Chemotaxis of Sperm Cells

Sperm cells are guided to the egg by chemoattractants in many species. Sperm cells are propelled in a liquid by the regular beat of their flagellum. In the presence of a concentration gradient of a chemoattractant, they can steer upwards the concentration gradient, a process called chemotaxis. Eggs release chemoattractants to guide the sperm cells to the egg. Sperm chemotaxis is best studied experimentally in the sea urchin. There, specific receptors in the flagellar membrane of the sperm cells are activated upon binding of chemoattractant molecules and trigger a signaling cascade which ultimately changes the activity of the molecular motors which drive the flagellar beat and result in a swimming response. Sea urchin sperm cells swim along circular and helical paths. Sperm cells of the sea urchin and several other species swim along helical paths far from boundary surfaces in the absence of chemoattractant. In a two-dimensional experimental geometry, sperm swimming paths are planar circles. The non-zero curvature of their swimming paths is a direct consequence of an asymmetry of their flagellar beat. In a concentration gradient of chemoattractant, sperm swimming path are drifting circles in two dimensions and bend helices in three dimensions. What is the working mechanism of sperm chemotaxis? In this thesis, we develop a theoretical description of sperm chemotaxis which can be subsumed as follows: While swimming along an approximately circular path in a concentration gradient a sperm cell traces a periodic concentration stimulus from the concentration field that has the frequency of circular swimming. The chemotactic signaling system processes this stimulus and causes a periodic modulation of the curvature of the swimming path which then gives rise to a swimming path which is a drifting circle. The relative direction of the drift with respect to the gradient direction is determined by the phase shift between the stimulus and the curvature oscillations. This picture is in perfect agreement with recent experimental findings. The mechanism is more general and also works in three dimensions for swimming along helical paths. Our results. Our theoretical description of sperm chemotaxis clarifies the concepts underlying sperm chemotaxis. In particular, we derive the role of internal timing of the chemotactic signaling system for sperm chemotaxis. We conclude that sampling a concentration field along circular and helical paths is a robust strategy for chemotaxis that does not require fine-tuning of parameters and which works reliable also in the presence of fluctuations. In a last chapter of this thesis, we discuss sperm chemotaxis in the more general context of an abstract search problem