Spike-to-Spike Correlation and Neural Coding: Basic Roles for Membrane and Circuit Dynamics

Correlations among neural spike times are ubiquitous, and questions of how these correlations develop, and of the impact they have on the neural code, are central in neuroscience. Their analysis also poses rich applied mathematics problems. We address two of the most basic ones here.

First, we ask: How do correlations among different neurons depend on the cells' operating range -- their rate and regularity of spiking? We use linear response calculations, asymptotics, and in vitro experiments to show that correlations between pairs of neurons vary sharply with their firing rates, almost universally. We illustrate the consequences via Fisher information, which quantifies the accuracy of encoding.

Next, we ask: How do correlations among different trials depend on architecture of neural circuits? (Here, the same stimulus is received by the circuit on each 'trial.') We take a first step toward the answer by identifying a surprising role for some, but not all, feedback connections in creating positive (and hence decorrelating) Lyapunov exponents.

This is joint work with Jaime de la Rocha, Brent Doiron, Kreso Josic, Kevin Lin, Alex Reyes, and Lai-Sang Young.