Morphological Effects on Bacterial Brownian Motion: Validation of a Chiral Two-Body Model

TL;DR

The essential role of flagella in stabilizing bacterial Brownian motion is demonstrated and the effectiveness of the chiral two-body model used for simulating this phenomenon is confirmed.

Abstract

We systematically investigate how flagellar morphology governs the stability of bacterial Brownian motion, evaluating the effectiveness of a simplified chiral two-body model. This model, which effectively captures the specific bacterial morphology and significantly reduces computational cost, is used for simulating bacterial Brownian motion. Our results demonstrate that the model accurately reproduces the Brownian motion of bacteria for contour lengths $Λ\ge5.0$~\si{μm}, helix radii $0.2\le R\le 0.5$~\si{μm}, and pitch angles $π/6\leθ\le2π/9$. We find that the translational and rotational velocities of bacteria depend linearly on the motor rotation rate, independent of dynamic viscosity. Increasing helix radius and contour length leads to more elongated trajectories and enhances their linearity. Furthermore, longer contour lengths improve the stability of the bacterial forward motion. Collectively, these findings demonstrate the essential role of flagella in stabilizing bacterial Brownian motion and confirm the effectiveness of the chiral two-body model for simulating this phenomenon.

Figures (9)

• Figure 1: Schematic diagram of a bacterium model. The flagellar axis is along the $x$-axis. The flagellum is characterized by a helix radius $R$, a filament radius $a$, a pitch $\lambda$, a pitch angle $\theta$, an axial length $L$, and a contour length $\Lambda=L/\cos\theta$, where $\tan\theta=2\pi R/\lambda$. The radius of the spherical cell body is denoted as $R_{b}$. The axial direction of the flagellum and the rotation direction of the motor are represented by $\mathbf{e}_{a}$ and $\mathbf{e}_{m}$, respectively.
• Figure 2: (a) and (c) Standard deviations of the translational and rotational velocities of the flagellar center as a function of contour length $\Lambda$, respectively. Solid lines represent quantities along the $x$-axis, while the dashed lines represent quantities along the $y$-axis. Correspondingly, (b) and (d) Relative differences between the analytical solutions and RFT simulations for these translational and rotational velocity standard deviations.
• Figure 3: Standard deviations of the flagellar center's (a) translational and (c) rotational velocities as a function of helix radius $R$. The solid and dashed lines represent the $x$-axis and $y$-axis quantities, respectively. (b) and (d) Relative differences between the analytical solutions and RFT simulations for these translational and rotational velocity standard deviations, respectively.
• Figure 4: Probability distribution of the angle $\phi$ for different contour lengths at helix radii (a) $R=0.20$ μ m and (b) $R=0.50$ μ m, respectively. Probability distribution of the angle $\phi$ for different pitch angles for contour lengths (c) $\Lambda=5.00$ μ m and (d) $\Lambda=10.0$ μ m, respectively. The solid lines represent the results obtained from RFT simulations, while dashed lines correspond to those from the chiral body model.
• Figure 5: Thrust and torque exerted by the motor on the cell body, obtained from the analytical solutions and the TMM simulations, depend on the following parameters: (a) filament radius $a$, (b) helix radius $R$, (c) contour length $\Lambda$, and (d) pitch angle $\theta$. The solid lines represent the thrust, while dashed lines represent the torque.