School of Interdisciplinary Mathematical Sciences, Meiji University, Tokyo, Japan.
Graduate School of Advanced Mathematical Sciences, Meiji University, Tokyo, Japan.
Sci Rep. 2023 May 20;13(1):8173. doi: 10.1038/s41598-023-34788-3.
Taxic behavior as a response to an external stimulus is a fundamental function of living organisms. Some bacteria successfully implement chemotaxis without directly controlling the direction of movement. They periodically alternate between run and tumble, i.e., straight movement and change in direction, respectively. They tune their running period depending on the concentration gradient of attractants around them. Consequently, they respond to a gentle concentration gradient stochastically, which is called "bacterial chemotaxis." In this study, such a stochastic response was reproduced by a non-living self-propelled object. We used a phenanthroline disk floating on an aqueous solution of Fe[Formula: see text]. The disk spontaneously alternated between rapid motion and rest, similar to the run-and-tumble motion of bacteria. The movement direction of the disk was isotropic independent of the concentration gradient. However, the existing probability of the self-propelled object was higher at the low-concentration region, where the run length was longer. To explain the mechanism underlying this phenomenon, we proposed a simple mathematical model that considers random walkers whose run length depends on the local concentration and direction of movement against the gradient. Our model adopts deterministic functions to reproduce the both effects, which is instead of stochastic tuning the period of operation used in the previous reports. This allows us to analyze the proposed model mathematically, which indicated that our model reproduces both positive and negative chemotaxis depending on the competition between the local concentration effect and it's gradient effect. Owing to the newly introduced directional bias, the experimental observations were reproduced numerically and analytically. The results indicate that the directional bias response to the concentration gradient is an essential parameter for determining bacterial chemotaxis. This rule might be universal for the stochastic response of self-propelled particles in living and non-living systems.
作为对外界刺激的反应，趋性行为是生物的基本功能。有些细菌在不直接控制运动方向的情况下成功地实施了趋化作用。它们周期性地在奔跑和翻滚之间交替，即分别进行直线运动和方向变化。它们根据周围吸引物浓度梯度调整其奔跑周期。因此，它们对温和的浓度梯度做出随机反应，这被称为“细菌趋化性”。在这项研究中，一种非生命的自主推进物体再现了这种随机反应。我们使用漂浮在 Fe[Formula: see text]水溶液上的菲咯啉盘。该盘会自发地在快速运动和静止之间交替，类似于细菌的奔跑和翻滚运动。盘的运动方向是各向同性的，与浓度梯度无关。然而，在低浓度区域，即奔跑长度较长的区域，自主推进物体的存在概率更高。为了解释这种现象的机制，我们提出了一个简单的数学模型，该模型考虑了随机游动者，其奔跑长度取决于局部浓度和运动方向与梯度的关系。我们的模型采用确定性函数来再现这两种效应，而不是在以前的报告中使用随机调整操作周期的方法。这使得我们可以对提出的模型进行数学分析，结果表明，我们的模型根据局部浓度效应和梯度效应之间的竞争，再现了正趋化性和负趋化性。由于引入了新的方向偏差，实验观察结果在数值和分析上都得到了再现。结果表明，方向偏差对浓度梯度的响应是决定细菌趋化性的一个基本参数。这一规则可能适用于生命和非生命系统中自主推进粒子的随机响应。
