Single spikes drive sequential propagation and routing of activity in a cortical network
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eLife assessment
This manuscript is relevant to experimental and theoretical neuroscientists interested in the trade-off between chaos and reliability in the brain, and may also pique the interest of the machine learning community, particularly those seeking to understand the computational capacity of recurrent neural networks. The findings are valuable, with practical and theoretical implications for this subfield. Using a spiking neural network model firmly anchored in experimental data from the turtle brain, the authors examine the reliability and flexibility of spike train sequences and determine the differential roles of strong and weak connections. The results show clearly that strong but sparse connections in a sub-network can produce a highly reliable response to single spikes, with reliability and multiplexing across sub-networks controlled by weak connectivity. The strength of evidence for the claims is convincing, using appropriate and validated methodology in line with current state-of-the-art.
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Abstract
Single spikes can trigger repeatable firing sequences in cortical networks. The mechanisms that support reliable propagation of activity from such small events and their functional consequences remain unclear. By constraining a recurrent network model with experimental statistics from turtle cortex, we generate reliable and temporally precise sequences from single spike triggers. We find that rare strong connections support sequence propagation, while dense weak connections modulate propagation reliability. We identify sections of sequences corresponding to divergent branches of strongly connected neurons which can be selectively gated. Applying external inputs to specific neurons in the sparse backbone of strong connections can effectively control propagation and route activity within the network. Finally, we demonstrate that concurrent sequences interact reliably, generating a highly combinatorial space of sequence activations. Our results reveal the impact of individual spikes in cortical circuits, detailing how repeatable sequences of activity can be triggered, sustained, and controlled during cortical computations.
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Author Response
Reviewer #3 (Public Review):
Weaknesses
The spontaneous activity of the network is extremely low, with [0.02 0.09] spks/s considered as a high activity range. Granted, this is based on ex vivo measurements. However, if this phenomenon is to be considered computationally relevant, as the authors claim, the paper should have examined the reliability of propagation and routing with in vivo activity levels.
The above weakness is a special case of the issue that the limits of applicability/robustness of results to model assumptions have not been well established. In particular, it is not clear how strong the strongest weights must be whilst still enabling long sequences, and what is the dependence of the results on the parameters of the distance-dependent connectivity.
Regarding the two first weaknesses listed in …
Author Response
Reviewer #3 (Public Review):
Weaknesses
The spontaneous activity of the network is extremely low, with [0.02 0.09] spks/s considered as a high activity range. Granted, this is based on ex vivo measurements. However, if this phenomenon is to be considered computationally relevant, as the authors claim, the paper should have examined the reliability of propagation and routing with in vivo activity levels.
The above weakness is a special case of the issue that the limits of applicability/robustness of results to model assumptions have not been well established. In particular, it is not clear how strong the strongest weights must be whilst still enabling long sequences, and what is the dependence of the results on the parameters of the distance-dependent connectivity.
Regarding the two first weaknesses listed in Reviewer #3 Public Review, we wish to note that:
● The statement that our estimate of spontaneous activity “is based on ex vivo measurements” is incorrect. Our single-cell and connectivity parameters are certainly based on ex vivo measurements, but the range of spontaneous activity that the Reviewer cites ([0.02 0.09] spks/s) is an estimate from in vivo recordings. Furthermore, in our model, we explored mean firing rates higher than this in vivo range and still observed sequences.
● While the Reviewer states that “it is not clear how strong the strongest weights must be”, we do provide a lower-bound estimate. We explored simulations where we truncated sections of the distribution of synaptic strengths and observed that networks that included the bottom 90% of connections did not produce sequences.
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eLife assessment
This manuscript is relevant to experimental and theoretical neuroscientists interested in the trade-off between chaos and reliability in the brain, and may also pique the interest of the machine learning community, particularly those seeking to understand the computational capacity of recurrent neural networks. The findings are valuable, with practical and theoretical implications for this subfield. Using a spiking neural network model firmly anchored in experimental data from the turtle brain, the authors examine the reliability and flexibility of spike train sequences and determine the differential roles of strong and weak connections. The results show clearly that strong but sparse connections in a sub-network can produce a highly reliable response to single spikes, with reliability and multiplexing across …
eLife assessment
This manuscript is relevant to experimental and theoretical neuroscientists interested in the trade-off between chaos and reliability in the brain, and may also pique the interest of the machine learning community, particularly those seeking to understand the computational capacity of recurrent neural networks. The findings are valuable, with practical and theoretical implications for this subfield. Using a spiking neural network model firmly anchored in experimental data from the turtle brain, the authors examine the reliability and flexibility of spike train sequences and determine the differential roles of strong and weak connections. The results show clearly that strong but sparse connections in a sub-network can produce a highly reliable response to single spikes, with reliability and multiplexing across sub-networks controlled by weak connectivity. The strength of evidence for the claims is convincing, using appropriate and validated methodology in line with current state-of-the-art.
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Reviewer #1 (Public Review):
There were two parts to this paper. The first was to build a network model with parameters carefully adjusted to match those seen in the turtle cortex. The second was to simulate the circuit, and show that it could produce reasonably repeatable patterns of activity in response to a single, externally added, spike.
As a model of the turtle cortex, the paper was pretty convincing. And the explanation for the repeatable patterns of activity - a small number of very strong connections and a very low background firing rate - seemed eminently reasonable. This paper should serve as a very good starting point for understanding computing in the turtle cortex.
However, average firing rates in the turtle are extremely low - 0.1 Hz, at least in these simulations. Their model is unlikely, therefore, to account for …
Reviewer #1 (Public Review):
There were two parts to this paper. The first was to build a network model with parameters carefully adjusted to match those seen in the turtle cortex. The second was to simulate the circuit, and show that it could produce reasonably repeatable patterns of activity in response to a single, externally added, spike.
As a model of the turtle cortex, the paper was pretty convincing. And the explanation for the repeatable patterns of activity - a small number of very strong connections and a very low background firing rate - seemed eminently reasonable. This paper should serve as a very good starting point for understanding computing in the turtle cortex.
However, average firing rates in the turtle are extremely low - 0.1 Hz, at least in these simulations. Their model is unlikely, therefore, to account for activity in the mammalian cortex, which exhibits a much higher background firing rate, and for which there's not a lot of evidence for the extremely strong connections seen in the turtle.
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Reviewer #2 (Public Review):
This modeling paper looks at how single spikes in the cortex are able to evoke patterns of sequential neural response in the surrounding neural network, an effect observed in the visual cortex of turtles, rodents, and the middle temporal cortex of humans, and possibly generalizable across many other species and brain areas. The results are anchored by population recordings from the turtle cortex, recapitulating those data and exploring how single spikes might be able to have such an outsized effect on broad-scale neural activity. The authors aim to show which kinds of network connectivity support this kind of response.
The results reveal that sparse, but strong connections in a neural network are the necessary ingredient for the reliable triggering of network sequences by single spikes. Dense, but weaker …
Reviewer #2 (Public Review):
This modeling paper looks at how single spikes in the cortex are able to evoke patterns of sequential neural response in the surrounding neural network, an effect observed in the visual cortex of turtles, rodents, and the middle temporal cortex of humans, and possibly generalizable across many other species and brain areas. The results are anchored by population recordings from the turtle cortex, recapitulating those data and exploring how single spikes might be able to have such an outsized effect on broad-scale neural activity. The authors aim to show which kinds of network connectivity support this kind of response.
The results reveal that sparse, but strong connections in a neural network are the necessary ingredient for the reliable triggering of network sequences by single spikes. Dense, but weaker networks can give rise to different sequences when triggered. One of the most intriguing results of the paper is the interaction of sequences triggered by different single spikes that are part of a strong, sparse sub-network. These concurrent sequences appear to be separable and potentially supported a wide repertoire of response states to very targeted and combinatorially expressive inputs.
The work is careful and well-executed and the work will be of interest to systems and computational neuroscientists. In particular, the work speaks to how to reliably trigger a wide array of broad-scale population sequence patterns. This could be important for signaling salient, complex external stimuli, especially in a dynamic environment. The work will also be of interest to the machine learning community working on recurrent neural networks and their computational capacity.
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Reviewer #3 (Public Review):
Riquelme et al. develop a spiking neural network model based on experimental measurements from ex vivo turtle visual cortex (neuronal parameters, connectivity profiles, synaptic strength distributions). Within the constraints given, the connectivity is random. The analyses in the manuscript are based on multiple instantiations (300) of the network and multiple simulations of each. The principle finding is that, if a randomly selected excitatory neuron is induced to emit an action potential, a reliable sequence of spikes follows (in more than 90% of cases). They then examine the role of connectivity in this phenomenon, including the frequency of specific motifs in the spike cascade and the comparative role of strong and weak connections. In particular, the authors show that rare strong connections are vital …
Reviewer #3 (Public Review):
Riquelme et al. develop a spiking neural network model based on experimental measurements from ex vivo turtle visual cortex (neuronal parameters, connectivity profiles, synaptic strength distributions). Within the constraints given, the connectivity is random. The analyses in the manuscript are based on multiple instantiations (300) of the network and multiple simulations of each. The principle finding is that, if a randomly selected excitatory neuron is induced to emit an action potential, a reliable sequence of spikes follows (in more than 90% of cases). They then examine the role of connectivity in this phenomenon, including the frequency of specific motifs in the spike cascade and the comparative role of strong and weak connections. In particular, the authors show that rare strong connections are vital for producing (long) reliable sequences. The authors then examine how the sequences can be broken down into sub-sequences that may or may not occur for a given trigger. They show that the sub-sequences are characterized by strong internal connections (compared to those between sub-sequences). Moreover, they show that the spike sequence can be routed by exciting or depressing the 'gate' neurons (i.e. those at the beginning of a particular sub-sequence) raising the intriguing possibility of context-driven routing of activity. Finally, the authors demonstrate that their model has interesting combinatorial properties, as the results of triggering two sequences at once cannot be accounted for in a linear fashion. All in all, this is a solid piece of work with well-thought-through analyses which is an interesting contribution to the fundamental question of how the brain manages reliable computation in a noisy world.
Strengths
"Ensemble approach" I appreciated the approach to generate many networks from the same distributions rather than (as is often the case) basing all their conclusions on one instantiation. In general, the statistical rigour is high.
Well-chosen analyses to tease apart the relationships between structure and dynamics.
Figures (for the most part) clearly support the conclusions of the paper.
Weaknesses
The spontaneous activity of the network is extremely low, with [0.02 0.09] spks/s considered as a high activity range. Granted, this is based on ex vivo measurements. However, if this phenomenon is to be considered computationally relevant, as the authors claim, the paper should have examined the reliability of propagation and routing with in vivo activity levels.
The above weakness is a special case of the issue that the limits of applicability/robustness of results to model assumptions have not been well established. In particular, it is not clear how strong the strongest weights must be whilst still enabling long sequences, and what is the dependence of the results on the parameters of the distance-dependent connectivity.
The figures are too densely packed and many of the elements are too small or too fine to be distinguished, especially if your eyesight is not the greatest. Although many people read online, where zooming is possible, the aim should still be that all elements of the figure can be perceived by a person over 45 who has printed the paper on regular A4 paper.
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