Impulsive system modelling in neurophysiology
by
S. A. Belbas
Mathematics Dept, University of Alabama, Tuscaloosa, AL. 35487-0350. USA.
Coauthors: S. A. Belbas and Sunghee Kim

Several models arising in neurophysiology involve coupling among periodic or intermitent signals, that can be specified by a finite or countable set of parameters, and generic continuous-time signals in continuous-time differential or integro-differential equations. We propose a model based on the theory of impulsive differential equations, for biochemical reactions described by nonlinear differential equations, when the input is a train of action potentials or a series of calcium spikes. One of the systems we introduce is a novel model for the phosphorylation and dephosphorylation of proteins under the stimulation of a train of action potentials.We prove and analyze the following: (i) an identification algorithm for the unknown parameters of the model; (ii) the frequency encoding of the applied electrical signal via protein phosphorylation and dephosphorylation; (iii) the effect of different stimulation patterns on the amplitude of the oscillations of the concentration of the percentage of phosphorylated protein.

Date received: February 25, 2003