Sriyab Somchai, Yojina Jiraporn, Ngamsaad Waipot, Kanthang Paisan, Modchang Charin, Nuttavut Narin, Lenbury Yongwimon, Krittanai Chartchai, Triampo Wannapong
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand.
Comput Biol Med. 2009 May;39(5):412-24. doi: 10.1016/j.compbiomed.2009.02.003. Epub 2009 Apr 1.
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.
我们展示了格子玻尔兹曼方法（LBM）在研究大肠杆菌中Min蛋白振荡动力学方面的应用。这种振荡涉及MinC、MinD和MinE蛋白，它们对于细菌细胞中部隔膜的正确定位是必需的。在这里，LBM被应用于一组描述Min蛋白动力学的确定性反应扩散方程。这在细胞水平上确定了细胞中部的分裂平面。我们特别使用LBM来研究二维空间中Min蛋白从极点到极点的动态振荡。我们观察到Min蛋白的模式形成取决于细胞的形状。LBM的数值结果与使用其他方法的先前发现高度一致，并且在定性上与实验结果吻合良好。我们的结果表明，LBM可以作为一种替代的计算工具，用于模拟这些Min蛋白系统的动力学，并且可能用于研究由反应扩散方程描述的复杂生物系统。此外，这些发现表明LBM对于研究大肠杆菌细胞形状与细胞分裂之间可能的进化联系也可能是有用的。结果表明，当细胞尺寸为1×2时，Min蛋白的振荡模式与实验结果最为一致。这表明，当细胞形状接近正方形时，振荡模式不再能将大肠杆菌的细胞分裂定位在正确位置。这些发现可能对于为什么通过自然选择大肠杆菌保持杆状或芽孢杆菌形态具有重要意义。
