Comparative Mathematical Modelling and Numerical Analysis of Chemotactic Signaling Dynamics in Escherichia coli

Abstract

Chemotaxis enables Escherichia coli to respond to changes in its chemical environment through coordinated receptor activity, intracellular phosphorylation and flagellar motor regulation. Mathematical models provide a quantitative framework for investigating these coupled signalling processes. This study compares the five-equation Clausznitzer chemotaxis model with the four-dimensional Edgington–Tindall reduction and examines the influence of four receptor free-energy formulations on signalling behaviour. The nonlinear ordinary differential equations were integrated in MATLAB with the stiff solver ode15s, and the reduced model was converted to physical time with its published scaling. Responses to a step in attractant concentration were evaluated through receptor activity, adaptation, CheY phosphorylation and predicted flagellar motor bias, and the robustness of the results was tested by tolerance refinement and a one-at-a-time parameter sensitivity analysis. Both models gave an adaptation precision of 1.0000. The adaptation times were 86.4 s for the five-equation model and 165.2 s for the reduced model; with the same Tar-only free energy, the five-equation model adapted in 173.6 s, which indicates that most of the difference arises from receptor composition rather than from model reduction. The three Tar-only free-energy formulations gave adapted-state slopes of −1.000, a value that follows from their mathematical structure, whereas the corresponding experimental value is −0.920 ± 0.003; the mixed-receptor formulation gave −0.423. The predicted motor bias differed markedly between the models because of their different protein totals. Quantitative interpretation therefore requires attention to parameter consistency, time scaling and the limited scope of the experimental benchmarks.