A Synaptical Story of Persistent Activity with Graded Lifetime in a Neural System
Persistent activity refers to the phenomenon that cortical neurons keep firing even after the stimulus triggering the initial neuronal responses is moved. Persistent activity is widely believed to be the substrate for a neural system retaining a memory trace of the stimulus information. In a conventional view, persistent activity is regarded as an attractor of the network dynamics, but it faces a challenge of how to be closed properly. Here, in contrast to the view of attractor, we consider that the stimulus information is encoded in a marginally unstable state of the network which decays very slowly and exhibits persistent firing for a prolonged duration. We propose a simple yet effective mechanism to achieve this goal, which utilizes the property of short-term plasticity (STP) of neuronal synapses. STP has two forms, short-term depression (STD) and short-term facilitation (STF), which have opposite effects on retaining neuronal responses. We find that by properly combining STF and STD, a neural system can hold persistent activity of graded lifetime, and that persistent activity fades away naturally without relying on an external drive. The implications of these results on neural information representation are discussed.
Summary: The authors present a model of persistent activity in neural networks as typically observed in working memory tasks and modeled as attractor dynamics. The authors note the shortcomings of existing models, namely the reliance on implausible global excitatory or inhibitory signals to reset the network dynamics after settling into an attractor state and the superfluousness of such a stable attractor, since in working memory tasks, the dynamics need only persistent as long as the task requires, not indefinitely. In the proposed model, these issues are confronted by incorporating short term synaptic facilitation and depression into a network model. Using a mean-field approach, the authors identify stable fixed points of the rate dynamics and how these fixed-points change as a function of network connectivity and timescale parameters. Using this formalism, the authors identify a family of parameters for which the network exhibits only 1 true stable fixed point- corresponding to network quiescence- but also exhibits a second, "slow point", i.e. a point which under different network parameters would correspond to a 2nd unstable fixed point of the rate dynamics, but for the chosen parameters yields network dynamics that evolve extremely slowly towards the true, stable fixed point. The primary effect of this “slow point” is to create a quasi-stable firing rate, similar to the attractor dynamics of existing models, but different in that the dynamics will eventually collapse to the quiescent state. The authors illustrate the existence of this state over a range of timescales of the synaptic plasticity and instantiate the presented framework in a full, spiking neural network.Review: This is an exceptionally clear-written submission of great interest to the theoretical neuroscience community. It stands out compared to alternative work in attractor dynamics in that it assigns a useful computation role for short-term synaptic plasticity in generating these dynamics and for noting that real biological systems have limited use for “true” fixed-points. The authors eloquently note that neural dynamics need only remain stable for finite, not infinite time, and propose a biologically plausible mechanism to both generate and terminate this quasi-stability. The reduced, mean-field model is clearly presented and illustrates quite nicely the relationship between network parameters and the stability of the slow dynamics. All the figures positively contribute to the submission and create a simple visual representation of the text’s mathematical details. The authors do a great job of explaining the opposing roles facilitation and depression play in generating the slow network dynamics, as most clearly displayed in Figure 4. All-around a solid submission, however, two small points for improvement. 1. The authors claim that the spiking model exhibits irregular, independent activity (critical to invoke a mean-field assumption)  which is difficult to see in Figure 5a, and upon closer inspection, appears to be untrue. As best as I can tell, the spike trains appear extremely regular, and even begin to synchronize a bit (as can be seen in the firing rate, around 2.75 seconds in Figure 5B). The main analytical results seem to hold true as presented here, but rely on this assumption. Clearly displaying the irregularity and independence in the spiking simulations would improve the submission. 2. The main analytical results are derived under the assumption that the synaptic plasticity variables have reached a steady-state, despite the fact that, as the authors note, these variables evolve slowly compared to the rate. A discussion of the conditions under which this assumption is valid would be helpful.