Fred Wolf, Max Planck, Dynamical entropy production in recurrent neuronal circuits
Max Planck Institute for Dynamics and Self-Organization
Neurons in the cerebral cortex fire action potentials in highly irregular, seemingly random sequences. Since neurons in isolation reliably respond to the repeated injection of identical temporally varying inputs, irregular activity in the cortex is not believed to result from a randomness in the spike generating mechanism, but rather from strongly fluctuating synaptic inputs. Several explanations for the origin of such fluctuating inputs have been proposed. The prevailing explanation is a dynamic balance between excitatory and inhibitory inputs, also known as the balanced state of cortical networks. Such a balance in neuronal circuits has been demonstrated experimentally in vitro and in vivo. Its statistical characteristics have been extensively studied theoretically. The dynamical nature of the balanced state, however, remained controversial and poorly understood.
Here, we characterize the dynamical properties of balanced model circuits compose of different single neuron models. We obtain the complete spectrum of Lyapunov exponents, the Kolgomorov-Sinai entropy rate and attractor dimension and establish the extensive nature of these properties. In stark contrast to statistical properties of balanced state networks (such as distributions of spike train cv and unit firing rates), their collective dynamics turns out to be extremely sensitive to minute details of the single neuron dynamics. Intriguingly, we find that modifying the time scale of action potential initiation can reduce dynamical entropy production in the network by orders of magnitude. In models of identical topological circuit structure, dynamical entropy production can be tuned from about one bit of information loss per neuron and spike to arbitrary small values. Very crisp action potential generators can even render the irregular network dynamics formally stable. Our results indicate that information flow through complex neural circuits should be expected extremely sensitive to minute features of the single neuron dynamics.
Location: Carl Icahn Lab 101
Date/Time: 11/19/12 at 12:00 pm - 11/19/12 at 1:00 pm
Department: Lewis-Sigler Institute