Department of Chemistry, University of Cambridge, Cambridge, UK.
Adv Exp Med Biol. 2012;736:381-96. doi: 10.1007/978-1-4419-7210-1_22.
Various sensing mechanisms in nature can be described by the Weber-Fechner law stating that the response to varying stimuli is proportional to their relative rather than absolute changes. The chemotaxis of bacteria Escherichia coli is an example where such logarithmic sensing enables sensitivity over large range of concentrations. It has recently been experimentally demonstrated that under certain conditions E. coli indeed respond to relative gradients of ligands. We use numerical simulations of bacteria in food gradients to investigate the limits of validity of the logarithmic behavior. We model the chemotactic signaling pathway reactions, couple them to a multi-flagella model for propelling and take the effects of rotational diffusion into account to accurately reproduce the experimental observations of single cell swimming. Using this simulation scheme we analyze the type of response of bacteria subject to exponential ligand profiles and identify the regimes of absolute gradient sensing, relative gradient sensing, and a rotational diffusion dominated regime. We explore dependance of the swimming speed, average run time and the clockwise (CW) bias on ligand variation and derive a small set of relations that define a coarse grained model for bacterial chemotaxis. Simulations based on this coarse grained model compare well with microfluidic experiments on E. coli diffusion in linear and exponential gradients of aspartate.
自然界中的各种感应机制可以用韦伯-费希纳定律来描述，该定律指出，对不同刺激的反应与它们的相对变化而非绝对变化成正比。细菌大肠杆菌的趋化性就是一个例子，这种对数感应使它能够在很大的浓度范围内保持敏感性。最近的实验表明，在某些条件下，大肠杆菌确实对配体的相对梯度做出反应。我们使用食物梯度中细菌的数值模拟来研究对数行为的有效性极限。我们对趋化信号通路反应进行建模，将它们与多鞭毛模型耦合，以推动细菌运动，并考虑旋转扩散的影响，从而准确再现单细胞游动的实验观察。使用这种模拟方案，我们分析了受指数配体分布影响的细菌的响应类型，并确定了绝对梯度感应、相对梯度感应和旋转扩散主导的响应类型。我们探索了细菌游动速度、平均奔跑时间和顺时针（CW）偏差对配体变化的依赖性，并得出了一组定义细菌趋化性的粗粒模型的关系。基于此粗粒模型的模拟与大肠杆菌在天冬氨酸线性和指数梯度中的扩散的微流控实验吻合良好。
