Single neuron local rational arithmetic revealed in phase space of input conductances

Abstract

We present a phase space analysis to explore the potential of single neuron local arithmetic operations on its input conductances. This analysis was conducted first by deriving a rational function model of local spatial summation by using the equivalent circuits for steady-state membrane potentials. It is shown that developed functional phases exist in the space of input conductances, where a single neuron's local operation on input conductances can be described in terms of a set of well-defined arithmetic functions. It is further suggested that this single neuron local rational arithmetic is programmable, in the sense that the selection of these functional phases can be effectively instructed by presynaptic activities. This programmability adds the degree of freedom in a single neuron's ability to process the input information.

Multi-mode single neuron arithmetics and logics

“…We studied the phase structure of mapping from gated conductances(G) to the local membrane potentials(V), and the transition from membrane potentials(V) to gated conductance((=) both in arithmetic and logic models. Starting with a pavement of membrane using a simplified circuit model, a rational function model was formulated as a general relation between the gated conductances and postsynaptic potentials [7,81, that is:…”