Decision letter: Synaptic input sequence discrimination on behavioral timescales mediated by reaction-diffusion chemistry in dendrites

Full text Figures and data Side by side Abstract Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Sequences of events are ubiquitous in sensory, motor, and cognitive function. Key computational operations, including pattern recognition, event prediction, and plasticity, involve neural discrimination of spatio-temporal sequences. Here, we show that synaptically-driven reaction-diffusion pathways on dendrites can perform sequence discrimination on behaviorally relevant time-scales. We used abstract signaling models to show that selectivity arises when inputs at successive locations are aligned with, and amplified by, propagating chemical waves triggered by previous inputs. We incorporated biological detail using sequential synaptic input onto spines in morphologically, electrically, and chemically detailed pyramidal neuronal models based on rat data. Again, sequences were recognized, and local channel modulation downstream of putative sequence-triggered signaling could elicit changes in neuronal firing. We predict that dendritic sequence-recognition zones occupy 5 to 30 microns and recognize time-intervals of 0.2 to 5 s. We suggest that this mechanism provides highly parallel and selective neural computation in a functionally important time range. https://doi.org/10.7554/eLife.25827.001 Introduction Activity sequences have long been recognized as a fundamental constituent of neural processing. Lorente de No suggested that reverberatory activity sequences in small networks could sustain activity (Lorente de No, 1938). Hebb's idea of cell assemblies suggested that ensembles of cells encoded a particular neuronal concept, but also that there was sequential activation within the group of cells forming the assembly (Hebb, 1949). Many sensory systems process sequential stimuli, and these are typically mapped to ensembles of sequentially active neurons (Bouchard and Brainard, 2016; Broome et al., 2006; Carrillo-Reid et al., 2015). Deeper in the brain, hippocampal place cells represent a higher-order cognitive map of space, yet here too sequences occur when the animal moves through spatial locations represented by the place cells (Wilson and McNaughton, 1994). The hippocampus exhibits other forms of sequential activity in the form of fast replay events (Jadhav et al., 2012; Wilson and McNaughton, 1994) and stimulus-bridging activity that emerges during associative learning (MacDonald et al., 2011) and trace conditioning (Modi et al., 2014). Thus, there are numerous neural correlates both of sequences, and of processing steps that recognize them. The idea of synfire chains examines conditions for self-sustaining sequential activity to occur in multiple layers of a network (Abeles, 1982). This is non-trivial, as excessive activation can lead to runaway epileptiform activity, whereas insufficient activation causes decay of the activity wave (Kumar et al., 2008; Mehring et al., 2003). Neural networks that can recognize such sequences are well-established. For example, events may be run through a delay line, so that the oldest event is delayed more, the next event less, and so on, so that they all arrive at the neural network at the same time. Thus, the time-sequence is flattened in time and classical attractor networks can recognize patterns in the sequence (Tank and Hopfield, 1987). Time-varying attractor networks have also been shown to be able to implement and recognize sequences (Lee, 2002). Time-invariance is a desirable feature of sequence recognition circuits, since the same order of events may take place at different speeds. Recursive networks using supervised learning, and short-term synaptic plasticity have been shown to be implement time-invariance (Barak and Tsodyks, 2006; Goudar and Buonomano, 2015; Laje and Buonomano, 2013). While networks can carry out sequence recognition, they make limited use of the rich dynamics of biological neurons. The theory of Hierarchical Temporal Memory builds on the idea of sequence-recognizing neurons and networks as a way to perform complex temporal computation (George and Hawkins, 2009; Hawkins and Ahmad, 2016). Even the ability to recognize simultaneous closely-localized synaptic input has interesting computational implications (Hawkins and Ahmad, 2016), The current study extends this to patterns of input both in time and space. One of the first biophysical proposals for subcellular sequence recognition was made by Rall, who showed theoretically that synaptic events propagate down the dendritic tree with a small delay. By timing synaptic inputs to coincide with this delay, Rall predicted that ordered input should yield a larger response than reversed input (Rall, 1964). A stronger version of this mechanism was experimentally demonstrated by Branco et al. (2010) who used glutamate uncaging to provide sequential input along a pyramidal neuron dendrite. They showed that NMDA receptor amplification of 'inward' sequences (distal to proximal) gave rise to about 40% larger somatic depolarization than 'outward' sequences, for rapid (~40 ms) sequences. However, many interesting neural sequences occur at slower time-scales. At least three attributes should converge for single neurons to achieve and report sequence recognition in the noisy context of neural activity. First, the neurons should recognize inputs coming in the correct order in space and time. Second, the selectivity for the correct input over scrambled input and background noise should be strong enough for there to be reliable discrimination. Third, recognized sequences should trigger activity changes either by way of changed firing, or by way of plasticity. In the current study, we use theory and reaction-diffusion modeling to show how the first condition may be achieved, and develop detailed multi-scale models to address the second and third. Results As the setting for this study, we considered a network in which ensembles of neurons are active in sequence, for example, place cells in the hippocampus as an animal moves along a linear track (Figure 1). We assumed that a single neuron from each of these ensembles projects onto a given postsynaptic cell, which is the focus of our analysis. The projections are ordered such that they converge onto a succession of spines located on a short stretch of dendrite on this cell, in the same spatial and temporal order as the activation of the ensembles. We ignored all other network context. We first treated this system in the abstract, as sequentially ordered activation of segments of a one-dimensional reaction-diffusion system with abstract chemistry. We asked if the reaction system could discriminate sequential from scrambled input. We then mapped the discrimination mechanism to a signaling pathway modeled as mass-action reaction-diffusion chemistry in a similar cylindrical geometry, but ornamented with dendritic spines. We then tested discrimination when we embedded mass-action chemistry into a morphologically and electrically detailed neuronal model receiving sequential input on a series of synapses, through ligand-gated ion channels. Finally, we asked if ion channel modulation by sequence discrimination chemistry in small dendritic zones, could affect neuronal firing. Figure 1 Download asset Open asset Sequential activity, from behavior to dendrite. Top: Linear arena in which a rat moves, with indicated locations of 5 place cells (color coded green, yellow, orange, red, and maroon in order.). The place cells are representatives of 5 neuronal ensembles (colored clouds), each active in one of the five locations on the arena. The neuronal ensembles each send a single axonal projection in spatial order to a small dendritic segment on a postsynaptic neuron, with an average spacing S between connected spines. Note that spines need not be immediately adjacent to each other. Below, buildup of reactant following input activity with the appropriate timing, corresponding to the rat moving at a speed which the dendritic chemistry recognizes. https://doi.org/10.7554/eLife.25827.002 Abstract reaction-diffusion systems support sequence recognition We first analyzed the requirements for chemical reaction-diffusion systems to achieve selectivity for spatially and temporally ordered inputs. In doing these calculations, we utilized 'spherical cow' models of chemistry: highly reduced formulations with just two diffusive state variables A and B, interpreted as molecules undergoing 1-dimensional diffusion (Figure 2A,B). The reaction system received input from a third molecule, designated as Ca (Figure 2A,B). In all cases, molecule B inhibited A. Figure 2 Download asset Open asset Responses and sequence selectivity of four abstract models involving molecules A and B. Columns are the respective models. (A) Model equations. (B) Model schematics. Arrows indicate excitation, plungers indicate inhibition. In the FHN model, A has a fast self-excitation and a slow self-inhibition. In the Switch model, we indicate a multiplicative inhibition of A by an arrow from B onto the self-inhibition arrow of A. (C) Response of point (non-spatial) model to a 1 s wide Gaussian input of Ca2+ (red dot) and a steady pulse of Ca2+ (green line). Input amplitudes: 1, 10, 0.4, and 1 respectively. (D-G) Response of molecule A in one-dimensional reaction-diffusion form of model to sequential input at five locations. (D) Time-course of response at five locations to ordered input. Locations are color-coded in the sequential order blue, green, red, cyan, purple. (E) Time-course of response at five locations to scrambled input. Note that the FHN and Switch models have much lower responses to scrambled as compared to ordered input. The Neg. FF model has a lower response at two of its locations. (F, G) Snapshot of spatial profile of response to ordered (F) and scrambled (G) input. Snapshot is at time 18.4, 14.2, 16.3 and 18.4 s respectively. https://doi.org/10.7554/eLife.25827.003 The abstract models were initially formulated to implement reaction-diffusion wave propagation at a speed that matched the arrival of sequential input. We implemented two models with this property: the FitzHugh-Nagumo form, which is a known stimulus-triggered, oscillating, and propagating wave system (Fitzhugh, 1961; Nagumo et al., 1962); and a bistable reaction-diffusion system, which again is a known substrate for propagating waves (Keener and Sneyd, 1998). To the bistable switch system, we added inhibitory feedback to restore the switch to baseline after a delay. In addition to these models with complex dynamics, we implemented a system with feedback inhibition, and a system with feedforward inhibition. These simpler models were designed to test if inhibitory feedback or feedforward systems, coupled with diffusion, could achieve selectivity in the absence of an amplifying positive feedback process. Our criterion for sequence recognition was that ordered inputs should elicit high total activity of a signaling molecule A, whereas scrambled inputs should elicit low levels of activity. Total activity here means the sum of activity of A over the duration and spatial extent of the stimulus. To investigate the temporal responses of these 'reaction' systems, we first delivered impulse (red dot) and step-function (green line) input to non-spatial versions of the models (Figure 2C). Each model exhibited a large impulse response. Two of the models (feedforward inhibition and state-switching) exhibited only a transient response to the sustained input. The negative feedback model, as expected, had a transient strong response followed by a shallow sustained response. The FitzHugh-Nagumo model, again as expected, oscillated. We then implemented 1-dimensional reaction-diffusion versions of these models (Figure 2, methods). We delivered Ca2+ stimuli at five equally spaced points on the reaction system. Each Ca2+ stimulus followed a Gaussian time-profile: (1) Ca=exp(−((phase−t)2)/(2 width2)) Here, phase defines the timing of each input, t is time, and width is the duration of the Ca2+ pulse. The only difference between the sequential and scrambled stimuli was their order ([0,1,2,3,4] and [2,1,4,3,0], respectively (methods)). The results of these simulations are compared in Figure 2D–G. First, we found that the simple feedback inhibition model showed no input sequence-dependent difference in total activity. This can be seen in terms of time-response at the five stimulus points (Figure 2D,E), and also in terms of spatial profile of A at the end of the stimulus (Figure 2F,G, Video 1). Video 1 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Time-and-space series of response of negative feedback model to sequential (blue) and scrambled (red) input. https://doi.org/10.7554/eLife.25827.004 Then, we observed that the feedforward inhibition model showed a small amount of selectivity (Figure 2D–G). This arose because the A response was diminished at two of the input points when the input was scrambled (Video 2). Video 2 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Time-and-space series of response of negative feedforward model to sequential (blue) and scrambled (red) input. https://doi.org/10.7554/eLife.25827.005 The FitzHugh-Nagumo (FHN) model was strongly selective, with a large buildup of response only when the input was sequential (Figure 2 third column, Video 3). We interpret this as arising when the propagating wave from the FHN equation arrived at successive input points just when the input was also present. Video 3 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Time-and-space series of response of FitzHuge-Nagumo model to sequential (blue) and scrambled (red) input. https://doi.org/10.7554/eLife.25827.006 The switching model was the most selective (Figure 2 last column, Video 4). This was because it built up to a large, sustained response lasting several seconds, provided the successive inputs were in the same position as the diffusively propagating activity of A. Video 4 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Time-and-space series of response of bistable switch model to sequential (blue) and scrambled (red) input. https://doi.org/10.7554/eLife.25827.007 Thus, this set of simulations showed that several reaction-diffusion like systems were capable of sequence selectivity. Strong selectivity emerged from a supralinear buildup of responses when diffusively propagating activity was aligned with successive inputs, and suppression due to inhibition when the alignment was off. Reaction systems select for distinct speeds and length-scales of sequential input We next asked how the different reaction systems were tuned to different spatial and temporal intervals. We devised a scalar metric, Q, of the degree of sequential ordering of stimuli, as a first step. We plotted the ordinal position of the input against the ordinal value of its arrival time. Thus, a perfect sequence would arrive at positions [0,1,2,3,4] at times [0,1,2,3,4]. We used the quantity (2) Q=mR2 as the measure of how ordered the sequence was. Here, m = slope and R = regression coefficient of best-fit line. R2 provides a measure of linearity of the sequence, and m assigns it a magnitude and sign. With this measure, the sequence [0,1,2,3,4] has Q = 1; [4,3,2,1,0] has Q = −1, and [4,0,2,1,3] has Q = −0.001. Examples of regression plots used to generate Q for different sequences are presented in Figure 3A,B. Figure 3 Download asset Open asset Sequence selectivity for different models. (A, B) Regression plots for sample sequences. (A) Perfect forward sequence [0,1,2,3,4] (red, Q = 1) and reverse sequence [4,3,2,1,0] (blue, Q = −1). (B) Scrambled sequence [4,0,2,1,3] (red, Q = −0.001) and [0,1,3,2,4] (blue, Q = 0.729). (C, E, G, I) Scatter plots of chemical system selectivity (measured as total activation of molecule A over time and space) against Q. There are 5! = 120 points, each being the outcome of a single simulation with a different sequence. In each plot the blue cross is the perfect forward sequence (whose timeseries is shown in Figure 2D), and the red cross is the scrambled sequence [2,1,4,3,0], whose timeseries is shown in Figure 2E. (D, F, H, J) Matrix of selectivity as a function of total length of stimulus zone and interval time between successive stimuli. In each plot, the asterisk is placed on the matrix entry obtained from the spacing and interval parameters used for the scatter plot to its left. In other words, the selectivity value for that matrix entry is obtained from Equation 3 using the Atot scores from the scatter plot. (C,D) Feedback model. This shows no selectivity. (E, F) Inhibitory feedforward model. Scatter plot in E represents calculations performed at time/distance values of (3 s, 4 mm). This shows low selectivity, as seen by slightly higher Atot for Q values of +1 and −1. (G,H) FitzHugh-Nagumo, scatter plot at (2 s, 2 mm). The model is selective in a narrow, diagonal range of time and distance. Its score is somewhat reduced because of the high baseline of Atot. (I,J) Switching model, scatter plot at (3 s, 4 mm). This is highly selective over a wide range of time and distance. Only the perfect forward and reverse sequences have high values of Atot. https://doi.org/10.7554/eLife.25827.008 We then compared our reaction readout A with the metric Q, to see how well each of our four reaction systems could discriminate sequence order (Figure 3C,E,G,I). Here, we ran simulations with each of the possible permuted input sequences. In each run, we summed the level of A over all five stimulus points, and from the time of the first stimulus till the end of the run, in order to obtain a cumulative estimate of the response. This total A value (Atot) was plotted against the Q metric for each of these permuted sequences (Figure 3C,E,G,I). If the chemical system was highly selective, we expected that only one or two points in the scatter plot should have a high value of Atot, and these should be the points with Q around +1 or −1. Chemical systems that did not exhibit sequence discrimination should have similar values of Atot for all sequences. The results were as expected from the individual runs from Figure 2. Specifically, the inhibitory feedback system had poor tuning, there was a small amount of selectivity for the feedforward inhibition case, and strong selectivity for the FitzHugh-Nagumo and switching cases. Each of these outcomes had been observed in Figure 2 for just the sequential and a single scrambled stimulus, and in Figure 3 we found that it generalized to the entire set of sequence permutations. Note that the modeled reaction-diffusion system was spatially symmetric and did not distinguish between forward and backward sequences. An analysis of symmetry breaking arising from incorporation of biological detail is out of the scope of the current paper. We next asked how selective each reaction system became, when the inputs were delivered at different time and space intervals. The time and space intervals were specified as parameters for each simulation run. We devised a metric for reaction network sequence selectivity, based on a comparison of responses to sequential vs. scrambled inputs: (3) the system strongly to sequential input than to other selectivity should be in the range from to one is Atot for the sequential stimulus, is the of Atot over all of the stimulus and is the value of Atot for all of stimulus To we out simulations of the model for all possible patterns of input, and obtained Atot in each (Figure first was then as Equation We these calculations for each point in the matrix of timing and spacing to obtain a of selectivity values (Figure As seen from Figure 2, the feedback inhibition model had low selectivity in all cases. The feedforward inhibition model showed a diagonal of selectivity such that rapid stimuli in as well as slower stimuli at were The FitzHugh-Nagumo was much strongly selective, but also had a similar diagonal In both these we interpret this as there being an propagation speed of the chemical activity and if the inputs were and spaced the response built The switching model was strongly selective, and had a large zone of strong selectivity around (2 s, 4 Thus, each of the three reaction systems had a range of stimulus timing and but the FHN and switch forms had much higher selectivity. Sequence speed selectivity with reaction and diffusion As a analysis on our abstract we asked how sequence speed selectivity with and diffusion This is important because it the spatial extent of the sequence selective zones that we to in the dendritic is also important as it defines the of sequential events that may be recognized by such reaction-diffusion We first tested the most that sequence propagation speed was to chemical and diffusion To we all and the diffusion by the same and reduced the stimulus width by the same We ran the same of stimulus space and time intervals as As expected, all the chemical and diffusion also the sequence speed to which the network had the response. As the were the was at time intervals but the same spatial intervals. (Figure However, different stimulus were to obtain strong in these We also of on stimulus and observed that the zone also on stimulus (Figure This is because the selectivity when the stimulus is strong enough that the ordered sequence to pathway but not so strong that the stimulus the inhibitory and To the range of sequence selectivity, we each of the parameters of the model one at a time with to the model. We out this 1-dimensional for the FHN and switching models (Figure 1 and 2). In each we and compared it to over input of which were scrambled (green methods). We also sequence selectivity as Equation 3 (red We found that selectivity was to such as diffusion but with to and stimulus These models were to be and to the of we did not the models for Figure 4 with 2 see all Download asset Open asset Sequence in space and time. for of 1, 2, 3 and 4 times respectively. (E) of speed of sequence as a function of the (F, G) of with stimulus (F) (G) Thus, by for and diffusion, we were able to achieve sequence selectivity over a range of time-intervals s between and spatial intervals between reaction-diffusion system based on feedback sequences We next asked if for sequence selectivity could be to a mass-action reaction-diffusion system. We based our mass-action model on a reduced model of feedback and The model exhibited the behavior of our abstract model. The other of the abstract model was delayed of activity. There are several known inhibitory feedback for the pathway et al., 2016). We added a to delayed of the The other changes we made to the model were to the synaptic signaling to receptor in the and to as a Ca2+ With the of active and the ion all molecules were The model is shown in Figure and the model is presented in This model is a map to the detailed and models of this pathway in the and et al., 2003). Ca2+ stimuli were delivered in the and into the dendrite Model responses to and function Ca2+ inputs are shown in Figure both in the dendrite. As expected, there is a strong to Ca2+ stimuli, followed by delayed inhibition. We ran this model in a cylindrical ornamented with spines at intervals and Figure We provided sequential and scrambled Ca2+ input to 5 of the spines by and observed sequence selectivity (Figure Figure 5 Download asset Open asset model of a switch exhibits sequence selectivity. (A) of model chemistry. indicate or activation inhibition, and arrow activity. indicate diffusion of Ca2+ and between and dendrite. the Ca2+ from the (B) Ca2+ responses seen at the to input delivered at stimulus was two of 1 s, by s. a delay of s, a of Ca2+ was delivered for s. (C) response to the Ca2+ stimulus. Note strong inhibition of the response to the second and rapid of response to the stimulus. (D) of reaction-diffusion model, with spines. was 1 and length was The five spines are in red, each by a coded (E) Response of system to sequential input [0,1,2,3,4] on indicated spines spaced at intervals of 3 s. Each input was delivered to the of the at for s. was from the dendrite to each of the spines. indicate from (F) Response to scrambled input, in the order The response to scrambled input had a and for a time. are as in Thus, we showed that a mass-action reaction-diffusion system exhibited sequence selectivity when it had with delayed by negative This had been predicted by the abstract models. Sequence selectivity in a detailed neuronal model with noisy input We then asked sequence recognition would in the complex context of active neurons receiving background activity in a We in biological detail at the following Model neuron based on including spines spaced at ion the cell, based on models. synaptic input at on all spines. synaptic input with an modulation on dendritic to the background synaptic input, the model exhibited with activity at (Figure in the form of on and NMDA on of spines. Ca2+ dynamics following synaptic ion including diffusion between and and

Topic: Neural dynamics and brain function
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences