Abstract
Sperm have thin structures known as flagella whose motion must be regulated in order to reach the egg for fertilization. Large numbers of sperm are typically needed in this process and some species have sperm that exhibit collective or aggregate motion when swimming in groups. The purpose of this study is to model planar motion of flagella in groups to explore how collective motion may arise in three-dimensional fluid environments. We use the method of regularized Stokeslets and a three-dimensional preferred curvature model to simulate groups of undulating flagella, where flagellar waveforms are modulated via hydrodynamic coupling with other flagella and surfaces. We find that collective motion of free-swimming flagella is an unstable phenomenon in long-term simulations unless there is an external mechanism to keep flagella near each other. However, there is evidence that collective swimming can result in significant gains in velocity and efficiency. With the addition of an ability for sperm to attach and swim together as a group, velocities and efficiencies can be increased even further, which may indicate why some species have evolved mechanisms that enable collective swimming and cooperative behavior in sperm.
Highlights
Many biological cell types rely upon tail-like appendages known as flagella to propel them towards optimal environments or environments where the cell serves a specific function
Cells have a single flagellum but flagellar motion may be impacted by neighboring sperm or other structures in the environment
Each simulation was run for many beats in order to observe motility patterns that arise in populations over long timescales
Summary
Many biological cell types rely upon tail-like appendages known as flagella to propel them towards optimal environments or environments where the cell serves a specific function. These flagella must typically move through highly viscous fluids, perhaps in the presence of other objects and cells within the fluid. Sperm must maneuver through a variety of environments in order to reach the egg and this process involves a complex choreography of biochemical reactions that mediate changes in motility patterns. These motility patterns are undulatory and often characterized by a nearly planar, sinusoidal beat form, though helical or “Figure 8”
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