The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli) is sufficient to accomplish division.bacterial cell division ͉ FtsZ-ring ͉ mathematical model ͉ peptidoglycan synthesis I n rod-like bacteria, such as Escherichia coli and Bacillus subtilis, a conserved cell division gene is FtsZ, which forms a filamentous ring structure (Z-ring) at the mid cell before division (1, 2). The positioning of the Z-ring at the mid cell in E. coli is related to spatial-temporal oscillations in the MinCDE system (3-5). For the actual division step, the radius of the Z-ring is seen to decrease over several minutes, after which a septum is formed and the bacterium separates into two daughter cells (1, 6). It has been postulated that the Z-ring generates forces and ''pinches'' the cell into halves (7), although whether FtsZ generates force is debatable. In addition to the Fts family of proteins, other proteins are also essential for cell division. In particular, disabling peptidoglycan (PG) synthesis proteins or penicillin binding proteins (PBP) just before division stops cytokinesis (8, 9). A systematic study showed that some PBPs are localized near the Z-ring during division (10). Therefore, cell wall synthesis is important in cell division. The mechanics and the dynamics of the cell wall must be considered on an equal footing for quantifying bacterial cell division.Growth and synthesis of the bacterial cell wall is a complex process. The wall is composed of saccharide strands interconnected by polypeptides (7,(11)(12)(13). Indeed, families of PBPs are found in bacteria, with some localized near the furrow during division and some uniformly distributed (10,14,15). Coordinated activity of PBPs synthesizes new PG strands, cross-linking them into the existing wall structure. In a proposed growth model, old strands are also depolymerized, thereby removing them from the wall structure (a process that we will generically call ''turnover'') (7, 11, 16), although models for E. coli growth without turnover also have been proposed (12, 13). Using radio-active labeling, turnover in the PG layer has been investigated (17-19). It was found that the c...