Differences in MinC/MinD sensitivity between polar and internal Z rings in Escherichia coli

In Escherichia coli the Z ring has the potential to assemble anywhere along the cell length but is restricted to midcell by the action of negative regulatory systems, including Min. In the current model for the Min system, the MinC/MinD division inhibitory complex is evenly distributed on the membrane and can disrupt Z rings anywhere in the cell; however, MinE spatially regulates MinC/MinD by restricting it to the cell poles, thus allowing Z ring formation at midcell. This model assumes that Z rings formed at different cellular locations have equal sensitivity to MinC/MinD in the absence of MinE. However, here we report evidence that differences in MinC/MinD sensitivity between polar and nonpolar Z rings exists even when there is no MinE. MinC/MinD at proper levels is able to block minicell production in Δmin strains without increasing the cell length, indicating that polar Z rings are preferentially blocked. In the FtsZ-I374V strain (which is resistant to MinC(C)/MinD), wild-type morphology can be easily achieved with MinC/MinD in the absence of MinE. We also show that MinC/MinD at proper levels can rescue the lethal phenotype of a min slmA double deletion mutant, which we think is due to the elimination of polar Z rings (or FtsZ structures), which frees up FtsZ molecules for assembly of Z rings at internal sites to rescue division and growth. Taken together, these data indicate that polar Z rings are more susceptible to MinC/MinD than internal Z rings, even when MinE is absent.     

Dynamic localization cycle of the cell division regulator MinE in Escherichia coli

The MinC protein directs placement of the division septum to the middle of Escherichia coli cells by blocking assembly of the division apparatus at other sites. MinD and MinE regulate MinC activity by modulating its cellular location in a unique fashion. MinD recruits MinC to the membrane, and MinE induces MinC/MinD to oscillate rapidly between the membrane of opposite cell halves. Using fixed cells, we previously found that a MinE-green fluorescent protein fusion accumulated in an annular structure at or near the midcell, as well as along the membrane on only one side of the ring. Here we show that in living cells, MinE undergoes a rapid localization cycle that appears coupled to MinD oscillation. The results show that MinE is not a fixed marker for septal ring assembly. Rather, they support a model in which MinE stimulates the removal of MinD from the membrane in a wave-like fashion. These waves run from a midcell position towards the poles in an alternating sequence such that the time-averaged concentration of division inhibitor is lowest at midcell.     

The conserved C-terminal tail of FtsZ is required for the septal localization and division inhibitory activity of MinCC/MinD

The Escherichia coli Min system contributes to spatial regulation of cytokinesis by preventing assembly of the Z ring away from midcell. MinC is a cell division inhibitor whose activity is spatially regulated by MinD and MinE. MinC has two functional domains of similar size, both of which have division inhibitory activity in the proper context. However, the molecular mechanism of the inhibitory action of either domain is not very clear. Here, we report that the septal localization and division inhibitory activity of MinC^C/MinD requires the conserved C-terminal tail of FtsZ. This tail also mediates interaction with two essential division proteins, ZipA and FtsA, to link FtsZ polymers to the membrane. Overproduction of MinC^C/MinD displaces FtsA from the Z ring and eventually disrupts the Z ring, probably because it also displaces ZipA. These results support a model for the division inhibitory action of MinC/MinD. MinC/MinD binds to ZipA and FtsA decorated FtsZ polymers located at the membrane through the MinC^C/MinD–FtsZ interaction. This binding displaces FtsA and/or ZipA, and more importantly, positions MinC^N near the FtsZ polymers making it a more effective inhibitor.     

MinC mutants deficient in MinD- and DicB-mediated cell division inhibition due to loss of interaction with MinD, DicB, or a septal component

The min locus encodes a negative regulatory system that limits formation of the cytokinetic Z ring to midcell by preventing its formation near the poles. Of the three Min proteins, MinC is the inhibitor and prevents Z-ring formation by interacting directly with FtsZ. MinD activates MinC by recruiting it to the membrane and conferring a higher affinity on the MinCD complex for a septal component. MinE regulates the cellular location of MinCD by inducing MinD, and thereby MinC, to oscillate between the poles of the cell, resulting in a time-averaged concentration of MinCD on the membrane that is lowest at midcell. MinC can also be activated by the prophage-encoded protein DicB, which targets MinC to the septum without recruiting it first to the membrane. Previous studies have shown that the C-terminal domain of MinC is responsible for the interaction with MinD, DicB, and the septal component. In the present study, we isolated mutations in the C-terminal domain of MinC that affected its interaction with MinD, DicB, and the septal component. Among the mutations isolated, R133A and S134A are specifically deficient in the interaction with MinD, E156A is primarily affected in the interaction with DicB, and R172A is primarily deficient in the interaction with the septum. These mutations differentiate the interactions of MinC with its partners and further support the model of MinCD- and MinC-DicB-mediated cell division inhibition.     

Bacterial cell division: a moving MinE sweeper boggles the MinD

Placement of the division site in Escherichia coli is determined in part by three Min proteins. Recent studies have shown that MinE, previously thought to form a static ring near the division site at the midcell position, actually joins MinC and MinD in their rapid oscillation between the cell poles.     

MinC/MinD copolymers are not required for Min function

In Escherichia coli, precise placement of the cytokinetic Z ring at midcell requires the concerted action of the three Min proteins. MinD activates MinC, an inhibitor of FtsZ, at least in part, by recruiting it to the membrane and targeting it to the Z ring, while MinE stimulates the MinD ATPase inducing an oscillation that directs MinC/MinD activity away from midcell. Recently, MinC and MinD were shown to form copolymers of alternating dimers of MinC and MinD, and it was suggested that these copolymers are the active form of MinC/MinD. Here, we use MinD mutants defective in binding MinC to generate heterodimers with wild‐type MinD that are unable to form MinC/MinD copolymers. Similarly, MinC mutants defective in binding to MinD were used to generate heterodimers with wild‐type MinC that are unable to form copolymers. Such heterodimers are active and in the case of MinC were shown to mediate spatial regulation of the Z ring demonstrating that MinC/MinD copolymer formation is not required. Our results are consistent with a model in which a membrane anchored MinC/MinD complex is targeted to the Z ring through the conserved carboxy tail of FtsZ leading to breakage of FtsZ filaments.     

Recruitment of MinC,an inhibitor of Z-ring formation,to the membrane in Escherichia coli: role of MinD and MinE

In Escherichia coli, the min system prevents division away from midcell through topological regulation of MinC, an inhibitor of Z-ring formation. The topological regulation involves oscillation of MinC between the poles of the cell under the direction of the MinDE oscillator. Since the mechanism of MinC involvement in the oscillation is unknown, we investigated the interaction of MinC with the other Min proteins. We observed that MinD dimerized in the presence of ATP and interacted with MinC. In the presence of a phospholipid bilayer, MinD bound to the bilayer and recruited MinC in an ATP-dependent manner. Addition of MinE to the MinCD-bilayer complex resulted in release of both MinC and MinD. The release of MinC did not require ATP hydrolysis, indicating that MinE could displace MinC from the MinD-bilayer complex. In contrast, MinC was unable to displace MinE bound to the MinD-bilayer complex. These results suggest that MinE induces a conformational change in MinD bound to the bilayer that results in the release of MinC. Also, it is argued that binding of MinD to the membrane activates MinC.     

Membrane redistribution of the Escherichia coli MinD protein induced by MinE

Escherichia coli cells contain potential division sites at midcell and adjacent to the cell poles. Selection of the correct division site at midcell is controlled by three proteins: MinC, MinD, and MinE. It has previously been shown (D. Raskin and P. de Boer, Cell 91:685-694, 1997) that MinE-Gfp localizes to the midcell site in an MinD-dependent manner. We use here Gfp-MinD to show that MinD associates with the membrane around the entire periphery of the cell in the absence of the other Min proteins and that MinE is capable of altering the membrane distribution pattern of Gfp-MinD. Studies with the isolated N-terminal and C-terminal MinE domains indicated different roles for the two MinE domains in the redistribution of membrane-associated MinD.     

The C-terminal domain of MinC inhibits assembly of the Z ring in Escherichia coli

In Escherichia coli, the Min system, consisting of three proteins, MinC, MinD, and MinE, negatively regulates FtsZ assembly at the cell poles, helping to ensure that the Z ring will assemble only at midcell. Of the three Min proteins, MinC is sufficient to inhibit Z-ring assembly. By binding to MinD, which is mostly localized at the membrane near the cell poles, MinC is sequestered away from the cell midpoint, increasing the probability of Z-ring assembly there. Previously, it has been shown that the two halves of MinC have two distinct functions. The N-terminal half is sufficient for inhibition of FtsZ assembly, whereas the C-terminal half of the protein is required for binding to MinD as well as to a component of the division septum. In this study, we discovered that overproduction of the C-terminal half of MinC (MinC(122-231)) could also inhibit cell division and that this inhibition was at the level of Z-ring disassembly and dependent on MinD. We also found that fusing green fluorescent protein to either the N-terminal end of MinC(122-231), the C terminus of full-length MinC, or the C terminus of MinC(122-231) perturbed MinC function, which may explain why cell division inhibition by MinC(122-231) was not detected previously. These results suggest that the C-terminal half of MinC has an additional function in the regulation of Z-ring assembly.     

Analysis of MinD mutations reveals residues required for MinE stimulation of the MinD ATPase and residues required for MinC interaction

The MinD ATPase is critical to the oscillation of the Min proteins, which limits formation of the Z ring to midcell. In the presence of ATP, MinD binds to the membrane and recruits MinC, forming a complex that can destabilize the cytokinetic Z ring. MinE, which is also recruited to the membrane by MinD, displaces MinC and stimulates the MinD ATPase, resulting in the oscillation of the Min proteins. In this study we have investigated the role of lysine 11, present in the deviant Walker A motif of MinD, and the three residues in helix 7 (E146, S148, and D152) that interact electrostatically with lysine 11. Lysine 11 is required for interaction of MinD with the membrane, MinC, MinE, and itself. In contrast, the three residues in helix 7 that interact with lysine 11 are not required for binding to the membrane or activation of MinC. They are also not required for MinE binding; however, they are required for MinE to stimulate the MinD ATPase. Interestingly, the D152A mutant self-interacts, binds to the membrane, and recruits MinC and MinE in the presence of ADP as well as ATP. This mutant provides evidence that dimerization of MinD is sufficient for MinD to bind the membrane and recruit its partners.     

ATP-dependent interactions between Escherichia coli Min proteins and the phospholipid membrane in vitro

Proper placement of the division apparatus in Escherichia coli requires pole-to-pole oscillation of the MinC division inhibitor. MinC dynamics involves a membrane association-dissociation cycle that is driven by the activities of the MinD ATPase and the MinE topological specificity factor, which themselves undergo coupled oscillatory localization cycles. To understand the biochemical mechanisms underlying Min protein dynamics, we studied the interactions of purified Min proteins with phospholipid vesicles and the role of ATP in these interactions. We show that (i) the ATP-bound form of MinD (MinD.ATP) readily associates with phospholipid vesicles in the presence of Mg(2+), whereas the ADP-bound form (MinD.ADP) does not; (ii) MinD.ATP binds membrane in a self-enhancing fashion; (iii) both MinC and MinE can be recruited to MinD.ATP-decorated vesicles; (iv) MinE stimulates dissociation of MinD.ATP from the membrane in a process requiring hydrolysis of the nucleotide; and (v) MinE stimulates dissociation of MinC from MinD.ATP-membrane complexes, even when ATP hydrolysis is blocked. The results support and extend recent work by Z. Hu et al. (Z. Hu, E. P. Gogol, and J. Lutkenhaus, Proc. Natl. Acad. Sci. USA 99:6761-6766, 2002) and support models of protein oscillation wherein MinE induces Min protein dynamics by stimulating the conversion of the membrane-bound form of MinD (MinD.ATP) to the cytoplasmic form (MinD.ADP). The results also indicate that MinE-stimulated dissociation of MinC from the MinC-MinD.ATP-membrane complex can, and may, occur prior to hydrolysis of the nucleotide.     

细菌细胞分裂位点的调控机制及其研究进展

大肠杆菌细胞内共有3个潜在的分裂位点,一个在细胞中部,另外两个位于细胞的两极。正常情况下,细菌仅利用中部的分裂位点以二分裂方式进行细胞的对称分裂。大肠杆菌细胞分裂时,中部潜在分裂位点的选择受到min操纵子(含minC、minD、minE3个基因)的精细调控。minC基因所编码的MinC蛋白是细胞分裂的抑制因子,与具有ATPase活性的MinD蛋白结合后被激活。在MinE蛋白的作用下,MinC和MinD蛋白在大肠杆菌细胞的两极问来回振荡。整个振荡周期中,MinC蛋白在细胞两极的两个潜在分裂位点处所停留的时间较长,分裂复合物无法正常组装,因而细胞两极的潜在分裂位点被屏蔽;而MinC蛋白在细胞中部的分裂位点所停留的时间较短,不能有效地抑制分裂复合物的组装,因此,各种细胞分裂蛋白在中部的分裂位点组装形成稳定的分裂复合物,使正常的细胞分裂得以进行。     

Division site placement in E.coli: mutations that prevent formation of the MinE ring lead to loss of the normal midcell arrest of growth of polar MinD membrane domains

The MinE protein functions as a topological specificity factor in determining the site of septal placement in Escherichia coli. MinE assembles into a membrane-associated ring structure near midcell and directs the localization of MinD and MinC into a membrane- associated polar zone that undergoes a characteristic pole-to-pole oscillation cycle. Single (green fluorescent protein) and double label (yellow fluorescent protein/cyan fluorescent protein) fluorescence labeling experiments showed that mutational alteration of a site on the alpha-face of MinE led to a failure to assemble the MinE ring, associated with loss of the ability to support a normal pattern of division site placement. The absence of the MinE ring did not prevent the assembly and disassembly of the MinD polar zone. Mutant cells lacking the MinE ring were characterized by the growth of MinD polar zones past their normal arrest point near midcell. The results suggested that the MinE ring acts as a stop-growth mechanism to prevent the MinCD polar zone from extending beyond the midcell division site.     

Selection of the midcell division site in Bacillus subtilis through MinD-dependent polar localization and activation of MinC

Bacterial cell division commences with the assembly of the tubulin-like protein, FtsZ, at midcell to form a ring. Division site selection in rod-shaped bacteria is mediated by MinC and MinD, which form a division inhibitor. Bacillus subtilis DivIVA protein ensures that MinCD specifically inhibits division close to the cell poles, while allowing division at midcell. We have examined the localization of MinC protein and show that it is targeted to midcell and retained at the mature cell poles. This localization is reminiscent of the pattern previously described for MinD. Localization of MinC requires both early (FtsZ) and late (PbpB) division proteins, and it is completely dependent on MinD. The effects of a divIVA mutation on localization of MinC now suggest that the main role of DivIVA is to retain MinCD at the cell poles after division, rather than recruitment to nascent division sites. By overexpressing minC or minD, we show that both proteins are required to block division, but that only MinD needs to be in excess of wild-type levels. The results suggest a mechanism whereby MinD is required both to pilot MinC to the cell poles and to constitute a functional division inhibitor.     

Asymmetric Constriction of Dividing Escherichia coli Cells Induced by Expression of a Fusion between Two Min Proteins

The Min system, consisting of MinC, MinD, and MinE, plays an important role in localizing the Escherichia coli cell division machinery to midcell by preventing FtsZ ring (Z ring) formation at cell poles. MinC has two domains, MinCn and MinCc, which both bind to FtsZ and act synergistically to inhibit FtsZ polymerization. Binary fission of E. coli usually proceeds symmetrically, with daughter cells at roughly 180° to each other. In contrast, we discovered that overproduction of an artificial MinCc-MinD fusion protein in the absence of other Min proteins induced frequent and dramatic jackknife-like bending of cells at division septa, with cell constriction predominantly on the outside of the bend. Mutations in the fusion known to disrupt MinCc-FtsZ, MinCc-MinD, or MinD-membrane interactions largely suppressed bending division. Imaging of FtsZ-green fluorescent protein (GFP) showed no obvious asymmetric localization of FtsZ during MinCc-MinD overproduction, suggesting that a downstream activity of the Z ring was inhibited asymmetrically. Consistent with this, MinCc-MinD fusions localized predominantly to segments of the Z ring at the inside of developing cell bends, while FtsA (but not ZipA) tended to localize to the outside. As FtsA is required for ring constriction, we propose that this asymmetric localization pattern blocks constriction of the inside of the septal ring while permitting continued constriction of the outside portion.     

Changes in the Min Oscillation Pattern before and after Cell Birth

The Min system regulates the positioning of the cell division site in many bacteria. In Escherichia coli, MinD migrates rapidly from one cell pole to the other. In conjunction with MinC, MinD helps to prevent unwanted FtsZ rings from assembling at the poles and to stabilize their positioning at midcell. Using time-lapse microscopy of growing and dividing cells expressing a gfp-minD fusion, we show that green fluorescent protein (GFP)-MinD often paused at midcell in addition to at the poles, and the frequency of midcell pausing increased as cells grew longer and cell division approached. At later stages of septum formation, GFP-MinD often paused specifically on only one side of the septum, followed by migration to the other side of the septum or to a cell pole. About the time of septum closure, this irregular pattern often switched to a transient double pole-to-pole oscillation in the daughter cells, which ultimately became a stable double oscillation. The splitting of a single MinD zone into two depends on the developing septum and is a potential mechanism to explain how MinD is distributed equitably to both daughter cells. Septal pausing of GFP-MinD did not require MinC, suggesting that MinC-FtsZ interactions do not drive MinD-septal interactions, and instead MinD recognizes a specific geometric, lipid, and/or protein target at the developing septum. Finally, we observed regular end-to-end oscillation over very short distances along the long axes of minicells, supporting the importance of geometry in MinD localization.Rod-shaped bacteria, such as Escherichia coli, divide by binary fission and thus assemble their cell division apparatus (the divisome) at the cell midpoint. Tubulin-like FtsZ is the major cytoskeletal protein of the divisome (17) and assembles into a polymeric ring on the inner surface of the cytoplasmic membrane (the Z ring). Assembly and eventual contraction of the Z ring are crucial for divisome function, and thus it is not surprising that many regulatory factors control FtsZ assembly (25). Notably, two negatively acting spatial regulatory systems, the Min system and nucleoid occlusion, ensure that the Z ring is located properly at the cell midpoint (18). Whereas a major component of the nucleoid occlusion system can be deleted with no major effects on cell division (2), inactivation of the Min system causes cells to divide either at midcell or aberrantly at cell poles (27). The result of polar cell division is the formation of chromosome-free minicells.The Min system consists of three proteins, MinC, MinD, and MinE (7). MinC has two separate domains, each of which binds to FtsZ and promotes disassembly of FtsZ polymers and polymer bundles (6, 29, 30). MinC also binds to MinD, an ATPase with a carboxy-terminal amphipathic helix that binds to the membrane only when the protein is bound to ATP (11, 12). MinD also forms polymers (31). Finally, MinE is a small protein that binds to MinD and stimulates hydrolysis of its bound ATP in the presence of membranes. By doing so, MinE helps to dislodge MinD from the membrane, although MinE itself can bind to the membrane (10). The result is that MinD and MinE form zones that oscillate from one cell pole to the other, with an oscillation period of seconds to minutes, depending on a number of factors, including temperature (9, 23, 24, 34). In typical cells, MinD spends most of its time bound to the membrane at a cell pole, forming a U-shaped zone, and its transit to the opposite pole is rapid compared to its dwell time (23). MinE typically forms a ring at the edge of the MinD zone (22, 24). The direction of the oscillation is determined strongly by cell geometry (5, 35). Other factors, such as membrane phospholipid composition, also influence MinD oscillation; MinD-ATP preferentially binds anionic phospholipids, such as cardiolipin, which is enriched at cell poles (15, 21, 32).Because MinC binds to MinD, MinC oscillates in concert with MinD and therefore is present at the cell poles for longer times than anywhere else in the cell (13, 22). This sets up a gradient of MinC, with the average smallest amount of MinC at midcell at any one time. The current model is that Z rings are most likely to assemble at the trough of the MinC gradient and are discouraged from assembling at cell poles at the peak of the gradient (14). This is supported by the observation that nonring FtsZ itself oscillates from pole to pole, presumably being chased back and forth by the alternating zones of high MinC concentration (33).However, recent work in Bacillus subtilis has shed new light on the possible function of MinC on the Z ring and the divisome. B. subtilis lacks MinE and thus relies on a static MinC gradient. This is set up by the recruitment of MinC and MinD (MinCD) to the Z ring during formation of the division septum (19, 20). This seems paradoxical, as the presence of MinCD at the Z ring is predicted to destabilize it. However, in B. subtilis, Z rings containing MinCD remain functional. Therefore, MinCD seems to have an important role in preventing the immediate reassembly of Z rings at developing cell poles next to a recently used ring (4, 8).This recruitment of MinCD to the Z ring of B. subtilis prompted us to examine in more detail Min oscillations in E. coli cells undergoing septation. We hypothesized that MinCD might bind to the Z ring at later stages of septation, perhaps helping the Z ring to function by stimulation of FtsZ disassembly. Previous results with green fluorescent protein (GFP)-MinC suggested that MinC could transiently localize to the Z ring during septation (13). Consequently, we tested if MinD, the driving force of the oscillation, could also localize to the Z ring and if this localization was dependent on MinC. We also hypothesized that a more central localization of MinCD during the time of septum formation might explain how Min proteins are partitioned equitably to both daughter cells.     

MinDE-Dependent Pole-to-Pole Oscillation of Division Inhibitor MinC in Escherichia coli

By inhibiting FtsZ ring formation near the cell ends, the MinC protein plays a critical role in proper positioning of the division apparatus in Escherichia coli. MinC activity requires that of MinD, and the MinE peptide provides topological specificity by suppressing MinC-MinD-mediated division inhibition specifically at the middle of the cell. We recently presented evidence that MinE not only accumulates in an FtsZ-independent ring structure at the cell's middle but also imposes a unique dynamic localization pattern upon MinD in which the latter accumulates alternately in either one of the cell halves in what appears to be a rapidly oscillating membrane association-dissociation cycle. Here we show that functional green fluorescent protein-MinC displays a very similar oscillatory behavior which is dependent on both MinD and MinE and independent of FtsZ. The results support a model in which MinD recruits MinC to its site of action and in which FtsZ ring assembly at each of the cell ends is blocked in an intermittent and alternate fashion.     

Determination of the structure of the MinD-ATP complex reveals the orientation of MinD on the membrane and the relative location of the binding sites for MinE and MinC

The three Min proteins spatially regulate Z ring positioning in Escherichia coli and are dynamically associated with the membrane. MinD binds to vesicles in the presence of ATP and can recruit MinC or MinE. Biochemical and genetic evidence indicate the binding sites for these two proteins on MinD overlap. Here we solved the structure of a hydrolytic-deficient mutant of MinD truncated for the C-terminal amphipathic helix involved in binding to the membrane. The structure solved in the presence of ATP is a dimer and reveals the face of MinD abutting the membrane. Using a combination of random and extensive site-directed mutagenesis additional residues important for MinE and MinC binding were identified. The location of these residues on the MinD structure confirms that the binding sites overlap and reveals that the binding sites are at the dimer interface and exposed to the cytosol. The location of the binding sites at the dimer interface offers a simple explanation for the ATP dependence of MinC and MinE binding to MinD.     

Topological regulation of cell division in E. coli. spatiotemporal oscillation of MinD requires stimulation of its ATPase by MinE and phospholipid.

Topological regulation of cell division in E. coli requires positioning a cell division inhibitor, MinC, at the poles of the cell, thus restricting the potential for division to midcell. This positioning is achieved through a rapid oscillation of MinC from pole to pole, a process requiring MinD and MinE. However, the mechanistic basis for this oscillation is not known. Here we report that MinE stimulates MinD ATPase activity, but only in the presence of phospholipid vesicles. Analysis of MinE mutants demonstrates that this stimulation is required for MinD oscillation and suggests that the level of stimulation determines the period of the oscillation. A model is presented in which the requirements for the MinD ATPase contribute spatial and temporal inputs that provide the mechanistic basis for the oscillation.     

Mathematical model for positioning the FtsZ contractile ring in Escherichia coli

During bacterial cytokinesis, a proteinaceous contractile ring assembles in the cell middle. The Z ring tethers to the membrane and contracts, when triggered, to form two identical daughter cells. One mechanism for positioning the ring involves the MinC, MinD and MinE proteins, which oscillate between cell poles to inhibit ring assembly. Averaged over time, the concentration of the inhibitor MinC is lowest at midcell, restricting ring assembly to this region. A second positioning mechanism, called Nucleoid Occlusion, acts through protein SlmA to inhibit ring polymerization in the location of the nucleoid. Here, a mathematical model was developed to explore the interactions between Min oscillations, nucleoid occlusion, Z ring assembly and positioning. One-dimensional advection-reaction-diffusion equations were built to simulate the spatio-temporal concentrations of Min proteins and their effect on various forms of FtsZ. The resulting partial differential equations were numerically solved using a finite volume method. The reduced chemical model assumed that the ring is composed of overlapping FtsZ filaments and that MinC disrupts lateral interactions between filaments. SlmA was presumed to break long FtsZ filaments into shorter units. A term was developed to account for the movement of FtsZ subunits in membrane-bound filaments as they touch and align with other filaments. This alignment was critical in forming sharp stable rings. Simulations qualitatively reproduced experimental results showing the incorrect positioning of rings when Min proteins were not expressed, and the formation of multiple rings when FtsZ was overexpressed.