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

为了理解大肠杆菌等细菌的游动机制，建立了一个新的数学模型。大肠杆菌是一种单细胞生物，它通过旋转螺旋鞭毛丝在粘性流体中游动。细胞运动涉及两种连续的运动：奔跑（鞭毛束推动的直线游动）和翻滚（穿插鞭毛的随机重新定向）。该项目将重点研究鞭毛和鞭毛细丝形状之间的流体动力学相互作用，这些形状是通过多态转化产生的。螺旋波长、螺旋直径和旋向性的局部变化？在游泳。将广义浸入边界法与无约束Kirchhoff杆理论相结合，研究了细菌体内的生物流体力学。该方法的一个新特点是浸入边界与流体的相互作用现在不仅涉及浸入边界点在局部流体速度下的平移，而且涉及相关三元组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，其中丝状结构与粘性流体相互作用。例子包括转录和复制过程中DNA的超卷曲以及蛋白质折叠。此外，纳米技术面临的挑战之一是开发可用于治疗疾病的纳米级机器。通过旋转马达了解游泳机制将有助于创造一种纳米机器，由自推进的生物分子纳米马达操作，可用于体内药物输送。此外，这样的跨学科项目产生的问题和活动可以用来吸引学生的科学通过研究者的工作在科学和工程项目（WISE）在她的大学。

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.