Gallagher Meurig T, Kirkman-Brown Jackson C, Smith David J
Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham B15 2TT, UK.
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK.
PNAS Nexus. 2023 Mar 9;2(3):pgad072. doi: 10.1093/pnasnexus/pgad072. eCollection 2023 Mar.
Flagellar motility is critical to natural and many forms of assisted reproduction. Rhythmic beating and wave propagation by the flagellum propels sperm through fluid and enables modulation between penetrative progressive motion, activated side-to-side yaw and hyperactivated motility associated with detachment from epithelial binding. These motility changes occur in response to the properties of the surrounding fluid environment, biochemical activation state, and physiological ligands, however, a parsimonious mechanistic explanation of flagellar beat generation that can explain motility modulation is lacking. In this paper, we present the Axonemal Regulation of Curvature, Hysteretic model, a curvature control-type theory based on switching of active moment by local curvature, embedded within a geometrically nonlinear elastic model of the flagellum exhibiting planar flagellar beats, together with nonlocal viscous fluid dynamics. The biophysical system is parameterized completely by four dimensionless parameter groupings. The effect of parameter variation is explored through computational simulation, revealing beat patterns that are qualitatively representative of penetrative (straight progressive), activated (highly yawing) and hyperactivated (nonprogressive) modes. Analysis of the flagellar limit cycles and associated swimming velocity reveals a cusp catastrophe between progressive and nonprogressive modes, and hysteresis in the response to changes in critical curvature parameter. Quantitative comparison to experimental data on human sperm exhibiting typical penetrative, activated and hyperactivated beats shows a good fit to the time-average absolute curvature profile along the flagellum, providing evidence that the model is capable of providing a framework for quantitative interpretation of imaging data.
鞭毛运动对自然生殖和多种辅助生殖形式至关重要。鞭毛的有节奏摆动和波动传播推动精子在液体中前进，并能在穿透性的渐进运动、激活的左右偏航运动以及与脱离上皮结合相关的超激活运动之间进行调节。这些运动变化是对周围流体环境特性、生化激活状态和生理配体的响应而发生的，然而，缺乏一种能够解释运动调节的简洁的鞭毛摆动产生机制解释。在本文中，我们提出了曲率轴丝调节滞后模型，这是一种基于局部曲率激活力矩切换的曲率控制型理论，嵌入到一个表现出平面鞭毛摆动的鞭毛几何非线性弹性模型中，并结合非局部粘性流体动力学。该生物物理系统完全由四个无量纲参数组进行参数化。通过计算模拟探索参数变化的影响，揭示出定性代表穿透性（直线前进）、激活（高度偏航）和超激活（非前进）模式的摆动模式。对鞭毛极限环和相关游泳速度的分析揭示了前进和非前进模式之间的尖点突变，以及对临界曲率参数变化响应中的滞后现象。与表现出典型穿透性、激活和超激活摆动的人类精子实验数据的定量比较表明，该模型与沿鞭毛的时间平均绝对曲率分布拟合良好，这为该模型能够为成像数据的定量解释提供框架提供了证据。
