Temporal resolution of spike coding in feedforward networks with signal convergence and divergence

Abstract

Convergent and divergent structures in the networks that make up biological brains are found across many species and brain regions at various spatial scales. Neurons in these networks fire action potentials, or "spikes", whose precise timing is becoming increasingly appreciated as large sources of information about both sensory input and motor output. While previous theories on coding in convergent and divergent networks have largely neglected the role of precise spike timing, our model and analyses place this aspect at the forefront. For a suite of stimuli with different timescales, we demonstrate that structural bottlenecks- small groups of neurons post-synaptic to network convergence - have a stronger preference for spike timing codes than expansion layers created by structural divergence. Additionally, we found that a simple network model based on convergence and divergence ratios of a hawkmoth (Manduca sexta) nervous system can reproduce the relative contribution of spike timing information in its motor output, providing testable predictions on optimal temporal resolutions of spike coding across the moth sensory-motor pathway at both the single-neuron and population levels. Our simulations and analyses suggest a relationship between the level of convergent/divergent structure present in a feedforward network and the loss of stimulus information encoded by its population spike trains as their temporal resolution decreases, which could be tested experimentally across diverse neural systems in future studies. We further show that this relationship can be generalized across different spike-generating models and measures of coding capacity, implying a potentially fundamental link between network structure and coding strategy using spikes. Author summaryWithin the complex anatomy of the brain, there are certain structures that appear more often than expected. One example of this is when large populations of neurons connect to much smaller populations, and vice versa. We refer to these structural patterns as network convergence and divergence; they are observed in systems like the cerebellum, insect olfactory networks, visuomotor pathways, and the early visual system of mammals. Despite the ubiquity of this connectivity pattern, we are only beginning to understand its functional implications from a computational point of view. Here, we construct and analyze mathematical models of spiking neural networks to understand how convergent and divergent structure shapes the way that information is represented in each part of the network, as a function of the temporal resolution of population spiking activity. We then developed a simple feedforward network model of the visuomotor pathway of a moth, with similar convergent/divergent network structure, and reproduce a similar proportion of spike timing to spike count information as observed experimentally. Our results form predictions about spike coding in populations previously unobserved in experiment.