Mathematical Modeling of Zebrafish Social Behavior in Response to Acute Caffeine Administration

Abstract

Zebrafish is a model organism that is receiving considerable attention in preclinical research. Particularly important is the use of zebrafish in behavioral pharmacology, where a number of high-throughput experimental paradigms have been proposed to quantify the effect of psychoactive substances consequences on individual and social behavior. In an effort to assist experimental research and improve animal welfare, we propose a mathematical model for the social behavior of groups of zebrafish swimming in a shallow water tank in response to the administration of psychoactive compounds to select individuals. We specialize the mathematical model to caffeine, a popular anxiogenic compound. Each fish is assigned to a Markov chain that describes transitions between freezing and swimming. When swimming, zebrafish locomotion is modeled as a pair of coupled stochastic differential equations, describing the time evolution of the turn-rate and speed in response to caffeine administration. Comparison with experimental results demonstrates the accuracy of the model and its potential use in the design of in-silico experiments.