Application of agent-based modelling to assess single-molecule transport across the cell envelope of E. coli

Abstract

Motivation Single cells often show stochastic behaviour and variations in the physiological state of individual cells affect the behaviour observed in cell populations. This may be partially explained by variations in the concentration and spatial location of molecules within and in the vicinity of each cell. Methods This paper introduces an agent-based model that represents single-molecule transport through the cellular envelope of Escherichia coli at the micrometre scale. This model enables broader observation of molecular transport throughout the different membrane layers and the study of the effect of molecular concentration in cellular noise. Simulations considered various low molecular weight molecules, i.e. ampicillin, bosentan, coumarin, saquinavir, and terbutaline, and a gradient of molecular concentrations. The model ensured stochasticity in the location of the agents, using diffusing spherical particles with physical dimensions. Results Simulation results were validated against theoretical and experimental data. For example, theoretically, ampicillin molecules take 0.6s to cross the entire cell envelope, and computational simulations took 0.68s, 0.68s, 0.70s, and 0.69s, for concentrations of 1.44M, 13.21M, 26.4M and 105.61M, respectively. Replicate standard deviation decreased with growing initial concentrations of the molecules. In turn, no clear relationship could be observed between molecular size and variability. Conclusions This work presented a novel agent-based model to study the effect of the initial concentration of low molecular weight molecules on cellular noise. Cellular noise during molecule diffusion was found to be concentration-dependent and size-independent. The new model holds considerable potential for future, more complex analyses, when emerging experimental data may enable modelling of membrane transport mechanisms.