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Volume 4,     Number 2,     Spring 1996

 

PARAMETER ESTIMATION IN
A REACTION-DIFFUSION MODEL
FOR SYNAPTIC TRANSMISSION
AT A NEUROMUSCULAR JUNCTION
J.C. CLEMENTS AND B.R. SMITH

Abstract. A reaction-diffusion system with nonlinear time-dependent boundary conditions is developed to model the uptake and release of neural transmitter at an invertebrate neuromuscular junction. The system of differential equations is transformed into an equivalent normalized, nonlinear integrodifferential equation problem which is solved using standard techniques for nonlinear Volterra integral equations. A statistical procedure for estimating the model parameters by fitting the model to specific experimental data is described and the goodness of fit of the model to the data in the presence of correlated errors is assessed.

 

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