Department of Mathematical Sciences, University of Cincinnati, 4199 French Hall West, Cincinnati, Ohio 45221, USA.
National Institute for Mathematical Sciences, KT Daeduk 2 Research Center, 70, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea.
Phys Rev E. 2017 Jun;95(6-1):063106. doi: 10.1103/PhysRevE.95.063106. Epub 2017 Jun 14.
The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.
螺旋菌鞭毛附着在细菌的细胞体上，如大肠杆菌和鼠伤寒沙门氏菌，使细胞能够在液体环境中游动。这些鞭毛能够进行多态转化，即它们呈现出不同的螺旋形状，在螺旋间距、半径和手性上有所不同。我们提出了一个由 Kirchhoff 杆理论描述的单鞭毛的数学模型，该模型沉浸在由 Stokes 方程控制的流体中。我们进行数值模拟，以演示两种实验中观察到的多态转化机制。首先，我们考虑一个附着在旋转电机上的鞭毛丝，其中通过电机旋转方向的反转来触发转化[L. Turner 等人，J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]。然后，我们考虑一个固定在一端并沉浸在外部流体流中的丝[H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]。讨论了螺旋菌鞭毛与粘性流体相互作用的详细动力学，并提供了与实验和理论结果的比较。
