Functional Identification of Spike-Processing Neural Circuits

Functional Identification of Spike-Processing Neural Circuits
Aurel A. Lazar and Yevgeniy B. Slutskiy
Neural Computation, MIT Press, February 2014.


We introduce a novel approach for a complete functional identification of
biophysical spike-processing neural circuits. The circuits considered accept
multidimensional spike trains as their input and comprise a multitude of
temporal receptive fields and conductance-based models of action potential
generation. Each temporal receptive field describes the spatiotemporal
contribution of all synapses between any two neurons and incorporates the
(passive) processing carried out by the dendritic tree. The aggregate dendritic
current produced by a multitude of temporal receptive fields is encoded into a
sequence of action potentials by a spike generator modeled as a nonlinear
dynamical system. Our approach builds on the observation that during any
experiment, an entire neural circuit, including its receptive fields and
biophysical spike generators, is projected onto the space of stimuli used to
identify the circuit. Employing the reproducing kernel Hilbert space (RKHS) of
trigonometric polynomials to describe input stimuli, we quantitatively describe
the relationship between underlying circuit parameters and their projections. We
also derive experimental conditions under which these projections converge to
the true parameters. In doing so, we achieve the mathematical tractability
needed to characterize the biophysical spike generator and identify the
multitude of receptive fields. The algorithms obviate the need to repeat
experiments in order to compute the neurons' rate of response, rendering our
methodology of interest to both experimental and theoretical neuroscientists.

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