Navigation of sperm cells in scalar turbulence: Theory of sperm chemotaxis in turbulent flow and its adaptation to dynamic concentration and velocity gradients

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Chemotaxis - the navigation of biological cells guided by chemical gradients - is crucial for bacterial foraging, immune responses, and guidance of sperm cells to the egg during fertilization. Cellular navigation represents a model system for the physics of autonomous motility at the microscale and its control by sensory cues. Previous work focused predominantly on idealized conditions of perfect chemical gradients. Yet, natural environments are characterized by perturbations, which distort extracellular chemical gradients. A prototypical example are turbulent flows of the ocean.In the model species of marine invertebrates, sperm and egg cells are directly spawned into open water, where sperm cells employ a dedicated gradient-sensing algorithm along helical paths to steer up concentration gradients of signaling molecules released by the egg. Small-scale turbulence distorts these concentration gradients and convects swimming cells. We propose to develop a theory of sperm chemotaxis in turbulent flow conditions, by combining an existing simulation framework of helical chemotaxis with hydrodynamic computations of turbulent advection, which is novel. Using this model system, we will target a gap in knowledge between (i) turbulent stirring of passive particles and (ii) chemotaxis of actively swimming cells studied previously in the absence of external flow. Thereby, we will address a fundamental and largely unexplored question: how biological cells navigate in dynamic and disordered environments. We will elucidate the competition between positive and negative effects of turbulence, i.e. faster establishment of concentration gradients and random distortion of these gradients. By this, we will confirm and explain the existence of an optimal turbulence strength that maximizes the probability of sperm-egg encounters. On a finer scale, our preliminary simulations suggest that small-scale turbulence creates extended filaments of high concentration along which sperm cell can 'surf' towards the egg. We will understand the mechanism of 'filament surfing' in terms of chemotactic steering and rotation by local shear flow. Next, we will study trapping of sperm cells in local concentration maxima and stochastic transitions between such maxima, and its dependence on the spatial and temporal resolution of gradient sensing. Thereby, we expect genuine physical insight into the exploration/exploitation trade-off in the context of cellular navigation. Previously, we pioneered the theory of helical chemotaxis, which represents one out of three basic gradient-sensing strategies of biological cells. Additionally, our group established a solid competence in hydrodynamic simulations. The proposed project will combine these two research fields into a new direction. Thereby, we will provide a concise understanding of cellular navigation in dynamic and disordered external fields in an important model system.