Viscoelastic Effects on Emergent Oscillations of Elastic Filament Models with Motor Activity Regulation.*

Abstract: It is well know that microorganisms, such as bacteria and eukaryotes, often move in intricate environments experiencing mechano-chemical dynamics. These environments consist of rheologically complex substances such as mucus and other biofilms that are more complicated than water. Spermatozoa (sperm), for example, swim in viscoelastic mucus via deformations of their flagella, which are slender threadlike structures that are powered by internal molecular motors. The motor activity generates flagellar bending, resulting in an undulatory beat. The effects of a fading-memory fluid on emergent properties of these spontaneous oscillations are not entirely known. Here we combine analysis with numerical simulations of finite-length, elastic filaments subject to motor activity regulation to elucidate the Hopf bifurcation that occurs with increased motor activity in a viscoelastic fluid. Additionally, we determine characteristics of the flapping motion, specifically frequency and amplitude changes and how those changes nonlinearly depend on motor activity as well as fluid elasticity.

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