exact spike-timing distribution reveals higher-order interactions of neurons

Safura Rashid Shomali¹, Majid Nili Ahmadabadi¹,², Hideaki Shimazaki³, S Nader Rasuli⁴,⁵

¹School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran; ²School of ECE, College of Engineering, University of Tehran, Tehran, 14155-6619, Iran; ³RIKEN Brain Science Institute, Wako, Saitama, 351-0198, Japan; ⁴Department of Physics, University of Guilan, Rasht, 41335-1914, Iran; ⁵School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran

**Correspondence:** Safura Rashid Shomali - safura@ipm.ir

BMC Neuroscience 2016, 17(Suppl 1):P73
It has been suggested that variability in spike patterns of individual neuron is largely due to noisy fluctuations caused by asynchronous synaptic inputs balanced near the threshold regime [1–3]. In this regime, small fluctuations in synaptic inputs to a neuron do cause output spikes; because the membrane potential is maintained below but close enough to the threshold potential. To successfully transfer signals under such noisy conditions, it is proposed that a few relatively stronger synapses and/or an assembly of nearly synchronous ones form "signaling inputs" [4]. Thus one fundamental question is how such relatively strong signaling input modifies the spiking activity of a post-synaptic neuron which receives noisy background inputs balanced near the threshold regime. Nonetheless, analytical studies on the effect of the signaling input under such conditions are scarce even with the popular leaky integrate-and-fire (LIF) neuron model. Here we analytically study the impact of a specified signaling input on spike timing of the postsynaptic LIF neuron which receives noisy inputs at the threshold regime. To this end, we first revisit Fokker-Planck analysis of a first spike-timing distribution when the LIF neuron receives noisy synaptic inputs, but no signaling input, at the threshold regime. We then perform perturbation analysis to investigate how a signaling input modifies this first spike-timing distribution. Fortunately, we could solve all terms of perturbation analytically and find the exact first spike-timing distribution of the postsynaptic neuron; it is applicable to not only excitatory but also inhibitory input. This analytical solution allows us to describe the statistics of output spiking activity as a function of background noise, membrane dynamics, and signaling input's timing and amplitude.

The proposed analysis of signaling input provides a powerful framework for studying information transmission, neural correlation, and timing-dependent synaptic plasticity. Among them, we investigate the impact of common signaling inputs on population activities of postsynaptic neurons. Using mixture models based on our analytical first spike-timing distribution, we calculate the higher-order interactions [5] of postsynaptic neurons in different network architectures. Comparing these results with higher-order interactions, measured from experimental data in monkey V1 [6], we try to answer whether one can reveal network architecture, responsible for the ubiquitously observed sparse activities.

### References

1. Vreeswijk C, Sompolinsky H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science. 1996;274: 1724–6.

2. Renart A, De La Rocha J, Bartho P, Hollender L, Parga N, Reyes A, Harris KD. The asynchronous state in cortical circuits. Science. 2010;327:587–90.

3. Tan AY, Chen Y, Scholl B, Seidemann E, Priebe NJ. Sensory stimulation shifts visual cortex from synchronous to asynchronous states. Nature. 2014;509:226–9.

4. Teramae Jn, Tsubo Y, Fukai T. Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links. Sci Rep. 2:485.

5. Nakahara H, Amari S. Information-geometric measure for neural spikes. Neural Comput. 2002;14:2269–316.

6. Ohiorhenuan IE, Victor JD. Information-geometric measure of 3-neuron firing patterns characterizes scale dependence in cortical networks. J Comput Neurosci. 2011;30:125–41.

## P74

### Neural mechanism of visual perceptual learning using a multi-layered neural network

Xiaochen Zhao¹, Malte J. Rasch¹

¹State Key Lab of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing 100875, China

**Correspondence:** Malte J. Rasch - malte.rasch@bnu.edu.cn

BMC Neuroscience 2016, 17(Suppl 1):P74

Recently, a study [1] has found by recording the activities of neurons in monkeys performing a contour detection task that the response properties of the primary visual cortex (V1) change continuously

during perceptual learning. In particular, the figure-background contrast was continuously enhanced in the course of learning. However, the exact neural circuit mechanisms that causes the V1 responses to change during perceptual learning remain unclear. In order to understand how the underlying neural network needs to change, we here train a multi-layered neural network model to perform the contour detection task on the very same visual stimuli as in the experiments and investigate the network's performance and the resulting synaptic weight structure.

In this study, we first model the V1 representation of each visual stimulus by using a non-classical receptive field model (NCRF) which takes into account orientation selective inhibition [3]. We further assume that the higher visual areas (up to a decision unit) are hierarchically structured, read out the V1 activity, and learn to change their synaptic weights to optimally perform the contour detection task. AGREL (attention-gated reinforcement learning) algorithm [2], which considers feedback connections and biologically plausible local synaptic adjustments, is applied to train the network (see Fig. 46). We found that the multi-layered model trained with AGREL could replicate the behavioral performance increase in a contour detection task as observed in experiments. Moreover, learning the network model structure showed enhanced synaptic weights in the region of the detected contour. It further demonstrated that "predictive" feedback signals from higher layers facilitate the responses of V1 neurons to the contour and thus increased the figure-background contrast in V1 with improved behavioral performance. The results suggest that the experimental observed V1 response facilitation could be caused by selective synaptic strengthening of feed-forward and feed-back pathways.

### References

1. Yan Y, Rasch MJ, Chen M, et al. Perceptual training continuously refines neuronal population codes in primary visual cortex. Nat Neurosci. 2014;17(10):1380–7.

2. Roelfsema PR, van Ooyen A. Attention-gated reinforcement learning of internal representations for classification. Neural Comput. 2005;17(10):2176–214.

3. Zeng C, Li Y, Yang K, et al. Contour detection based on a non-classical receptive field model with butterfly-shaped inhibition subregions. Neurocomputing. 2011;74(10):1527–34.

<figure><img src="image_51.png" /><figcaption>**Fig. 46** V1 representations of the stimuli and simulation results of the model. A V1 representations of the stimuli by using NCRF model.</figcaption></figure>

B Model performance increases with perceptual training. C Synaptic

weight changes after perceptual learning
P75

Inferring collective spiking dynamics from mostly unobserved systems

Jens Wilting¹, Viola Priesemann¹,²

¹Max-Planck-Institute for Dynamics and Self-Organization, D-37077

Göttingen, Germany; ²Bernstein Center for Computational Neuroscience, University of Göttingen, D-37075 Göttingen, Germany

**Correspondence:** Jens Wilting - jwilting@nld.ds.mpg.de

BMC Neuroscience 2016, 17(Suppl 1):P75

What can we know about a high-dimensional dynamical system if we
can only observe a very small part of it? This problem of spatial sub-
sampling is common to almost every area of research where spatially
extended, time evolving systems are investigated, and is particularly
severe when assessing population spiking dynamics in neuroscience.
Previous studies have shown that subsampling can lead to spuri-
ous results when assessing the dynamical state of spiking activity, in
particular when discriminating whether neural networks operates at
criticality [1, 2]. Here we present further insight why the distance to
criticality is systematically overestimated, and introduce a novel esti-
mator which for the first time allows to correctly infer the distance to
criticality even under strong subsampling.

Neuronal systems have been proposed to operate close to criticality, because in models criticality maximizes information processing capacities [e.g. 3]. Indeed, power-law distributions of the avalanche size, an indication of criticality, have been found for local field potentials from in vitro systems [1] to humans in vivo [4]. However, for neuronal systems criticality also comes with the risk of spontaneous runaway activity, which may lead to pathological states like epilepsy. Experiments indeed indicate that spiking activity in rats, cats, and monkeys is in a sub-critical regime, thereby keeping a safety-margin from criticality [5]. Quantifying the precise distance to criticality may help to shed light on how the brain maximizes its information processing capacities without risking runaway activity.

In neural systems, critical dynamics is typically compared to dynam-
ics from models that resemble branching processes [1]. Their dynam-
ics are controlled by a single parameter, the expected number σ of
postsynaptic spikes generated by one individual spike, showing either
stationary dynamics (sub-critical, σ < 1) or transient growth (super-
critical, σ > 1). For σ = 1 branching processes are critical and produce
heavy tailed avalanche size distributions. We used a driven branching
process, which allows to exactly match the model neuron firing rate to
that observed in experiments for any σ. We propose a stochastic rep-
resentation of subsampling and show that under subsampling estab-
lished approaches to inferring σ are substantially biased. We derived
a novel approach based on multistep regression [6], which for the first
time allows to quantify the distance to criticality even under strong
subsampling. Our method generalizes to auto-regressive processes
with both additive and multiplicative noise, making it widely applica-
ble in diverse fields of research. We validate our method by applying
subsampling to simulated branching networks with invasion, and also
to a network of integrate-and-fire neurons.

We applied this method to spike recordings from awake macaque
monkeys prefrontal cortex, cat visual cortex, and rat hippocampus. We
found that neuronal population activity operates close to criticality,
but in a subcritical regime with 0.94 < σ < 0.995. These results point
at a novel universal organization principle: spiking dynamics in vivo is
in a subcritical regime which does not yield maximum, but sufficient
information processing capacity, and at the same time keeps a safety-
margin from unstable supercritical states.

**References**

1. Beggs J, Plenz D. Neuronal avalanches in neocortical circuits. J Neurosci. 2003;23(35):11167-77.

2. Priesemann V, Munk MHJ, Wibral M. Subsampling effects in neuronal avalanche distributions recorded in vivo. BMC Neurosci. 2009;10:40.

3. Boedecker J, Obst O, Lizier JT, Mayer NM, Asada M. Information processing in echo state networks at the edge of chaos. Theory Biosci. 2012;131:205-13.

4. Priesemann V, Valerrame M, Wibral M, Le Van Quyen M. Neuronal avalanches differ from wakefulness to deep sleep—evidence from intracranial depth recordings in humans. PloS Comput Biol. 2013;9(3):e1002985.

5. Arviv O, Goldstein A, Shriki O. Near-critical dynamics in stimulus-evoked activity of the human brain and its relation to spontaneous resting-state activity. J Neurosci. 2015;35(41):13927-42.

6. Priesemann V, et al. Spike avalanches in vivo suggest a driven, slightly subcritical brain state. Front Syst Neurosci. 2014;8:108.

7. Wilting J, Priesemann V. Quantifying the distance to criticality under subsampling. BMC Neurosci. 2015;16:O3.

P76

How to infer distributions in the brain from subsampled
observations

Anna Levina¹, Viola Priesemann²

¹IST Austria, Klosterneuburg, 3400, Austria; ²BCCN & MPI for Dynamics and Self-Organization, Göttingen, 37077, Germany

**Correspondence:** Anna Levina - anna.levina@ist.ac.at

BMC Neuroscience 2016, 17(Suppl 1):P76

Infering the dynamics of a system from observations is a challenge, even if one can observe all system units or components. The same task becomes even more challenging if one can sample only a small fraction of the units at a time. As a prominent example, spiking activity in the brain can be accessed only for a very small fraction of all neurons in parallel. These limitations do not affect our ability to infer single neuron properties, but it influences our understanding of the global network dynamics or connectivity: Subsampling can hamper inferring whether a system shows scale-free topology or scale-free dynamics (criticality) [1, 2]. Criticality is a dynamical state that maximizes information processing capacity in models, and therefore is a favorable candidate state for brain function. Experimental approaches to test for criticality extract spatio-temporal clusters of spiking activity, called avalanches, and test whether they followed power laws. Avalanches can propagate over the entire system, thus observations are strongly affected by subsampling. We developed a formal ansatz to infer avalanche distributions in the full system from spatial subsampling using both analytical and numerical approaches.

In the mathematical model subsampling from exponential distribu-
tion does not change the class of distribution, but only its parameters.
In contrast, power law distributions, despite their alias "scale-free", do
not manifest as power laws under subsampling [2]. We study changes
in distributions to derive "subsampling scaling" that allows to extrap-
olate the results from subsampling to a full system: P(s) = p<sub>sub</sub>p<sub>sub</sub>(s/
p<sub>sub</sub>) where P(s) is the original distribution, p<sub>sub</sub> is the one under sub-
sampling, and p<sub>sub</sub> = N/M is the probability to sample a unit, N—
number of sampled units, M—system size. In the model with critical
avalanches, subsampling scaling collapses distributions for any N
(Fig. 47B). However, for subcritical models, no distribution collapse is
observed (Fig. 47D). Thus we demonstrate that subsampling scaling
allows to distinguish critical from non-critical systems. With the help of
this novel method we studied dissociated cortical cultures. For these
we artificially subsampled recordings by considering only fraction of
all 60 electrodes. We find that in the first days subsampling scaling
does not collapse distributions well, whereas mature cultures (~from
day 21) allow for a good collapse, indicating development toward criti-
cality (Fig. 47C, E).

**Acknowledgements:** AL received funding from the Marie Curie Actions (FP7/2007–2013) under REA Grant Agreement No. (291734). VP received funding from BMBF Bernstein 01GQ1005B.

**References**

1. Stumpf, MPH, Wiuf C, May RM. Subnets of scale-free networks are not scale-free: sampling properties of networks. PNAS 2005;102(12):4221-24.

2. Priesemann V, Munk MH, Wibral M. Subsampling effects in neuronal avalanche distributions recorded in vivo. BMC Neurosci. 2009;10(1):40.

3. Uhlig M, Levina A, Geisel T, Herrmann JM. Critical dynamics in associative memory networks. Front Comp Neurosci. 2013;7.
<figure><img src="image_52.png" /></figure>

P77
Influences of embedding and estimation strategies on the
inferred memory of single spiking neurons

Lucas Rudelt¹, Joseph T. Lizier², Viola Priesemann¹

¹Department of Non-linear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; ²School of Civil Engineering, The University of Sydney, Sydney, NSW, Australia

**Correspondence:** Lucas Rudelt - l.rudelt@gmail.com

BMC Neuroscience 2016, 17(Suppl 1):P77

Information theory provides a generic framework for study-
ing statistical dependencies, and is widely used in neuroscience.
However, a correct estimation of the involved quantities can be
challenging. For example, a correct estimation of transfer entropy
(TE), TE(X → Y) = I(X⁻, Y⁻), or active information storage (AIS),
AIS(X) = I(X⁻, X), requires past state variables X⁻ and Y⁻ that encode
all information about the past that is relevant when predicting X or Y
[1]. For a spiking neuron, states can be defined by transforming the
spike train into a binary sequence of spike counts in sufficiently small,
equally spaced bins with some bin size Δt (Fig. 48A). For neurons, how-
ever, it is unclear how many past bins a sufficient state variable typi-
cally comprises. In practice, past states have often been limited to only
one time bin to reduce the complexity of estimation. This points at the
main challenge one faces when estimating TE and AIS: A reliable esti-
mation of probabilities from recorded data becomes more and more
difficult with increasing complexity of the state variables, i.e. with
considering more past bins. We used AIS for single spiking neurons to
estimate (a) how much memory there is, (b) how long it reaches typi-
cally into the past, (c) the (non-)linear contributions of the memory. To
this end, we first examined the performance of different estimators

<figure><img src="image_53.png" /></figure>

for a realistic model neuron [2] whose AIS can be directly computed (dashed line, Fig. 48B). Using constant external drive we simulated a recording of 12 h. In a model-free approach, probabilities were directly estimated from relative frequencies using the standard 'plugin' estimator or the 'NSB' estimator [3]. In addition, we fitted a generalized linear model (GLM) whose predictions constitute an estimator that is constrained to linear contributions. For all these estimation strategies, the number of past bins k and thus the time range was systematically varied (Fig. 48B). We then applied the same estimators to in vitro and in vivo recordings (Fig. 48c, d) of 3 h and 1 h duration.

Considering a very small number k of past bins can lead to a sub-
stantial underestimation of AIS. Increasing the number of past bins,
however, leads to severe positive bias of the model-free estimators
when the complexity of the past state becomes too large. This mani-
fests in the estimators exceeding the true AIS (Fig. 48B). Assuming
a point process with linear contributions (GLM), in contrast, allows
a robust estimation but does not capture non-linear effects. This
approach can also be used to take the global past activity of the
neural population into account, thereby unveiling redundancies in
the activity of the single neuron with the population activity. While
the model neuron intrinsically has only linear dependencies on its
past, it is surprising that, in vitro, there also seem to be very little
non-linear contributions and a lot of redundancy. In vivo, the non-
linear contributions are more prominent and the memory is clearly
non-redundant.

We thus showed that appropriate embedding is necessary, otherwise
AIS is underestimated and likewise, TE might be mis-estimated. Fur-
thermore, our results suggest that in vivo the information processing
is more evolved.

**References**

1. Wibral M, Lizier J, Priesemann V. Bits from brains for biologically-inspired computing. Comput Intell. 2015;2:5.

2. Pozzorini, C, Naud R, Mensi S, Gerstner W. Temporal whitening by power-law adaptation in neocortical neurons. Nat Neurosci. 2013;16(7):9428.

3. Nemenman I, Shafee F, Bialek W. Entropy and inference, revisited. Adv Neural Inf Process Syst. 2002;14:471–478.
P78

A nearest-neighbours based estimator for transfer entropy between spike trains

Joseph T. Lizier¹, Richard E. Spinney¹, Mikail Rubinov²,³, Michael Wibral⁴,
Viola Priesemann⁵,⁶

¹Complex Systems Research Group, Faculty of Engineering & IT, The University of Sydney, NSW 2006, Australia; ²Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA 20147, USA; ³Department of Psychiatry, University of Cambridge, Cambridge, UK; ⁴MEG Unit, Brain Imaging Center, Goethe University, 60528 Frankfurt am Main, Germany; ⁵Department of Nonlinear Dynamics, Max Planck Institute for Dynamics & Self-Organization, Göttingen, Germany; ⁶Bernstein Center for Computational Neuroscience, Göttingen, Germany

*Correspondence*: Joseph T. Lizier - joseph.lizier@sydney.edu.au

BMC Neuroscience 2016, 17(Suppl 1):P78

The nature of a directed relationship (or lack thereof) between brain areas is a fundamental topic of inquiry in computational neuroscience [1]. A particular focus of such inquiry is in regards to the analysis of information flows in a network [2], and such investigations take place at all levels of analysis, from interregional connectivity in fMRI imaging data [3] down to directed relationships between spike trains at the neuronal level [4].

In all of the aforementioned studies, information theory provides the primary tool, transfer entropy (TE) [5], for analysis of such directed relationships. TE measures the predictive gain about state transitions in a target time-series from observing some source time-series. While the TE has been used extensively to analyse recordings from fMRI, MEG and EEG for example [1–3], fewer applications [4] have been made to spiking time-series. Although one can apply temporal binning on such time-series before measuring TE on the resultant binary time-series [4], it remains unclear: (a) how to set parameters for this approach (e.g. bin sizes), (b) whether an estimate can be achieved by avoiding temporal binning and instead working directly with continuous-valued time stamps of spikes, and (c) whether such an estimate would actually improve on binning approaches.

Recent theoretical developments have pointed to how transfer entropy may be derived from continuous-valued time-stamps of spikes directly, using spike rates conditioned on previous spike histories [6]. Yet, it is not immediately obvious how an estimator for this form would be constructed, and indeed construction of such an estimator has previously defaulted to a binning or discretisation of time [7]. Here, we propose an estimator for this continuous-time point-process formulation of TE that remains in the continuous-time regime by harnessing a nearest-neighbours approach [8] to matching (rather than binning) inter-spike interval (ISI) histories and future spike-times. By retaining as much information about ISIs as possible, this estimator is expected to improve on properties of TE such as robustness to noise and undersampling, bias removal, and sensitivity, etc. We are currently implementing the proposed estimation algorithm in open-source code (i.e. contributing to JIDT [9] and TRENTOOL [10]), and evaluating the properties of the algorithm particularly in comparison to temporal binning approaches.

References

1. Wibral M, Vicente R, Lizier JT, editors. Directed information measures in neuroscience. Berlin: Springer-Verlag; 2014.

2. Vicente R, Wibral M, Lindner M, Pipa G. Transfer entropy—a model-free measure of effective connectivity for the neurosciences. J Comp Neurosci. 2011;30(1):45–67.

3. Lizier JT, Heinzle J, Horstmann A, Haynes J-D, Prokopenko M. Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity. J Comp Neurosci. 2011;30(1):85–107.

4. Ito S, Hansen ME, Heiland R, Lumsdaine A, Litke AM, Beggs JM. Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model. PLoS One. 2011;6(11):e27431.

5. Schreiber T. Measuring information transfer. Phys Rev Lett. 2000;85:461–4.

6. Bossomaier T, Barnett L, Harré M, Lizier JT. An introduction to transfer entropy: information flow in complex systems. Berlin: Springer; 2016 (in press).

7. Kim S, Putrino D, Ghosh S, Brown EN. A Granger causality measure for point process models of ensemble neural spiking activity. PLoS Comput Biol. 2011;7(3):e1001110.

8. Kraskov A, Stögbauer H, Grassberger P. Estimating mutual information. Phys Rev E. 2004;69(6):066138.

9. Lizier JT. JIDT: an information-theoretic toolkit for studying the dynamics of complex systems. Front Robot AI. 2014;1:11.

10. Lindner M, Vicente R, Priesemann V, Wibral M. TRENTOOL: a Matlab open source toolbox to analyse information flow in time series data with transfer entropy. BMC Neurosci. 2011;12(1):119.

P79

Active learning of psychometric functions with multinomial
logistic models

Ji Hyun Bak¹, Jonathan Pillow²

¹Department of Physics & Lewis-Sigler Institute for Integrative
Genomics, Princeton University, Princeton, NJ 08544, USA; ²Department
of Psychology & Princeton Neuroscience Institute, Princeton University,
Princeton, NJ 08544, USA

*Correspondence*: Ji Hyun Bak - jhbak@princeton.edu

BMC Neuroscience 2016, 17(Suppl 1):P79

As new technologies expand the capacity for making large-scale
measurements of neural activity, there is a growing need for meth-
ods to rapidly characterize behavior and its dependence on stimuli. In
typical experiments, an animal is presented with a stimulus on each
trial and has to select a response among several options. Since such
experiments are costly, a problem of practical importance is to learn
the animal's psychometric choice functions from a minimal amount of
data. Here we show that one can achieve substantial speedups over
traditional randomized designs via active learning, in which stimuli are
selected adaptively on each trial according to an information-theoretic
criterion, as shown in Fig. 49. Specifically, we model behavior with a
multinomial logistic regression model, in which the probability of
each choice given a stimulus depends on a set of linear weights. Our
work extends previous work on this problem [1-3] in several impor-
tant ways. First, we incorporate an explicit lapse rate to account for the
fact that observers may occasionally make errors on "easy" trials due
to lapses in concentration or memory [4]. Second, we develop an effi-
cient method based on Markov Chain Monte Carlo (MCMC) sampling
that is accurate in settings in which the log-likelihood is not concave,
for example as in the presence of lapse rates. Third, we extend consid-
eration for multiple-alternative responses, extending previous work
for binary responses. We compare the performance of our sampling-
based method to one based on a local (Laplace) approximation to

<figure><img src="image_54.png" /><figcaption>**Fig. 49** Example of active learning, simulated with a three-alternatives model on 1D stimulus. After each observation, the psychometric functions are estimated based on the accumulated data, and the next stimulus is chosen to maximize the expected information gain. The estimated psychometric functions (*solid lines*) quickly approach the true functions (*dashed lines*) through the adaptive and optimal choice of stimuli</figcaption></figure>
the posterior [5], and show that failure to incorporate lapse rates can have deleterious effects on the accuracy of inferred parameters under both methods. We test our method on simulated data, as well as on an experimental dataset concerning the multiple-alternative choice behavior of monkeys [6], demonstrating that active sampling of the stimulus space facilitates the learning of the psychometric function significantly, as well as suggesting that the full range of the multi-dimensional stimulus could have been exploited more efficiently using our active learning framework. Finally, we discuss the comparative advantages and disadvantages of the different methods, and how one might adapt these algorithms to achieve best results.

**Acknowledgements:** We thank Anne Churchland for providing the data. JP was supported by the McKnight Foundation, Simons Global Brain Initiative, NSF CAREER Award IIS-1150186, and NIMH grant MH099611. JHB was supported by NSF grant PHY-1521553.

## References

1. Kontsevich LL, Tyler CW. Bayesian adaptive estimation of psychometric slope and threshold. Vis Res. 1999;39:2729-37.

2. Zocchi SS, Atkinson AC. Optimum experimental designs for multinomial logistic models. Biometrics. 1999;55:437-44.

3. DiMattina C. Fast adaptive estimation of multidimensional psychometric functions. J Vis. 2015;15:1-20.

4. Kuss M, Jakel F, Wichmann FA. Bayesian inference for psychometric functions. J Vis. 2005;5:478-92.

5. Lewi J, Butera R, Paninski L. Sequential optimal design of neurophysiology experiments. Neural Comput. 2009;21:616-87.

6. Churchland AK, Kiani R, Shadlen MN. Decision-making with multiple alternatives. Nat Neurosci. 2008;11:693-702.

## P81

### Inferring low-dimensional network dynamics with variational latent Gaussian process

Yuan Zaho¹,², Il Memming Park¹,³

¹Department of Neurobiology and Behavior, Stony Brook University, Stony Brook, NY 11794, USA; ²Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA;

³Institute for Advanced Computational Science, Stony Brook University, Stony Brook, NY 11794, USA

**Correspondence:** Il Memming Park - memming.park@stonybrook.edu

BMC Neuroscience 2016, 17(Suppl 1):P81

Surprisingly, large-scale population recordings often show signatures of low-dimensional dynamics, that is, variations in a small number of common factors explain most of the dependence among neurons [1-3]. This supports the idea that a large neuronal network is implementing necessary computations described by continuous low-dimensional nonlinear dynamics. Sufficient amount of redundancy in the population activity would allow us access to the internal computation process of interest even when we only observe a small subset of neurons. Thus, it is necessary to deduce the latent dynamics from neural time series in order to understand if and how neural systems operate in this regime. There are several latent variable models that aim at recovering the latent dynamics, however, they make inadequate assumptions in favor of fast inference [4]. Here we describe an approximate inference method that recovers the latent dynamics under a natural generative model with minimal assumptions.

We implemented a probabilistic method to extract shared low-dimensional latent dynamics from multi-channel neural recordings (LFP and spike trains) to reveal how neural population encodes information, and how multiple functional neural populations dynamically interact with each other. Key assumptions of our model are: (1) each neural signal represent a noisy mixture of common latent dynamics, and (2) latent dynamics are independent and temporally smooth (with possibly different time scales). We use autoregressive generalized linear model driven by latent dynamics. Unlike most of the literature [5], we do not impose linear dynamics as a prior on the latent process, instead we use a general gaussian process prior which provides a flexible framework for imposing structure such as smoothness. However, as a

result, the exact posterior inference is intractable, thus we developed a variational method to find a Gaussian approximation to the posterior [6]. Our inference algorithm is memory-efficient and fast: both linear in time using a low-rank approximation of the covariance. We compare our method on both simulated systems and real data from V1 driven by drifting gratings. For a population of 148 V1 neurons, 11.4 % of the variance was explained by a shared 4-dimensional latent process, while 10 % of the variance was explained by independent variability of each neuron. We recovered orientation dependent embedding that faithfully encode the stimulus drive on average, and the population-wide trial-to-trial modulation. In conclusion, we present an efficient and scalable method to recover underlying dynamics from noisy partial observations to study neural code and computation.

## References

1. Okun M, Steinmetz NA, Cossell L, Iacaruso MF, Ko H, Barthó P, Moore T, Hofer SB, Mrsic-Flogel TD, Carandini M, Harris KD. Diverse coupling of neurons to populations in sensory cortex. Nature. 2015;521(7553):511-15.

2. Goris RLT, Movshon JA, Simoncelli EP. Partitioning neuronal variability. Nat Neurosci. 2014;17(6):858-65.

3. Luczak A, Bartho P, Harris KD. Gating of sensory input by spontaneous cortical activity. J Neurosci. 2013;33(4):1684-95.

4. Yu BM, Cunningham JP, Santhanam G, Ryu SI, Shenoy KV, Sahani M. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. J Neurophysiol. 2009;102(1):614-35.

5. Paninski L, Ahmadian Y, Ferreira DGG, Koyama,S, Rahnama Rad K, Vidne M, Vogelstein J, Wu W. A new look at state-space models for neural data. Journal of Comput Neurosci. 2010;29(1-2):107-26.

6. Blei DM, Kucukelbir A, McAuliffe JD. Variational inference: a review for statisticians. arXiv 2016 1601.00670 [http://arxiv.org/abs/1601.00670 arXiv]

## P82

### Computational investigation of energy landscapes in the resting state subcortical brain network

Jiyoung Kang¹, Hae-Jeong Park²

¹Graduate School of Life Science, University of Hyogo, 3-2-1 Koto, Kamigori, Ako, Hyogo, 678-1297, Japan; ²Department of Nuclear Medicine, Radiology and Psychiatry, Yonsei University College of Medicine, Department of Cognitive Science, Yonsei University, 50 Yonsei-ro, Sinchon-dong Seodaemoon-gu, Seoul, 120-752, Republic of Korea

**Correspondence:** Hae-Jeong Park - parkhj@yuhs.ac

BMC Neuroscience 2016, 17(Suppl 1):P82

Recently, energy landscapes of the resting state functional brain network have been researched using the pairwise maximum entropy model (MEM). This approach considers not only activities of nodes but also interactions among nodes in modeling brain networks and thus estimating energy landscapes of the brain state [1, 2]. From the energy landscape models, we can identify major stable states (local minima) and estimate transition rates among stable states.

The brain networks of the resting states are known to be affected by brain diseases or treatments. In the pairwise MEM, such effects correspond to changes in the parameters of the baseline activities and pairwise interactions.

In the present study, we investigated the energy landscape and its robustness of the subcortical human brain network that plays a central role in the human brain. The subcortical brain regions we examined were 15 regions of interests (ROIs); hippocampus, amygdala, caudate, putamen, pallidum, thalamus, nucleus accumbens, and brainstem. To construct a pairwise MEM for spontaneous interactions among subcortical brain regions, we used resting state fMRI (rs-fMRI) data of the human connectome projects, which contains 468 people's data. The blood oxygen level-dependent signals in the ROI were first binarized to represent states (zero for inactive, one for active states) of the ROI, and thereby 2¹⁵ brain states were considered. The parameters of the MEM were fitted to reproduce observed activation patterns of the rs-fMRI data. The constructed MEM showed high accuracy of fit (~92.6 %) and reliability (~99.9 %).
We found symmetric properties for the left and right hemispheres, and confirmed estimated parameters grossly reflecting the known anatomical connectivity of the subcortical brain. We further investigated the robustness of the system by perturbing the global weight for interactions, parameters for baseline activities of ROI and parameters for interactions between pairs of all ROIs (1906 edges), one by one from the original MEM. Alteration of the energy landscapes after perturbation was measured with respect to the number of local minima. We found that the number of the local minima of the subcortical system without any perturbation is very high. This implies that the subcortical brain system is optimal in the sense of its largest coverage of local minima (maximal number of local minima). This result suggests that brain was built to have multiple stable states. We also found different categories of parameters that affect the energy landscape of the resting state. For example, small increase in the pairwise parameter between the caudate and putamen dramatically reduced the numbers of the local minima while reduction in this parameter did not change the energy landscape.

In conclusion, MEM analysis of resting state functional network would be an important tool to understand principles of the brain organization and could be useful in researching brain disease.

## References

1. Watanabe T, Hirose S, Wada H, Imai Y, Machida T, Shirouzu I, Konishi S, Miyashita Y, Masuda N. A pairwise maximum entropy model accurately describes resting-state human brain networks. Nat Commun. 2013;4:1370.

2. Watanabe T, Hirose S, Wada H, Imai Y, Machida T, Shirouzu I, Konishi S, Miyashita Y, Masuda N. Energy landscapes of resting-state brain networks. Front Neuroinform. 2014;8:12.

## P83

### Local repulsive interaction between retinal ganglion cells can generate a consistent spatial periodicity of orientation map

Jaeson Jang¹, Se-Bum Paik¹,²

¹Department of Bio and Brain engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea; ²Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea

**Correspondence:** Jaeson Jang - jaesonjang@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P83

Orientation map in the primary visual cortex (V1) is of great interest among functional maps in the brain, but its developmental mechanism has been under debate. A recently suggested idea is that a moiré interference pattern between ON and OFF retinal ganglion cells (RGCs) can develop a quasi-periodic structure of orientation map [1] (Fig. 50A). In this model, the mosaics of ON and OFF RGCs that are in hexagonal lattice patterns generate a periodic interference pattern and induce a cortical orientation preference map. This model successfully explains the mechanism of map development, but two questions remain unanswered yet; (1) How does the hexagonal pattern of RGC mosaic develop and (2) how is the angle alignment (θ) between ON and OFF RGC mosaics (Fig. 50A) restricted to seed the consistent spatial periodicity of orientation map? Here, we suggest that a local repulsive interaction between the nearby cells is enough to develop hexagonal RGC mosaics and consistent alignment of ON and OFF mosaics.

To validate this idea of developmental process of cell mosaic, we assumed a local repulsive force between the nearby cells as a function of distance between two cells (Fig. 50B), which induces a gradual shift of cell position. In our model simulations, we confirmed that this model could develop a hexagonal pattern in the monotypic RGC mosaic (Fig. 50C, D). Next, we examined how the angle alignment between ON and OFF mosaics can be achieved by homotypic (ON-ON or OFF-OFF) and heterotypic (ON-OFF) interaction between RGCs. We simulated the development of ON and OFF mosaics as we allow a heterotypic interaction and gradually reduce the distance between two mosaics (Fig. 50E). When two mosaics get closer enough, we observed that the angle alignment between ON and OFF mosaics was limited to low angles (Fig. 50F). Finally, we analyzed previously reported cat RGC mosaic data [2, 3] and concluded that the data suggests the existence

of heterotypic repulsive interaction between ON and OFF mosaics, as our model predicted.

Our results suggest that a local repulsive interaction between RGCs can develop a hexagonal pattern in mosaics and restrict the angle alignment between ON and OFF RGC mosaics to generate a constant spatial period of orientation map. This model may provide a complementary mechanism of the retinal origin of periodic functional maps in the brain.

## References

1. Paik S-B, Ringach DL. Retinal origin of orientation maps in visual cortex. Nat Neurosci. 2011;14:919–925.

2. Zhan XJ, Troy JB. Modeling cat retinal beta-cell arrays. Vis Neurosci. 2000;17:23–39.

3. Wassle H, Boycott BB, Illing R-B. Morphology and mosaic of ON- and OFF-beta cells in the cat retina and some functional considerations. Proc R Soc B Biol Sci. 1981;212:177–95.

## P84

### Phase duration of bistable perception reveals intrinsic time scale of perceptual decision under noisy condition

Woochul Choi¹,², Se-Bum Paik¹,²

¹Department of Bio and Brain Engineering, KAIST, Daejeon 34141, Republic of Korea; ²Program of Brain and Cognitive Engineering, KAIST, Daejeon 34141, Republic of Korea

**Correspondence:** Woochul Choi - choiwc1128@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P84

When we see an ambiguous visual stimulus such as Necker cube, our perceived state switches periodically between two possible interpretations. This phenomenon, called bistable perception, is considered important to the study of dynamic mechanism of sensory perception. In particular, the time duration of each perceptual state, termed “phase duration”, seems to be a crucial factor to understanding the temporal features of underlying neural activity during sensory perception under this condition, which has not been studied intensively yet.

In this study, we assume that phase duration is intrinsically correlated with time delay in cognitive tasks, such as decision making from sensory information. Our hypothesis is that the periodic switching in bistable perception is a repeated process of decision making and reveals the time scale required for this decision task. To confirm our hypothesis, we performed a human psychophysics experiment using the “racetrack” type stimulus [1], which can induce a motion perception from both bistable illusion and real motion by varying the coherence parameter, c (Fig. 51A). We examined the relationship between

<figure><img src="image_55.png" /></figure>
<figure><img src="image_56.png" /></figure>

the phase duration, τ, under illusory motion (c = 0) and the response delay for coherent motion with different degrees of ambiguity (c > 0, Fig. 51B). Our result showed that the response delay in the coherent motion detection task (c > 0) was highly correlated with the phase duration in the bistable illusory motion perception (c = 0) (Fig. 51C, N = 19, R = 0.61, p < 0.01, Pearson's correlation coefficient). For a systematic analysis of subjects' performance for these two tasks, we designed a theoretical model of simple double-well energy potential [2] (Fig. 51D). The model could successfully replicate the correlation between phase duration and response delay in each task, suggesting that bistable perception and perceptual decision making processes may share a common neural mechanism (Fig. 51C).

**Conclusions** Our findings show that the phase duration of bistable perception is highly correlated with the response time of a cognitive task. Our simple model suggests that the bistable perception can be interpreted as perceptual decision making process under highly ambiguous condition and share similar temporal dynamics.

## References

1. Jain S. Performance characterization of Watson Ahumada motion detector using random dot rotary motion stimuli. PLoS One. 2009;4.

2. Kornmeier J, Bach M. Ambiguous figures—what happens in the brain when perception changes but not the stimulus. Front Hum Neurosci. 2012;6:51.

## P85

### Feedforward convergence between retina and primary visual cortex can determine the structure of orientation map

Changju Lee¹, Jaeson Jang¹, Se-Bum Paik¹,²

¹Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea; ²Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea

**Correspondence:** Changju Lee - lcj110808@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P85

Orientation map in the primary visual cortex (V1) is one of the most studied functional maps in the brain. In higher mammals such as

monkeys and cats, preferred orientation of each V1 neuron appears continuous and periodic across cortical space. On the other hand, in rodents, it appears completely discontinuous, forming a structure called salt-and-pepper map. However, the developmental mechanism of salt-and-pepper orientation maps remains unclear. Previously, a model study suggested that a moiré interference pattern between ON and OFF retinal ganglion cell (RGC) mosaics can seed a periodic orientation maps (Fig. 52A), and a salt-and-pepper map can also be developed when the spatial periodicity of interference pattern is very short [1]. However, our analysis suggests that the spatial periodicity of map, estimated from rat RGC mosaics data, is not small enough to generate a salt-and-pepper structure (Fig. 52B, C). To address this issue, here we suggest that feedforward convergent wiring between retina and V1 is a crucial factor that decides the structure of orientation map. To find a convergence condition that develops salt-and-pepper map, we modulated two parameters in our simulations: (1) the convergence range of V1 cells and (2) the sampling ratio of RGCs within the range. The regularity of orientation map was estimated from the measurement of the preferred orientation difference between local neurons (Fig. 52D). We found that a salt-and-pepper map was developed with low sampling ratio and large convergence range, while a smooth map was developed when convergence range was relatively small and sampling ratio was high (Fig. 52E). To further analyze the map structure generated by our model, we compared the profile of correlation between local receptive fields structure in our simulated V1 map to the previous observation in animal experiment [2]. We confirmed that our salt-and-pepper map model well matched the statistics of observed experimental data.

**Conclusions** Our result suggests that a salt-and-pepper map can be developed by sparse and long-range convergence in feedforward wiring, while smooth map can be developed by localized convergence. We suggest that the condition of feedforward convergence between retina and V1 is a critical factor to determine the structure of orientation map.

<figure><img src="image_57.png" /></figure>
## References

1. Paik S-B, Ringach DL. Retinal origin of orientation maps in visual cortex. Nat Neurosci. 2011;14:919–25.

2. Bonin V, Histed MH, Yurgenson S, Reid RC. Local diversity and fine-scale organization of receptive fields in mouse visual cortex. J Neurosci. 2011;31:18506–21.

## P86

### Computational method classifying neural network activity patterns for imaging data

Min Song<sup>1,2</sup>, Hyeonsu Lee<sup>1</sup>, Se-Bum Paik<sup>1,2</sup>

<sup>1</sup>Department of Bio and Brain Engineering, KAIST, Daejeon 34141, Republic of Korea; <sup>2</sup>Program of Brain and Cognitive Engineering, KAIST, Daejeon 34141, Republic of Korea

**Correspondence:** Min Song - night@kaist.ac.kr, Hyeonsu Lee - hslee9305@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P86

In neural imaging data, various types of spatio-temporal activity patterns are observed which may reflect dynamic features of information processing in the brain [1, 2]. Classification of these patterns is required to analyze the brain activity further. However, development of analysis tool for spatio-temporal neural activity pattern has been regarded difficult because of highly complex connections between neurons and nonlinearity of activity patterns. In this study, we suggest a novel method of classifying activity patterns in two aspects: spatial geometry and temporal dynamics. We show that our method efficiently categorizes complicated spatio-temporal patterns in brain. First, we defined meaningful activity as salient distribution of highly activated parts. Its spatial feature could be described by size and peak amplitude (Fig. 53A), temporal feature by velocity and dispersion of activity (Fig. 53A). Thus, we designed geometric profile as two-dimensional profile of instantaneous neural activity, by measuring the topography of supra-threshold area with a shifting threshold. This profile contains the information of size, peak amplitude, and geometric contours of meaningful activity. With this method, we could readily estimate similarity or correlation of different activities in terms of size, peak amplitude, and amplitude contour (Fig. 53B).

Next, we defined propagation profile as a characteristic of temporal displacement of activity on each direction against time and angle axis. We measured trajectory and speed of activity using a normalized cross-correlation. This profile intuitively shows dominant trajectory, speed change and dispersion of the activity: how disperse to every direction. So we can compare activities: whether the activity is moving straight or curved trajectories, or whether the activity propagation is accelerating or not (Fig. 53C).

Our new method can easily perform not only classification of overall dynamics in brain, but also a simplified description of complex

patterns (Fig. 53D), that may be applicable to the analysis of various kinds of brain imaging data.

## P87

### Symmetry of spike-timing-dependent-plasticity kernels regulates volatility of memory

Youngjin Park<sup>1</sup>, Woochul Choi<sup>1,2</sup>, Se-Bum Paik<sup>1,2</sup>

<sup>1</sup>Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea; <sup>2</sup>Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea

**Correspondence:** Youngjin Park - yodamaster@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P87

Synaptic plasticity is considered the core mechanism of learning and memory [1]. However, how plasticity can specifically modulate synaptic connections to generate short term or long term memory has not been understood completely. Here we introduce a theoretical model which suggests that a key mechanism of short term and long term memory can be implemented by a small difference in spike-timing-dependent-plasticity (STDP) rule. (Fig. 54A).

To test our idea, we designed simulations using a model feedforward neural network where two types of synaptic plasticity are implemented; asymmetric STDP (AS) [2] and symmetric STDP (SS). We defined the memory as the ability of a system to retrieve a consistent response spike pattern when we repeatedly introduce an identical pattern of spikes, and then we examined the performance of the system in terms of memory sustainability and appendability.

In our simulations, a network with AS showed performances similar to short-term memory while a network with SS showed long-term memory like properties. Memory in an AS Network decayed as a function of time, while memory in a SS network did not show a noticeable decay (Fig. 54B). Moreover, when a new input pattern was given to the network in addition to old memory, AS system replaced old memory with new memory pattern (Fig. 54C), while SS system maintained the old memory together with a newly trained memory (Fig. 54D).

Based on our findings, we suggest a new memory system called hybrid memory that is capable of showing intermediate properties between a long-term memory and a short-term memory (Fig. 54B, hybrid). This model suggests that transition between short term and long term memory might not be discrete but gradual.

**Conclusions** We have shown that our model network can implement different types of memory performance from the variation of plasticity,

<figure><img src="image_58.png" /><figcaption>**Fig. 53** A novel index effectively describes different neural activity patterns obtained from imaging. **A** Neural activity obtained from optical imaging could be analyzed with appearance and propagation. **B** Appearance index of four distinct sample. **C** Propagation index of straight trajectory (**top**) and curved trajectory (**bottom**). **D** Propagation Index of non-dispersive sample (**top**) and dispersive sample (**bottom**)</figcaption></figure>

<figure><img src="image_59.png" /><figcaption>**Fig. 54** Different learning rules reproduce volatile/nonvolatile memory system. **A** Spike timing dependent plasticity. **B** Memory decaying properties of different learning rule. Poisson spikes are given for 1000 s to simulate decaying environment. **C, D** Multiple patterns was given to the system every 200 s. **C** Memory performance of each pattern in AS memory system. **D** Memory performance of each pattern in SS memory system</figcaption></figure>