Mechanisms of marine invertebrate sperm chemotaxis: from cellular signaling to flagellar swimming

为了充分了解精子是如何到达卵子的，我们需要了解精子是如何改变其波形以应对周围环境的。由于精子运动是一个复杂系统的紧急性质，我们需要有多尺度模型来解释化学信号、力学和流体动力学。对于海洋无脊椎动物的精子，化学吸引剂能够通过启动信号通路将精子引导到卵子，导致钙的增加。钙的这种增加改变了波形，并最终改变了轨迹。该项目将开发一系列模型，用于研究趋化作用的相关生物化学，钙如何以及在哪里作用于改变鞭毛波形，以及这种作用如何与允许精子到达卵子的轨迹相结合。将开发趋化信号通路的模型，并将实施几何离合器假说，以获得钙如何影响动力蛋白臂激活(鞭毛轴丝中的主动力和力矩生成器)的准确模型。将开发多尺度模型，将细胞水平上的相关生物化学与宏观尺度上的轨迹和鞭毛弯曲联系起来。为了准确地计算三维流体中鞭毛的非平面弯曲，我们将发展广义浸没边界方法的一种新的正则化形式。这种方法将提供一个框架来数值求解包括浸没在粘性流体中的结构的耦合系统，其中精子鞭毛施加在液体上的力和扭矩取决于生物化学。通过开发综合的、多尺度的模型，我们将研究趋化性和由此导致的鞭毛内钙浓度的增加如何使无脊椎动物的精子在海洋环境中到达卵子并受精。即将开发的建模框架将允许我们测试有关钙在鞭毛中作用的不同假设，以了解这与精子的出现波形和轨迹是如何耦合的。这项研究处于数学和生物学的交界处，因为有必要考虑到相关的生物化学、力学和流体动力学来模拟精子的运动。参与这一研究项目的学生将接受跨学科培训，并将获得基于该项目相关生物学和计算方面的模型开发经验。虽然这个项目的主要重点是研究无脊椎动物精子的运动性，但即将开发的新的数值方法也将适用于其他微生物(如大肠杆菌)的运动性研究。该项目的目的是开发数学模型，以了解海胆精子如何到达海洋环境中的卵子并使其受精。这项研究还将阐明哺乳动物精子运动的各个方面，并将与诊断不孕症和开发避孕药具相关。

In order to fully understand how the sperm reaches the egg, we need to have an understanding of how the sperm is able to modify its waveform in response to the surrounding environment. Since sperm motility is an emergent property of a complex system, we need to have multiscale models that account for chemical signaling, mechanics, and hydrodynamics. For marine invertebrate sperm, a chemoattractant is able to guide sperm to the egg by initiating a signaling pathway that results in an increase in calcium. This increase in calcium modifies the waveform, and ultimately the trajectory. This project will develop a hierarchy of models that will be used to investigate the relevant biochemistry of chemotaxis, how and where calcium is acting to modify the flagellar waveform, and how this couples to trajectories that allow the sperm to reach the egg. A model for the chemotactic signaling pathway will be developed and the Geometric Clutch Hypothesis will be implemented to have an accurate model of how calcium effects dynein arm activation (active force and torque generators in the axoneme of the flagellum). Multiscale models will be developed to couple the relevant biochemistry at the cellular level to trajectories and flagellar bending at the macroscale. In order to accurately account for nonplanar bending of the flagellum in a 3-dimensional fluid governed by the Stokes equations, we will develop a new regularized formulation of the generalized immersed boundary method. This method will provide a framework to numerically solve a coupled system that includes an immersed structure in a viscous fluid, where the force and torque that the sperm flagellum exerts on the fluid can depend on the biochemistry. Through the development of integrative, multiscale models, we will examine how chemotaxis and the resulting increase in calcium concentration within the flagellum enables invertebrate sperm to reach and fertilize the egg in a marine environment. The modeling framework that will be developed will allow us to test different hypotheses about where calcium is acting in the flagellum to understand how this couples to emergent waveforms and trajectories of sperm. This research lies at the interface of mathematics and biology, as it is necessary to account for the relevant biochemistry, mechanics, and hydrodynamics to model sperm motility. Students involved in this research project will receive interdisciplinary training and will gain experience in model development based on the relevant biology and computational aspects of the project. Although the main focus of this project is on studying aspects of invertebrate sperm motility, the new numerical method that will be developed will also be applicable to study aspects of motility in other microorganisms such as Escherichia coli. The aim of this project is to develop mathematical models to understand how sea urchin sperm reach and fertilize the egg in a marine environment. This research will also shed light onto aspects of mammalian sperm motility and will be relevant to diagnosing infertility and developing contraceptives.