Computers in Biology and Medicine 39 (2009) 412--424 Contents lists available at ScienceDirect Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/cbm Mesoscale modeling technique for studying the dynamics oscillation of Min protein: Pattern formation analysis with lattice Boltzmann method Somchai Sriyab a,b , Jiraporn Yojina a,b , Waipot Ngamsaad b , Paisan Kanthang b , Charin Modchang b , Narin Nuttavut b , Yongwimon Lenbury a,e , Chartchai Krittanai c , Wannapong Triampo b,d,f, ∗ a Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand b R&D Group of Biological and Environmental Physics, Department of Physics, Faculty of Science, Mahidol University, Bangkok, Thailand c Center of Excellence for Vector and Vector-Borne Diseases, Faculty of Science, Mahidol University, Nakhonpathom, Thailand d Institute of Molecular Biology and Genetics, Mahidol University, Nakhonpathom, Thailand e Center of Excellence in Mathematics, PERDO, Commission on Higher Education, Thailand f Thailand Center of Excellence in Physics, PERDO, Commission on Higher Education, Thailand ARTICLE INFO ABSTRACT Article history: Received 12 May 2008 Accepted 11 February 2009 Keywords: Lattice Boltzmann method Protein oscillation Min proteins Pattern formation Mesoscale 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 × 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. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Cell division is the process that a cell separates into two daughter cells after the DNA has been duplicated and distributed into two re- gions. For a successful cell division, the cell has to determine where to separate in Escherichia coli and other rod-shape bacteria, two pro- cesses are known to determine the division site: nucleoid occlusion [1] and the oscillation of Min proteins [2]. Min proteins which are involved in determining the division site are the MinC, MinD, and MinE proteins [2]. Experiments involving ∗ Corresponding author at: R&D Group of Biological and Environmental Physics, Department of Physics, Faculty of Science, Mahidol University, Rama 6 Rd., Ratchate- wee, Bangkok 10400, Thailand. Tel.: +66 2 441 9816x1131; fax: +66 2 441 9322. E-mail addresses: scwtr@mahidol.ac.th, wtriampo@gmail.com (W. Triampo). 0010-4825/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2009.02.003 the use of modified proteins have shown that MinC is able to inhibit the formation of the filamentous temperature sensitiveZ (FtsZ)-ring [3]. It has been reported that tubules of FtsZ protein form cytoskele- ton structure that is involved in septum formation [46]. The FtsZ moves from the cytoplasm to inner membrane at the midcell loca- tion just prior to cell division and assembles the Z-ring which then relocates to the cytoplasm after division. MinD, on the other hand, is an ATPase which is connected peripherally to the cytoplasmic membrane. It can bind and activate MinC into function [4,5]. Recent studies have demonstrated that MinD recruits MinC to the mem- brane. This suggests that MinD stimulates MinC by concentrating them near the presumed site of activation [6,7]. MinE is required to give site specificity to division inhibitor, which suggests that MinE acts as a topological specificity protein capable of recognizing the midcell site and preventing the MinC division inhibitor from acting at that site [8]. Its expression results in a site-specific suppression