Abstract
Although hydrodynamic interactions and cooperative swimming of mammalian sperm are observed, the key factors that lead to attraction or repulsion in different confined geometries are not well understood. In this study, we simulate the 3-dimensional fluid-structure interaction of pairs of swimmers utilizing the Method of Regularized Stokeslets, accounting for a nearby wall via a regularized image system. To investigate emergent trajectories of swimmers, we look at different preferred beat forms, planar or quasi-planar (helical with unequal radii). We also explored different initializations of swimmers in either the same plane (co-planar) or with centerlines in parallel planes. In free space, swimmers with quasi-planar beat forms and those with planar beat forms that are co-planar exhibit stable attraction. The swimmers reach a maintained minimum distance apart that is smaller than their initial distance apart. In contrast, for swimmers initialized in parallel beat planes with a planar beat form, we observe alternating periods of attraction and repulsion. When the pairs of swimmers are perpendicular to a nearby wall, for all cases considered, they approach the wall and reach a constant distance between swimmers. Interestingly, we observe sperm rolling in the case of swimmers with preferred planar beat forms that are initialized in parallel beat planes and near a wall.
Highlights
The tumultuous journey of the mammalian sperm involves navigating the female reproductive tract
Using the method of regularized Stokeslets with an image system to account for the wall, we study swimmers propagating both preferred planar and quasi-planar beat forms
The baseline parameters used for the numerical methods and preferred beat form are given in Table 1; we assume that in a given simulation, all sperm flagella have the same preferred configuration given by Eqs 3, 4, with values in the range of mammalian sperm [10]
Summary
The tumultuous journey of the mammalian sperm involves navigating the female reproductive tract. Even though millions of sperm are deposited at the beginning of the tract, only a select few are able to traverse the long distances and overcome all of the hurdles to make it to the egg [1, 2]. Sperm progress through a wide range of environments and their motility patterns must change in response to various chemical and physical cues; this could act to group sperm together or separate them [3,4,5]. A sperm senses other nearby sperm and surfaces via hydrodynamic interactions, which results in a wide range of collective motion, from alignment in trains and vortices to synchronization and attraction [6,7,8]. Sperm are able to propel themselves through different fluid environments by bending their elastic and flexible flagellum or tail. The emergent beat form and trajectory will depend on the local fluid environment and the particular
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