In-silico experiments of zebrafish behaviour: modeling swimming in three dimensions

Mathematical modeling of zebrafish social behavior in response to acute caffeine administration

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.

Biohybrid soft robots with self-stimulating skeletons

Bioinspired hybrid soft robots that combine living and synthetic components are an emerging field in the development of advanced actuators and other robotic platforms (i.e., swimmers, crawlers, and walkers). The integration of biological components offers unique characteristics that artificial materials cannot precisely replicate, such as adaptability and response to external stimuli. Here, we present a skeletal muscle-based swimming biobot with a three-dimensional (3D)-printed serpentine spring skeleton that provides mechanical integrity and self-stimulation during the cell maturation process. The restoring force inherent to the spring system allows a dynamic skeleton compliance upon spontaneous muscle contraction, leading to a cyclic mechanical stimulation process that improves the muscle force output without external stimuli. Optimization of the 3D-printed skeletons is carried out by studying the geometrical stiffnesses of different designs via finite element analysis. Upon electrical actuation of the muscle tissue, two types of motion mechanisms are experimentally observed: directional swimming when the biobot is at the liquid-air interface and coasting motion when it is near the bottom surface. The integrated compliant skeleton provides both the mechanical self-stimulation and the required asymmetry for directional motion, displaying its maximum velocity at 5 hertz (800 micrometers per second, 3 body lengths per second). This skeletal muscle-based biohybrid swimmer attains speeds comparable with those of cardiac-based biohybrid robots and outperforms other muscle-based swimmers. The integration of serpentine-like structures in hybrid robotic systems allows self-stimulation processes that could lead to higher force outputs in current and future biomimetic robotic platforms.

Model-based feedback control of live zebrafish behavior via interaction with a robotic replica

The possibility of regulating the behavior of live animals using biologically-inspired robots has attracted the interest of biologists and engineers for over twenty-five years. From early work on insects to recent endeavors on mammals, we have witnessed fascinating applications that have pushed forward our understanding of animal behavior along new directions. Despite significant progress, most of the research has focused on open-loop control systems, in which robots execute predetermined actions, independent of the animal behavior. We integrate mathematical modeling of social behavior toward the design of realistic feedback laws for robots to interact with a live animal. In particular, we leverage recent advancements in data-driven modeling of zebrafish behavior. Ultimately, we establish a novel robotic platform that allows real-time actuation of a biologically-inspired 3D-printed zebrafish replica to implement model-based control of animal behavior. We demonstrate our approach through a series of experiments, designed to elucidate the appraisal of the replica by live subjects with respect to conspecifics and to quantify the biological value of closed-loop control.

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.

Data-driven modeling of zebrafish behavioral response to acute caffeine administration

Over the last thirty years, we have witnessed a dramatic rise in the use of zebrafish in preclinical research. Every year, more than 5000 technical papers are published about zebrafish, many of them seeking to explain the underpinnings of anxiety through animal testing. In-silico experiments could significantly contribute to zebrafish research and welfare, by offering new means to support the 3Rs principles of replacement, reduction, and refinement. Here, we propose a data-driven modeling framework to predict the anxiety-related behavioral response of zebrafish to acute caffeine administration. The modeling framework unfolds along a two-time-scale dichotomy to capture freezing behavior along a slow temporal scale and burst-and-coast locomotion at a fast time-scale. Anchored in the theory of Markov chains and stochastic differential equations, we demonstrate a parsimonious, yet robust, modeling framework to accurately simulate experimental observations of zebrafish treated at different caffeine concentrations. Our results complement recent modeling efforts, laying the foundations for conducting in-silico experiments in zebrafish behavioral pharmacology.

A Comparison of Individual Learning and Social Learning in Zebrafish Through an Ethorobotics Approach

Social learning is ubiquitous across the animal kingdom, where animals learn from group members about predators, foraging strategies, and so on. Despite its prevalence and adaptive benefits, our understanding of social learning is far from complete. Here, we study observational learning in zebrafish, a popular animal model in neuroscience. Toward fine control of experimental variables and high consistency across trials, we developed a novel robotics-based experimental test paradigm, in which a robotic replica demonstrated to live subjects the correct door to join a group of conspecifics. We performed two experimental conditions. In the individual training condition, subjects learned the correct door without the replica. In the social training condition, subjects observed the replica approaching both the incorrect door, to no effect, and the correct door, which would open after spending enough time close to it. During these observations, subjects could not actively follow the replica. Zebrafish increased their preference for the correct door over the course of 20 training sessions, but we failed to identify evidence of social learning, whereby we did not register significant differences in performance between the individual and social training conditions. These results suggest that zebrafish may not be able to learn a route by observation, although more research comparing robots to live demonstrators is needed to substantiate this claim.

The zebrafish subcortical social brain as a model for studying social behavior disorders

Social behaviors are essential for the survival and reproduction of social species. Many, if not most, neuropsychiatric disorders in humans are either associated with underlying social deficits or are accompanied by social dysfunctions. Traditionally, rodent models have been used to model these behavioral impairments. However, rodent assays are often difficult to scale up and adapt to high-throughput formats, which severely limits their use for systems-level science. In recent years, an increasing number of studies have used zebrafish (Danio rerio) as a model system to study social behavior. These studies have demonstrated clear potential in overcoming some of the limitations of rodent models. In this Review, we explore the evolutionary conservation of a subcortical social brain between teleosts and mammals as the biological basis for using zebrafish to model human social behavior disorders, while summarizing relevant experimental tools and assays. We then discuss the recent advances gleaned from zebrafish social behavior assays, the applications of these assays to studying related disorders, and the opportunities and challenges that lie ahead.

Detecting intermittent switching leadership in coupled dynamical systems

Leader-follower relationships are commonly hypothesized as a fundamental mechanism underlying collective behaviour in many biological and physical systems. Understanding the emergence of such behaviour is relevant in science and engineering to control the dynamics of complex systems toward a desired state. In prior works, due in part to the limitations of existing methods for dissecting intermittent causal relationships, leadership is assumed to be consistent in time and space. This assumption has been contradicted by recent progress in the study of animal behaviour. In this work, we leverage information theory and time series analysis to propose a novel and simple method for dissecting changes in causal influence. Our approach computes the cumulative influence function of a given individual on the rest of the group in consecutive time intervals and identify change in the monotonicity of the function as a change in its leadership status. We demonstrate the effectiveness of our approach to dissect potential changes in leadership on self-propelled particles where the emergence of leader-follower relationship can be controlled and on tandem flights of birds recorded in their natural environment. Our method is expected to provide a novel methodological tool to further our understanding of collective behaviour.

Data-driven modelling of social forces and collective behaviour in zebrafish

Zebrafish are rapidly emerging as a powerful model organism in hypothesis-driven studies targeting a number of functional and dysfunctional processes. Mathematical models of zebrafish behaviour can inform the design of experiments, through the unprecedented ability to perform pilot trials on a computer. At the same time, in-silico experiments could help refining the analysis of real data, by enabling the systematic investigation of key neurobehavioural factors. Here, we establish a data-driven model of zebrafish social interaction. Specifically, we derive a set of interaction rules to capture the primary response mechanisms which have been observed experimentally. Contrary to previous studies, we include dynamic speed regulation in addition to turning responses, which together provide attractive, repulsive and alignment interactions between individuals. The resulting multi-agent model provides a novel, bottom-up framework to describe both the spontaneous motion and individual-level interaction dynamics of zebrafish, inferred directly from experimental observations.

A new paradigm in modelling the evolution of a stand via the distribution of tree sizes

Our study focusses on investigating a modern modelling paradigm, a bivariate stochastic process, that allows us to link individual tree variables with growth and yield stand attributes. In this paper, our aim is to introduce the mathematics of mixed effect parameters in a bivariate stochastic differential equation and to describe how such a model can be used to aid our understanding of the bivariate height and diameter distribution in a stand using a large dataset provided by the Lithuanian National Forest Inventory (LNFI). We examine tree height and diameter evolution with a Vasicek-type bivariate stochastic differential equation and mixed effect parameters. It is focused on demonstrating how new developed bivariate conditional probability density functions allowed us to calculate the evolution, in the forward and backward directions, of the mean diameter, height, dominant height, assortments, stem volume of a stand and uncertainties in these attributes for a given stand age. We estimate the parameters by considering discrete samples of the diameter and height at a given age and by using an approximated maximum likelihood procedure. The model performance criteria for the height and diameter growth models include statistical indexes and an analysis of residuals.

Symbolic dynamics of animal interaction

Since its introduction nearly two decades ago, transfer entropy has contributed to an improved understanding of cause-and-effect relationships in coupled dynamical systems from raw time series. In the context of animal behavior, transfer entropy might help explain the determinants of leadership in social groups and elucidate escape response to predator attacks. Despite its promise, the potential of transfer entropy in animal behavior is yet to be fully tested, and a number of technical challenges in information theory and statistics remain open. Here, we examine an alternative approach to the computation of transfer entropy based on symbolic dynamics. In this context, a symbol is associated with a specific locomotory bout across two or more consecutive time instants, such as reversing the swimming direction. Symbols encapsulate salient locomotory patterns and the associated permutation transfer entropy quantifies the ability to predict the patterns of an individual given those of another individual. We demonstrate this framework on an existing dataset on fish, for which we have knowledge of the underlying cause-and-effect relationship between the focal subject and the stimulus. Symbolic dynamics offers an intuitive and robust approach to study animal behavior, which could enable the inference of causal relationship from noisy experimental observations of limited duration.