Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train.
We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.
Rangan
Aaditya V
AV
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA.
Kovacic
Gregor
G
Cai
David
D
D000818:Animals; D003198:Computer Simulation; D004594:Electrophysiology; D019277:Entropy; D006801:Humans; D007700:Kinetics; D008433:Mathematics; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D011336:Probability; D013997:Time Factors