Modeling multi-sensory feedback control of zebrafish in a flow

Understanding how animals navigate complex environments is a fundamental challenge in biology and a source of inspiration for the design of autonomous systems in engineering. Animal orientation and navigation is a complex process that integrates multiple senses, whose function and contribution are yet to be fully clarified. Here, we propose a data-driven mathematical model of adult zebrafish engaging in counter-flow swimming, an innate behavior known as rheotaxis. Zebrafish locomotion in a two-dimensional fluid flow is described within the finite-dipole model, which consists of a pair of vortices separated by a constant distance. The strength of these vortices is adjusted in real time by the fish to afford orientation and navigation control, in response to of the multi-sensory input from vision, lateral line, and touch. Model parameters for the resulting stochastic differential equations are calibrated through a series of experiments, in which zebrafish swam in a water channel under different illumination conditions. The accuracy of the model is validated through the study of a series of measures of rheotactic behavior, contrasting results of real and in-silico experiments. Our results point at a critical role of hydromechanical feedback during rheotaxis, in the form of a gradient-following strategy.Author summary: The astounding feats of animal orientation and navigation have fascinated scientists and engineers for decades. The refined and elegant processes of orientation and navigation are generally thought to be the outcome of a complex feedback process, which involves the integration of multiple cues gathered from the surroundings. Fish rheotaxis is an innate behavior through which an animal is able to orient itself and swim against a current, even in the absence of visual cues. To date, little is known about the information pathways that underlie this behavior and how they are integrated. To help address this challenge, we propose a data-driven mathematical model of rheotaxis in zebrafish— an emerging species of choice in biomedical research. Our model explains how zebrafish make use of visual, hydrodynamic, and tactile cues in a feedback loop to adjust their heading and speed during swimming. We validate the accuracy of our model by comparing real and synthetic data across two experimental conditions, in which we vary the illumination of a water channel. Our results demonstrate how a simple, yet effective, feedback control mechanism can explain a complex process such as rheotaxis.