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Sherrington's Model of Successive Induction for Comparative Analysis of Zebrafish Motor Response
Citation:
Ball, K. AND S. Padilla. Sherrington's Model of Successive Induction for Comparative Analysis of Zebrafish Motor Response. Tutorial Workshop on Parameter Estimation for Biological Models, Raleigh, NC, July 28 - 29, 2016.
Impact/Purpose:
This work explores a mathematical model to describe chemical effects on fish locomotor activity. It will be used to calculate the potency of environmental chemical effects on fish behavior. This will lead to an improvement in the ability to test and prioritize chemicals for their ability to result in neurotoxicity.
Description:
The responses in motor activity of zebrafish to sudden changes in lighting conditions may be modeled by Sherrington’s model of successive induction. Fish left in the dark exhibit very little motion, when exposed to light zebrafish motion increases towards an apparent horizontal asymptote, and when lights are turned off again motor activity spikes before exponentially decaying back to zero. The full Sherrington model is a system of two first order linear nonhomogeneous ordinary differential equations with piecewise defined parameters depending on the lighting condition in a given interval. We suggest a simplification of the theoretical model to one equation and investigate a population-aggregated longitudinal analysis from maximum likelihood estimates of model parameters for groups of multiple fish.