Understanding the hydrodynamic interaction among flagella of E. coli using the immersed boundary method combined with the Kirchhoff rod theory

发展了一种新的数学模型来理解细菌的游动机制，如大肠杆菌。大肠杆菌是一种单细胞有机体，它通过旋转螺旋鞭毛细丝在粘性流体中游泳。细胞的运动涉及两个连续的运动：奔跑(鞭毛束推动的直线游泳)和翻滚(散布鞭毛进行随机重定向)。本项目将重点研究游泳过程中鞭毛和鞭毛细丝形状之间的水动力相互作用，这些形状是通过多态变化产生的，即螺旋形波长、螺旋形直径和惯用手的局部变化。结合无约束Kirchhoff杆理论和浸没边界法的推广版本被用来研究细菌中的生物流体力学。这种方法的一个新特点是，浸没边界与流体的相互作用现在不仅包括浸没边界点在局部流体速度下的平移，而且还包括相关三联体在局部流体角速度下的旋转。这种方法将在生物流体动力学中找到许多应用，在生物流体动力学中，丝状结构与粘性流体相互作用。例如，DNA在转录和复制过程中的超螺旋以及蛋白质折叠。此外，纳米技术的挑战之一是开发纳米级的机器，可以用于疾病的治疗。通过旋转马达了解游泳机制将有助于创造一种由自行式生物分子纳米马达操纵的纳米机器，可以用于体内的药物输送。此外，这种跨学科的项目产生了一些问题和活动，可以通过研究人员与她所在大学的女性科学与工程项目(WISE)合作来吸引学生学习科学。

A new mathematical model is developed to understand the swimming mechanism of bacteria such as Escherichia coli. The bacterium E. coli is a single-celled organism which swims in a viscous fluid by rotating its helical flagellar filaments. Two successive motions are involved in the cell motility: Runs (straight swimming propelled by flagellar bundling) and tumbles (random reorientation by interspersing flagella). This project will focus on the study of the hydrodynamic interaction among flagella and flagellar filament shapes that arise through polymorphic transformations?local changes in helical wavelength, helical diameter, and handedness?during swimming. A generalized version of the immersed boundary method combined with the unconstrained Kirchhoff rod theory is used to study biological fluid mechanics in the bacterium. A new feature of this method is that the interaction of the immersed boundary with the fluid now involves not only translation of the immersed boundary points at the local fluid velocity, but also rotation of the associated triads at the local fluid angular velocity. This method will find numerous applications in biological fluid dynamics, where filamentous structures interact with a viscous fluid. Examples include the supercoiling of DNA during transcription and replication and protein folding. In addition, one of the challenges in nanotechnology is to develop machines at the nanoscale which can be used in the treatment of disease. Understanding swimming mechanism by means of rotary motors will help to create a nanomachine, operated by self-propelled biomolecular nano motors, that could be used for drug delivery inside the body. Furthermore, such interdisciplinary projects give rise to problems and activities that can be used to attract students to science through the investigator's work with the Women in Science and Engineering program (WISE) at her university.