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# 25th Annual Computational Neuroscience Meeting: CNS-2016

Seogwipo City, Jeju-do, South Korea. 2-7 July 2016

Published: 18 August 2016

## A1

### Functional advantages of cell-type heterogeneity in neural circuits

Tatyana O. Sharpee¹

¹Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, San Diego, CA, USA

**Correspondence:** Tatyana O. Sharpee - sharpee@snl.salk.edu

BMC Neuroscience 2016, **17**(Suppl 1):A1

Neural circuits are notorious for the complexity of their organization. Part of this complexity is related to the number of different cell types that work together to encode stimuli. I will discuss theoretical results that point to functional advantages of splitting neural populations into subtypes, both in feedforward and recurrent networks. These results outline a framework for categorizing neuronal types based on their functional properties. Such classification scheme could augment classification schemes based on molecular, anatomical, and electro-physiological properties.

## A2

### Mesoscopic modeling of propagating waves in visual cortex

Alain Destexhe¹,²

¹UNIC, CNRS, Gif sur Yvette, France; ²The European Institute for Theoretical Neuroscience (EITN), Paris, France

**Correspondence:** Alain Destexhe - destexhe@unic.cnrs-gif.fr

BMC Neuroscience 2016, **17**(Suppl 1):A2

Propagating waves are large-scale phenomena widely seen in the nervous system, in both anesthetized and awake or sleeping states. Recently, the presence of propagating waves at the scale of microns-millimeters was demonstrated in the primary visual cortex (V1) of macaque monkey. Using a combination of voltage-sensitive dye (VSD) imaging in awake monkey V1 and model-based analysis, we showed that virtually every visual input is followed by a propagating wave (Muller et al., Nat Comm 2014). The wave was confined within V1, and was consistent and repeatable for a given input. Interestingly, two propagating waves always interact in a suppressive fashion, and sum sublinearly. This is in agreement with the general suppressive effect seen in other circumstances in V1 (Bair et al., J Neurosci 2003; Reynaud et al., J Neurosci 2012).

To investigate possible mechanisms for this suppression we have designed mean-field models to directly integrate the VSD experiments. Because the VSD signal is primarily caused by the summed voltage of all membranes, it represents an ideal case for mean-field models. However, usual mean-field models are based on neuronal transfer functions such as the well-known sigmoid function, or functions estimated from very simple models. Any error in the transfer function may result in wrong predictions by the corresponding mean-field model. To palliate this caveat, we have obtained semi-analytic forms of the transfer function of more realistic neuron models. We found that the same mathematical template can capture the transfer function for models such as the integrate-and-fire (IF) model, the

adaptive exponential (AdEx) model, up to Hodgkin-Huxley (HH) type models, all with conductance-based inputs.

Using these transfer functions we have built "realistic" mean-field models for networks with two populations of neurons, the regular-spiking (RS) excitatory neurons, showing spike frequency adaptation, and the fast-spiking (FS) inhibitory neurons. This mean-field model can reproduce the propagating waves in V1, due to horizontal interactions, as shown previously using IF networks. This mean-field model also reproduced the suppressive interactions between propagating waves. The mechanism of suppression was based on the preferential recruitment of inhibitory cells over excitatory cells by afferent activity, which acted through the conductance-based shunting effect of the two waves onto one another. The suppression was negligible in networks with identical models for excitatory and inhibitory cells (such as IF networks). This suggests that the suppressive effect is a general phenomenon due to the higher excitability of inhibitory neurons in cortex, in line with previous models (Ozeki et al., Neuron 2009).

Work done in collaboration with Yann Zerlaut (UNIC) for modeling, Sandrine Chemla and Frederic Chavane (CNRS, Marseille) for in vivo experiments. Supported by CNRS and the European Commission (Human Brain Project).

## A3

### Dynamics and biomarkers of mental disorders

Mitsuo Kawato¹

¹ATR Computational Neuroscience Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan

**Correspondence:** Mitsuo Kawato - kawato@hip.atr.co.jp

BMC Neuroscience 2016, **17**(Suppl 1):A3

Current diagnoses of mental disorders are made in a categorical way, as exemplified by DSM-5, but many difficulties have been encountered in such categorical regimes: the high percentage of comorbidities, usage of the same drug for multiple disorders, the lack of any validated animal model, and the situation where no epoch-making drug has been developed in the past 30 years. NIMH started RDoC (research domain criterion) to overcome these problems [1], and some successful results have been obtained, including common genetic risk loci [2] and common neuroanatomical changes for multiple disorders [3] as well as psychosis biotypes [4].

In contrast to the currently dominant molecular biology approach, which basically assumes one-to-one mapping between genes and disorders, I postulate the following dynamics-based view of psychiatric disorders. Our brain is a nonlinear dynamical system that can generate spontaneous spatiotemporal activities. The dynamical system is characterized by multiple stable attractors, only one of which corresponds to a healthy or typically developed state. The others are pathological states.

The most promising research approach within the above dynamical view is to combine resting-state functional magnetic resonance imaging, machine learning, big data, and sophisticated neurofeedback.
Yahata et al. developed an ASD biomarker using only 16/9730 functional connections, and it did not generalize to MDD or ADHD but moderately to schizophrenia [5]. Yamashita's regression model of working memory ability from functional connections [6] generalized to schizophrenia and reproduced the severity of working-memory deficits of four psychiatric disorders (in preparation).

With the further development of machine learning algorithms and accumulation of reliable datasets, we hope to obtain a comprehensive landscape of many psychiatric and neurodevelopmental disorders. Guided by this full-spectrum structure, a tailor-made neurofeedback therapy should be optimized for each patient [7].

### References

1. Insel T, Cuthbert B, Garvey M., et al. Research domain criteria (RDoC): toward a new classification framework for research on mental disorders. Am J Psychiatry. 2010;167:748-51.

2. Cross-disorder group of the psychiatric genomics consortium: identification of risk loci with shared effects on five major psychiatric disorders: a genome-wide analysis. Lancet. 2013;381:1371-9.

3. Goodkind M, et al. Identification of a common neurobiological substrate for mental illness. JAMA Psychiatry. 2015;72:305-15.

4. Clementz BA, et al. Identification of distinct psychosis biotypes using brain-based biomarkers. Am J Psychiatry. 2016;173:373-84.

5. Yahata N, Morimoto J, Hashimoto R, Lisi G, Shibata K, Kawakubo Y, Kuwabara H, Kuroda M, Yamada T, Megumi F, Imamizu H, Nanez JE, Takahashi H, Okamoto Y, Kasai K, Kato N, Sasaki Y, Watanabe T, Kawato M: A small number of abnormal brain connections predicts adult autism spectrum disorder. Nature Commun. 2016;7:11254. doi:10.1038/ncomms11254.

6. Yamashita M, Kawato M, Imamizu H. Predicting learning plateau of working memory from whole-brain intrinsic network connectivity patterns. Sci Rep. 2015;5(7622). doi:10.1038/srep07622.

7. ATR Brain Information Communication Research Laboratory Group. DecNef Project. Available at http://www.cns.atr.jp/decnefpro/ (2016).

## F1

### Precise recruitment of spiking output at theta frequencies requires dendritic h-channels in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneurons

Vladislav Sekulić¹,², Frances K. Skinner¹,²,³

¹Krembil Research Institute, University Health Network, Toronto, Ontario, Canada, M5T 2S8; ²Department of Physiology, University of Toronto, Toronto, Ontario, Canada, M5S 1A8; ³Department of Medicine (Neurology), University of Toronto, Toronto, Ontario, Canada, M5T 2S8

**Correspondence:** Vladislav Sekulić - vlad.sekulic@utoronto.ca

BMC Neuroscience 2016, 17(Suppl 1):F1

The theta rhythm (4–12 Hz) is a prominent network oscillation observed in the mammalian hippocampus and is correlated with spatial navigation and mnemonic processing. Inhibitory interneurons of the hippocampus fire action potentials at specific phases of the theta rhythm, pointing to distinct functional roles of interneurons in shaping this rhythmic activity. One hippocampal interneuron type, the oriens-lacunosum/moleculare (O-LM) cell, provides direct feedback inhibition and regulation of pyramidal cell activity in the CA1 region. O-LM cells express the hyperpolarization-activated, mixed-cation current ($I_h$) and, in vitro, demonstrate spontaneous firing at theta that is impaired upon blockade of $I_h$. Work using dynamic clamp has shown that in the presence of frequency-modulated artificial synaptic inputs, O-LM cells exhibit a spiking resonance at theta frequencies that is not dependent on $I_h$ [1]. However, due to the somatic injection limitation of dynamic clamp, the study could not examine the potential contributions of putative dendritic $I_h$ or the integration of dendritically-located synaptic inputs. To overcome this, we have used a database of previously developed multi-compartment computational models of O-LM cells [2].

We situated our OLM cell models in an in vivo-like context by injecting Poisson-based synaptic background activities throughout their dendritic arbors. Excitatory and inhibitory synaptic weights were tuned to produce similar baseline activity prior to modulation of the

inhibitory synaptic process at various frequencies (2–30 Hz). We found that models with dendritic inputs expressed enhanced resonant firing at theta frequencies compared to models with somatic inputs. We then performed detailed analyses on the outputs of the models with dendritic inputs to further elucidate these results with respect to $I_h$ distributions. The ability of the models to be recruited at the modulated input frequencies was quantified using the rotation number, or average number of spikes across all input cycles. Models with somatodendritic $I_h$ were recruited at >50 % of the input cycles for a wider range of theta frequencies (3–9 Hz) compared to models with somatic $I_h$ only (3–4 Hz). Models with somatodendritic $I_h$ also exhibited a wider range of theta frequencies for which phase-locked output (vector strength >0.75) was observed (4–12 Hz), compared to models with somatic $I_h$ (3–5 Hz). Finally, the phase of firing of models with somatodendritic $I_h$ given 8–10 Hz modulated input was delayed 180–230° relative to the time of release from inhibitory synaptic input.

O-LM cells receive phasic inhibitory inputs at theta frequencies from a subpopulation of parvalbumin-positive GABAergic interneurons in the medial septum (MS) timed to the peak of hippocampal theta, as measured in the stratum pyramidale layer [3]. Furthermore, O-LM cells fire at the trough of hippocampal pyramidal layer theta in vivo [4], an approximate 180° phase delay from the MS inputs, corresponding to the phase delay in our models with somatodendritic $I_h$. Our results suggest that, given dendritic synaptic inputs, O-LM cells require somatodendritic $I_h$ channel expression to be precisely recruited during the trough of hippocampal theta activity. Our strategy of leveraging model databases that encompass experimental cell type-specificity and variability allowed us to reveal critical biophysical factors that contribute to neuronal function within in vivo-like contexts.

**Acknowledgements:** Supported by NSERC of Canada, an Ontario Graduate Scholarship, and the SciNet HPC Consortium.

### References

1. Kipersky TJ, Fernandez FR, Economo MN, White JA. Spike resonance properties in hippocampal O-LM cells are dependent on refractory dynamics. J Neurosci. 2012;32(11):3637-51.

2. Sekulić V, Lawrence JJ, Skinner FK. Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells. PLOS One. 2014;9(10):e106567.

3. Borhegyi Z, Varga V, Szilágyi, Fabo D, Freund TF. Phase segregation of medial septal GABAergic neurons during hippocampal theta activity. J Neurosci. 2004;24(39):8470-9.

4. Varga C, Golshani P, Soltesz I. Frequency-invariant temporal ordering of interneuronal discharges during hippocampal oscillations in awake mice. Proc Natl Acad Sci USA. 2012;109(40):E2726-34.

## F2

### Kernel methods in reconstruction of current sources from extracellular potentials for single cells and the whole brains

Daniel K. Wójcik¹, Chaitanya Chintaluri¹, Dorottya Cserpán², Zoltán Somogyvári²

¹Department of Neurophysiology, Nencki Institute of Experimental Biology, Warsaw, Poland; ²Department of Theory, Wigner Research Centre for Physics of the Hungarian Academy of Sciences, Budapest, H-1121, Hungary

**Correspondence:** Daniel K. Wójcik - d.wojcik@nencki.gov.pl

BMC Neuroscience 2016, 17(Suppl 1):F2

Extracellular recordings of electric potential, with a century old history, remain a popular tool for investigations of brain activity on all scales, from single neurons, through populations, to the whole brains, in animals and humans, in vitro and in vivo [1]. The specific information available in the recording depends on the physical settings of the system (brain + electrode). Smaller electrodes are usually more selective and are used to capture local information (spikes from single cells or LFP from populations) while larger electrodes are used for subdural recordings (on the cortex, ECoG), on the scalp (EEG) but also as depth electrodes in humans (called SEEG). The advantages of extracellular electric potential are the ease of recording and its stability. Its problem
is interpretation: since electric field is long range one can observe neural activity several millimeters from its source [2-4]. As a consequence every recording reflects activity of many cells, populations and regions, depending on which level we focus. One way to overcome this problem is to reconstruct the distribution of current sources (CSD) underlying the measurement [5], typically done to identify activity on systems level from multiple LFP on regular grids [6].

We recently proposed a kernel-based method of CSD estimation from multiple LFP recordings from arbitrarily placed probes (i.e. not necessarily on a grid) which we called kernel Current Source Density method (kCSD) [7]. In this overview we present the original proposition as well as two recent developments, skCSD (single cell kCSD) and kESI (kernel Electrophysiological Source Imaging). skCSD assumes that we know which part of the recorded signal comes from a given cell and we have access to the morphology of the cell. This could be achieved by patching a cell, driving it externally while recording the potential on a multielectrode array, injecting a dye, and reconstructing the morphology. In this case we know that the sources must be located on the cell and this information can be successfully used in estimation. In kESI we consider simultaneous recordings with subdural ECoG (strip and grid electrodes) and with depth electrodes (SEEG). Such recordings are taken on some epileptic patients prepared for surgical removal of epileptogenic zone. When MR scan of the patient head is taken and the positions of the electrodes are known as well as the brain's shape, the idea of kCSD can be used to bound the possible distribution of sources facilitating localization of the foci.

**Acknowledgements:** Polish Ministry for Science and Higher Education (grant 2948/7.PR/2013/2), Hungarian Scientific Research Fund (Grant OTKA K113147), National Science Centre, Poland (Grant 2015/17/B/ST7/04123).

## 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. Hunt MJ, Falinska M, Łęski S, Wójcik DK, Kasicki S. Differential effects produced by ketamine on oscillatory activity recorded in the rat hippocampus, dorsal striatum and nucleus accumbens. J Psychopharmacol. 2011;25:808–21.

3. Lindén H, Tetzlaff T, Potjans TC, Pettersen KH, Gruen S, Diesmann M, Einevoll GT. Modeling the spatial reach of the LFP. Neuron. 2011;72:859–72.

4. Łęski S, Lindén H, Tetzlaff T, Pettersen KH, Einevoll GT. Frequency dependence of signal power and spatial reach of the local field potential. PLoS Comput Biol. 2013;9:e1003137.

5. Wójcik DK. Current source density (CSD) analysis. In: Jaeger D, Jung R, editors. Encyclopedia of computational neuroscience. SpringerReference. Berlin: Springer; 2013.

6. Mitzdorf U. Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomena. Physiol Rev. 1985;65:37–100.

7. Potworowski J, Jakuczun W, Łęski S, Wójcik DK. Kernel current source density method. Neural Comput. 2012;24:541–75.

## F3

### The synchronized periods depend on intracellular transcriptional repression mechanisms in circadian clocks

Jae Kyoung Kim¹, Zachary P. Kilpatrick², Matthew R. Bennett³, Kresimir Josić²,⁴

¹Department of Mathematical Sciences, KAIST, Daejoen 34141, Republic of Korea; ²Department of Mathematics, University of Houston, Houston, TX 77004, USA; ³Department of Biochemistry and Cell Biology and Institute of Biosciences and Bioengineering, Rice University, Houston, TX 77005, USA; ⁴Department of Biology and Biochemistry, University of Houston, Houston, TX 77004, USA

**Correspondence:** Jae Kyoung Kim - jaekkim@kaist.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):F2

In mammals, circadian (~24 h) rhythms are mainly regulated by a master circadian clock located in the suprachiasmatic nucleus (SCN) [1]. The SCN consists of ~20,000 neurons, each of which generates own rhythms via intracellular transcriptional negative feedback loop

involving PER-CRY and BMAL1-CLOCK. These individual rhythms of each neuron are synchronized through intercellular coupling via neurotransmitters including VIP [2]. In this talk, I will discuss that the synchronized periods via coupling signal strongly depend on the mechanism of intracellular transcription repression [3–4]. Specifically, using mathematical modeling and phase response curve analysis, we find that the synchronized period of SCN stays close to the population mean of cells' intrinsic periods (~24 h) if transcriptional repression occurs via protein sequestration. However, the synchronized period is far from the population mean when repression occurs via Hill-type regulation (e.g. phosphorylation-based repression). These results reveal the novel relationship between two major functions of the *SCN-intracellular* rhythm generation and *intercellular* synchronization of rhythms. Furthermore, this relationship provides an explanation for why the protein sequestration is commonly used in circadian clocks of multicellular organisms, which have a coupled master clock, but not in unicellular organisms [4].

**Acknowledgements:** This work was funded by the National Institutes of Health, through the joint National Science Foundation/National Institute of General Medical Sciences Mathematical Biology Program grant No. R01GM104974 (to M.R.B. and K.J.), National Science Foundation grants Nos. DMS-1311755 (to Z.P.K.) and DMS-1122094 (to K.J.), the Robert A. Welch Foundation grant No. C-1729 (to M.R.B.), National Science Foundation grant No. DMS-0931642 to the Mathematical Biosciences Institute (to J.K.K.), KAIST Research Allowance Grant G04150020 (to J.K.K.) and the TJ Park Science Fellowship of POSCO TJ Park Foundation G01160001 (to J.K.K).

## References

1. Dibner C, Schibler U, Albrecht U. The mammalian circadian timing system: organization and coordination of central and peripheral clocks. Annu Rev Physiol. 2010;72:517–49.

2. Welsh DK, Takahashi JS, Kay SA. Suprachiasmatic nucleus: cell autonomy and network properties. Annu Rev Physiol. 2010;72:551.

3. Kim JK, Kilpatrick ZP, Bennett MR, Josić K. Molecular mechanisms that regulate the coupled period of the mammalian circadian clock. Biophys J. 2014;106(9):2071–81.

4. Kim JK. Protein sequestration vs Hill-type repression in circadian clock models (in revision).

## O1

### Assessing irregularity and coordination of spiking-bursting rhythms in central pattern generators

Irene Elices¹, David Arroyo¹, Rafael Levi¹,², Francisco B. Rodriguez¹, Pablo Varona¹

¹Grupo de Neurocomputación Biológica, Dpto. de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, Spain;

²Department of Biological Sciences, University of Southern California, CA, USA

**Correspondence:** Irene Elices - irene.elices@uam.es

BMC Neuroscience 2016, 17(Suppl 1):O1

Found in all nervous systems, central pattern generators (CPGs) are neural circuits that produce flexible rhythmic motor patterns. Their robust and highly coordinated spatio-temporal activity is generated in the absence of rhythmic input. Several invertebrate CPGs are among the best known neural circuits, as their neurons and connections have been identified and mapped. The crustacean pyloric CPG is one of these flagship neural networks [1, 2]. Experimental and computational studies of CPGs typically examine their rhythmic output in periodic spiking-bursting regimes. Aiming to understand the fast rhythm negotiation of CPG neurons, here we present experimental and theoretical analyses of the pyloric CPG activity in situations where irregular yet coordinated rhythms are produced. In particular, we focus our study in the context of two sources of rhythm irregularity: intrinsic damage in the preparation, and irregularity induced by ethanol. The analysis of non-periodic regimes can unveil important properties of the robust dynamics controlling rhythm coordination in this system.

Adult male and female shore crabs (*Carcinus maenas*) were used for the experimental recordings. The isolated stomatogastric ganglion was kept
in *Carcinus maenas* saline. Membrane potentials were recorded intracellularly from the LP and PD cells, two mutually inhibitory neurons that form a half-center oscillator in the pyloric CPG. Extracellular electrodes allowed monitoring the overall CPG rhythm. Conductance-based models of the pyloric CPG neurons and their associated graded synapses as described in [3, 4] were also used in this dual experimental and theoretical study.
Irregularity and coordination of the CPG rhythms were analyzed using measures characterizing the cells' instantaneous waveform, period, duty cycle, plateau, hyperpolarization and temporal structure of the spiking activity, as well as measures describing instantaneous phases among neurons in the irregular rhythms and their variability. Our results illustrate the strong robustness of the circuit to keep LP/PD phase relationships in intrinsic and induced irregularity conditions while allowing a large variety of burst waveforms, durations and hyperpolarization periods in these neurons. In spite of being electrically coupled to the pacemaker cell of the circuit, the PD neurons showed a wide flexibility to participate with larger burst durations in the CPG rhythm (and larger increase in variability), while the LP neuron was more restricted in sustaining long bursts in the conditions analyzed. The conductance-based models were used to explain the role of asymmetry in the dynamics of the neurons and synapses to shape the irregular activity observed experimentally. Taking into account the overall experimental and model analyses, we discuss the presence of preserved relationships in the non-periodic but coordinated bursting activity of the pyloric CPG, and their role in the fast rhythm negotiating properties of this circuit.

**Acknowledgements:** We acknowledge support from MINECO DPI2015-65833-P, TIN2014-54580-R, TIN-2012-30883 and ONRG grant N62909-14-1-N279.

## References

1. Marder E, Calabrese RL. Principles of rhythmic motor pattern generation. Physiol Rev. 1996;76:687-717.

2. Selterston AI, Rabinovich MI, Abarbanel HDJ, Elson R, Szücs A, Pinto RD, Huerta R, Varona P. Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. J Physiol. 2000;94:357-74.

3. Latorre R, Rodríguez FB, Varona P. Neural signatures: multiple coding in spiking-bursting cells. Biol Cybern. 2006;95:169-83.

4. Elices I, Varona P. Closed-loop control of a minimal central pattern generator network. Neurocomputing. 2015;170:55-62.

# O2
## Regulation of top-down processing by cortically-projecting parvalbumin positive neurons in basal forebrain

Eunjin Hwang¹, Bowon Kim¹,², Hiio-Been Han¹,³, Tae Kim⁴, James T. McKenna⁵, Ritchie E. Brown⁵, Robert W. McCarley⁵, Jee Hyun Choi¹,²
¹Center for Neuroscience, Korea Institute of Science and Technology, Hwarang-ro 14-gil 5, Seongbuk-gu, Seoul 02792, South Korea;
²Department of Neuroscience, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejon 34113, South Korea; ³Department of Psychology, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, South Korea; ⁴Department of Psychiatry, Kyung Hee University Hospital at Gangdong, 892, Dongnam-ro, Gangdong-gu, Seoul 05278, South Korea; ⁵Department of Psychiatry, Veterans Administration Boston Healthcare System and Harvard Medical School, Brockton, MA 02301, USA

**Correspondence:** Jee Hyun Choi - jeechoi@kist.re.kr

BMC Neuroscience 2016, 17(Suppl 1):O2

Particular behaviors are associated with different spatio-temporal patterns of cortical EEG oscillations. A recent study suggests that the cortically-projecting, parvalbumin-positive (PV+) inhibitory neurons in the basal forebrain (BF) play an important role in the state-dependent control of cortical oscillations, especially ~40 Hz gamma oscillations [1]. However, the cortical topography of the gamma oscillations which are controlled by BF PV+ neurons and their relationship to behavior are unknown. Thus, in this study, we investigated the spatio-temporal patterns and the functional role of the cortical oscillations induced or entrained by BF PV+ neurons by combining optogenetic stimulation

of BF PV+ neurons with high-density EEG [2, 3] in channelrhodopsin-2 (ChR2) transduced PV-cre mice. First, we recorded the spatio-temporal responses in the cortex with respect to the stimulation of BF PV+ neurons at various frequencies. The topographic response patterns were distinctively different depending on the stimulation frequencies, and most importantly, stimulation of BF PV+ neurons at 40 Hz (gamma band frequency) induced a preferential enhancement of gamma band oscillations in prefrontal cortex (PFC) with a statistically significant increase in intracortical connectivity within PFC. Second, optogenetic stimulation of BF PV+ neurons was applied while the mice were exposed to auditory stimuli (AS) at 40 Hz. The time delay between optogenetic stimulation and AS was tested and the phase response to the AS was characterized. We found that the phase responses to the click sound in PFC were modulated by the optogenetic stimulation of BF PV+ neurons. More specifically, the advanced activation of BF PV+ neurons by $\pi/2$ (6.25 ms) with respect to AS sharpened the phase response to AS in PFC, while the anti-phasic activation ($\pi$, 12.5 ms) blunted the phase response. Interestingly, like PFC, the primary auditory cortex (A1) also showed sharpened phase response for the $\pi/2$ advanced optogenetic BF PV+ neuron activation during AS. Considering that no direct influence of BF PV+ neurons on A1 was apparent in the response to stimulation of BF PV+ neurons alone, the sharpened phase response curve of A1 suggests a top-down influence of the PFC. This result implies that the BF PV+ neurons may participate in regulating the top-down influence that PFC exerts on primary sensory cortices during attentive behaviors, and supports the idea that the modulating activities of BF PV+ neurons might be a potential target for restoring top-down cognitive functions as well as abnormal frontal gamma oscillations associated with psychiatric disorders.

**Acknowledgements:** This research was supported by the Department of Veterans Affairs, the Korean National Research Council of Science & Technology (No. CRC-15-04-KIST), NIMH R01 MH039683 and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01059119). The contents of this report do not represent the views of the US Department of Veterans Affairs or the United States government.

## References

1. Kim T, et al. Cortically projecting basal forebrain parvalbumin neurons regulate cortical gamma band oscillations. Proc Natl Acad Sci. 2015;112(11):3535-40.

2. Choi JH, et al. High resolution electroencephalography in freely moving mice. J Neurophysiol. 2010;104(3):1825-34.

3. Lee M, et al. High-density EEG recordings of the freely moving mice using polyimide-based microelectrode. J Vis Exp. 2011;47. http://www.jove.com/details.php?id=2562. doi:10.3791/2562.

# O3
## Modeling auditory stream segregation, build-up and bistability

James Rankin¹, Pamela Osborn Popp¹, John Rinzel¹,²
¹Center for Neural Science, New York University, New York 10003, NY;
²Courant Institute of Mathematical Sciences, New York University, New York 10012, NY

**Correspondence:** James Rankin - james.rankin@nyu.edu

BMC Neuroscience 2016, 17(Suppl 1):O3

With neuromechanistic modelling and psychoacoustic experiments we study the perceptual dynamics of auditory streaming (cocktail party problem). The stimulus is a sequence of two interleaved tones, A and B in a repeating triplet pattern: ABA_ABA_ ('_' is a silent gap). Initially, subjects hear a single integrated pattern, but after some seconds they hear segregated A_A_A_ and _B__B__ streams (build-up of streaming segregation). For long presentations, build-up is followed by irregular alternations between integrated and segregated (auditory bistability). We recently presented [1] the first neuromechanistic model of auditory bistability; it incorporates common competition mechanisms of mutual inhibition, slow adaptation and noise [2]. Our competition network is
<figure><img src="image_2.png" /></figure>

**Fig. 1** A Model schematic: tone inputs $I_A$ and $I_B$ elicit pulsatile responses in A1, which are pooled as inputs to a three-population competition network. Central unit AB encodes integrated, peripheral units A and B encode segregated. Mutual inhibition between units and recurrent excitation are incorporated with adaptation and noise. B A1 inputs show early initial adaptation, also if a pause is present. Build-up function shows proportion segregated increasing over time, here shown for three tone-frequency differences, DF, with no pause (*dashed*) or with a pause (*solid curves*). Time-snapshots from model (*filled circles*) agree with data (*empty circles* with SEM error bars, N = 8)

formulated to reside downstream of primary auditory cortex (A1). Neural responses in macaque A1 to triplet sequences [3] encode stimulus features and provide the inputs to our network (Fig. 1A). In our model recurrent excitation with an NMDA-like timescale links responses across gaps between tones and between triplets. It captures the dynamics of perceptual alternations and the stimulus feature dependence of percept durations. To account for build-up we incorporate early adaptation of A1 responses [3] (Fig. 1B, upper). Early responses in A1 are broadly tuned and do not reflect the frequency difference between the tones; later responses show a clear tonotopic dependence. This adaptation biases the initial percept towards integration, but occurs faster (~0.5 s) than the gradual build-up process (~5–10 s). The low initial probability of segregation gradually builds up to the stable probability of later bistable alternations (Fig. 1B, lower). During build-up, a pause in presentation may cause partial reset to integrated [4]. Our extended model shows this behavior assuming that after a pause A1 responses recover on the timescale of early adaptation. Moreover, the modeling results agree with our psychoacoustic experiments (compare filled and open circles in Fig. 1B, lower).

**Conclusions** For the first time, we offer an explanation of the discrepancy in the timescales of early A1 responses and the more gradual build-up process. Recovery of A1 responses can explain resetting for stimulus pauses. Our model offers, to date, the most complete account of the early and late dynamics for auditory streaming in the triplet paradigm.

## References

1. Rankin J, Sussman E, Rinzel J. Neuromechanistic model of auditory bistability. PLoS Comput Biol. 2015;11:e1004555.

2. Shpiro A, Moreno-Bote R, Rubin N, Rinzel J. Balance between noise and adaptation in competition models of perceptual bistability. J Comp Neurosci. 2009;27:37–54.

3. Micheyl C, Tian B, Carlyon R, Rauschecker J. Perceptual organization of tone sequences in the auditory cortex of awake macaques. Neuron. 2005;48:139–48.

4. Beauvois MW, Meddis R. Time decay of auditory stream biasing. Percept Psychophys. 1997;59:81–6.

## O4

### Strong competition between tonotopic neural ensembles explains pitch-related dynamics of auditory cortex evoked fields

Alejandro Tabas¹, André Rupp²,¹, Emili Balaguer-Ballester¹,³,¹

¹Faculty of Science and Technology, Bournemouth University, Bournemouth, England, UK; ²Heidelberg University, Baden-Württemberg, Germany; ³Bernstein Center for Computational Neuroscience, Heidelberg-Mannheim, Baden-Württemberg, Germany

**Correspondence:** Alejandro Tabas - atabas@bournemouth.ac.uk

¹Equal contribution

BMC Neuroscience 2016, 17(Suppl 1):O4

Auditory evoked fields (AEFs) observed in MEG experiments systematically present a transient deflection known as the N100 m, elicited around 100 ms after the tone onset in the antero-lateral Heschl's Gyrus. The exact N100m's latency is correlated with the perceived pitch of a wide range of stimulus [1, 2], suggesting that the transient component reflects the processing of pitch in auditory cortex. However, the biophysical substrate of such precise relationship remains an enigma. Existing models of pitch, focused on perceptual phenomena, did not explain the mechanism generating cortical evoked fields during pitch processing in biophysical detail. In this work, we introduce a model of interacting neural ensembles describing, for the first time to our knowledge, how cortical pitch processing gives rise to observed human neuromagnetic responses and why its latency strongly correlates with pitch.

To provide a realistic cortical input, we used a recent model of the auditory periphery and realistic subcortical processing stages. Subcortical processing was based on a delay-and-multiply operation carried out in cochlear nucleus and inferior colliculus [3], resulting in realistic patterns of neural activation in response to the stimulus periodicities. Subcortical activation is transformed into a tonotopic receptive-field-like representation [4] by a novel cortical circuit composed by functional blocks characterised by a best frequency. Each block consist of an excitatory and an inhibitory population, modelled using mean-field approximations [5]. Blocks interact with each other through local AMPA- and NMDA-driven excitation and GABA-driven global inhibition [5].

The excitation-inhibition competition of the cortical model describes a general pitch processing mechanism that explains the N100m deflection as a transient state in the cortical dynamics. The deflection is rapidly triggered by a rise in the activity elicited by the subcortical input, peaks after the inhibition overcomes the input, and stabilises when model dynamics reach equilibrium, around 100 ms after onset. As a direct consequence of the connectivity structure among blocks, the time necessary for the system to reach equilibrium depends on the encoded pitch of the tone. The model quantitatively predicts observed latencies of the N100m in agreement with available empirical data [1, 2] in a series of stimuli (see Fig. 2), suggesting that the mechanism potentially accounts for the N100 m dynamics.

## References

1. Seither-Preisler A, Patterson R, Krumbholz K, Seither S, Lütkenhöner B. Evidence of pitch processing in the N100 m component of the auditory evoked field. Hear Res. 2006;213(1–2):88–98.

2. Roberts TP, Ferrari P, Stufflebeam SM, Poeppel D. Latency of the auditory evoked neuromagnetic field components: stimulus dependence and insights toward perception. J Clin Neurophysiol. 2000;17(2):114–29.

3. Meddis R, O'Mard LP. Virtual pitch in a computational physiological model. J Acoust Soc Am. 2006;36:8361–9.

4. Balaguer-Ballester E, Clark, N. Understanding pitch perception as a hierarchical process with top-down modulation. PLoS Comput Biol. 2009;5(3):e1000301.

5. Wong K-F, Wang X-J. A recurrent network mechanism of time integration in perceptual decisions. J Neurosci. 2006;26(4):1314–28.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** N100 m predictions in comparison with available data [1, 2] for a range of pure tones (A) and HCTs (B)</figcaption></figure>
O5

**A simple model of retinal response to multi-electrode stimulation**

Matias I. Maturana¹,², David B. Grayden²,³, Shaun L. Cloherty⁴, Tatiana Kameneva², Michael R. Ibbotson¹,⁵, Hamish Meffin¹,⁵

¹National Vision Research Institute, Australian College of Optometry, 3053, Australia; ²NeuroEngineering Laboratory, Dept. Electrical & Electronic Eng., University of Melbourne, 3010, Australia; ³Centre for Neural Engineering, University of Melbourne, 3010, Australia; ⁴Department of Physiology, Monash University, 3800, Australia; ⁵ARC Centre of Excellence for Integrative Brain Function, Department Optometry and Vision Sciences, University of Melbourne, 3010, Australia

**Correspondence:** Hamish Meffin - hmeffin@unimelb.edu.au

BMC Neuroscience 2016, 17(Suppl 1):O5

Retinal implants can restore vision to patients suffering photoreceptor loss by stimulating surviving retinal ganglion cells (RGCs) via an array of microelectrodes implanted within the eye [1]. However, the acuity offered by existing devices is low, limiting the benefits to patients. Improvements may come by increasing the number of electrodes in new devices and providing patterned vision, which necessitates stimulation using multiple electrodes simultaneously. However, simultaneous stimulation poses a number of problems due to cross-talk between electrodes and uncertainty regarding the resulting activation pattern.

Here, we present a model and methods for estimating the responses of RGCs to simultaneous electrical stimulation. Whole cell in vitro patch clamp recordings were obtained from 25 RGCs with various morphological types in rat retina. The retinae were placed onto an array of 20 stimulating electrodes. Biphasic current pulses with 500 µs phase duration and 50 µs interphase gap were applied simultaneously to all electrodes at a frequency of 10 Hz, with the amplitude of current on each electrode sampled independently from a Gaussian distribution.

A linear-nonlinear model was fit to the responses of each RGC using spike-triggered covariance analyses on 80 % of the recorded data. The analysis revealed a single significant principle component corresponding to the electrical receptive field for each cell, with the second largest principle component having negligible effect on the neural response (Fig. 3a). This indicates that interactions between electrodes are approximately linear in their influence on the cells' responses.

Furthermore, the spike-triggered ensemble showed two clusters (red and blue in Fig. 3a) corresponding to stimulation that had a net effect that was either anodic first or cathodic first. The electrical receptive fields for both anodic first and cathodic first stimulation were highly similar (Fig. 3b). They consisted of a small number (1–4) of electrodes that were close to the cell body (green dot).

<figure><img src="image_4.png" /></figure>

The remaining 20 % of data were used to validate the model. The average model prediction root-mean-square error was 7 % over the 25 cells. The accuracy of the model indicates that the linear-nonlinear model is appropriate to describe the responses of RGCs to electrical stimulation.

**Acknowledgements:** This research was supported by the Australian Research Council (ARC). MI, HM, and SC acknowledge support through the Centre of Excellence for Integrative Brain Function (CE140100007), TK through ARC Discovery Early Career Researcher Award (DE120102210) and HM and TK through the ARC Discovery Projects funding scheme (DP140104533).

**Reference**

1. Hadjinićolaou AE, Meffin H, Maturana M, Cloherty SL, Ibbotson MR. Prosthetic vision: devices, patient outcomes and retinal research. Clin Exp Optom. 2015;98(5):395–410.

O6

**Noise correlations in V4**

**area correlate with behavioral performance in visual discrimination task**

Veronika Koren¹,², Timm Lochmann¹,², Valentin Dragoi³, Klaus Obermayer¹,²

¹Institute of Software Engineering and Theoretical Computer Science, Technische Universitaet Berlin, Berlin, 10587, Germany; ²Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universitaet zu Berlin, Berlin, 10115, Germany; ³Department of Neurobiology and Anatomy, University of Texas-Houston Medical School, Houston, TX 77030, USA

**Correspondence:** Veronika Koren - veronika.koren@bccn-berlin.de

BMC Neuroscience 2016, 17(Suppl 1):O6

Linking sensory coding and behavior is a fundamental question in neuroscience. We have addressed this issue in behaving monkey visual cortex (areas V1 and V4) while animals were trained to perform a visual discrimination task in which two successive images were either rotated with respect to each other or were the same. We hypothesized that the animal's performance in the visual discrimination task depends on the quality of stimulus coding in visual cortex. We tested this hypothesis by investigating the functional relevance of neuronal correlations in areas V1 and V4 in relation to behavioral performance. We measured two types of correlations: noise (spike count) correlations and correlations in spike timing. Surprisingly, both methods showed that correct responses are associated with significantly higher correlations in V4, but not V1, during the delay period between the two stimuli. This suggests that pair-wise interactions during the spontaneous activity preceding the arrival of the stimulus sets the stage for subsequent stimulus processing and importantly influences behavioral performance.

Experiments were conducted in 2 adult monkeys that were previously trained for the task. After 300 ms of fixation, the target stimulus, consisting of a naturalistic stimulus, is shown for 300 ms, and after a random delay period (500–1200 ms), a test stimulus is shown for 300 ms. The test can either be identical to the target stimulus (match) or rotated with respect to the target (non-match). Monkey responded by pressing a button and was rewarded for a correct response with fruit juice. Two linear arrays with 16 recording channels each were used to record population activity in areas V1 and V4. The difficulty of the task is calibrated individually to have 70 % correct responses on average. The analysis is conducted on non-match condition, comparing activity in trials with correct responses with trials where the monkey responded incorrectly. Noise correlations were assessed as pair-wise correlations of spike counts (method 1) and of spike timing (method 2). For method 1, z-scores of spike counts of binned spike trains are computed in individual trials. r_sc is computed as Pearson correlation coefficient of z-scores in all available trials, balanced across correct/incorrect condition. For the method 2, cross-correlograms were computed, from which the cross-correlograms from shuffled trials are subtracted. Resulting function was summed around zero lag and normalized with sum of autocorrelograms [1].
While firing rates of single units or of the population did not significantly change for correct and incorrect responses, noise correlations during the delay period were significantly higher in V4 pairs, computed with both r_sc method (p = 0.0005 in monkey 1, sign-rank test) and with r_ccg method (p = 0.0001 and p = 0.0280 in monkey 1 and 2, respectively, 50 ms integration window). This result is robust to changes in the length of the bin (method 1) and to the length of the summation window (method 2). In agreement with [2], we confirm the importance of spontaneous activity preceding the stimulus on performance and suggest that higher correlations in V4 might be beneficial for successful read-out and reliable transmission of the information downstream.

## References

1. Bair W, Zohary E, Newsome WT. Correlated firing in macaque visual area MT: time scales and relationship to behavior. J Neurosci. 2001; 21(5):1676-97.

2. Gutnisky DA, Beaman CB, Lew SE, Dragoi V. Spontaneous fluctuations in visual cortical responses influence population coding accuracy. Cereb Cortex. 2016;1-19.

3. Cohen MR, Maunsell JH. Attention improves performance primarily by reducing interneuronal correlations. Nat Neurosci. 2009;12(12):1594-1600.

4. Nienborg HR, Cohen MR, Cumming BG. Decision-related activity in sensory neurons: correlations among neurons and with behavior. Annu Rev Neurosci. 2012;35:463-83.

## O7

### Input-location dependent gain modulation in cerebellar nucleus neurons

Maria Psarrou¹, Maria Schilstra¹, Neil Davey¹, Benjamin Torben-Nielsen¹, Volker Steuber¹

Centre for Computer Science and Informatics Research, University of Hertfordshire, Hatfield, AL10 9AB, UK

**Correspondence:** Maria Psarrou - m.psarrou@herts.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):O7

Gain modulation is a brain-wide principle of neuronal computation that describes how neurons integrate inputs from different presynaptic sources. A gain change is a multiplicative operation that is defined as a change in the sensitivity (or slope of the response amplitude) of a neuron to one set of inputs (driving input) which results from the activity of a second set of inputs (modulatory input) [1, 2].

Different cellular and network mechanisms have been proposed to underlie gain modulation [2-4]. It is well established that input features such as synaptic noise and plasticity can contribute to multiplicative gain changes [2-4]. However, the effect of neuronal morphology on gain modulation is relatively unexplored. Neuronal inputs to the soma and dendrites are integrated in a different manner: whilst dendritic saturation can introduce a strong non-linear relationship between dendritic excitation and somatic depolarization, the relationship between somatic excitation and depolarization is more linear. The non-linear integration of dendritic inputs can enhance the multiplicative effect of shunting inhibition in the presence of noise [3].

Neurons in the cerebellar nuclei (CN) provide the main gateway from the cerebellum to the rest of the brain. Understanding how inhibitory inputs from cerebellar Purkinje cells interact with excitatory inputs from mossy fibres to control output from the CN is at the center of understanding cerebellar computation. In the present study, we investigated the effect of inhibitory modulatory input on CN neuronal output when the excitatory driving input was delivered at different locations in the CN neuron. We used a morphologically realistic conductance based CN neuron model [5] and examined the change in output gain in the presence of distributed inhibitory input under two conditions: (a) when the excitatory input was confined to one compartment (the soma or a dendritic compartment) and, (b), when the excitatory input was distributed across particular dendritic regions at different distances from the soma. For both of these conditions, our results show that the arithmetic operation performed by inhibitory synaptic input depends on the location of the excitatory

synaptic input. In the presence of distal dendritic excitatory inputs, the inhibitory input has a multiplicative effect on the CN neuronal output. In contrast, excitatory inputs at the soma or proximal dendrites close to the soma undergo additive operations in the presence of inhibitory input. Moreover, the amount of the multiplicative gain change correlates with the distance of the excitatory inputs from the soma, with increasing distances from the soma resulting in increased gain changes and decreased additive shifts along the input axis. These results indicate that the location of synaptic inputs affects in a systematic way whether the input undergoes a multiplicative or additive operation.

## References

1. Salinas E, Sejnowski TJ. Gain modulation in the central nervous system: where behavior, neurophysiology, and computation meet. Neuroscience. 2001;7(5):430-40.

2. Silver RA. Neuronal arithmetic. Nat Rev Neurosci. 2010;11(7):474-89.

3. Prescott SA, De Koninck Y. Gain control of firing rate by shunting inhibition: roles of synaptic noise and dendritic saturation. Proc Natl Acad Sci USA. 2003;100(4):2076-81.

4. Rothman J, Cathala L, Steuber V, Silver RA. Synaptic depression enables neuronal gain control. Nature. 2009;475:1015-18.

5. Steuber V, Schultheiss NW, 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 Comput Neurosci. 2011;30(3):633-58.

## O8

### Analytic solution of cable energy function for cortical axons and dendrites

Huiwen Ju¹, Jiao Yu², Michael L. Hines³, Liang Chen⁴ and Yuguo Yu¹
¹School of Life Science and the Collaborative Innovation Center for Brain Science, Fudan University, Shanghai, 200438, China; ²Linyi Hospital of Traditional Chinese Medicine, 211 Jiefang Road, Lanshan, Linyi, Shandong Province, 276000, China; ³Department of Neuroscience, Yale University School of Medicine, New Haven, CT 06520, USA; ⁴Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai, China

**Correspondence:** Yuguo Yu - yuyuguo@fudan.edu.cn

BMC Neuroscience 2016, 17(Suppl 1):O8

Accurate estimation of action potential (AP)-related metabolic cost is essential for understanding energetic constraints on brain connections and signaling processes. Most previous energy estimates of the AP were obtained using the Na⁺-counting method [1, 2], which seriously limits accurate assessment of metabolic cost of ionic currents that underlie AP generation. Moreover, the effects of axonal geometry and ion channel distribution on energy consumption related to AP propagation have not been systematically investigated.

To address these issues, we return to the cable theory [3] that underlies our HH-type cortical axon model [4], which was constructed based on experimental measurements. Based on the cable equation that describes how ion currents flow along the cable as well as analysis of the electrochemical energy in the equivalent circuit, we derived the electrochemical energy function for the cable model,

$$ \begin{aligned} \frac{\partial^2 E}{\partial x \partial t} &= I_{Na}(V - V_{Na}) + I_{K}(V - V_{K}) + I_{L}(V - V_{L}) - \frac{1}{2\pi a} i_a \frac{\partial V}{\partial x} \\ &= g_{Na} \max_{m} m^3 h(V(x, t) - V_{Na})^2 + g_{K} \max_{h} h^4 (V(x, t) - V_{K})^2 \\ &\quad + g_{L} (V(x, t) - V_{L})^2 + G_a \left(\frac{\partial V}{\partial x}\right)^2 \end{aligned} $$

where $g_{Na}^{max}$ (in a range of 50-650 mS/cm²), $g_{K}^{max}$ (5-100 mS/cm²), and $g_L = 0.033$ mS/cm² are the maximal sodium, maximal potassium, and leak conductance per unit membrane area, respectively; and $V_{Na} = 60$, $V_K = -90$, $V_L = -70$ mV are the reversal potentials of the sodium, potassium, and leak channels, respectively. The gate variables m, h, and n are dimensionless activation and inactivation variables, which describe the activation and inactivation processes of the sodium and
potassium channels [4]. This equation describes the AP-related energy
consumption rate per unit membrane area (cm²/s) at any axonal dis-
tance and any time. The individual terms on the right-hand side of the
equation represent the contributions of the sodium, potassium, leak,
and axial currents, respectively. Then we employed the cable energy
function to calculate energy consumption for unbranched axons and
axons with several degrees of branching (branching level, BL). Calcula-
tions based on this function distinguish between the contributions of
each item toward total energy consumption.

Our analytical approach predicts an inhomogeneous distribution of
metabolic cost along an axon with either uniformly or nonuniformly
distributed ion channels. The results show that the Na⁺-counting
method severely underestimates energy cost in the cable model by
20–70%. AP propagation along axons that differ in length may require
over 15% more energy per unit of axon area than that required by a
point model. However, actual energy cost can vary greatly depending
on axonal branching complexity, ion channel density distributions,
and AP conduction states. We also infer that the metabolic rate (i.e.
energy consumption rate) of cortical axonal branches as a function of
spatial volume exhibits a 3/4 power law relationship.

**Acknowledgements:** Dr. Yu thanks for the support from the National Natural Science Foundation of China (31271170, 31571070), Shang-hai program of Professor of Special Appointment (Eastern Scholar SHH1140004).

References

1. Alle H, Roth A, Geiger JR. Energy-efficient action potentials in hippocampal mossy fibers. Science. 2009;325(5946):1405-8.

2. Carter BC, Bean BP. Sodium entry during action potentials of mammalian neurons: incomplete inactivation and reduced metabolic efficiency in fast-spiking neurons. Neuron. 2009;64(6):898-909.

3. Rall W. Cable theory for dendritic neurons. In: Methods in neuronal modeling. MIT Press; 1989. p. 9-92.

4. Yu Y, Hill AP, McCormick DA. Warm body temperature facilitates energy efficient cortical action potentials. PLoS Comput Biol. 2012;8(4):e1002456.

O9

C. elegans interactome: interactive visualization of *Caenorhabditis elegans* worm neuronal network

Jimin Kim¹, Ruth Leahy², Eli Shlizerman¹,³

¹Department of Applied Mathematics, University of Washington, Seattle WA 98195, USA; ²Amazon.com Inc., Seattle, WA 98108, USA; ³Department of Electrical Engineering, University of Washington, Seattle, WA 98195, USA

Correspondence: Eli Shlizerman - shlizee@uw.edu

BMC Neuroscience 2016, 17(Suppl 1):O9

Modeling neuronal systems involves incorporating the two layers: a
static map of neural connections (connectome), and biophysical pro-
cesses that describe neural responses and interactions. Such a model
is called the ‘dynome’ of a neuronal system as it integrates a dynamical
system with the static connectome. Being closer to reproducing the
activity of a neuronal system, investigation of the dynome has more
potential to reveal neuronal pathways of the network than the static
connectome [1]. However, since the two layers of the dynome are
considered simultaneously, novel tools have to be developed for the
dynome studies. Here we present a visualization methodology, called
‘interactome’, that allows to explore the dynome of a neuronal system
interactively and in real-time, by viewing the dynamics overlaid on a
graph representation of the connectome.

We apply our methodology to the nervous system of *Caenorhabditis elegans* (*C. elegans*) worm, which connectome is almost fully resolved [2], and a computational model of neural dynamics and interactions (gap and synaptic) based on biophysical experimental findings was recently introduced [3]. Integrated together, *C. elegans* dynome

defines a unique set of neural dynamics of the worm. To visualize the
dynome, we propose a dynamic force-directed graph layout of the
connectome. The layout is implemented using D3 visualization plat-
form [4], and is designed to communicate with an integrator of the
dynome. The two-way communication protocol between the layout
and the integrator allows for stimulating (injecting current) into any
subset of neurons at any time point (Fig. 4B). It also allows for simulta-
neously viewing the response of the network on top of the layout visu-
alized by resizing graph nodes (neurons) according to their voltage. In
addition, we support structural changes in the connectome, such as
ablation of neurons and connections.

Our visualization and communication protocols thereby display the
stimulated network in an interactive manner and permit to explore dif-
ferent regimes that the stimulations induce. Indeed, with the interac-
tome we are able to recreate various experimental scenarios, such as
stimulation of forward crawling (PLM/AVB neurons and/or ablation of
AVB) and show that its visualization assists in identifying patterns of
neurons in the stimulated network. As connectomes and dynomes of
additional neuronal systems are being resolved, the interactome will
enable exploring their functionality and inference to its underlying
neural pathways [5].

References

1. Kopell NJ, Gritton HJ, Whittington MA, Kramer MA. Beyond the connectome: the dynome. Neuron. 2014;83(6):1319-28.

2. Varshney LR, Chen BL, Paniagua E, Hall DH, Chkolvski DB. Structural properties of the caenorhabditis elegans neuronal network. PLoS Comput Biol. 2011;7(2):e1001066.

3. Kunert J, Shlizerman E, Kutz JN. Low-dimensional functionality of complex network dynamics: neurosensory integration in the *Caenorhabditis elegans* connectome. Phys Rev E. 2014;89(5):052805.

4. Bostock M, Ogievetsky V, Heer J. D3 data-driven documents. IEEE. 2011;17(12):2301-9.

5. Kim J, Leahy W, Shlizerman E. *C. elegans* interactome: interactive visualization of *Caenorhabditis elegans* worm neuronal network. 2016 (in submission).

O10

Is the model any good? Objective criteria for computational neuroscience model selection

Justas Birgiolas¹, Richard C. Gerkin¹, Sharon M. Crook¹,²

¹School of Life Science, Arizona State University, Tempe, AZ 85287, USA;

²School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

Correspondence: Justas Birgiolas - justas@asu.edu

BMC Neuroscience 2016, 17(Suppl 1):O10

Objectively evaluating and selecting computational models of bio-
logical neurons is an ongoing challenge in the field. Models vary in
morphological detail, channel mechanisms, and synaptic transmission
implementations. We present the results of an automated method for
evaluating computational models against property values obtained

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5** The average deviations of models and cell electrophysiology properties as measured in multiples of the 95 % CI bounds of experimental data means. Dashed line represents 1 CI bound threshold. Top rows show average deviations across all models for each cell property. Bottom rows show deviations across all cell properties for each model</figcaption></figure>

from published cell electrophysiology studies. Seven published deterministic models of olfactory bulb mitral cells were selected from ModelDB [1] and simulated using NEURON's Python interface [2]. Passive and spike properties in response to step current stimulation pulses were computed using the NeuronUnit [3] package and compared to their respective, experimentally obtained means of olfactory bulb mitral cell properties found in the NeuroElectro database [4].

Results reveal that across all models, the resting potential and input resistance property means deviated the most from their experimentally measured means ($R_{input}$, $t$ test $p = 0.02$, $V_{rest}$, Wilcoxon-test $p = 0.01$). The time constant, spike half-width, spike amplitude, and spike threshold properties, in the order of decreasing average deviation, matched well with experimental data ($p > 0.05$) (Fig. 5 top).

In three models, the property deviations were, on average, outside the 95 % CI of the experimental means (Fig. 5 bottom), but these averages were not significant ($t$ test $p > 0.05$). All other models were within the 95 % CI, while the model of Chen et al. had the lowest deviation [5].

Overall, the majority of these olfactory bulb mitral cell models display some properties that are not significantly different from their experimental means. However, the resting potential and input resistance properties significantly differ from the experimental values. We demonstrate that NeuronUnit provides an objective method for evaluating the fitness of computational neuroscience cell models against publicly available data.

**Acknowledgements:** The work of JB, RG, and SMC was supported in part by R01MH1006674 from the National Institutes of Health.

## References

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

2. Hines M, Davison AP, Muller E. NEURON and Python. Front Neuroinform. 2009;3:1.

3. Omar C, Aldrich J, Gerkin RC. Collaborative infrastructure for test-driven scientific model validation. In: Companion proceedings of the 36th international conference on software engineering. ACM; 2014. p. 524–7.

4. Tripathy SJ, Savitskaya J, Burton SD, Urban NN, Gerkin RC. NeuroElectro: a window to the world's neuron electrophysiology data. Front Neuroinform. 2014;8.

5. Chen WR, Shen GY, Shepherd GM, Hines ML, Midtgaard J. Multiple modes of action potential initiation and propagation in mitral cell primary dendrite. J Neurophysiol. 2002;88(5):2755–64.

## O11

### Cooperation and competition of gamma oscillation mechanisms

Atthaphon Viriyopase¹,²,³, Raoul-Martin Memmesheimer¹,³,⁴, and Stan Gielen¹,²

¹Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen (Medical Centre), The Netherlands; ²Department for Biophysics, Faculty of Science, Radboud University Nijmegen, The Netherlands; ³Department for Neuroinformatics, Faculty of Science, Radboud University Nijmegen, The Netherlands; ⁴Center for Theoretical Neuroscience, Columbia University, New York, NY, USA

**Correspondence:** Atthaphon Viriyopase - a.viriyopase@science.ru.nl

BMC Neuroscience 2016, 17(Suppl 1):O11

Two major mechanisms that underlie gamma oscillations are InterNeuronal Gamma ("ING"), which is related to tonic excitation of reciprocally coupled inhibitory interneurons (I-cells), and Pyramidal InternNeuron Gamma ("PING"), which is mediated by coupled populations of excitatory pyramidal cells (E-cells) and I-cells. ING and PING are thought to serve different biological functions. Using computer simulations and analytical methods, we [1] therefore investigate which mechanism (ING or PING) will dominate the dynamics of a network when ING and PING interact and how the dominant mechanism may switch.

We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency "wins". It determines the frequency of the network oscillations and suppresses the other mechanism. The network oscillation frequency (green lines corresponding to the network topology given in Fig. 6C) corresponding to

<figure><img src="image_7.png" /><figcaption>**Fig. 6** Oscillations in full and reduced networks of reciprocally coupled pyramidal cells and interneurons. **A, B** Illustrate topologies of reduced networks that generate “pure” ING and “pure” PING, respectively, while **C** highlights the topology of a “full” network that could in principle generate either ING or PING oscillations or mixtures of both. **D, E** Frequency of pure ING-rhythm generated by the reduced network in **A** (blue line), pure PING-rhythm generated by the reduced network in **b** (red line), and rhythms generated by the full network in **C** (green line) as a function of mean current to I-cells $I_{0,I}$ and as function of mean current to E-cells $I_{0,E}$, respectively. **D** Results for networks with type-I interneurons while **E** shows results for networks with type-II interneurons. Pyramidal cells are modeled as type-I Hodgkin–Huxley neurons</figcaption></figure>
the network with type-I-phase-response-curve interneurons and type-II-phase-response-curve interneurons is plotted in Fig. 6D, E, respectively. We explain our simulation results by a theoretical model that allows a full theoretical analysis.

Our study suggests experimental approaches to decide whether oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and whether the participating interneurons belong to class I or II. Consider as an example networks with type-I interneurons where the external drive to the E-cells, $I_{0,E}$, is kept constant while the external drive to the I-cells, $I_{0,I}$, is varied. For both ING and PING dominated oscillations the frequency of the rhythm increases when $I_{0,I}$ increases (cf. Fig. 6D). Observing such an increase does therefore not allow to determine the underlying mechanism. However, the absolute value of the first derivative of the frequency with respect to $I_{0,I}$ allows a distinction, as it is much smaller for PING than for ING (cf. Fig. 6D). In networks with type-II interneurons, the non-monotonic dependence near the ING-PING transition may be a characteristic hallmark to detect the oscillation character (and the interneuron type): Decrease (increase) of the frequency when increasing $I_{0,E}$ indicates ING (PING), cf. Fig. 6E. These theoretical predictions are in line with experimental evidence [2].

## References

1. Viriyopase A, Memmesheimer RM, Gielen S. Cooperation and competition of gamma oscillation mechanisms. J Neurophysiol. 2016.

2. Craig MT, McBain CJ. Fast gamma oscillations are generated intrinsically in CA1 without the involvement of fast-spiking basket cells. J Neurosci. 2015;35(8):3616-24.

## O12

### A discrete structure of the brain waves

Yuri Dabaghian¹,², Justin DeVito¹, Luca Perotti³

¹Department of Neurology Pediatrics, Baylor College of Medicine, Houston, TX 77030, USA; ²Department of Computational and Applied Mathematics, Rice University, Houston, TX, 77005, USA; ³Physics Department, Texas Southern University, 3100 Cleburne St, Houston, TX 77004, USA

**Correspondence:** Yuri Dabaghian - dabaghian@rice.edu

BMC Neuroscience 2016, 17(Suppl 1):O12

A physiological interpretation of the biological rhythms, e.g., of the local field potentials (LFP) depends on the mathematical and computational approaches used for its analysis. Most existing mathematical methods of the LFP studies are based on braking the signal into a combination of simpler components, e.g., into sinusoidal harmonics of Fourier analysis or into wavelets of the Wavelet Analysis. However, a common feature of all these methods is that their prime components are presumed from the onset, and the goal of the subsequent analysis reduces to identifying the combination that best reproduces the original signal.

We propose a fundamentally new method, based on a number of deep theorems of complex function theory, in which the prime components of the signal are not presumed a priori, but discovered empirically [1]. Moreover, the new method is more flexible and more sensitive to the signal's structure than the standard Fourier method.

Applying this method reveals a fundamentally new structure in the hippocampal LFP signals in rats in mice. In particular, our results suggest that the LFP oscillations consist of a superposition of a small, discrete set of frequency modulated oscillatory processes, which we call "oscillons". Since these structures are discovered empirically, we hypothesize that they may capture the signal's actual physical structure, i.e., the pattern of synchronous activity in neuronal ensembles. Proving this hypothesis will help enormously to advance a principal, theoretical understanding of the neuronal synchronization mechanisms. We anticipate that it will reveal new information about the structure of the LFP and other biological oscillations, which should provide insights into the underlying physiological phenomena and the organization of brains states that are currently poorly understood, e.g., sleep and epilepsy.

**Acknowledgements:** The work was supported by the NSF 1422438 grant and by the Houston Bioinformatics Endowment Fund.

## Reference

1. Perotti L, DeVito J, Bessis D, Dabaghian Y, Dabaghian Y, Brandt VL, Frank LM. Discrete spectra of brain rhythms (in submision).

## O13

### Direction-specific silencing of the *Drosophila* gaze stabilization system

Anmo J. Kim¹,†, Lisa M. Fenk¹,†, Cheng Lyu¹, Gaby Maimon¹

¹Laboratory of Integrative Brain Function, The Rockefeller University, New York, NY 10065, USA

**Correspondence:** Anmo J. Kim - anmo.kim@gmail.com

† Authors contributed equally

BMC Neuroscience 2016, 17(Suppl 1):O13

Many animals, including insects and humans, stabilize the visual image projected onto their retina by following a rotating landscape with their head or eyes. This stabilization reflex, also called the optomotor response, can pose a problem, however, when the animal intends to change its gaze. To resolve this paradox, von Holst and Mittelstaedt proposed that a copy of the motor command, or efference copy, could be routed into the visual system to transiently silence this stabilization reflex when an animal changes its gaze [1]. Consistent with this idea, we recently demonstrated that a single identified neuron associated with the optomotor response receives silencing motor-related inputs during rapid flight turns, or saccades, in tethered, flying *Drosophila* [2]. Here, we expand on these results by comprehensively recording from a group of optomotor-mediating visual neurons in the fly visual system: three horizontal system (HS) and six vertical system (VS) cells. We found that the amplitude of motor-related inputs to each HS and VS cell correlates strongly with the strength of each cell's visual sensitivity to rotational motion stimuli around the primary turn axis, but not to the other axes (Fig. 7). These results support the idea that flies send rotation-axis-specific efference copies to the visual system during saccades—silencing the stabilization reflex only for a specific axis, but leaving the others intact. This is important because saccades consist of stereotyped banked turns, which involve body rotations around all three primary axes of rotation. If the gaze stabilization

<figure><img src="image_8.png" /><figcaption>**Fig. 7** The amplitudes of saccade-related potentials (SRPs) to HS and VS cells are strongly correlated with each cell's visual sensitivity to rightward yaw motion stimuli. **A** Experimental apparatus. **B** Maximal-intensity z-projections of the lobula plate to visualize HS- or VS-cell neurites that are marked by a GAL4 enhancer trap line. **C, D** The amplitude of saccade-related potentials (SRPs) were inversely correlated with visual responses, when measured under rightward yaw motion stimuli, but not under clockwise roll motion stimuli. Each sample point corresponds to each cell type. *Error bars* indicate SEM</figcaption></figure>
system is impaired for only one of these axes, then the fly is expected to attempt to maintain gaze stability, through a combination of head and body movements, for the other two. This prediction is consistent with behavioral measurements of head and body kinematics during saccades in freely flying blow flies [3]. Together, these studies provide an integrative model of how efference copies counteract a specific aspect of visual feedback signals to tightly control the gaze stabilization system.

### References

1. von Holst E, Mittelstaedt H. The principle of reafference. Naturwissenschaften.1950;37:464-76.

2. Kim AJ, Fitzgerald JK, Maimon G. Cellular evidence for efference copy in *Drosophila* visuomotor processing. Nat Neurosci. 2015;18:1247-55.

3. Schilstra C, van Hateren JH. Stabilizing gaze in flying blowflies. Nature. 1998;395:654.

## O14

### What does the fruit fly think about values? A model of olfactory associative learning

Chang Zhao<fnref n="1" />, Yves Widmer<fnref n="2" />, Simon Sprecher<fnref n="2" />, Walter Senn<fnref n="1" />

**Correspondence:** Chang Zhao - zhao@pyl.unibe.ch

BMC Neuroscience 2016, 17(Suppl 1):O14

Associative learning in the fruit fly olfactory system has been studied from the molecular to the behavior level [1, 2]. Fruit flies are able to associate conditional stimuli such as odor with unconditional aversive stimuli such as electrical shocks, or appetitive stimuli such as sugar or water. The mushroom body in the fruit fly brain is considered to be crucial for olfactory learning [1, 2]. The behavioral experiments show that the learning can not be explained simply by an additive Hebbian (i.e. correlation-based) learning rule. Instead, it depends on the timing between the conditional and unconditional stimulus presentation. Yarali and colleagues suggested a dynamic model on the molecular level to explain event timing in associative learning [3]. Here, we present new experiments together with a simple phenomenological model for learning that shows that associative olfactory learning in the fruit fly represents value learning that is incompatible with Hebbian learning.

In our model, the information of the conditional odor stimulus is conveyed by Kenyon cells from the projection neurons to the mushroom output neurons; the information of the unconditional shock stimulus is represented by dopaminergic neurons to the mushroom output neurons through direct or indirect pathways. The mushroom body output neurons encode the internal value (v) of the odor (o) by synaptic weights (w) that conveys the odor information, v = w·o. The synaptic strength is updated according to the value learning rule, Δw = η(s - v), o, where s represents the (internal) strength of the shock stimulus, o represents the synaptic odor trace, and η is the learning rate. The value associated with the odor determines the probability of escaping from that odor. This simple model reproduces the behavioral data and shows that olfactory conditioning in the fruit fly is in fact value learning. In contrast to the prediction of Hebbian learning, the escape probability for repeated odor-shock pairings is much lower than the escape probability for a single pairing with a correspondingly stronger shock.

### References

1. Aso Y, Sitaraman D, Ichinose T, Kaun KR, Vogt K, Belliart-Gurin G, Plaais PY, Robie AA, Yamagata N, Schnaitmann C, Rowell WJ, Johnston RM, Ngo TB, Chen N, Korff W, Nitabach MN, Heberlein U, Preat T, Branson KM, Tanimoto H, Rubin GM: Mushroom body output neurons encode valence and guide memory-based action selection in Drosophila. ELife. 2014;3:e04580.

2. Heisenberg M. Mushroom body memoir: from maps to models. Nat Rev Neurosci. 2003;4:266-75.

3. Yarali A, Nehrkorn J, Tanimoto H, Herz AVM. Event timing in associative learning: from biochemical reaction dynamics to behavioural observations. PLoS One. 2012;7(3):e32885.

## O15

### Effects of ionic diffusion on power spectra of local field potentials (LFP)

Geir Halnes<fnref n="1" />, Tuomo Mäki-Marttunen<fnref n="2" />, Daniel Keller³, Klas H.

Pettersen<fnref n="4" />,⁵, Ole A. Andreassen<fnref n="2" />, Gaute T. Einevoll<fnref n="1" />,<fnref n="6" />

**Correspondence:** Geir Halnes - geir.halnes@nmbu.no

BMC Neuroscience 2016, 17(Suppl 1):O15

The local field potential (LFP) in the extracellular space (ECS) of the brain, is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the LFP and its underlying neurophysiological processes are commonly used in the interpretation such measurements. Standard methods, such as volume conductor theory [1], assume that ionic diffusion in the ECS has negligible impact on the LFP. This assumption could be challenged during endured periods of intense neural signalling, under which local ion concentrations in the ECS can change by several millimolars. Such concentration changes are indeed often accompanied by shifts in the ECS potential, which may be partially evoked by diffusive currents [2]. However, it is hitherto unclear whether putative diffusion-generated potential shifts are too slow to be picked up in LFP recordings, which typically use electrode systems with cut-off frequencies at ~0.1 Hz.

To explore possible effects of diffusion on the LFP, we developed a hybrid simulation framework: (1) The NEURON simulator was used to compute the ionic output currents from a small population of cortical layer-5 pyramidal neurons [3]. The neural model was tuned so that simulations over ~100 s of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments [2]. (2) In parallel, a novel electrodiffusive simulation framework [4] was used to compute the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. To explore the relative role of diffusion, we compared simulations where ECS diffusion was absent with simulations where ECS diffusion was included.

Our key findings were: (i) ECS diffusion shifted the local potential by up to ~0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f<fnref n="2" /> power law. (iii) Diffusion effects

<figure><img src="image_9.png" /></figure>

<footnote n="1">¹Department of Physiology, University of Bern, Bern, 3012, Switzerland;</footnote>

<footnote n="2">²Department of Biology, University of Fribourg, Fribourg, 1700, Switzerland</footnote>

<footnote n="1">¹Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway; ²NORMENT, Institute of Clinical Medicine, University of Oslo, Oslo, Norway; ³The Blue Brain Project, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland;</footnote>

<footnote n="4">⁴Letten Centre and Glialab, Department of Molecular Medicine, Institutue of Basic Medical Sciences, University of Oslo, Oslo, Norway; ⁵Centre for Molecular Medicine Norway, University of Oslo, Oslo, Norway;</footnote>

<footnote n="6">⁶Department of Physics, University of Oslo, Oslo, Norway</footnote>
dominated the PSD of the ECS potential for frequencies up to ~10 Hz (Fig. 8). We conclude that for large, but physiologically realistic ECS concentration gradients, diffusion could affect the ECS potential well within the frequency range considered in recordings of the LFP.

## References

1. Holt G, Koch C. Electrical interactions via the extracellular potential near cell bodies. J Comput Neurosci. 1999;6:169–84.

2. Dietzel I, Heinemann U, Lux H. Relations between slow extracellular potential changes, glial potassium buffering, and electrolyte and cellular volume changes during neuronal hyperactivity in cat. Glia. 1989;2:25–44.

3. Hay E, Hill S, Schürmann F, Markram H, Segev I. Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active properties. PLoS Comput Biol. 2011;7(7):e1002107.

4. Halnes G, Østby I, Pettersen KH, Ohnholt SW, Einevoll GT: Electrodiffusive model for astrocytic and neuronal ion concentration dynamics. PLoS Comput Biol. 2013;9(12):e1003386.

## O16

### Large-scale cortical models towards understanding relationship between brain structure abnormalities and cognitive deficits

Yasunori Yamada¹

¹IBM Research - Tokyo, Japan

**Correspondence:** Yasunori Yamada - ysnr@jp.ibm.com

BMC Neuroscience 2016, 17(Suppl 1):O16

Brain connectivity studies have revealed fundamental properties of normal brain network organization [1]. In parallel, they have reported structural connectivity abnormalities in brain diseases such as Alzheimer's disease (AD) [1, 2]. However, how these structural abnormalities affect information processing and cognitive functions involved in brain diseases is still poorly understood. To deepen our understanding of this causal link, I developed two large-scale cortical models with normal and abnormal structural connectivity of diffusion tensor imaging on aging APOE-4 non-carriers and carriers in the USC Multimodal Connectivity Database [2, 3]. The possession of the APOE-4 allele is one of the major risk factors in developing later AD, and it has known abnormalities in structural connectivity characterized by lower network communication efficiency in terms of local interconnectivity and balance of integration and interconnectivity [2]. The two cortical models share other parameters and consist of 2.4 million spiking neurons and 4.8 billion synaptic connections. First, I demonstrate the biological relevance of the models by confirming that they reproduce normal patterns of cortical spontaneous activities in terms of the following distinctive properties observed in vivo [4]: low firing rates of individual neurons that approximate log-normal distributions, irregular spike trains following a Poisson distribution, a network balance between excitation and inhibition, and greater depolarization of the average membrane potentials. Next, to investigate how the difference in structural connectivity affects cortical information processing, I compare cortical response properties to an input during spontaneous activity between the cortical models. The results show that the cortical model with the abnormal structural connectivity decreased the degree of cortical response as well as the number of cortical regions responding to the input (Fig. 9), suggesting that the structural connectivity abnormality observed in APOE-4 carriers might reduce cortical information propagation and lead to negative effects in information integration. Indeed, imaging studies support this suggestion by reporting structural abnormality with lower network communication efficiency

observed in the structural connectivity of both APOE-4 carriers and AD patients [1, 2]. This computational approach allowing for manipulations and detailed analyses that are difficult or impossible in human studies can help to provide a causal understanding of how cognitive deficits in patients with brain diseases are associated with their underlying structural abnormalities.

**Acknowledgements:** This research was partially supported by the Japan Science and Technology Agency (JST) under the Strategic Promotion of Innovative Research and Development Program.

## References

1. Stam CJ. Modern network science of neurological disorders. Nat Rev Neurosci. 2014;15(10):683–695.

2. Brown JA, Terashima KH, Burggren AC, Ercoli LM, Miller KJ, Small GW, Bookheimer SY. Brain network local interconnectivity loss in aging APOE-4 allele carriers. Proc Natl Acad Sci USA. 2011;108(51):20760–5.

3. Brown JA, Rudie JD, Bandrowski A, van Horn JD, Bookheimer SY. The UCLA multimodal connectivity database: a web-based platform for brain connectivity matrix sharing and analysis. Front Neuroinform. 2012;6(28).

4. Ikegaya Y, Sasaki T, Ishikawa D, Honma N, Tao K, Takahashi N, Minamisawa G, Ujita S, Matsuki N. Interpyramid spike transmission stabilizes the sparseness of recurrent network activity. Cereb Cortex. 2013;23(2):293–304.

## O17

### Spatial coarse-graining the brain: origin of minicolumns

Moira L. Steyn-Ross¹, D. Alistair Steyn-Ross¹

¹School of Engineering, University of Waikato, Hamilton 3240, New Zealand

**Correspondence:** Moira L. Steyn-Ross - msr@waikato.ac.nz

BMC Neuroscience 2016, 17(Suppl 1):O17

The seminal experiments of Mountcastle [1] over 60 years ago established the existence of cortical minicolumns: vertical column-like arrays of approximately 80–120 neurons aligned perpendicular to the pial surface, penetrating all six cortical layers. Minicolumns have been proposed as the fundamental unit for cortical organisation. Minicolumn formation is thought to rely on gene expression and thalamic activity, but exactly why neurons cluster into columns of diameter 30–50 µm containing approximately 100 neurons is not known.

In this presentation we describe a mechanism for the formation of minicolumns via gap-junction diffusion-mediated coupling in a network of spiking neurons. We use our recently developed method of cortical "reblocking" (spatial coarse-graining) [2] to derive neuronal dynamics equations at different spatial scales. We are able to show that for sufficiently strong gap-junction coupling, there exists a minimum block size over which neural activity is expected to be coherent. This coherence region has cross-sectional area of order (40–60 µm)², consistent with the areal extent of a minicolumn. Our scheme regrids a 2D continuum of spiking neurons using a spatial rescaling theory, established in the 1980s, that systematically eliminates high-wave-number modes [3]. The rescaled neural equations describe the bulk dynamics of a larger block of neurons giving "true" (rather than mean-field) population activity, encapsulating the inherent dynamics of a continuum of spiking neurons stimulated by incoming signals from neighbors, and buffeted by ion-channel and synaptic noise.

Our method relies on a perturbative expansion. In order for this coarse-graining expansion to converge, we require not only a sufficiently strong level of inhibitory gap-junction coupling, but also a sufficiently large blocking ratio B. The latter condition establishes a lower bound for the smallest "cortical block": the smallest group of neurons that can respond to input as a collective and cooperative unit. We find that this minimum block-size ratio lies between 4 and 6. In order to relate this 2D geometric result to the 3D extent of a 3-mm-thick layered cortex, we project the cortex onto a horizontal surface and count the number of neurons contained within each *l* × *l* grid micro-cell. Setting *l* ≈ 10 µm and assuming an average of one interneuron per grid cell, a blocking ratio at the mid-value *B* = 5 implies that the side-length of a coherent "macro-cell" will be *L* = *Bl* = 50 µm containing ~25 inhibitory plus 100 excitatory neurons (assuming an *l* to *e*

<figure><img src="image_10.png" /></figure>
abundance ratio of 1:4) in cross-sectional area $L^2$. Thus the minicolumn volume will contain roughly 125 neurons. We argue that this is the smallest diffusively-coupled population size that can support cooperative dynamics, providing a natural mechanism defining the functional extent of a minicolumn.

We propose that minicolumns might form in the developing brain as follows: Inhibitory neurons migrate horizontally from the ganglionic eminence to form a dense gap-junction coupled substrate that permeates all layers of the cortex [4]. Progenitor excitatory cells ascend vertically from the ventricular zone, migrating through the inhibitory substrate of the cortical plate. Thalamic input provides low-level stimulus to activate spiking activity throughout the network. Inhibitory diffusive coupling allows a "coarse graining" such that neurons within a particular areal extent respond collectively to the same input. The minimum block size prescribed by the coarse graining imposes constraints on minicolumn geometry, leading to the spontaneous emergence of cylindrical columns of coherent activity, each column centered on an ascending chain of excitatory neurons and separated from neighboring chains by an annular surround of inhibition. This smallest aggregate is preferentially activated during early brain development, and activity-based plasticity then leads to the formation of tangible structural columns.

### References

1. Mountcastle VB. Modality and topographic properties of single neurons of cat's somatic sensory cortex. J Neurophysiol. 1957;20(4):408-34.

2. Steyn-Ross ML, Steyn-Ross DA. From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes. Phys Rev E. 2016;93(2):022402.

3. Steyn-Ross ML, Gardiner CW. Adiabatic elimination in stochastic systems III. Phys Rev A. 1984;29(5):2834-44.

4. Jones EG. Microcolumns in the cerebral cortex. Proc Natl Acad Sci USA. 2000;97(10):5019-21.

## O18

### Modeling large-scale cortical networks with laminar structure

Jorge F. Mejias¹, John D. Murray², Henry Kennedy³, and Xiao-Jing Wang¹,⁴
¹Center for Neural Science, New York University, New York, NY, 10003, USA; ²Department of Psychiatry, Yale School of Medicine, New Haven, CT, 06511, USA; ³INSERM U846, Stem Cell and Brain Research Institute, Bron Cedex, France; ⁴NYU-ECNU Institute of Brain and Cognitive Science, NYU Shanghai, Shanghai, China

**Correspondence:** Jorge F. Mejias - jorge.f.mejias@gmail.com

BMC Neuroscience 2016, 17(Suppl 1):O18

Visual cortical areas in the macaque are organized according to an anatomical hierarchy, which is defined by specific patterns of anatomical projections in the feedforward and feedback directions [1, 2]. Recent macaque studies also suggest that signals ascending through the visual hierarchy are associated with gamma rhythms, and top-down signals with alpha/low beta rhythms [3-5]. It is not clear, however, how oscillations presumably originating at local populations can give rise to such frequency-specific large-scale interactions in a mechanistic way, or the role that anatomical projections patterns might have in this.

To address this question, we build a large-scale cortical network model with laminar structure, grounding our model on a recently obtained anatomical connectivity matrix with weighted directed inter-areal projections and information about their laminar origin. The model involves several spatial scales—local or intra-laminar microcircuit, inter-laminar circuits, inter-areal interactions and large-scale cortical network—and a wide range of temporal scales—from slow alpha oscillations to gamma rhythms. At any given level, the model is constrained anatomically and then tested against electrophysiological observations, which provides useful information on the mechanisms modulating the oscillatory activity at different scales. As we ascend through the local to the inter-laminar and inter-areal levels, the model allows us to explore the sensory-driven enhancement of gamma rhythms, the inter-laminar phase-amplitude coupling, the relationship between alpha waves and local inhibition, and the frequency-specific

inter-areal interactions in the feedforward and feedback directions [3, 4], revealing a possible link with the predictive coding framework. When we embed our modeling framework into the anatomical connectivity matrix of 30 areas (which includes novel areas not present in previous studies [2, 6]), the model gives insight into the mechanisms of large-scale communication across the cortex, accounts for an anatomical and functional segregation of FF and FB interactions, and predicts the emergence of functional hierarchies, which recent studies have found in macaque [4] and human [5]. Interestingly, the functional hierarchies observed experimentally are highly dynamic, with areas moving across the hierarchy depending on the behavioral context [4]. In this regard, our model provides a strong prediction: we propose that these hierarchical jumps are triggered by laminar-specific modulations of input into cortical areas, suggesting a strong link between hierarchy dynamics and context-dependent computations driven by specific inputs.

### References

1. Felleman DJ, Van Essen DC. Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex. 1991;1(1):1-47.

2. Markov NT, Vezoli J, Chameau P, Falchier A, Quilodran R, Huissoud C, Lamy C, Misery P, Giroud P, Ullman S, et al. Anatomy of hierarchy: feedforward and feedback pathways in macaque visual cortex. J Comp Neurol. 2014;522:225-259.

3. van Kerkoerle T, Self MW, Dagnino B, Gariel-Mathis MA, Poort J, van der Togt C, Roelfsema PR. Alpha and gamma oscillations characterize feedback and feedforward processing in monkey visual cortex. Proc Natl Acad Sci USA. 2014;111:14332-41.

4. Bastos AM, Vezoli J, Bosman CA, Schoffelen JM, Oostenveld R, Dowdall JR, De Weerd P, Kennedy H, Fries P. Visual areas exert feedforward and feedback influences through distinct frequency channels. Neuron. 2015;85:390-401.

5. Michalareas G, Vezoli J, van Pelt S, Schoffelen JM, Kennedy H, Fries. Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human visual cortical areas. Neuron. 2016;89:384-97.

6. Chaudhuri R, Knoblauch K, Gariel MA, Kennedy H, Wang XJ. A large-scale circuit mechanism for hierarchical dynamical processing in the primate cortex. Neuron. 2015;88:419-31.

## O19

### Information filtering by partial synchronous spikes in a neural population

Alexandra Kruscha¹,², Jan Grewe³,⁴, Jan Benda³,⁴ and Benjamin Lindner¹,²
¹Bernstein Center for Computational Neuroscience, Berlin, 10115, Germany; ²Institute for Physics, Humboldt-Universität zu Berlin, Berlin, 12489, Germany; ³Institute for Neurobiology, Eberhardt Karls Universität Tübingen, Germany; ⁴Bernstein Center for Computational Neuroscience, Munich, Germany

**Correspondence:** Alexandra Kruscha - alexandra.kruscha@bccn-berlin.de
BMC Neuroscience 2016, 17(Suppl 1):O19

Synchronous firing of neurons is a prominent feature in many brain areas. Here, we are interested in the information transmission by the synchronous spiking output of a noisy neuronal population, which receives a common time-dependent sensory stimulus. Earlier experimental [1] and theoretical [2] work revealed that synchronous spikes encode preferentially fast (high-frequency) components of the stimulus, i.e. synchrony can act as an information filter. In these studies a rather strict measure of synchrony was used: the entire population has to fire within a short time window. Here, we generalize the definition of the synchronous output, for which only a certain fraction $\gamma$ of the population needs to be active simultaneously—a setup that seems to be of more biological relevance. We characterize the information transfer in dependence of this fraction and the population size, by the spectral coherence function between the stimulus and the partial synchronous output. We present two different analytical approaches to derive this frequency-resolved measure (one that is more suited for small population sizes, while the second one is applicable to larger populations). We show that there is a critical synchrony fraction, namely the probability at which a single neuron spikes within the
predefined time window, which maximizes the information transmis-
sion of the synchronous output. At this value, the partial synchronous
output acts as a low-pass filter, whereas deviations from this critical
fraction lead to a more and more pronounced band-pass filtering
effect. We confirm our analytical findings by numerical simulations for
the leaky integrate-and-fire neuron. We also show that these findings
are supported by experimental recordings of P-Units electroreceptors
of weakly electric fish, where the filtering effect of the synchronous
output occurs in real neurons as well.

**Acknowledgement:** This work was supported by Bundesministerium für Bildung und Forschung Grant 01GQ1001A and DFG Grant 609788-L1 1046/2-1.

References

1. Middleton JW, Longtin A, Benda J, Maler L. Postsynaptic receptive field size and spike threshold determine encoding of high-frequency information via sensitivity to synchronous presynaptic activity. J Neurophysiol. 2009;101:1160–70.

2. Sharafi N, Benda J, Lindner B. Information filtering by synchronous spikes in a neural population. J Comp Neurosc. 2013;34:285–301.

O20

Decoding context-dependent olfactory valence in *Drosophila*

Laurent Badel¹, Kazumi Ohta¹, Yoshiko Tsuchimoto¹, Hokto Kazama¹

¹RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, 351-0198, Japan

Correspondence: Laurent Badel - laurent@brain.riken.jp

BMC Neuroscience 2016, 17(Suppl 1):O20

Many animals rely on olfactory cues to make perceptual decisions
and navigate the environment. In the brain, odorant molecules are
sensed by olfactory receptor neurons (ORNs), which convey olfactory
information to the central brain in the form of sequences of action
potentials. In many organisms, axons of ORNs expressing the same
olfactory receptor converge to one or a few glomeruli in the first cen-
tral region (the antennal lobe in insects and the olfactory bulb in fish
and mammals) where they make contact with their postsynaptic tar-
gets. Therefore, each glomerulus can be considered as a processing
unit that relays information from a specific type of receptor. Because
different odorants recruit different sets of glomeruli, and most glomer-
uli respond to a wide array of odors, olfactory information at this stage
of processing is contained in spatiotemporal patterns of glomerular
activity. How these patterns are decoded by the brain to guide odor-
evoked behavior, however, remains largely unknown.

In *Drosophila*, attraction and aversion to specific odors have been
linked to the activation of one or a few glomeruli (reviewed in [1]) in
the antennal lobe (AL). These observations suggest a “labeled-line”
coding strategy, in which individual glomeruli convey signals of spe-
cific ethological relevance, and their activation triggers the execution
of hard-wired behavioral programs. However, because these studies
used few odorants, and a small fraction of glomeruli were tested, it is
unclear how the results generalize to broader odor sets, and whether
similar conclusions hold for each of the ~50 glomeruli of the fly AL.
Moreover, how compound signals from multiple glomeruli are inte-
grated is poorly understood.

Here, we combine optical imaging, behavioral and statistical tech-
niques to address these questions systematically. Using two-photon
imaging, we monitor Ca²⁺ activity in the AL in response to 84 odors.
We next screen behavioral responses to the same odorants. Compar-
ing these data allows us to formulate a decoding model describing
how olfactory behavior is determined by glomerular activity patterns
in a quantitative manner. We find that a weighted sum of normal-
ized glomerular responses recapitulates the observed behavior and
predicts responses to novel odors, suggesting that odor valence is
not determined solely by the activity a few privileged glomeruli. This
conclusion is supported by genetic silencing and optogenetic activa-
tion of individual ORN types, which are found to evoke modest biases
in behavior in agreement with model predictions. Finally, we test the
model prediction that the relative valence of a pair of odors depends
on the identity of other odors presented in the same experiment. We
find that the relative valence indeed changes, and may even switch,

suggesting that perceptual decisions can be modulated by the olfac-
tory context. Surprisingly, our model correctly captured both the
direction and the magnitude of the observed changes. These results
indicate that the valence of olfactory stimuli is decoded from AL activ-
ity by pooling contributions over a large number of glomeruli, and
highlight the ability of the olfactory system to adapt to the statistics of
its environment, similarly to the visual and auditory systems.

Reference

1. Li Q, Liberles SD. Aversion and attraction through olfaction. Curr Biol. 2015;25(3):R120-9.

P1

Neural network as a scale-free network: the role of a hub

B. Kahng¹

¹Department of Physics and Astronomy, Seoul National University, 08826, Korea

Correspondence: B. Kahng - bkahng@snu.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P1

Recently, increasing attention has been drawn to human neurosci-
ence in network science communities. This is because recent fMRI and
anatomical experiments have revealed that neural networks of normal
human brain are scale-free networks. Thus, accumulated knowledges
in a broad range of network sciences can be naturally applied to neu-
ral networks to understand functions and properties of normal and
disordered human brain networks. Particularly, the degree exponent
value of the human neural network constructed from the fMRI data
turned out to be approximately two. This value has particularly impor-
tant meaning in scale-free networks, because the number of connec-
tions to neighbors of a hub becomes largest and thus functional role
of the hub becomes extremely important. In this talk, we present the
role of the hub in pattern recognition and dynamical problems in asso-
ciation with neuroscience.

P2

Hemodynamic responses to emotions and decisions using
near-infrared spectroscopy optical imaging

Nicoladie D. Tam¹

¹Department of Biological Sciences, University of North Texas, Denton, TX 76203, USA

Correspondence: Nicoladie D. Tam - nicoladie.tam@unt.edu

BMC Neuroscience 2016, 17(Suppl 1):P2

This study focuses on the relationship between the emotional
response, decision and the hemodynamic responses in the prefron-
tal cortex. This is based on the computational emotional model that
hypothesizes the emotional response is proportional to the discrep-
ancy between the expectancy and the actuality. Previous studies had
shown that emotional responses are related to decisions [1, 2]. Specifi-
cally, the emotional responses of happy [3], sad [4], angry [5], jealous
[6] emotions are proportional to the discrepancy between what one
wants and what one gets [1, 3–7].

**Methods** Human subjects are asked to perform the classical behavio-
ral economic experiment called Ultimatum Game (UG) [8]. This experi-
mental paradigm elicits the interrelationship between decision and
emotion in human subjects [3–6]. The hemodynamic responses of the
prefrontal cortex were recorded while the subjects performed the UG
experiment.

**Results** The results showed that the hemodynamic response, which corresponds to the neural activation and deactivation based on the metabolic activities of the neural tissues, are proportional to the emotional intensity and the discrepancy between the expectancy and the actuality. This validates the hypothesis of the proposed emotional theory [9–11] that the intensity of emotion is proportional to the discrepancy between the expected and the actual outcomes. These responses are also related to the fairness perception [7], with respect to the survival functions [9, 10] similar to the responses established for happy [1] emotion, and for fairness [12] experimentally. This is consistent with the computational relationship between decision and fairness [13].
## References

1. Tam ND. Quantification of happy emotion: dependence on decisions. Psychol Behav Sci. 2014;3(2):68-74.

2. Tam ND. Rational decision-making process choosing fairness over monetary gain as decision criteria. Psychol Behav Sci. 2014;3(6-1):16-23.

3. Tam ND. Quantification of happy emotion: Proportionality relationship to gain/loss. Psychol Behav Sci. 2014;3(2):60-7.

4. Tam ND. Quantitative assessment of sad emotion. *Psychol Behav Sci* 2015, 4(2):36-43.

5. Tam DN. Computation in emotional processing: quantitative confirmation of proportionality hypothesis for angry unhappy emotional intensity to perceived loss. Cogn Comput. 2011;3(2):394-415.

6. Tam ND, Smith KM. Cognitive computation of jealous emotion. Psychol Behav Sci. 2014;3(6-1):1-7.

7. Tam ND. Quantification of fairness perception by including other regarding concerns using a relativistic fairness-equity model. Adv Soc Sci Research J. 2014;1(4):159-69.

8. von Neumann J, Morgenstern O, Rubinstein A. Theory of games and economic behavior. Princeton: Princeton University Press; 1953.

9. Tam D. EMOTION-I model: A biologically-based theoretical framework for deriving emotional context of sensation in autonomous control systems. Open Cybern Syst J. 2007;1:28-46.

10. Tam D. EMOTION-II model: a theoretical framework for happy emotion as a self-assessment measure indicating the degree-of-fit (congruency) between the expectancy in subjective and objective realities in autonomous control systems. Open Cybern Syst J. 2007;1:47-60.

11. Tam ND. EMOTION-III model. A theoretical framework for social empathic emotions in autonomous control systems. Open Cybern Syst J. 2016 (in press).

12. Tam ND: Quantification of fairness bias in relation to decisions using a relativistic fairness-equity model. *Adv in Soc Sci Research J* 2014, 1(4):169-178.

13. Tam ND. A decision-making phase-space model for fairness assessment. Psychol Behav Sci. 2014;3(6-1):8-15.

## P3

### Phase space analysis of hemodynamic responses to intentional movement directions using functional near-infrared spectroscopy (fNIRS) optical imaging technique

Nicoladie D. Tam¹, Luca Pollonini², George Zouridakis³

¹Department of Biological Sciences, University of North Texas, Denton, TX 76203, USA; ²College of Technology, the University of Houston, TX, 77204, USA; ³Departments of Engineering Technology, Computer Science, and Electrical and Computer Engineering, University of Houston, Houston, TX, 77204, USA

**Correspondence:** Nicoladie D. Tam - nicoladie.tam@unt.edu

BMC Neuroscience 2016, 17(Suppl 1):P3

We aim to extract the intentional movement directions of the hemodynamic signals recorded from noninvasive optical imaging technique, such that a brain-computer-interface (BCI) can be built to control a wheelchair based on the optical signals recorded from the brain. Real-time detection of neurodynamic signals can be obtained using functional near-infrared spectroscopy (fNIRS), which detects both oxy-hemoglobin (oxy-Hb) and deoxy-hemoglobin (deoxy-Hb) levels in the underlying neural tissues. In addition to the advantage of real-time monitoring of hemodynamic signals using fNIRS over fMRI (functional magnetic resonance imaging), fNIRS also can detect brain signals of human subjects in motion without any movement artifacts. Previous studies had shown that hemodynamic responses are correlated with the movement directions based on the temporal profiles of the oxy-Hb and deoxy-Hb levels [1-5]. In this study, we will apply a phase space analysis to the hemodynamic response to decode the movement directions instead of using the temporal analysis in the previous studies.

**Methods** In order to decode the movement directions, human subjects were asked to execute two different orthogonal directional movements in the front-back and right-left directions while the optical hemodynamic responses were recorded in the motor cortex of the dominant hemisphere. We aim to decode the intentional movement directions without a priori any assumption on how arm movement directions are correlated with the hemodynamic signals. Therefore,

we used the phase space analysis to determine how the trajectories of oxy-Hb and deoxy-Hb are related to each other during these arm movements.

**Results** The results show that there are subpopulations of cortical neurons that are task-related to the intentional movement directions. Specifically, using phase space analysis of the oxy-Hb and deoxy-Hb levels, opposite movement direction is represented by the different hysteresis of the trajectories in opposite direction in the phase space. Since oxy-Hb represents the oxygen delivery and deoxy-Hb represents the oxygen extraction by the underlying brain tissues, the phase space analysis provides a means to differentiate the movement direction by the ratio between oxygen delivery and oxygen extraction. In other words, the oxygen demands in the subpopulation of neurons in the underlying tissue differ depending on the movement direction. This also corresponds to the opposite patterns of neural activation and deactivation during execution of opposite movement directions. Thus, phase space analysis can be used as an analytical tool to differentiate different movement directions based on the trajectory of the hysteresis with respect to the hemodynamic variables.

## References

1. Tam ND, Zouridakis G. Optical imaging of motor cortical activation using functional near-infrared spectroscopy. BMC Neurosci. 2012;13(Suppl 1):P27.

2. Tam ND, Zouridakis G. Optical imaging of motor cortical hemodynamic response to directional arm movements using near-infrared spectroscopy. Int J Biol Eng. 2013;3(2):11-17.

3. Tam ND, Zouridakis G. Decoding of movement direction using optical imaging of motor cortex. BMC Neurosci. 2013; P380.

4. Tam ND, Zouridakis G. Temporal decoupling of oxy- and deoxy-hemoglobin hemodynamic responses detected by functional near-infrared spectroscopy (fNIRS). J Biomed Eng Med Imaging. 2014;1(2):18-28.

5. Tam ND, Zouridakis G. Decoding movement direction from motor cortex recordings using near-infrared spectroscopy. In: Infrared spectroscopy: theory, developments and applications. Hauppauge: Nova Science; 2014.

## P4

### Modeling jamming avoidance of weakly electric fish

Jaehyun Soh¹, DaeEun Kim¹

¹Biological Cybernetics, School of Electrical and Electronic Engineering, Yonsei University, Shinchon, Seoul, 120-749, South Korea

**Correspondence:** DaeEun Kim - daeeun@yonsei.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P4

Weakly electric fish use electric field generated by the electric organ in the tail of the fish. They detect objects by sensing the electric field with electroreceptors on the fish's body surface. Obstacles in the vicinity of the fish distort the electric field generated by the fish and the fish detect this distortion to recognize environmental situations. Generally, weakly electric fish produce species-dependent electric organ discharge (EOD) signals. Frequency bands of the fish's signals include a variety of frequencies, 50-600 Hz or higher than 800 Hz. The EOD signals can be disturbed by similar frequency signals emitted by neighboring weakly electric fish. They change their EOD frequencies to avoid jamming signals when they detect the interference of signals. This is called jamming avoidance response (JAR).

Electroreceptors of the fish read other electric fish's EOD while they sense their own EOD. Therefore, when two weakly electric fish are close enough and they sense similar frequencies, their sensing ability by EOD is impaired because of signal jamming [1, 2]. The fish lowers its EOD frequency in response to the jamming signals when a slightly higher frequency of signals are detected and otherwise, raises its EOD. This response is shown in Fig. 10. The fish shift their EOD frequency almost immediately without trial and error.

The method of how to avoid jamming has been studied for a long time, but the corresponding neural mechanisms have not been revealed yet so far. The JAR of *Eigenmannia* can be analyzed by Lissajous graphs which consist of amplitude modulations and differential phase modulations. Relative intensity of signals at each skin can show that the signal frequency is higher than its own signal frequency or lower [3].
<figure><img src="image_11.png" /><figcaption>**Fig. 10** Jamming avoidance response</figcaption></figure>

We suggest an algorithm of jamming avoidance for EOD signals, especially for wave-type fish. We explore the diagram of amplitude modulation versus phase modulation, and analyze the shape over the graph. The phase differences or amplitude differences will contribute to the estimation of the signal jamming situation. From that, the jammed signal frequency can be detected and so it can guide the jamming avoidance response. It can provide a special measure to predict the jamming avoidance response. However, what type of neural structure is available in weakly electric fish is an open question. We need further study on this subject.

**Acknowledgements:** This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2014R1A2A1A11053839).

## References

1. Heiligenberg W. Electrolocation of objects in the electric fish eigenmannia (rhamphichthyidae, gymnotoidei). J Comp Physiol. 1973;87(2):137–64.

2. Heiligenberg W. Principles of electrolocation and jamming avoidance in electric fish. Berlin: Springer; 1977.

3. Heiligenberg W. Neural nets in electric fish. Cambridge: MIT Press; 1991.

## P5

### Synergy and redundancy of retinal ganglion cells in prediction

Minsu Yoo¹, S. E. Palmer¹,²

¹Committee on Computational Neuroscience, University of Chicago, Chicago, IL, USA; ²Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL, USA

**Correspondence:** Minsu Yoo - minsu@uchicago.edu

BMC Neuroscience 2016, 17(Suppl 1):P5

Recent work has shown that retina ganglion cells (RGC) of salamanders predict future sensory information [1]. It has also been shown that these RGC's carry significant information about the future state of their own population firing patterns [2]. From the perspective of downstream neurons in the visual system that do not have independent access to the visual scene, the correlations in the RGC firing, itself, may be important for predicting the future visual input. In this work, we explore the structure of the generalized correlation in firing patterns in the RGC, with a particular focus on coding efficiency. From the perspective of efficient neural coding, we might expect neurons to code for their own future state independently (decorrelation across cells), and to have very little predictive information extending forward in time (decorrelation in the time domain).

In this work, we quantify whether neurons in the retina code for their own future input independently, redundantly, or synergistically, and how long these correlations persist in time. We use published extracellular multi-electrode data from the salamander retina in response to repeated presentations of a natural movie [1]. We find significant mutual information in the population firing that is almost entirely independent except at very short time delays, where the code is weakly redundant (Fig. 11). We also find that the information persists to delays of up to a few 100 ms. In addition, we find that individual neurons vary widely in the amount of predictive information they carry about the future population firing state. This heterogeneity may

<figure><img src="image_12.png" /><figcaption>**Fig. 11** Predictive information in the retinal response is coded for independently. Red the mutual information between the binary population firing patterns at times t and t + Δt, for 1000 randomly selected groups of 5 cells from our 31-cell population. Time is binned in 16.67 ms bins, and the (rare) occurrence of two spikes in a bin is recorded as a '1'. Blue the sum of the mutual information between a single cell response at time t and the future response of the group at time t + Δt. Error bars indicate the standard error of the mean across groups. All information quantities are corrected for finite-size effects using quadratic extrapolation [3]</figcaption></figure>

contribute to the diversity of predictive information we find across groups in this experiment.

The results in this study may provide useful information for building a model of the RGC population that can explain why redundant coding is only observed at short delays, or what makes one RGC more predictive than another. Building this type of model will illustrate how the retina represents the future.

## References

1. Palmer SE, Marre O, Berry MJ, Bialek W. Predictive information in a sensory population. Proc. Natl. Acad. Sci. 2015;112:6908–13.

2. Salisbury J, Palmer SE. Optimal prediction and natural scene statistics in the retina. ArXiv150700125 Q-Bio [Internet]. 2015 [cited 2016 Feb 25]; Available from: http://arxiv.org/abs/1507.00125.

3. Panzeri S, Senatore R, Montemurro MA, Petersen RS. Correcting for the sampling bias problem in spike train information measures. J. Neurophysiol. 2007;98:1064–72.

## P6

### A neural field model with a third dimension representing cortical depth

Viviana Culmone¹, Ingo Bojak¹

¹School of Psychology, University of Reading, Reading, Berkshire, RG1 6AY, UK

**Correspondence:** Viviana Culmone - v.culmone@pgr.reading.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P6

Neural field models (NFMs) characterize the average properties of neural ensembles as a continuous excitable medium. So far, NFMs have largely ignored the extension of the dendritic tree, and its influence on the neural dynamics [1]. As shown in Fig. 12A, we implement a 3D-NFM, including the dendritic extent through the cortical layers, starting from a well-known 2D-NFM [2]. We transform the equation for the average membrane potential $h_e$ for the point-like soma in the 2D-NFM [2] to a full cable equation form (added parts in bold):

$$ \tau_e \frac{\partial h_e(x, z, t)}{\partial t} = -[h_e(x, z, t) - h_e^r] + \lambda^2 \frac{\partial^2 h_e(x, z, t)}{\partial z^2} + f_{\text{syn}} \sum_k \psi_{ke}(h_e) I_{ke}(x, z, t) $$
<figure><img src="image_13.png" /><figcaption>**Fig. 12 A** The 3D-NFM adds a dendritic dimension to the 2D one [1]. One single macrocolumn has inhibitory (I) and excitatory (E) subpopulations. **B** (Top) Discretization of the dendrite. (Bottom) Equilibrium membrane potential along the dendrite for two different synaptic inputs. **C** PSDs of $h_e$ for the 2D- and 3D-NFM. Increasing the synaptic input recovers the lost alpha rhythm</figcaption></figure>

The 3D-NFM is modeled considering the dendritic tree as a single linear cable. Figure 12B shows the resulting resting potential along the extended dendrite for synaptic input in two different locations. Naively keeping the parameters of the 2D-NFM for the 3D-NFM results in a power spectral density (PSD) without an alpha rhythm resonance, see Fig. 12C. However, increasing the synaptic input by a factor $f_{syn}$ can compensate for the dispersion along the dendrite and recovers the peak in the alpha band. We study the influence of varying the distribution of synaptic inputs along the dendritic (vertical) dimension and of changing the (horizontal) area of the simulated cortical patch. We also provide an outlook on how to compare our results with local field potential recordings from real cortical tissues. We expect that 3D-NFMs will be used widely in the future for describing such experimental data, and that the methods used to extend the specific 2D-NFM used here [2] will generalize to other 2D-NFMs.

## References

1. Spruston N. Pyramidal neurons: dendritic structure and synaptic integration. Nat Rev Neurosci. 2008;9:206-221.

2. Bojak I, Liley DTJ. Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E. 2005;71:041902.

# P7

## Network analysis of a probabilistic connectivity model of the Xenopus tadpole spinal cord

Andrea Ferrario¹, Robert Merrison-Hort¹, Roman Borisyuk¹

¹School of Computing and Mathematics, Plymouth University, Plymouth, PL4 8AA, United Kingdom

**Correspondence:** Andrea Ferrario - andrea.ferrario@plymouth.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P7

Our previous results [1, 2] describe a computational anatomical model of the Xenopus tadpole spinal cord which includes about 1400 neurons of seven types allocated on two sides of the body. This model is based on a developmental approach, where axon growth is simulated and synapses are created (with some probability) when axons cross dendrites. A physiological model of spiking neurons with the

generated connectivity of about 85,000 synapses produces a very reliable swimming pattern of anti-phase oscillations in response to simulated sensory input [2].

Using the developmental model we generate 100 different sets of synaptic connections ("connectomes"), and use this information to create a generalized probabilistic model. The probabilistic model provides a new way to easily generate tadpole connectomes and, remarkably, these connectomes produce similar simulated physiological behavior to those generated using the more complex developmental approach (e.g. they swim when stimulated). Studying these generated connectivity graphs allows us to analyze the structure of connectivity in a typical tadpole spinal cord.

Many complex neuronal networks have been found to have "small world" properties, including those in the nematode worm *C. elegans* [3, 6], cat and macaque cortex and the human brain [4]. Small world networks are classified between regular and random networks, and are characterized by a high value of the clustering coefficient *C* and a relatively small value of the average path length *L*, when compared with Erdős-Rényi and degree matched graphs of a similar size. We used graph theory tools to calculate the strongly connected component of each network, which was then used to measure *C* and *L*. For the degree-matched network, these computations have been based on finding the probabilistic generating function [5]. By comparing these measures with those of degree matched random graphs, we found that tadpole's network can be considered a small world graph. This is also true for the sub-graph consisting only of neurons on one side of the body, which displays properties very similar to those of the *C. elegans* network. Another important subgraph, comprising only the two main neuron types in the central pattern generator (CPG) network also shows small world properties, but is less similar to the *C. elegans* network.

Our approach allows us to study the general properties of the architecture of the tadpole spinal cord, even though in reality the actual network varies from individual to individual (unlike in *C. elegans*). This allows us to develop ideas about the organizing principles of the network, as well as to make predictions about the network's functionality that can be tested first in computer simulations and later in real animal experiments. In this work we combine several graph theory techniques in a novel way to analyze the structure of a complex neuronal network where not all biological details are known. We believe that this approach can be applied widely to analyze other animals' nervous systems.

## References

1. Borisiuk R, al Azad AK, Conte D, Roberts A, Soffe SR. A developmental approach to predicting neuronal connectivity from small biological datasets: a gradient-based neuron growth model. PloS One. 2014;9(2):e89461.

2. Roberts A, Conte A, Hull M, Merrison-Hort R, al Azad AK, Buhl E, Borisyuk R, Soffe SR. Can simple rules control development of a pioneer vertebrate neuronal network generating behavior? J Neurosci. 2014;34(2):608-21.

3. Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature. 1998;440-2.

4. Kaiser M. A tutorial in connectome analysis: topological and spatial features of brain networks. Neurolmage. 2011;892-907.

5. Newman MEJ, Strogatz SH, Watts DJ. Random graphs with arbitrary degree distribution and their applications. Phys. Rev. 2001;E64:026118.

6. Vershney LR, Chen BL, Paniagua E, Hall DH Chklovskii DB. Structural properties of the *Caenorhabditis elegans* neuronal network. PloS Comput Biol. 2011;7(2):e1001066.

# P8

## The recognition dynamics in the brain

Chang Sub Kim¹

¹Department of Physics, Chonnam National University, Gwangju, 61186, Republic of Korea

**Correspondence:** Chang Sub Kim - cskim@jnu.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P8

Over the years an extensive research endeavor has been given to understanding the brain's cognitive function in a unified principle
and to providing a formulation of the corresponding computational scheme of the brain [1]. The explored free-energy principle (FEP) claims that the brain's operation on perception, learning, and action rests on brain's internal mechanism of trying to avoid aberrant events encountering in its habitable environment. The theoretical measure for this biological process has been suggested to be the informational free-energy (IFE). The computational actualization of the FEP is carried out via the gradient descent method (GDM) in machine learning theory.

The information content of the cognitive processes is encoded in the biophysical matter as spatiotemporal patterns of the neuronal correlates of the external causes. Therefore, any realistic attempt to account for the brain function must conform to the physics laws and the underlying principles. Notwithstanding the grand simplicity, however, the FEP framework embraces some extra-physical constructs. Two major such extra-physical constructs are the generalized motions, which are non-Newtonian objects, and the GDM in executing the brain's computational mechanism of perception and active inference. The GDM is useful in finding mathematical solutions in the optimal problems, but not derived from a physics principle.

In this work, we cast the FEP in the brain science into the framework of the principle of least action (PLA) in physics [2]. The goal is to remove the extra-physical constructs embedded in the FEP and to reformulate the GDM within the standard mechanics arena. Previously, we suggested setting up the minimization scheme of the IFE in the Lagrange mechanics formalism [3] which contained only primitive results. In the present formulation we specify the IFE as the information-theoretic Lagrangian and thus formally define the informational action (IA) as time-integral of the IFE. Then, the PLA prescribes that the viable brain minimizes the IA when encountering uninhabitable events by selecting an optimal path among all possible dynamical configurations in the brain's neuronal network. Specifically, the minimization yields the mechanistic equations of motion of the brain states, which are inverting algorithms of sensory inputs to infer their external causes. The obtained Hamilton-Jacobi-Bellman-type equation prescribes the brain's recognition dynamics which do not require the extra-physical concept of higher order motions. Finally, a neurobiological implementation of the algorithm is presented which complies with the hierarchical, operative structure of the brain. In doing so, we adopt the local field potential and the local concentration of ions in the Hodgkin-Huxley model as the effective brain states [4]. Thus, the brain's recognition dynamics is operatively implemented in a neuro-centric picture. We hope that our formulation, conveying a wealth of structure as an interpretive and mechanistic description of explaining how the brain's cognitive function may operate, will provide with a helpful guidance for future simulation.

### References

1. Friston K. The free-energy principle: a unified brain theory? Nat Reivew Neurosci. 2010;11:127-38.

2. Landau LP. Classical mechanics. 2nd ed. New York: Springer; 1998.

3. Kim CS. The adaptive dynamics of brains: Lagrangian formulation. Front Neurosci Conf Abstr Neuroinform. 2010. doi:10.3389/conf.fnins.2010.13.00046.

4. Hodgkin A, Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952;117:500-44.

## P9

### Multivariate spike train analysis using a positive definite kernel

Taro Tezuka¹

¹Faculty of Library, Information and Media Science, University of Tsukuba, Tsukuba, 305-0821, Japan

**Correspondence:** Taro Tezuka - tezuka@slis.tsukuba.ac.jp

BMC Neuroscience 2016, 17(Suppl 1):P9

Multivariate spike trains, obtained by recording multiple neurons simultaneously, is a key to uncovering information representation in the brain [1]. Other expressions used to refer to the same type of data include "multi-neuron spike train" [2] and "parallel spike train" [3]. One approach

to analyze spike trains is to use kernel methods, which are known to be among the most powerful machine learning methods. Kernel methods rely on defining a symmetric positive-definite kernel suited to the given data. This work proposes a general way of extending kernels on univariate (or single-unit) spike trains to multivariate spike trains.

In this work, the mixture kernel, which naturally extends a kernel defined on univariate spike trains, is proposed and evaluated. There are many univariate spike train kernels proposed [4–9], and the mixture kernel is applicable to any of these kernels. Considered abstractly, a multivariate spike train is a set of time points at which different types of events occurred. In other words, it is a sample taken from a marked point process. The method proposed in this paper is therefore applicable to other data with the same structure.

The mixture kernel is defined as a linear combination of symmetric positive-definite kernels on the components of the target data structure, in this case univariate spike trains. The name "mixture kernel" derives from the common use of the word "mixture" to indicate a linear combination in physics and machine learning, for example in Gaussian mixture models. One can prove that the mixture kernel is symmetric positive-definite if coefficient matrix of the mixture is a symmetric positive-semidefinite matrix.

The performance of the mixture kernel was evaluated by kernel ridge regression for estimating the value of the parameter for generating synthetic spike train data, and also the stimulus given to the animal as the spike trains were recorded. For synthetic data, multivariate spike trains were generated using homogenous Poisson processes. For real data, the pvc-3 data set [2] in the CRCNS (Collaborative Research in Computational Neuroscience) data sharing website was used, which is a 10-unit multivariate spike trains recorded from the primary visual cortex of a cat.

**Acknowledgement:** This work was supported in part by JSPS KAKENHI Grant Numbers 21700121, 25280110, and 25540159.

### References

1. Gerstner W, Kistler WM, Naud R, Paninski L. Neuronal dynamics. Cambridge: Cambridge University Press; 2014.

2. Blanche T. Multi-neuron recordings in primary visual cortex, CRCNS.org; 2009.

3. Grun S, Rotter S. Analysis of parallel spike trains. Berlin: Springer; 2010.

4. Paiva A, Park IM, Principe JC. A reproducing kernel Hilbert space framework for spike train signal processing, Neural Comput. 2009;21(2):424–49.

5. Park IM, Seth S, Rao M, Principe JC. Strictly positive definite spike train kernels for point process divergences. Neural Comput. 2012;24:2223–50.

6. Park IM, Seth S, Paiva A, Li L, Principe JC. Kernel methods on spike train space for neuroscience: a tutorial. Signal Process Mag. 2013;30(4):149–60.

7. Li L, Park IM, Brockmeier AJ, Chen B, Seth S, Francis JT, Sanchez JC, Principe JC. Adaptive inverse control of neural spatiotemporal spike patterns with a reproducing kernel Hilbert space (RKHS) framework. IEEE Trans Neural Syst Rehabil Eng. 2013;21(4):532–43.

8. Shpgelman L, Singer Y, Paz R, Vaadia E. Spikernels: embedding spiking neurons in inner product spaces. Adv Neural Inf Process Syst. 2003;15:125–32.

9. Eichhorn J, Tolias A, Zien A, Kuss M, Rasmussen CE, Weston J, Logothetis N, Scholkopf B. Prediction on spike data using kernel algorithms. Adv Neural Inf Process Syst. 2004;16:1367–74.

## P10

### Synchronization of burst periods may govern slow brain dynamics during general anesthesia

Pangyu Joo¹

¹Physics, POSTECH, Pohang, 37673, Republic of Korea

**Correspondence:** Pangyu Joo - pangyu32@postech.ac.kr

BMC Neuroscience 2016, 17(Suppl 1):P10

Researchers have utilized electroencephalogram (EEG) as an important key to study brain dynamics in general anesthesia. Representative features of EEG in deep anesthesia are slow wave oscillation and burst suppression [1], and they have so different characteristics that they seem to have different origins. Here, we propose that the two feature may be a different aspect of same phenomenon and show that the slow oscillation could arise from partial synchronization of
<figure><img src="image_14.png" /><figcaption>**Fig. 13** A The convoluted signal with different ATP recovery rates ($J_{ATP}$) and relative connection strengths (C). B Standard deviation of the convoluted signals</figcaption></figure>

bursting periods. To model the synchronization of burst periods, modified version of Ching's model of burst suppression [2] is used. 20 pyramidal neurons and 20 fast spiking neurons are divided into 10 areas composed of 2 pyramidal and 2 fast spiking neurons so that each area exhibit burst suppression behavior independently. Then, all the pyramidal neurons are all to all connected and the connection strength modulates the amount of synchronization of burst periods. The action potentials of pyramidal neurons are substituted by 1 when the action potential larger than 0, and all other case 0. Then they are averaged over the neurons and convoluted with 50 ms square function to see the collective activity of the neurons. As shown in Fig. 13A, At high level of ATP recovery rate ($J_{ATP} > 1$), there are no suppression period so that slow oscillation does not appear regardless of synchronization. At low level of ATP recovery rate ($J_{ATP} = 0.5$), we can observe that the slow oscillation appears with increasing amplitude and finally become burst suppression as relative connection strength increases (Fig. 13B). When the ATP recovery rate is 0, then the pyramidal neurons do not fire at all. These results suggest that the burst period synchronization model could explain some important features of EEG during general anesthesia: the increasing slow oscillation amplitude as anesthesia deepen, significantly high activity in bursting period, and the peak max phase amplitude coupling in deep anesthesia.

## References

1. Purdon PL, Pierce ET, Mukamel EA, et al. Electroencephalogram signatures of loss and recovery of consciousness from propofol. PNAS. 2013;110(12):E1142–51.

2. Ching S, Purdon PL, Vijayan S, Kopell NJ, Brown EN. A neurophysiological–metabolic model for burst suppression. PNAS. 2012;109(8):3095–100.

# P11
## The ionic basis of heterogeneity affects stochastic synchrony

Young-Ah Rho¹,⁴, Shawn D. Burton2,3, G. Bard Ermentrout¹,³, Jaesung Jeong⁴, Nathaniel N. Urban²,³

¹Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA 15260; ²Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, PA, USA 15213; ³Center for the Neural Basis of Cognition, Pittsburgh, PA, USA 15213; ⁴Department of Bio and Brain Engineering/Program of Brain and Cognitive Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea 34141

**Correspondence:** Young-Ah Rho - yarho75@gmail.com

BMC Neuroscience 2016, 17(Suppl 1):P11

Synchronization in neural oscillations is a prominent feature of neural activity and thought to play an important role in neural coding. Theoretical and experimental studies have described several mechanisms for synchronization based on coupling strength and correlated noise input. In the olfactory systems, recurrent and lateral inhibition mediated by dendrodendritic mitral cell–granule cell synapses are critical for synchronization, and intrinsic biophysical heterogeneity reduce the ability to synchronize. In our previous study, a simple phase model was used to examine how physiological heterogeneity in biophysical properties and firing rates across neurons affects correlation-induced synchronization (stochastic synchrony). It has showed that heterogeneity in the firing

rates and in the shapes of the phase response curves (PRCs) reduced output synchrony. In this study, we extend the previous phase model to a conductance based model to examine how the density of specific ion channels in mitral cells impacts on stochastic synchrony. A recent study revealed that mitral cells are highly heterogeneous in the expression of the sag current, a hyperpolarization-activated inward current (Angelo, 2011). The variability in the sag contributes to the diversity of mitral cells and thus we wanted to know how this variability influences synchronization. Mitral cell oscillations and bursting are also regulated by an inactivating potassium current ($I_A$). Based on these ion channels, we examined the effect of changing the current densities ($g_A$, $g_H$) on diversity of PRCs and of synchrony. In order to identify oscillatory patterns of bursting and repetitive spiking across $g_A$ and $g_H$ to the model, two parameter bifurcation analysis was performed in the presence and absence of noise. Increasing $g_H$ alone reduces the region of bursting, but does not completely eliminate bursting, and PRCs changed much more with respect to $g_A$ than $g_H$. Focusing on varying $g_A$, we next examined a role of $g_A$ density and firing rate in stochastic synchrony by introducing the fluctuating correlated input resembling the shared presynaptic drives. We found that heterogeneity in A-type current mainly influenced on stochastic synchrony as we predicted in PRCs investigated theoretically, and diversity in firing rate alone didn't account for it. In addition, heterogeneous population with respect to $g_A$, given decent amount of $g_A$ density, showed better stochastic synchrony than homogeneous population in same firing rate.

# P12
## Circular statistics of noise in spike trains with a periodic component

Petr Marsalek¹,²

¹Institute of Pathological Physiology, First Faculty of Medicine, Charles University in Prague, 128 53, Czech Republic; ²Czech Technical University in Prague, Zikova 1903/4, 166 36, Czech Republic

**Correspondence:** Petr Marsalek - petr.marsalek@lf1.cuni.cz

BMC Neuroscience 2016, 17(Suppl 1):P12

**Introduction** We estimate parameters of the inter-spike interval distributions in binaural neurons of the mammalian sound localization neural circuit, neurons of the lateral and medial superior olive [1]. We present equivalent descriptions of spike time probabilities using both standard and circular statistics. We show that the difference between sine function and beta density in the circular domain is negligible.

**Results** Estimation of the spike train probability density function parameters is presented in relation to harmonic and complex sound input. The resulting densities are expressed analytically with the use of harmonic and Bessel functions. Parameter fits are verified by numerical simulations of spike trains (Fig. 14).

<figure><img src="image_15.png" /><figcaption>**Fig. 14** Comparison of circular probability density functions of sine and beta density. A Beta density with parameters $a = b = 3.3818$, matches closely that of the sine function, used as a probability density function (PDF). Beta density with parameters $a = b = 3$ solid line, is matched by sine function $y = 1.05 - 1.1 \cos(2\pi x/1.1)$. B Cumulative distribution function (CDF) is shown for these densities together with the difference between the two CDFs multiplied by 100 to visualize the comparison of the two distributions. C For testing different vector strengths we use uniform distributions with pre-set vector strengths ($p = 0.8, 0.5$ and 0.08)</figcaption></figure>
**Conclusions** We use analytical techniques, where it is possible. We calculate the one-to-one correspondence of vector strength parameters and parameters of circular distributions used for description of data. We show here introductory figure of our paper with the two representative circular densities. We also use experimental data [2, 3] and simulated data to compare them with these theoretical distributions.

**Acknowledgements:** Supported by the PRVOUK program no. 205024 at the Charles University in Prague. I acknowledge contributions to the analytical computations by Ondrej Pokora and simulation in Matlab by Peter G. Toth.

## References

1. Bures Z, Marsalek P. On the precision of neural computation with interaural level differences in the lateral superior olive. Brain Res. 2013;1536:16-26.

2. Joris P, Carney L, Smith P, Yin T. Enhancement of neural synchronization in the anteroventral cochlear nucleus. I. Responses to tones at the characteristic frequency. J Neurophysiol. 1994;71(3):1022-36.

3. Joris P, Smith P, Yin T. Enhancement of neural synchronization in the anteroventral cochlear nucleus. II. Responses in the tuning curve tail. J Neurophysiol. 1994;71(3):1037-51.

## P14

### Representations of directions in EEG-BCI using Gaussian readouts

Hoon-Hee Kim¹,², Seok-hyun Moon³, Do-won Lee³, Sung-beom Lee³, Ji-yong Lee³, Jaeseung Jeong¹,²

¹Department of Bio and Brain Engineering and ²Program of Brain and Cognitive Engineering, College of Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea, 34141; ³Korea Science Academy of KAIST, Busan, South Korea, 10547

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

BMC Neuroscience 2016, 17(Suppl 1):P14

EEG (electroencephalography) is one of most useful neuroimaging technology and best options for BCI (Brain-Computer Interface) because EEG has portable size, wireless and well-wearing design in any situations. The key objective of BCI is physical control of machine such as cursor movement in screen and robot movement [1, 2]. In previously study, the motor imagery had used for represent of direction to movement [1, 2]. For example, the left hand imagery mapping to move the left, the right hand imagery mapping to move the right and both hand imagery mapping to move the forward. In this study, however, we considered only brain signals when a subject thinks directions to movements not motor imageries. We designed the recurrent neural networks which consist of 300-10,000 artificial linear neurons using Echo State Networks paradigm [3]. We also recorded EEG signals using Emotiv EPOC+ which has 16 channels (AF3, F7, F3, FC5, T7, P7, O1, O2, P8, T8, FC6, F4, F8, AF4 and two of reference). All raw data of channels

were normalized and then used inputs to recurrent neural networks. For representation of directions, we had built Gaussian readouts which has preferred directions and fitted the Gaussian functions (Fig. 15). The firing rate of readout were high when the subject thought preferred direction. However, when the subject thought not preferred direction, the firing rate of readout slightly low down. For implement these readouts, all of neuros in recurrent neural networks had linearly connected to all readouts and weights of these connections were trained by linear learning rules. In result, we considered 5 healthy subjects and recorded EEG signals for each directions. The readouts were showed well Gaussian fitted direction preference. In this study, we considered only two dimensions but many situations of BCI has three dimensional space. Therefore, our study which using Gaussian readouts should be extended to three dimensional version.

## References

1. Chae Y, Jeong J, Jo S. Toward brain-actuated humanoid robots: asynchronous direct control using an EEG-based BCI. IEEE Trans Robot. 2012;28(5):1131-44.

2. LaFleur K, Cassady K, Doud A, Shades K, Rogin E, He B. Quadcopter control in three-dimensional space using a noninvasive motor imagery-based brain-computer interface. J Neural Eng. 2013;10(4):046003.

3. Jaeger H, Haas H. Harnessing nonlinearity predicting chaotic systems and saving energy in wireless communication. Science. 2004;304(5667):78-80.

## P15

### Action selection and reinforcement learning in basal ganglia during reaching movements

Yaroslav I. Molkov¹, Khaldoun Hamade², Wondimu Teka³, William H. Barnett¹, Taegyo Kim², Sergey Markin², Ilya A. Rybak²

¹Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA; ²Department of Neurobiology and Anatomy, Drexel University, Philadelphia, PA 19129, USA; ³Department of Mathematical Sciences, Indiana University - Purdue University, Indianapolis, IN 46202, USA

**Correspondence:** Yaroslav I. Molkov - ymolkov@gsu.edu

BMC Neuroscience 2016, 17(Suppl 1):P15

The basal ganglia (BG) comprise a number of interconnected nuclei that are collectively involved in a wide range of motor and cognitive behaviors. The commonly accepted theory is that the BG play a pivotal role in action selection and reinforcement learning facilitated by the activity of dopaminergic neurons of substantia nigra pars compacta (SNC). These dopaminergic neurons encode prediction errors when reward outcomes exceed or fall below anticipated values. The BG gate appropriate behaviors from multiple moto-cortical command candidates arriving at the striatum (BG's input nuclei) but suppress competing inappropriate behaviors. The selected motor action is realized when the internal segment of the globus pallidus (GPI) (BG's output nuclei) disinhibits thalamic neurons corresponding to the gated behavior. The BG network performs motor command selection through the facilitation of the appropriate behavior via the "direct" striatonigral (GO) pathway and inhibition of competing behaviors by the "indirect" striatopallidal (NOGO) pathway.

Several modeling studies have showed plausibility of the above concept in simplified cases, e.g. for binary action selection in response to a binary cue. However, in these previous models, the possible actions/behaviors were represented in an abstract way, and did not have a detailed implementation as specific neuronal patterns actuating the muscular-skeletal apparatus. To address these details, the motor system in the present study includes a 2D-biomechanical arm model in the horizontal plane to simulate realistic reaching movements. The arm consists of two segments (upper arm and forearm) and has two joints (shoulder and elbow) controlled by four monoarticular (flexor and extensor at each joint) and two bi-articular (shoulder and elbow flexor, and shoulder and elbow extensor) muscles. The neural component of the model includes the BG, the thalamus, the motor cortex, and spinal circuits. The low-level spinal circuitry contains six motor-neurons (each controlling one muscle), and receives proprioceptor feedback from muscles. Cortical neurons provide inputs to the spinal

<figure><img src="image_16.png" /></figure>
network. Their activity is calculated by solving an inverse problem (inverting the internal model) based on the initial position of the arm, reaching distance and direction.

In the model, reaching movements in different directions were used as a set of possible behaviors. We simulated movements in response to a sensory cue defining the target arm position. The cortex generated signals corresponding to the cue and all possible motor commands and delivered these signals to the BG. The resulting neuronal patterns in the motor cortex were calculated as a convolution of the thalamic activity and all possible motor commands. The function of BG was to establish the association between the cue and the appropriate action(s) by adjusting weights of plastic corticostriatal projections through reinforcement learning. The BG model contained an exploratory mechanism, operating through the subthalamic nucleus (STN) that allowed the model to constantly seek better cue-action associations that deliver larger rewards. Reinforcement learning relied on the SNc dopaminergic signal that measured trial-to-trial changes in the reward value, defined by performance errors.

Using this model, we simulated several learning tasks in the conditions of different unexpected perturbations. When a perturbation was introduced, the model was capable of quickly switching away from pre-learned associations and learning novel cue-action associations. The analysis of the model reveals several features, that can have general importance for brain control of movements: (1) potentiation of the cue-NOGO projections is crucial for quick destruction of preexisting cue-action associations; (2) the synaptic scaling (the decay of the cortical-striatal synaptic weights in the absence of dopamine-mediated potentiation/depression) has a relatively short time-scale (10–20 trials); (3) quick learning is associated with a relatively poor accuracy of the resultant movement. We suggest that BG may be involved in a quick search for behavioral alternatives when the conditions change, but not in the learning of skilled movements that require good precision.

## P17

**Axon guidance: modeling axonal growth in T-junction assay**

Csaba Forro¹, Harald Dermutz¹, László Demkó¹, János Vörös¹

¹LBB, ETH Zürich, Zürich, 8051, Switzerland

**Correspondence:** Csaba Forro - forro@biomed.ee.ethz.ch

BMC Neuroscience 2016, 17(Suppl 1):P17

The current field of neuroscience investigates the brain at scales varying from the whole organ, to brain slices and down to the single cell level. The technological advances miniaturization of electrode arrays has enabled the investigation of neural networks comprising several neurons by recording electrical activity from every individual cell in the network. This level of complexity is key in the study of the core principles at play in the machinery of the brain. Indeed, it is the first layer of complexity above the single cell that is still tractable for the human scientist without needing to resort to a 'Big Data' approach. In light of this, we strive to create topologically well-defined neural networks, akin to mathematical directed graphs, as a model systems in order to study the basic mechanisms emerging in networks of increasing complexity and varying topology. This approach will also yield statistically sound and reproducible observations, something which is sought after in neuroscience [1].

The first step in realizing such a well-defined neural network is to reliably control the guidance of individual axons in order to connect the network of cells in a controlled way. For this purpose, we present a method consisting of obstacles forcing the axon to turn one way or the other. The setup is made of PolyDiMethylSiloxane (PDMS) which is microstructured by ways of state of the art photolithography procedures. Two tunnels of 5 µ height are patterned into a block of 100 µ thick PDMS and connected in the shape of a T-junction (Fig. 16). Primary cortical neurons are inserted via entry holes at the base of the tunnels. The entry angle of the bottom tunnel ("vertical part of the T") into the junction is varied between 20° (steep entry) and 90° (vertical

<figure><img src="image_17.png" /><figcaption>**Fig. 16 A** The T-junction assay with an entry angle of 20°. The axon is expected to prefer a right-turn at this angle. **B** A simple model is constructed where the direction of growth of the axon is proportional to area (red) it can explore</figcaption></figure>

entry). We observe that the axons prefer to turn towards the smaller angle. We show how this observed angular selectivity in axon guidance can be explained by a simple model and how this principle can be used to create topologically well-defined neural networks (Fig. 16B).

## Reference

1. Button KS, et al. Power failure: why small sample size undermines the reliability of neuroscience. Nat Rev Neurosci. 2013;14(5):365–76.

## P19

**Transient cell assembly networks encode persistent spatial memories**

Yuri Dabaghian¹,², Andrey Babichev¹,²

¹Department of Neurology Pediatrics, Baylor College of Medicine, Houston, TX 77030, USA; ²Department of Computational and Applied Mathematics, Rice University, Houston, TX, 77005, USA

**Correspondence:** Yuri Dabaghian - dabaghian@rice.edu

BMC Neuroscience 2016, 17(Suppl 1):P19

The reliability of our memories is nothing short of remarkable. Thousands of neurons die every day, synaptic connections appear and disappear, and the networks formed by these neurons constantly change due to various forms of synaptic plasticity. How can the brain develop a reliable representation of the world, learn and retain memories despite, or perhaps because of, such complex dynamics? Here we consider the specific case of spatial navigation in mammals, which is based on mental representations of their environments—cognitive maps—provided by the network of the hippocampal place cells—neurons that become active only in a particular region of the environment, known as their respective place fields. Experiments suggest that the hippocampal map is fundamentally topological, i.e., more similar to a subway map than to a topographical city map, and hence amenable to analysis by topological methods [1]. By simulating the animal's exploratory movements through different environments we studied how stable topological features of space get represented by assemblies of simulated neurons operating under a wide range of conditions, including variations in the place cells' firing rate, the size of the place fields, the number of cells in the population [2,3]. In this work, we use methods from Algebraic Topology to understand how the dynamic connections between hippocampal place cells influence the reliability of spatial learning. We find that although the hippocampal network is highly transient, the overall spatial map encoded by the place cells is stable.

**Acknowledgements:** The work was supported by the NSF 1422438 grant and by the Houston Bioinformatics Endowment Fund.
## References

1. Dabaghian Y, Brandt VL, Frank LM. Reconceiving the hippocampal map as a topological template. *eLife*. 2014. doi:10.7554/eLife.03476.

2. Dabaghian Y, Mémoli F, Frank L, Carlsson G. A topological paradigm for hippocampal spatial map formation using persistent homology. *PLoS Comput Biol*. 2012;8:e1002581.

3. Arai M, Brandt V, Dabaghian Y. The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map. *PLoS Comput Biol*. 2014;10:e1003651.

## P20

### Theory of population coupling and applications to describe high order correlations in large populations of interacting neurons

Haiping Huang¹

¹RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

**Correspondence:** Haiping Huang - physhuang@gmail.com

BMC Neuroscience 2016, 17(Suppl 1):P20

Correlations among neurons spiking activities play a prominent role in deciphering the neural code. Various models were proposed to understand the pairwise correlations in the population activity. Modeling these correlations sheds light on the functional organization of the nervous system. In this study, we interpret correlations in terms of population coupling, a concept recently proposed to understand the multi-neuron firing patterns of the visual cortex of mouse and monkey [1]. We generalize the population coupling to its higher order (PC2), characterizing the relationship of pairwise firing with the population activity. We derive the practical dimensionality reduction method for extracting the low dimensional representation parameters, and test our method on different types of neural data, including ganglion cells in the salamander retina onto which a repeated natural movie was projected [2], and layer 2/3 as well as layer 5 cortical cells in the medial prefrontal cortex (MPC) of behaving rats [3].

For the retinal data, by considering the correlation between the pairwise firing activity and the global population activity, i.e., the second order population coupling, the three-cell correlation could be predicted partially (64.44 %), which suggests that PC2 acts as a key circuit variable for third order correlations. The interaction matrix revealed here may be related to the found overlapping modular structure of retinal neuron interactions [4]. In this structure, neurons interact locally with their adjacent neurons, and in particular this feature is scalable and applicable for larger networks.

About 94.79 % of three-cell correlations are explained by PC2 in the MPC circuit. The PC2 matrix shows clear hubs' structure in the cortical circuit. Some neuron interacts strongly with a large portion of neurons in the population, and such neurons may play a key role in shaping the collective spiking behavior during the working memory task. The hubs and non-local effects are consistent with findings reported in the original experimental paper [3].

**Acknowledgements:** We are grateful to Shigeyoshi Fujisawa and Michael J Berry for sharing us the cortical and retinal data, respectively. We also thank Hideaki Shimazaki and Taro Toyoizumi for stimulating discussions. This work was supported by the program for Brain Mapping by Integrated Neurotechnologies for Disease Studies (Brain/MINDS) from Japan Agency for Medical Research and development, AMED.

## References

1. Okun M, Steinmetz NA, Cossell L, Iacaruso MF, Ko H, Bartho P, et al. Diverse coupling of neurons to populations in sensory cortex. *Nature*. 2015;521:511–15.

2. Tkacik G, Marre O, Amodei D, Schneidman E, Bialek W, Berry II MJB. Searching for collective behavior in a large network of sensory neurons. *PLoS Comput Biol*. 2014;10:e1003408.

3. Fujisawa S, Amarasingham A, Harrison MT, Buzsaki G. Behavior-dependent short-term assembly dynamics in the medial prefrontal cortex. *Nat Neurosci*. 2008;11:823–33.

4. Ganmor E, Segev R, Schneidman E. The architecture of functional interaction networks in the retina. *J Neurosci*. 2011;31(8):3044–54.

## P21

### Design of biologically-realistic simulations for motor control

Sergio Verduzco-Flores¹

¹Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa 1919-1, Japan

**Correspondence:** Sergio Verduzco-Flores - sergio.verduzco@oist.jp

BMC Neuroscience 2016, 17(Suppl 1):P21

Several computational models of motor control, although apparently feasible, fail when simulated in 3-dimensional space with redundant manipulators [1, 2]. Moreover, it has become apparent that the details of musculoskeletal simulations, such as the muscle model used, can fundamentally affect the conclusions of a computational study [3]. There would be great benefits from being able to test theories involving motor control within a simulation framework that brings realism in the musculoskeletal model, and in the networks that control movements. In particular, it would be desirable to have: (1) a musculoskeletal model considered to be research-grade within the biomechanics community, (2) afferent information provided by standard models of the spindle afferent and the Golgi tendon organ, (3) muscle stimulation provided by a spiking neural network that follows the basic known properties of the spinal cord, and (4) a cerebellar network as part of adaptive learning.

Creating this type of model is only now becoming practical, not only due to faster computers, but due to properly validated musculoskeletal models and simulation platforms from the biomechanics community, as well as mature software and simulations techniques from the computational neuroscience community. We show how these can be harnessed in order to create simulations that are grounded both by physics and by neural implementation. This pairing of computational neuroscience and biomechanics is sure to bring further insights into the workings of the central nervous system.

## References

1. Gielen S. Review of models for the generation of multi-joint movements in 3D. In: Sternad D, editor. *Progress in motor control*. New-York: Springer; 2009.

2. Verduzco-Flores SO, O'Reilly RC. How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error. *Front Comput Neurosci*. 2015;9:39.

3. Gribble PL, Ostry DJ, Sanguineti V, Laboissière R. Are complex control signals required for human arm movement? *J Neurophysiol*. 1998;79:1409–24.

## P22

### Towards understanding the functional impact of the behavioural variability of neurons

Filipa Dos Santos¹, Peter Andras¹

¹School of Computing and Mathematics, Keele University, Newcastle-under-Lyme, ST5 5BG, UK

**Correspondence:** Filipa Dos Santos - f.d.s.brandao@keele.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P22

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance
<figure><img src="image_18.png" /><figcaption>**Fig. 17** The time distances between the first and second spikes of the simulated PD neurons as a function of the $g_K$ and $g_{CaT}$ conductances of the neuron with variable conductances. A first spikes. B Second spikes. The PD neuron with fixed conductances had $g_K = 1.5768$ µS and $g_{CaT} = 0.0225$ µS</figcaption></figure>

between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.

Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong.

## References

1. Hill ES, Vasireddi SK, Bruno AM, Wang J, Frost WN. Variable neuronal participation in stereotypic motor programs. PLoS One. 2012;7:e1–11.

2. Bucher D, Johnson CD, Marder E. Neuronal morphology and neuropil structure in the stomatogastric ganglion. J Comp Neurol. 2007;501:185–205.

3. Soto-Treviño C, Rabbah P, Marder E, Nadim F. Computational model of electrically coupled, intrinsically distinct pacemaker neurons. J Neurophysiol. 2005;94:590–604.

4. Golowasch J, Casey M, Abbott LF, Marder E. Network stability from activity-dependent regulation of neuronal conductances. Neural Comput. 1999;11:1079–96.

5. Khorkova O, Golowasch J. Neuromodulators, not activity, control coordinated expression of ionic currents. J Neurosci. 2007;27:8709–18.

## P23

### Different oscillatory dynamics underlying gamma entrainment deficits in schizophrenia

Christoph Metzner¹, Achim Schweikard², Bartosz Zurowski³

¹Science and Technology Research Institute, University of Hertfordshire, Hatfield, United Kingdom; ²Institute for Robotics and Cognitive Systems, University of Luebeck, Luebeck, Germany; ³Department of Psychiatry, University of Luebeck, Schleswig-Holstein, Luebeck, Germany

**Correspondence:** Filipa Dos Santos - c.metzner@herts.ac.uk

BMC Neuroscience 2016, 17(Suppl 1):P23

In recent years, a significant amount of biomarkers and endophenotypic signatures of psychiatric illnesses have been identified, however, only a very limited number of computational models in support thereof have been described so far [1]. Furthermore, the few existing computational models typically only investigate one possible mechanism in isolation, disregarding the potential multifactoriality of the network behaviour [2]. Here we describe a computational instantiation of an endophenotypic finding for schizophrenia, an impairment in gamma entrainment in auditory click paradigms [3].

We used a model of primary auditory cortex from Beeman [4] and simulated a click entrainment paradigm with stimulation at 40 Hz, to

investigate gamma entrainment deficits, and at 30 Hz as a control condition. We explored the multifactoriality by performing an extensive parameter search (approx. 4000 simulations). We focused on synaptic and connectivity parameters of the fast spiking inhibitory interneurons in the model (i.e. number and strength of and, GABAergic decay times at I-to-E and I-to-I connections, independently). We performed a time-frequency analysis of simulated EEG signals and extracted the power in the 40 Hz and the 30 Hz band, respectively. Using the power in the 40 Hz band for 40 Hz stimulation we identified regions in the parameter space showing strong reductions in gamma entrainment. For these we calculated cycle-averaged EEG signals and spike time histograms of both network populations, in order to explore the dynamics underlying the reduction in gamma power.

We find three regions in the parameter space which show strong reductions in gamma power. These three regions, however, have very different parameter settings and show very different oscillatory dynamics. The first, which produces the strongest reduction, is characterised by a strong prolongation of decay times at I-to-E synapses and strong and numerous I-to-E connections. Cycle-averaged spike histograms show a broadening of distributions which indicate that the overall synchrony is reduced, leading to the strong reduction in gamma power. However, this parameter setting also produced a strong reduction of power in the 30 Hz control condition, which is not seen experimentally. The second region, is characterized by prolonged I-to-I decay times together with numerous and strong I-to-I connectivity. Here, a second peak appears in the cycle-average spike histogram of the excitatory population, which leads to a loss of synchrony and thus a reduction in gamma power. The third parameter region, is also characterized by prolonged I-to-I decay times. Moreover, it is associated with a reduction in I-to-I connection numbers and strengths together with strong I-to-E connections. Here, we found that in every second cycle, the spike histogram of the inhibitory neurons showed two peaks, one at the beginning and one in the middle of the cycle. This second peak then inhibited the excitatory neurons' response to the next stimulation. Hence, the EEG signal showed beat-skipping, i.e. every second gamma peak was suppressed, resulting in a decrease in gamma power.

Performing an extensive parameter search in an in silico instantiation of an endophenotypic finding for schizophrenia, we have identified distinct regions of the parameter space that give rise to analogous network level behaviour found in schizophrenic patients using electrophysiology [3]. However, the oscillatory dynamics underlying this behaviour substantially differ across regions. These regions might correspond to different subtypes of schizophrenic patients and hence, subtypes of what might have different targets for alleviating the deficits because of their differences in underlying dynamics.

## References

1. Siekmeier P. Computational modeling of psychiatric illnesses via well-defined neurophysiological and neurocognitive biomarkers. Neurosci Biobehav Rev. 2015;57:365–80.

2. Pavão, R, Tort ABL, Amaral OB. Multifactoriality in psychiatric disorders: a computational study of schizophrenia. Schizophrenia Bull. 2015;41(4):980–88.

3. Kwon JS, O'Donnell BF, Wallenstein GV, Greene RW, Hirayasu Y, Nestor PG, Hasselmo ME, Potts GF, Shenton ME, McCarley RW. Gamma frequency-range abnormalities to auditory stimulation in schizophrenia. Arch Gen Psychiatry. 1999;56(11):1001–5.

4. Beeman D. A modeling study of cortical waves in primary auditory cortex. BMC Neurosci. 2013;14(Suppl. 1):P23.

## P24

### Memory recall and spike frequency adaptation

James P. Roach¹, Leonard M. Sander²,³, Michal R. Zochowski²,³,⁴

¹Neuroscience Graduate Program, University of Michigan, Ann Arbor, MI 48109, USA; ²Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA; ³Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA; ⁴Biophysics Program, University of Michigan, Ann Arbor, MI 48109, USA

**Correspondence:** James P. Roach - roachjp@umich.edu

BMC Neuroscience 2016, 17(Suppl 1):P24
In the brain, representations of the external world are encoded by patterns of neural activity. It is critical that representations be stable, but still easily moved between. This phenomenon has been modeled at the network level as auto associative memory. In auto associative network models, such as the Hopfield network, representations, or memories, are stored within synaptic weights and form stable fixed points, or attractors [1]. Spike frequency adaptation (SFA) provides a biologically plausible mechanism for switching between stable fixed points in the Hopfield network. In the present work we show that for low levels of SFA networks will stabilize in a representation that corresponds to the nearest memory activity space, regardless of strength. In networks with higher levels of SFA only the pattern corresponding to the strongest memory, or a global minimum in activity space. The effects of SFA are similar to fast, or thermodynamic noise, but also allows for deterministic destabilization of memories leading to periodic activation of memories through time. We argue that control of SFA level is a universal mechanism for network-wide attractor selectivity. SFA is tightly regulated by the neurotransmitter acetylcholine (ACh) and can be changed on behaviorally relevant timescales. To support this claim we demonstrate that SFA controls selectivity of spatial attractors in a biophysical model of cholinergic modulation in cortical networks [2, 3]. This model produces localized bumps of firing. A region with enhanced recurrent excitation acts as an attractor for the bump location and selectivity for these regions is quickly diminishes as SFA level increases [3]. When multiple spatial attractors of varying strengths are stored in a network moderate increases SFA level will lead to the weak attractors being destabilized and activity localizing within the strongest attractor. This effect is qualitatively similar to the effects of SFA in the Hopfield network. These results indicate that ACh controls memory recall and perception within the cortex by regulation of SFA and explain the important role cholinergic modulation plays in cognitive functions such as attention and memory consolidation [4].

**Acknowledgements:** JPR was supported by an NSF Graduate Research Fel- lowship Program under Grant No. DGE 1256260 and a UM Rackham Merit Fellowship. MRZ and LMS were supported by NSF PoLS 1058034.

## References

1. Hopfield JJ. Neural networks and physical systems with emergent collective computational abilities. PNAS. 1982;79: 2554-8.

2. Stiefel KM, Gutkin BS, Sejnowski TJ. The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons. J Comp Neurosci. 2008;26:289-301.

3. Roach JP, Ben-Jacob E, Sander LM, Zochowski MR. Formation and dynamics of waves in a cortical model of cholinergic modulation. PLoS Comput Biol. 2015;11(8): e1004449.

4. Hasselmo ME, Sarter M. Modes and models of forebrain cholinergic neuromodulation of cognition. Neuropsychopharmacology. 2011;36:52-73.

## P25

### Stability of neural networks and memory consolidation preferentially occur near criticality

Quinton M. Skilling¹, Nicolette Ognjanovski², Sara J. Aton², Michal Zochowski¹,³

¹Biophysics Program, University of Michigan, Ann Arbor, MI 48109 USA; ²Department of Molecular, Cellular, and Developmental Biology, University of Michigan, Ann Arbor, MI, 48109 USA; ³Department of Physics, University of Michigan, Ann Arbor, MI 48109 USA

**Correspondence:** Michal Zochowski - michalz@umich.edu

BMC Neuroscience 2016, 17(Suppl 1):P25

Dynamic neural representations underlie cognitive processing and are an outcome of complex interactions of network structural properties and cellular dynamics. We have developed a new framework to study dynamics of network representations during rapid memory formation in the hippocampus in response to contextual fear conditioning (CFC) [1]. Experimentally, this memory paradigm is achieved by exposing mice to foot shocks while in a novel environment and later testing for behavioral responses when reintroduced to that environment. We employ the average minimum distance (AMD) functional connectivity

algorithm to spiking data recorded before, during, and after CFC using implanted stereotrodes. Comparing changes in functional connectivity using cosine similarity, we find that stable functional representations correlate well with animal performance in learning. Using extensive computer simulations, we show that the most robust changes compared to baseline occur when the system resides near criticality. We attribute these results to emergence of long-range correlations during the initial process of memory formation. Furthermore, we have developed a generic model using a generalized Hopfield framework to link formation of novel memory representation to functional stability changes. The network initially stores a single representation, which is to exemplify biologically already stored (old) memories, and is then presented a new representation by freezing a randomly chosen fraction of nodes from a novel pattern. We show that imposing fractional input of the new representation may partially stabilize this representation near the phase transition (critical) point. We further show that invoking synaptic plasticity rules may fully stabilize this new representation only when the dynamics of the network reside near criticality. Taken together these results show, for the first time, that only when the network is at criticality can it stabilize novel memory representations, the dynamical regime which also yields an increase of network stability. Furthermore, our results match well experimental data observed from CFC experiments.

## Reference

1. Ognjanovski N, Maruyama D, Lashner N, Zochowski M, Aton SJ. CA1 hippocampal network activity changes during sleep-dependent memory consolidation. Front Syst Neurosci. 2014;8:61.

## P26

### Stochastic oscillation in self-organized critical states of small systems: sensitive resting state in neural systems

Sheng-Jun Wang¹,², Guang Ouyang², Jing Guang³, Mingsha Zhang³, K. Y. Michael Wong⁴, Changsong Zhou²,⁵,⁶

¹Department of Physics, Shaanxi Normal University, Xi'An City, ShaanXi Province, China; ²Department of Physics and Centre for Nonlinear Studies, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong; ³State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China; ⁴Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong; ⁵Beijing Computational Science Research Center, Beijing 100084, People's Republic of China; ⁶Research Centre, HKBU Institute of Research and Continuing Education, Shenzhen, China

**Correspondence:** Changsong Zhou - cszhou@hkbu.edu.hk

BMC Neuroscience 2016, 17(Suppl 1):P26

Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems [1], which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli. The results have been published in [2].

**Acknowledgements:** This work was partially supported by Hong Kong Baptist University Strategic Development Fund, NSFCRC Joint Research Scheme HKUST/NSFC/12-13/01 (or N-HKUST 606/12),
RGC (Grants No. 604512, No. 605813, and No. 12302914), NSFC (Grants No.11275027, No. 11328501, and No. 11305098), and the Fundamental Research Funds for the Central Universities (Grant No. GK201302008).

### References

1. Gireesh E, Plenz D, Neuronal avalanches organize as nested theta-and beta/gamma-oscillations during development of cortical layer 2/3. Proc Natl Acad Sci USA. 2008;105:7576-81.

2. Wang SJ, Ouyang G, Guang J, Zhang MS, Wong KYM, Zhou CS. Stochastic oscillation in self-organized critical states of small systems: sensitive resting state in neural systems. Phys Rev Lett. 2016;116:018101.

## P27

### Neurofield: a C++ library for fast simulation of 2D neural field models

Peter A. Robinson¹,², Paula Sanz-Leon¹,², Peter M. Drysdale¹,², Felix Fung¹,², Romesh G. Abeysuriya³, Chris J. Rennie¹,², Xuelong Zhao¹,²

¹School of Physics, University of Sydney, Sydney, New South Wales, 2006, Australia; ²Center for Integrative Brain Function, University of Sydney, Sydney, New South Wales, 2006, Australia

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

BMC Neuroscience 2016, 17(Suppl 1):P27

Neural field theory [1] has addressed numerous questions regarding brain dynamics and its interactions across many scales, becoming a highly flexible and unified framework for the study and prediction of experimental observables of the electrical activity of the brain. These include EEG spectra [2, 3], evoked response potentials, age-related changes to the physiology of the brain [4], epileptic seizures [5, 6], and synaptic plasticity phenomena [7]. However, numerical simulations of neural field models are not widely available despite their extreme usefulness in cases where analytic solutions are less tractable. This work introduces the features of NeuroField, a research-ready library applicable to simulate a wide range of neural field based systems involving multiple structures (e.g., cortex, cortex and thalamic nuclei, and basal ganglia). The link between a given neural field model, its mathematical representation (i.e., a delay-partial differential equations system with spatial periodic boundary conditions) and its computational implementation is described. The resulting computational model has the capability to represent from spatially extended to neural-mass-like systems, and it has been extensively validated against analytical solutions and against experiment [1-10]. To illustrate its flexibility, a range of simulations modeling a variety of arousal-, sleep- and epilepsy-state phenomena is presented [8, 9]. NeuroField has been written using object-oriented programming in C++ and is bundled together with MATLAB routines for quantitative offline analysis, such as spectral and dynamic spectral analysis.

### References

1. Robinson PA, Rennie CJ, Wright JJ. Propagation and stability of waves of electrical activity in the cortex. Phys Rev E. 1997;56:826-40.

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

3. Robinson PA, Rennie CJ, Rowe DL, O'Connor SC. Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Hum Brain Mapp. 2004;23:53-72.

4. van Albada SJ, Kerr CC, Chiang AKI, Rennie CJ, Robinson PA. Neurophysiological changes with age probed by inverse modeling of EEG spectra. Clin Neurophysiol. 2010;121:21-38.

5. Robinson PA, Rennie CJ, Rowe DL. Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E. 2002; 65:041924.

6. Breakspear M, Roberts JA, Terry JR, Rodrigues S, Mahant N, Robinson PA. A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb Cortex. 2006;16:1296-1313.

7. Fung PK, Haber AL, Robinson PA. Neural field theory of large-scale synaptic plasticity in the cerebral cortex. J Theor Biol. 2013; 318:44-57.

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

9. Robinson, PA, Postnova, S, Abeysuriya, RG, Kim, JK, Roberts, JA, McKenzie-Sell L, Karanjai, A, Kerr, CC, Fung, F, Anderson, R, Breakspear, MJ, Drysdale, PM, Fulcher, BD, Phillips, AKJ, Rennie, CJ, Yin G. Chapter 5: a multiscale "working brain" model. In: Validating neurocomputational models of neurological and psychiatric disorders. Paris: Springer; 2015.

10. O'Connor SC, Robinson PA. Spatially uniform and nonuniform analysis of electroencephalographic dynamics, with application to the topography of the alpha rhythm. Phys Rev E. 2004;70:110-9.

## P28

### Action-based grounding: Beyond encoding/decoding in neural code

Yoonsuck Choe¹, Huei-Fang Yang²

¹Department of Computer Science & Engineering, Texas A&M University, College Station, TX, 77845, USA; ²Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan

**Correspondence:** Yoonsuck Choe - choe@tamu.edu

BMC Neuroscience 2016, 17(Suppl 1):P28

How can we decode the neural activation patterns (Fig. 18A)? This is a key question in neuroscience. We as scientists have the luxury of controlling the stimulus, based on which we can find the meaning of the spikes (Fig. 18C-right). However, as shown in Fig. 18A (and C-left), the problem seems intractable from the point of view of the brain itself since neurons deeply embedded in the brain do not have direct access to the stimulus. In [1] and related work, we showed that the decoding problem seems intractable only because we left out the motor system from the picture. Figure 18D shows how motor action can help processes deeply embedded in the brain can understand the meaning of the spikes by generating motor behavior and observing the resulting change in the neural spikes. Here, a key principle is to generate motion that keeps the neural spike pattern invariant over time (Fig. 18E), which allows the following to coincide (1) the property of the motion (diagonal movement) and (2) the encoded property of the input (45° orientation). Using reinforcement learning, we showed that the invariance criterion leads to near optimal state-action mapping for synthetic and natural image inputs (Fig. 18F, G), where the encoded property of the input is mapped to congruent motor action. Furthermore, we showed that the receptive fields can be learned simultaneously with

<figure><img src="image_19.png" /></figure>
the state-action mapping (Fig. 18H). The main lesson we learned is that the encoding/decoding framework in neural code can lead to a dead end unless the problem is posed from the perspective of the brain itself; and the motor system can play an important role in the shaping of the sensory/perceptual primitives (also see [2]).

## References

1. Choe Y, Yang HF, Misra N. Motor system's role in grounding, receptive field development, and shape recognition. In: 7th IEEE international conference on development and learning (ICDL 2008). IEEE, p. 67–72.

2. Salinas E. How behavioral constraints may determine optimal sensory representations. PLoS Biol. 2006;4(12):e387.

## P29

### Neural computation in a dynamical system with multiple time scales

Yuanyuan Mi¹,†, Xiaohan Lin¹,†, Si Wu¹

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

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

†Y.M. and X.L. contributed equally to this work

BMC Neuroscience 2016, 17(Suppl 1):P29

The brain performs computation by updating its internal states in response to external inputs. Neurons, synapses, and the circuits are the fundamental units for implementing brain functions. At the single neuron level, a neuron integrates synaptic inputs and generates spikes if its membrane potential crosses the threshold. At the synapse level, neurons interact with each other to enhance or depress their responses. At the network level, the topology of neuronal connection pattern shapes the overall population activity. These fundamental computation units of different levels encompass rich short-term dynamics, for example, spike-frequency adaptation (SFA) at single neurons [1], short-term facilitation (STF) and depression (STD) at neuronal synapses [2]. These dynamical features typically expand a broad range of time scale and exhibit large diversity in different brain regions. Although they play a vital part in the rise of various brain functions, it remains unclear what is the computational benefit for the brain to have such variability in short-term dynamics.

In this study, we propose that one benefit for having multiple dynamical features with varied time scales is that the brain can fully exploit the advantages of these features to implement which are otherwise contradictory computational tasks. To demonstrate this idea, we consider STF, SFA and STD with increasing time constants in the dynamics of a CANN. The potential brain regions with these parameter values are the sensory cortex, where the neuronal synapses are known to be STD-dominating. We show that the network is able to implement three seemingly contradictory computations, which are persistent activity, adaptation and anticipative tracking (see Fig. 19). Simply state, the role of STF is to hold persistent activity in the absence of external drive, the role of SFA is to support anticipative tracking for a moving input, and the role of STD is to eventually suppress neural activity for a static or transient input. Notably, the time constants of SFA and STD can be swapped with each other, since SFA and STD have the similar effects on the network dynamics. Nevertheless, we need to include both of them, since a single negative feedback modulation is unable to achieve both anticipative tracking and plateau decay concurrently. The implementation of each individual computational task based on a single dynamical feature has been studied previously. Here, our contribution is on revealing that these tasks can be realized concurrently in a single neural circuit by combined dynamical features with coordinated time scales. We hope that this study will shed light on our understanding of how the brain orchestrates its rich dynamics at various levels to realize abundant cognitive functions.

## Reference

1. Benda J, Herz AVM. A universal model for spike-frequency adaptation. Neural Comput. 2003;15(11):2523–64.

2. 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.

<figure><img src="image_20.png" /></figure>

## P30

### Maximum entropy models for 3D layouts of orientation selectivity

Joscha Liedtke¹,², Manuel Schottdorf¹,², Fred Wolf¹,²

¹Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; ²Bernstein Center for Computational Neuroscience, Göttingen, Germany

**Correspondence:** Joscha Liedtke - joscha@nld ds.mpg.de, Manuel Schottdorf - manuel@nld ds.mpg.de

BMC Neuroscience 2016, 17(Suppl 1):P30

The neocortex is composed of 6 different layers. In the primary visual cortex (V1), the functional architecture of basic stimulus selectivity is experimentally found to be similar across these layers [1]. The organization in functional columns justifies the use of cortical models describing only two-dimensional layers and disregarding functional organization in the third dimension.

Here we show theoretically that already small deviations from an exact columnar organization can lead to non-trivial three-dimensional functional structures (see Fig. 20). Previously, two-dimensional orientation domains were modeled by Gaussian random fields, the maximum entropy ensemble, allowing for an exact calculation of pinwheel densities [2]. Pinwheels are points surrounded by neurons preferring all possible orientations and these points generalize to pinwheel strings in three dimensions. We extend the previous two-dimensional model characterized by its typical scale of orientation domains to a three-dimensional model by keeping the typical scale in each layer and introducing a columnar correlation length. We dissect in detail the three-dimensional functional architecture for flat geometries and for curved gyri-like geometries with different columnar correlation lengths. The model is analyzed analytically complemented by numerical simulations to obtain solutions for its intrinsic statistical parameters. We find that (i) pinwheel strings are generally curved, (ii) for large
<figure><img src="image_21.png" /><figcaption>**Fig. 20** A Three-dimensional orientation domains with columnar correlation length of Λ. B String singularities of orientation domains in A. Typical scale of cats Λ ≈ 1 mm</figcaption></figure>

curvatures closed loops and reconnecting pinwheel strings appear and (iii) for small columnar correlation lengths a novel transition to a rodent-like interspersed organization emerges.

This theory extends the work of [2, 3] by adding a columnar dimension and supplements the work of [4] by a rigorous statistical treatment of the three-dimensional functional architecture of V1. Furthermore, the theory sheds light on the required precision of experimental techniques for probing the fine structure of the columnar organization in V1.

## References

1. Hubel DN, Wiesel TN. Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J Physiol. 1962;160:106-54.

2. Schnabel M, Kaschube M, Löwel S, Wolf F. Random waves in the brain: symmetries and defect generation in the visual cortex. Eur Phys J Spec Topics. 2007;145(1):137-57.

3. Wolf F, Geisel T. Spontaneous pinwheel annihilation during visual development. Nature. 1998;395:73-8.

4. Tanaka S, Moon CH, Fukuda M, Kim SG: Three-dimensional visual feature representation in the primary visual cortex. Neural Networks 2011, 24(10):1022-1035.

## P31

### A behavioral assay for probing computations underlying curiosity in rodents

Yoriko Yamamura¹, Jeffery R. Wickens¹

¹Neurobiology Research Unit, Okinawa Institute of Science and Technology, Onna-son, Okinawa, 904-0412, Japan

**Correspondence:** Yoriko Yamamura - yoriko@oist.jp

BMC Neuroscience 2016, 17(Suppl 1):P31

Curiosity in humans appears to follow an inverted U-shaped function of unpredictability: stimuli that are neither too predictable nor too unpredictable evoke the greatest interest [1]. Rewarding moderate

sensory unpredictability is an effective strategy for reinforcing explorations that improve our predictive models of the world [1, 2]. However, the computations and neural circuits underlying this unpredictability-dependence of curiosity remain largely unknown.

A rodent model of curiosity would be useful for elucidating its underlying neural circuitry, because more specific manipulation techniques are available than in humans. It has been shown that mice prefer unpredictable sounds to predictable ones when the sounds are paired with light [3]. However, frequency of stimulus presentation was a potential confound in this study. Furthermore, a more systematic sampling of stimulus unpredictability is necessary to determine whether a rodent analogue of the U-shaped curve indeed exists.

We have devised an operant conditioning paradigm building on [3], using sensory stimuli as "reward" to quantify the rewardingness of various levels of sensory predictability for rats. Rats (Long Evans, male) are placed in a soundproofed chamber with two nosepoke holes. A combination of sound and light stimuli is presented whenever the rat pokes the active hole; no stimulus is associated with the inactive hole (counterbalanced across subjects).

We hypothesize that reward is also a U-shaped function of stimulus unpredictability in rats, and that this is due to a Bayesian precision weighting placing more importance on deviations from reliable predictions. This departs from previous learning-based accounts [2]. There are five experimental conditions, systematically varied in unpredictability of the sound stimuli (as quantified by entropy *H*), and a control condition, in which a nosepoke in neither hole has any consequence (Fig. 21). Specifically, the sound stimuli are random sequences of two possible 125-ms sound snippets of equal value to the rat, with their frequencies of occurrence varied across conditions to vary *H*. Each sequence contains eight such snippets. Across all conditions, the light stimulus simply remains on while the sound is being played; it is added to enhance the rats' responding to auditory stimuli [3]. We predict that the rats' active nosepoke responses will be maximally increased at intermediate *H* (Fig. 21).

In preliminary experiments for conditions 0 and 2 (N = 3 each; three sessions), rats preferred the active hole to the inactive, replicating the earlier results in mice [3]. Moreover, as hypothesized, rats responded more to the active hole in condition 2 (mean = 15.0, SD = 5.32) than in condition 0 (mean = 11.3, SD = 4.05); t(22) = 1.91, *p* = 0.0345 (one-tailed t test). We note that in mice, most across-condition differences did not emerge until around session 7 [3].

The proposed assay quantifies the rewardingness of sensory unpredictability in rats. By systematically varying the entropy of the sound sequence, we can probe the computations behind the putative unpredictability-driven reward. The assay can furthermore be used to study the effect of pharmacological or genetic manipulations on unpredictability-driven reward, in order to validate mechanistic implementations of such computations.

<figure><img src="image_22.png" /><figcaption>**Fig. 21** Schematic of the sound stimuli used in all conditions, and the predicted reward for each</figcaption></figure>