Probabilistic Neural Coding from Deterministic Neural Dynamics: mathematics and biophysics of adaptive single neuron computation

Abstract

The basic unit of computation in the nervous system is the transformation of input into output spikes performed by an individual neuron. The spiking response of the neuron to a complex, time-varying input can be characterized with two different classes of models: nonlinear dynamical systems represent the detailed biophysical properties a neuron, and probabilistic black box coding models identify abstract representations of the computation performed. However, the relationships between biophysical mechanisms and neural coding properties have very rarely been resolved. Here, the focus is on the task of feature selection, where a neuron extracts and encodes from its complex inputs a small number of relevant signal components. Feature selection is generally adaptive: both the relevant features and the encoding depend on the background statistical context in which the signal appears. This thesis presents a theory of conditional dynamical processes that associate abstract representations of the signal with sub-ensembles of states of the corresponding dynamical system. The theory provides a bridge to use meth- ods from either coding or dynamics to simultaneously study both. The unifying framework is used to derive how the interactions of the statistical properties of the input and the neural dynamics determine which features of the input are encoded by spikes. Adaptation of the encoding to changes in input statistics is shown to arise from corresponding changes in how the state space of the nonlinear system is probed by the input. First, we identify the mechanisms of adaptive feature selection in integrate-and-fire mod- els. Then, we demonstrate that integrate-and-fire models without any additional currents can perform a novel type of stochastically-emergent perfect contrast gain control--a sophis- ticated adaptive computation. We identify the general dynamical principles responsible and design from first principles a nonlinear dynamical model that implements automatic gain control. We conclude by fitting models to experimental data and relating the models to measurable biophysical properties to demonstrate that our proposed theoretical mechanism is consistent with the adaptive gain control observed in the developing cortex.