Mathematical modeling of navigational decisions based on intensity versus directionality in Drosophila larval phototaxis

Abstract

Organisms use environmental cues for directed navigation. Depending on the sensory modality and complexity of the involved sensory organs, different types of information may be processed. Understanding the basic logic behind navigational decisions critically depends on the complexity of the nervous system. Due to the comparably simple organization of the nervous system of the fruit fly larva, it stands as a powerful model to study decision-making processes that underlie directed navigation. Here, we formulate a stochastic method based on biased Markov chains to model the behavioral basis of negative phototaxis. We have quantitatively measured phototaxis in response to defined sensory inputs. We find that larvae make navigational decisions by taking into account both light intensities and its spatial gradients, and our model allows us to quantify how larvae minimize their exposure to light intensity and at the same time maximize their distance to the source of light. The response to the light field is a non-linear response and saturates above an intensity threshold. Our mathematical model simulates and predicts larval behavioral dynamics only using light intensity and directionality as input parameters. Moreover, it allows us to evaluate the relative importance of these two factors governing visual navigation. The model has been validated with experimental biological data yielding insight into the strategy that larvae use to achieve their goal with respect to the navigational cue of light, paving the way for future work to study the role of the different neuronal components in this mechanism.\n\nAuthor SummaryNavigational decision-making is a complex process during which the nervous system is able to decipher external input through molecular and cellular mechanisms to produce a spatially-coordinated behavioral output. Drosophila larvae provide an excellent model to understand these decision-making mechanisms as we can measure the behavioral output (larval navigation) in response to quantifiable external input (different light conditions). We have performed experiments to quantify larval light avoidance in order to subsequently design a mathematical model that quantitatively reproduces larval behavior. Our results allow us to characterize the relative importance of light intensity and directionality and yield insight into the neural algorithms used in the decision-making mechanism of larval phototaxis.