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Hyperactivation in mammalian sperm is characterized by highly asymmetrical waveforms and an increase in the amplitude of flagellar bends. It is important for the sperm to be able to achieve hyperactivated motility in order to reach and fertilize the egg. Calcium (Ca2+) dynamics are known to play a large role in the initiation and maintenance of hyperactivated motility. Here we present an integrative model that couples the CatSper channel mediated Ca2+ dynamics of hyperactivation to a mechanical model of an idealized sperm flagellum in a 3-d viscous, incompressible fluid. The mechanical forces are due to passive stiffness properties and active bending moments that are a function of the local Ca2+ concentration along the length of the flagellum. By including an asymmetry in bending moments to reflect an asymmetry in the axoneme’s response to Ca2+, we capture the transition from activated motility to hyperactivated motility. We examine the effects of elastic properties of the flagellum and the Ca2+ dynamics on the overall swimming patterns. The swimming velocities of the model flagellum compare well with data for hyperactivated mouse sperm.

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CatSpers are calcium (Ca(2+)) channels that are located along the principal piece of mammalian sperm flagella and are directly linked to sperm motility and hyperactivation. It has been observed that Ca(2+) entry through CatSper channels triggers a tail to head Ca(2+) propagation in mouse sperm, as well as a sustained increase of Ca(2+) in the head. Here, we develop a mathematical model to investigate this propagation and sustained increase in the head. A 1-d reaction-diffusion model tracking intracellular Ca(2+) with flux terms for the CatSper channels, a leak flux, and plasma membrane Ca(2+) clearance mechanism is studied. Results of this simple model exhibit tail to head Ca(2+) propagation, but no sustained increase in the head. Therefore, in this model, a simple plasma membrane pump-leak system with diffusion in the cytosol cannot account for these experimentally observed results. It has been proposed that Ca(2+) influx from the CatSper channels induce additional Ca(2+) release from an internal store. We test this hypothesis by examining the possible role of Ca(2+) release from the redundant nuclear envelope (RNE), an inositol 1,4,5-trisphosphate (IP(3)) gated Ca(2+) store in the neck. The simple model is extended to include an equation for IP(3) synthesis, degradation, and diffusion, as well as flux terms for Ca(2+) in the RNE. When IP(3) and the RNE are accounted for, the results of the model exhibit a tail to head Ca(2+) propagation as well as a sustained increase of Ca(2+) in the head.