Stochastic modeling of external electric field effect on Escherichia coli Min protein dynamics

Abstract

R&D Group of Biological and Environmental Physics, Department of Physics, Faculty of Science, Mahidol University, Rama 6 Rd., Ratchatewee, Bangkok, 10400 Thailand Cell division in Escherichia coli and other rod-shaped bacteria depends on the precise placement of a division septum at the cell center. The MinCDE system consisting of three proteins, MinC, MinD, and MinE, controls accurate cell division at the center of the cell through pole-to-pole oscillation. With simplifying assumptions and relying on a deterministic model, we present a one-dimensional stochastic model that describes the effects of an external electric field on the MinCDE system. Computer simulations were performed to investigate the response of the oscillatory dynamics to various strengths of the electric field and to the total number of Min proteins. A sufficient electric field strength was capable of interfering with MinCDE dynamics with possible changes to the cell division process. Interestingly, effects of an electric field were found not to depend on the total number of Min proteins. The noise involved shifted the correct trend of Min proteins behavior. However, as a consequence of the robustness of the dynamics, the oscillatory pattern of the proteins still existed even though the number of Min proteins was relatively low. When considering the correlations between the local and the global minimum (maximum) of MinD (MinE), the results suggest that using a high enough Min protein concentration will reduce the local minimum (maximum) effect, which is related to the probability of polar division in each single oscillator cycle. Although this model is simple and neglects some complex mechanisms concerning protein oscillation in correlation with cell division, it has been demonstrated to be good enough for positioning of the dividing site. Nevertheless, more experimental and theoretical studies are needed to provide a more realistic (but of course more complicated) model of bacterial cell division.