Complementarity of Spike- and Rate-Based Dynamics of Neural Systems

Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other. Author Summary: We develop and demonstrate a model that allows us to examine how the predictions of spiking and rate-based models of neurons and their interactions are related. First, the behavior of a chain of neurons is explored by simulating each spiking neuron and spike-mediated interactions between neurons individually. Second, the same chain is studied using approximations based on the firing rate of the neurons. The predictions for these two approaches are closely compared and it is found that the simpler, rate-based approach captures the major system behaviors of the spike-based approach, namely spiking rates and modulations in those rates. Strong interactions between these modes take place when the frequency of one mode is an integer or half-integer multiple of the frequency of the other mode.