Mesoscale modeling technique for studying the dynamics oscillation of Min protein: pattern formation analysis with lattice Boltzmann method.

We presented an application of the Lattice Boltzmann method (LBM) to study the dynamics of Min proteins oscillations in Escherichia coli. The oscillations involve MinC, MinD and MinE proteins, which are required for proper placement of the division septum in the middle of a bacterial cell. Here, the LBM is applied to a set of the deterministic reaction diffusion equations which describes the dynamics of the Min proteins. This determines the midcell division plane at the cellular level. We specifically use the LBM to study the dynamic pole-to-pole oscillations of the Min proteins in two dimensions. We observed that Min proteins' pattern formation depends on the cell's shape. The LBM numerical results are in good agreement with previous findings, using other methods and agree qualitatively well with experimental results. Our results indicate that the LBM can be an alternative computational tool for simulating the dynamics of these Min protein systems and possibly for the study of complex biological systems which are described by reaction-diffusion equations. Moreover, these findings suggest that LBM could also be useful for the investigation of possible evolutionary connection between the cell's shape and cell division of E. coli. The results show that the oscillatory pattern of Min protein is the most consistent with experimental results when the dimension of the cell is 1 x 2. This suggests that as the cell's shape is close to being a square, the oscillatory pattern no longer places the cell division of E. coli at the proper location. These findings may have a significant implication on why, by natural selection, E. coli is maintained in a rod shape or bacillus form.