Chromosome segregation by the Escherichia coli Min system

The mechanisms underlying chromosome segregation in prokaryotes remain a subject of debate and no unifying view has yet emerged. Given that the initial disentanglement of duplicated chromosomes could be achieved by purely entropic forces, even the requirement of an active prokaryotic segregation machinery has been questioned. Using computer simulations, we show that entropic forces alone are not sufficient to achieve and maintain full separation of chromosomes. This is, however, possible by assuming repeated binding of chromosomes along a gradient of membrane-associated tethering sites toward the poles. We propose that, in Escherichia coli, such a gradient of membrane tethering sites may be provided by the oscillatory Min system, otherwise known for its role in selecting the cell division site. Consistent with this hypothesis, we demonstrate that MinD binds to DNA and tethers it to the membrane in an ATP-dependent manner. Taken together, our combined theoretical and experimental results suggest the existence of a novel mechanism of chromosome segregation based on the Min system, further highlighting the importance of active segregation of chromosomes in prokaryotic cell biology.


Introduction
When cells divide, their genetic content has to be faithfully copied and equally distributed to the progeny. Several processes, therefore, exist and cooperate to carry out the delicate task of cell division, such as DNA replication, segregation, correct positioning of the division site, and cytokinesis itself. For prokaryotes, much is known about how the DNA is replicated (Scholefield et al, 2011;Badrinarayanan et al, 2012), how cells define their middle in a precise way (Thanbichler and Shapiro, 2008;de Boer, 2010;Lutkenhaus, 2012), and how cytokinesis is carried out (de Boer, 2010;Erickson et al, 2010). The mechanisms of chromosome segregation have, on the other hand, remained largely enigmatic (Pogliano et al, 2003;Reyes-Lamothe et al, 2012), and different models propose segregation to be either passive or active. In the model of purely passive segregation, the forces that separate sister chromosomes are internal to the chromosomes themselves and are generated by repulsion of two self-avoiding polymers in a rod-shaped geometry to maximize their conformational entropy (Jun and Mulder, 2006;Jun and Wright, 2010). Partitioning forces may also arise from a number of other processes  such as the interplay between the organization of the nucleiod and replication (Sawitzke and Austin, 2001) or co-transcriptional translation and translocation of membrane proteins (Woldringh, 2002). In the models of active segregation, external forces produced by specialized proteins use energy to move duplicated chromosomes each into one daughter cell, more closely resembling the function of the eukaryotic mitotic apparatus. The presence of a dedicated segregation machinery has been recently shown in Caulobacter crescentus (Ptacin et al, 2010;Schofield et al, 2010;Shebelut et al, 2010) and in Vibrio cholerae (Fogel and Waldor, 2006). This machinery was proposed to rely on the force generated by depolimerization of oligomers that are formed by the cytoplasmic DNA-binding ATPase ParA. Similar Par systems are also involved in the segregation of some low-copy-number plasmids in bacteria (Ringgaard et al, 2009;Gerdes et al, 2010). However, E. coli and many other bacteria lack a chromosomal Par system, suggesting that the ParA-dependent segregation mechanism is not universal.
The closest homolog of ParA in E. coli, the ATPase MinD, is part of the Min system that has a well-established function in restricting the division plane to mid-cell (Lutkenhaus, 2007(Lutkenhaus, , 2012. MinD has an additional C-terminal amphipathic helix that allows it to form membrane-associated, ATP-dependent dynamic filaments (Hu et al, 2002;Szeto et al, 2002;Hu and Lutkenhaus, 2003;Szeto et al, 2003;Zhou and Lutkenhaus, 2003), which exhibit periodic pole-to-pole oscillations in the cell. Min oscillations arise from the interplay between the ATPdependent membrane association and subsequent oligomerization of MinD, and MinE-stimulated local release of MinD from the membrane upon ATP hydrolysis (Hu et al, 2002;Lackner et al, 2003;Kruse et al, 2007;Loose et al, 2008). These oscillations create an intracellular gradient of the complex between MinD and the cell-division inhibitor MinC (Raskin and de Boer, 1999), with a minimum at mid-cell and maxima at the poles.
In this study, we use numerical computer simulations to demonstrate how a gradient of DNA binding sites at the cell membrane can act as a Brownian ratchet to bias the movement of chromosomes from mid-cell toward the poles, completing and maintaining chromosome segregation initially achieved by purely entropic repulsion forces. We further propose that such a gradient can be provided by the Min system, demonstrating that MinD can bind to DNA and tether it to the membrane in an ATP-dependent manner. These results suggest a novel mechanism of active chromosome segregation that might be common among bacteria.

Results
Polar gradients of DNA binding sites at the membrane can enhance entropy-driven segregation of chromosomes Previous computer models of chromosome segregation showed that entropic repulsion might be sufficient to promote the initial disentanglement of two self-avoiding ring polymers representing the duplicated DNA (Jun and Mulder, 2006;Jun and Wright, 2010). Yet because the entropic forces are expected to drop sharply after the initial unmixing of such polymers, entropy alone is unlikely to ensure clearance of chromosomes away from mid-cell, and therefore additional mechanism(s) must exist in E. coli to complete chromosome segregation.
We hypothesized that one such mechanism may be provided by polar gradients of DNA tethering sites at the membrane, whereby repeated binding and unbinding of chromosomes to these sites would prevent backward movement of the DNA toward mid-cell, effectively biasing its random diffusion toward the poles and thus resulting in a Brownian ratchettype mechanism of segregation. To test this hypothesis, we simulated the dynamics of two self-avoiding ring polymers ( ¼ chromosomes) confined in a volume with an aspect ratio of 1:8 corresponding to that of an E. coli cell (Supplementary Figure S1A). In these simulations, entropic repulsion is represented by the excluded volume interactions between the two ring polymers, as well as between the segments of one polymer, meaning that two segments cannot cross or overlap (Bohn and Heermann, 2010;Jun and Wright, 2010;Fritsche et al, 2012). We further considered membrane tethering of chromosomal segments, with either a homogenous or polar gradients distribution of such sites. A typical simulation starts with the two polymers being mixed (Supplementary Figure S1A) and is run by stepwise displacement of polymer segments using a Monte-Carlo method until the centers of mass of both polymers have reached their steady-state position. As shown in Figure 1A, polar gradients of DNA tethering sites on the membrane lead to a more pronounced separation of the two polymers than purely entropic repulsion. Similar improvement in segregation was obtained with static or dynamic gradients, whereby in the latter case the gradient was allowed to periodically oscillate (Supplementary Figure S1B and C). Notably, a uniform distribution of tethering sites does not improve and even slows segregation down. Decreasing the steepness of the gradient makes segregation less efficient but does not fully impair it (Supplementary Figure S1D). In contrast, increasing the dwell time (and therefore effective affinity) of DNA segments at tethering sites by 10-fold reduces the efficiency of segregation below that accomplished by the entropic repulsion alone (Supplementary Figure S1E). Thus, efficient segregation requires DNA tethering to be relatively weak and transient.
The benefit of the proposed mechanism for chromosome segregation is even more evident when comparing the polymer density profiles over time in simulations without ( Figure 1B) and with oscillating gradient of tethering sites ( Figure 1C). This confirms that while the entropic repulsion of the nucleoids is sufficient to initially push chromosomes apart, it subsequently becomes too weak to achieve full segregation away from mid-cell. At this point, the action of the Brownian ratchet that is mediated by a gradient of binding sites becomes important. Furthermore, comparing the distribution of the center of polymer mass upon equilibration in multiple simulations reveals that only with a gradient of tethering sites the center of mass is positioned with high precision ( Figure 1D). Importantly, such a gradient is able to efficiently segregate polymers even independent of the entropic forces ( Figure 1E), and while the entropic repulsive force drops rapidly with increasing distance between the centers of mass of the two polymers, the gradient of tethering sites can maintain the effective repulsion at larger distances where the entropic contribution becomes negligible ( Figure 1F). Notably, in our model chromosome segregation is primarily generated by tethering sites that are distributed along the lateral membrane. As a consequence, our computer simulations neither show any pronounced extension of the polymers toward the cell poles nor require such extension for segregation, which is consistent with the observed nucleoid morphology in E. coli cells.

Identification of MinD as a candidate tethering protein
In principle, the proposed mechanism of chromosome segregation can be mediated by any protein (or protein complex) that forms polar gradients at the membrane and binds DNA. Since MinD is known to form dynamic polar gradients in E. coli and given its homology to ParA, we decided to test whether it could also bind DNA. Indeed, we found that incubation with MinD alters the electrophoretic mobility of Active chromosome segregation by MinD gradients B Di Ventura et al DNA fragments in the electrophoretic mobility shift assay (EMSA), retaining a large fraction of the 155 bp doublestranded DNA probe in the well (Figure 2A). This shift largely in the upper portion of the gel indicated formation of high molecular weight (HMW) nucleoprotein filaments. The interaction was not sequence specific, being observed to a similar extent for DNA fragments that correspond to the P1 promoter of the E. coli minB operon and to the unrelated hybrid pTrc promoter. Confirming that HMW nucleoprotein complexes result from binding of multiple MinD proteins to the same DNA molecule rather than from MinD aggregation, smaller MinDbound DNA fragments migrated into the gel as distinct bands ( Figure 2B and C). The HMW MinD-DNA complexes appeared to be inhibited by ADP (Figure 2A and B), since they were much more pronounced in the presence of ATP or in the absence of any nucleotide added to the reaction. We further showed that in order for MinD to bind, the DNA fragment has to be longer than 10 bp ( Figure 2C). The distinct band observed for the 20-30 bp DNA fragments ( Figure 2B and C) thus likely corresponds to a DNA-bound dimer of MinD. In contrast, a variable number of MinD proteins can bind to longer DNA fragments, resulting in the formation of a smear due to the multiple species present (Figure 2A).   Only position of the right polymer along the long cell axis is shown. (F) Repulsive force between two polymers as a function of the distance between their CMs, for the model without tethering or with an oscillating gradient. The repulsive force was computed by applying a given attractive force between the polymers and measuring the distance at which they equilibrate.

Active chromosome segregation by MinD gradients B Di Ventura et al
ParA-family members, arginine 218 in Soj and lysine 340 in SopA (Hester and Lutkenhaus, 2007;Castaing et al, 2008). However, replacement of arginine 187, which aligns with another important DNA-binding residue of Soj, arginine 189 (Hayes and Barilla, 2006), had no effect ( Figure 2E). In an attempt to find other residues that could be involved in DNA binding, we tested two arginines at positions 251 and 254, but found that single (MinD R251E and MinD R254E ) or double (MinD R2E ) mutation of these residues to glutamates had no effect on DNA binding (Supplementary Table S2). We also mutated other, positively charged residues lying at the core of the MinD dimer, but found no effect (Supplementary Table S2). To our surprise, DNA binding was nearly abolished by truncation of the last 10 C-terminal residues that form the amphipathic helix, normally responsible for membrane association of MinD (MinD D10 ; Figure 2E and Supplementary Figure S2A). Similar results were obtained using surface plasmon resonance (SPR) assays ( Figure 2F), which also showed that DNA binding and dissociation of MinD in vitro occurs at the time scale of tens of seconds, with an apparent dissociation constant of B0.6 mM. Nevertheless, the amphipathic helix is unlikely to be directly involved in DNA binding, since the binding could be restored by introducing the R2E mutation in the context of the truncated MinD (MinD R2ED10 ; Figure 2E). Moreover, the ability of this mutant to bind to DNA strongly suggests that MinD non-sequence specific DNA binding is not due to its being positively charged at the C-terminus, since MinD R2ED10 not only lacks the positively Active chromosome segregation by MinD gradients B Di Ventura et al charged C-terminal helix but even contains two more negatively charged residues compared with wild-type MinD. We propose that the C-terminal helix modulates DNA binding of MinD via a conformational change, which may be mimicked by mutating arginines 251 and 254 to glutamates in the truncated MinD.

MinD forms HMW complexes with DNA
Formation of the HMW MinD complexes with DNA was further confirmed by sedimentation analysis of the labeled DNA probe with and without MinD. Indeed, DNA was found in the pellet in the presence of wild-type MinD and ATP ( Figure 2G). The sedimentation of DNA was strongly reduced in the presence of mutant MinD R219D ( Figure 2G). Interestingly, substantial sedimentation of DNA was observed for MinD K11A mutant that is not able to dimerize (Zhou et al, 2005) but is still able to bind ATP (Okuno et al, 2010), indicating that binding of multiple monomers to the same DNA fragment may be sufficient to form HMW nucleoprotein complexes. MinD K11A -DNA complexes were also detected in EMSAs (Supplementary Figure S2B).

MinD can tether DNA to the membrane in an ATPdependent manner
To test whether MinD is able to tether the DNA to the membrane, we used a flotation assay (Weber et al, 1998) in which a mixture of protein, DNA, and liposomes was separated by ultracentrifugation in a density gradient. Under our experimental conditions, liposomes and liposome-associated molecules move to the top of the gradient, whereas proteins and DNA that are not bound to liposomes remain at the bottom ( Figure 3A). The ultracentrifugation is carried out for 4 h allowing the material in the gradient to reach equilibrium (Steringer et al, 2012). As expected, when subject to separation individually, liposomes were primarily found in the top fraction 1 ( Figure 3B), whereas DNA was found in the bottom fractions 3 and 4 (Supplementary Figure S3A). When mixed together, DNA and MinD were found in fractions 3 and 4 (Supplementary Figure S3B). In the presence of MinD and ATP, liposomes were also found in fraction 2 ( Figure 3C; Supplementary Figure S3D), indicating the formation of complexes between MinD and liposomes that are substantially heavier than free liposomes and might correspond to the previously observed MinD-induced membrane tubules (Hu et al, 2002). In the presence of MinD, DNA also became enriched in fraction 2 in an ATP-dependent manner ( Figure 3D; Supplementary Figure S3D), suggesting that MinD oligomers are able to recruit DNA to the membrane. Certain liposomedependent enrichment of DNA in fraction 1 was observed even in the absence of MinD (Supplementary Figure S3C), presumably due to a non-specific binding. Nevertheless, the MinD-and ATP-dependent recruitment of DNA to liposomes in fraction 2 was much more efficient, confirming its specificity ( Figure 3E; Supplementary Figure S3C and D).
In the flotation assay, MinD also localized to the lighter liposome fraction 1, in the presence of either ATP or ADP (Supplementary Figure S3D), indicating that the assay is sensitive enough to detect the weak membrane binding of monomeric MinD (Szeto et al, 2003). However, the higher ratio of DNA to MinD in fraction 2 suggests that oligomeric ATP-bound MinD is much more potent in recruiting DNA to the liposomes ( Figure 3F). Consistent with this explanation, monomeric MinD K11A that, as expected, localized to Active chromosome segregation by MinD gradients B Di Ventura et al fraction 1 but was not able to shift liposomes to fraction 2, led only to a slight enrichment of DNA in fraction 1 ( Figure 3D; Supplementary Figure S3F). MinD D10 was completely deficient in liposome binding ( Figure 3D; Supplementary Figure S3G). The DNA-binding mutant MinD R219D was largely impaired in tethering DNA to the membrane ( Figure 3D). Yet this result cannot be unambiguously assigned to the impairment of MinD R219D DNA binding, since the R219D mutation also apparently affects binding of MinD to the membrane. MinD R219D could not efficiently shift the liposomes to fraction 2, although it was found in fraction 1 (Supplementary Figure S3E). Weaker binding of MinD R219D to the membrane was further confirmed using a liposome sedimentation assay, with significantly smaller amount of liposome-bound MinD R219D in the pellet compared with the wild-type MinD ( Figure 4A; Supplementary Figure S4). Considering the location of arginine 219 on the surface of MinD that faces toward the membrane (Wu et al, 2011), it is perhaps not surprising that this mutation affects MinD interaction with the membrane. Yet, to our knowledge, this is the first mutation mapped outside of the C-terminal helix that specifically affects binding of MinD to the membrane. Moreover, the involvement of residues outside of the C-terminal amphipathic helix in membrane binding was confirmed by weaker liposomemediated sedimentation of MinD carrying R251E and R254E mutations ( Figure 4B). We further investigated the behavior of these mutants in vivo. When fused to a yellow fluorescent protein (YFP), MinD R219D was able to bind to the membrane ( Figure 4C) and to support oscillations when expressed together with MinE ( Supplementary Movies 1 and 3). However, both membrane binding and oscillations required higher expression levels than for wild-type MinD, consistent with the lower affinity of this mutant for the membrane. Moreover, MinD R219D apparently could not support MinC oscillations even when using induction levels that led to MinDE oscillations (Supplementary Movies 2, 4 and 5), indicating that the R219D mutation might also directly affect MinD binding to MinC. The negative effect of R251E and R254E mutations on membrane binding of MinD could be also confirmed in vivo ( Figure 4D).

The cytoplasmic mutant MinD R2ED10 is enriched on the nucleiod in vivo
As previously mentioned, the R251E and R254E mutations in the context of the truncated MinD D10 can restore DNA binding. As this mutant (MinD R2ED10 ) is cytoplasmic, we reckoned that it might show co-localization with the nucleiod in E. coli cells that is otherwise obscured by binding of MinD to the membrane. We therefore constructed a fusion of MinD R2ED10 to EYFP and analyzed its in vivo localization. Albeit not in all cells, MinD R2ED10-EYFP clearly showed enrichment over the nucleiod area, as ascertained by imaging both the EYFP and the DAPI channels ( Figure 4E). The co-localization of MinD R2ED10-EYFP with DNA was only partial, supporting the prediction of our computer simulations that MinD-DNA binding has to be intrinsically weak.

Absence of MinD leads to an increase in anucleate cells
If MinD is involved in chromosome segregation, then one might expect to observe segregation defects in cells lacking MinD. To distinguish specific MinD-dependent segregation defects from those caused by the asymmetric cell division in the absence of the functional Min system, we compared the distribution of DAPI-stained DNA in a population of DminB cells lacking the entire Min system (MinC, MinD and MinE) to that in DminC cells lacking only the inhibitor of cell division MinC. Because of aberrant division near the cell poles in the absence of MinC, both these strains produce anucleate mini-cells, the hallmark of the min mutants. Nevertheless, cells lacking only MinC show visibly better separation of the nucleiods compared with those lacking all Min proteins ( Figure 5A; Supplementary Figure S5), supporting our idea that MinD has a role in chromosome segregation that is independent of its function in placement of the cell-division site. Moreover, we found an increase in anucleate cells in the DminB strain compared with the DminC strain ( Figure 5B) when excluding mini-cells from our analysis. Even assuming that the determined fraction of anucleate cells is overestimated because DAPI staining of DNA did not occur in all cells, the observed specific difference between the DminB and DminC strains strongly suggests that the defect in the MinD-dependent partitioning can lead to the loss of chromosomes also in non-mini cells.

Mutation of arginine 219 in MinD causes chromosome segregation defects in vivo
An even more direct proof of the involvement of MinD in chromosome segregation would be given by a MinD mutant that is not able to bind DNA, but can still oscillate and thus mediate the cell-size control. However, because of the observed interrelation between the two activities of MinD, we could not effectively decouple the defects in DNA and membrane binding. Indeed, consistent with its lower affinity for the membrane and for MinC, MinD R219D could not fully complement the mini-cell phenotype of DminB strain (deletion of all three Min proteins) even when co-expressed with MinC and MinE. Nonetheless, we reasoned that the effect of the R219D mutation on DNA segregation by MinD might become apparent when comparing DminB cells expressing either MinD/MinE or MinD R219D /MinE. In this experiment, we also expressed a basal level of MinC, since this gave us a similar distribution of cell sizes in both strains, decreasing the number of very long cells that were difficult to analyze. The analysis was restricted to cells of about double the size of a newborn cell, which likely originated from symmetric cell divisions and typically has two discernible nucleoids. To assay the extent of chromosome segregation in these cells, we stained the DNA with DAPI and determined the distribution of the DAPI signal along the long cell axis. Consistent with the involvement of MinD in chromosome segregation, we observed better separation of nucleoids in cells harboring wild-type MinD compared with those harboring the mutant MinD R219D (Figure 5C and D). This apparent difference could be confirmed by quantifying the distances between the centers of mass of the two nucleoids and also the depth of their separation ( Figure 5E and F).

MinD expression decreases mobility of chromosomal loci
According to our hypothesis, MinD molecules bind to the membrane and to the DNA and can tether the two, albeit only transiently. In agreement with that, we observed that expression of MinD in a DminB strain lowers the mobility of chromosomal loci associated with replication forks that were labeled with single-strand binding protein fused to YFP (SSB-YFP)   (Figure 5G-I). Estimated apparent diffusion coefficients of these foci were B1.5 times lower in the presence of MinD (Supplementary Figure S6). Importantly, since the expression of MinD alone does not change the minicell phenotype typical of DminB cells, we could rule out that the observed difference in the mobility of replication forks was due to differences in cell morphology.

Dynamics of the Min system can support proposed chromosome segregation
Taken together, our experimental results suggest that, in E. coli cells, the oscillating, membrane-bound MinD protein may indeed provide the source of the polar gradients of DNA tethering sites used for chromosome segregation. To confirm that the experimental parameters of the Min system are consistent with the proposed segregation mechanism, we  Figure 6C). This indicates that it is primarily the existence of a gradient with a minimum at mid-cell and maxima at the poles and not the details of its movement that is critical for the proposed segregation mechanism.

Discussion
Until now, the machinery used by E. coli and most other bacteria for the essential cellular function of chromosome segregation had remained elusive, with several previously proposed candidate processes being recently dismissed (Wang and Sherratt, 2010). In our model, we propose that nonsequence specific binding of MinD to DNA and at the same time to the membrane could create a dynamic gradient of DNA tethering sites on the membrane that progressively moves from mid-cell to the pole in each round of oscillation ( Figure 7). Repeated binding and unbinding of chromosomal segments to these tethering sites eventually can mediate   of sister chromosomes by biasing their random movement toward the poles in a Brownian ratchet-like manner. Our simulations demonstrate that the proposed mechanism can rely on either an oscillatory or a static gradient of tethering sites, meaning that may also function in bacterial species with static MinD localization (Marston et al, 1998). In the latter case of static gradient, the random movement of chromosomes is biased toward the poles at all times. In the former case of oscillatory gradient, each chromosome is biased in its movement toward the pole only during one half of the oscillation cycle, when MinD is mostly at the corresponding pole. During another half of the Min cycle, this chromosome is in principle freely diffusing, but because of the large size of the chromosome its diffusion is much slower than the cycle of Min oscillation (Jun and Mulder, 2006) and thus cannot randomize chromosome position on this time scale. Nevertheless, such alternating 'catch-and-release' can lead to oscillations of the center of mass of the chromosome above the gradual movement toward the pole, as observed in our simulations ( Figure 1A). Notably, Fisher et al (2013) recently showed similar oscillations of the chromosome ('longitudinal density waves') on the time scale of tens of seconds, which we believe may be explained by the proposed Min-dependent chromosome tethering. Importantly, to operate efficiently this mechanism requires the initial disentanglement of daughter nucleoids, which is likely achieved by entropic repulsion of self-avoiding ring chromosomes (Jun and Mulder, 2006) or by a related mechanism of minimization of radial confinement stress (Fisher et al, 2013). Consistent with previous reports (Jun and Mulder, 2006;Arnold and Jun, 2007;Jun and Wright, 2010;Bohn and Heermann, 2011), our work suggests that such entropic repulsion can efficiently push sister chromosomes apart during the early stages of segregation. However, because the entropic forces progressively weaken as the overlap between volumes occupied by the two chromosomes decreases, the entropic repulsion fails to achieve full segregation. Consistent with this analysis, daughter nucleoids show less efficient separation in the absence of the Min system butin most cases-not a complete segregation defect. Notably, our simulations demonstrate that the proposed MinD-driven segregation should function independently of the details that underlie the initial unmixing of the chromosomes.
Given its well-established role in another essential process of the cell cycle, it is perhaps not surprising that the Min system was not considered as a likely candidate for chromosome segregation machinery, despite the homology of MinD to ParA and the early work demonstrating chromosome segregation defects in min strains (Akerlund et al, 1992(Akerlund et al, , 2002. Consequently, previous comparisons between the ParA and the Min systems assumed that, despite similarities in their function and regulation, these systems have evolutionary diverged to execute two different key functions in bacterial cell division (Gerdes et al, 2010;Lutkenhaus, 2012). In contrast, our study proposes that the Min system in E. coli retained both functions, with the dynamic gradient of MinD on the membrane ensuring symmetric cell division and proper segregation of the daughter chromosomes. The interplay between these two functions apparently relies on an intimate intertwining of MinD interactions with the DNA and with the membrane. Different from the DNA binding by ParA-type proteins, MinD interaction with DNA is further regulated by its membrane-binding amphipathic helix, although this sequence is not per se required for the DNA binding. On the other hand, mutations in the amino-acid residues that affect the DNA binding of MinD also apparently modulate its interaction with the membrane, although those residues are not part of the amphipathic helix.
The ATP dependence of both interactions is further likely to ensure that, in the cell, chromosomal DNA primarily interacts with membrane-bound MinD, thus reducing the non-productive sequestration of MinD at the nucleoid. Free diffusion of cytoplasmic MinD is, in fact, essential for the maintenance of the Min oscillations, which may also explain the observed relatively weak binding of MinD to DNA. Nevertheless, high local concentration of MinD at the membrane ensures that even its weak interactions with the chromosomal DNA are able to generate sufficient tethering force.
Proper partitioning of the genetic material is a key feature of the cell division process and it is controlled by multiple systems in bacteria . It is therefore important to emphasize that during chromosome segregation, the Min machinery has to cooperate not only with the entropic forces but also with several other systems that have established roles in organizing the nucleoid throughout the cell cycle and in unlinking and translocating the concatenated daughter chromosomes through the closing septum (Wang et al, 2006;Danilova et al, 2007;Grainge et al, 2007;White et al, 2008;Madabhushi and Marians, 2009;Espeli et al, 2012;Reyes-Lamothe et al, 2012). Nevertheless, our work suggests that, similarly to eukaryotes, most bacteria employ a mitotic apparatus, although specific partitioning mechanisms in individual species might differ, relying either on the Min system or on the ParA system (Fogel and Waldor, 2006;Ptacin et al, 2010;Schofield et al, 2010;Shebelut et al, 2010).

Strains and expression constructs
All strains and plasmids used in this study are listed in Supplementary  Table S1. His-tagged MinD and its mutants were essentially purified as previously described (Loose et al, 2008). See Supplementary information for details of plasmid construction, cell growth conditions, and protein purification.

DNA EMSAs
Binding reactions were performed in a volume of 10 ml in EMSA buffer (38 mM HEPES/NaOH (pH 7.2), 38 mM NaCl, 5 mM MgCl 2 , 7% glycerol, 1 mM DTT). Each reaction contained 200 fmol of dsDNA labeled by 5 0 -hexachloro-fluorescein phosphoramidite (HEX) and 1 mM ATP or ADP (unless otherwise specified). Reactions were incubated at room temperature for 10 min and then separated on 10% polyacrylamide (PA) native gels for B30 min. Gels were run in 0.5X TBE plus 1 mM MgSO 4 at 150 V and subsequently visualized using a Typhoon gel scanner.

Co-sedimentation and flotation assays
Co-sedimentation of MinD and DNA with liposomes is described in Supplementary information. Flotation assays were performed with unilamellar liposomes prepared from synthetic DOPG (1,2-dioleoyl-snglycero-3-phospho-(1 0 -rac-glycerol), sodium salt; Avanti Polar Lipids) Active chromosome segregation by MinD gradients B Di Ventura et al and 0.1% DiO (3,3 0 -dioctadecyloxacarbocyanine perchlorate; Invitrogen). Liposomes were incubated with HEX-labeled DNA and/or with recombinant wild-type or mutant MinD (40 mg/ml) and 1 mM ATP or ADP for 10 min at room temperature, and subsequently subjected to ultracentrifugation for 4 h at 48 000 r.p.m. and 41C in the gradient of Nycodenz as described previously (Weber et al, 1998). All materials were recovered from the gradient in four fractions and fluorescence in respective fractions of the gradient was quantified using a Gemini XS plate reader (Molecular Devices). Additionally, MinD was quantified in each fraction using western blotting with anti-polyHistidine antibodies. See Supplementary information for details.
Modeling and simulation of chromosome dynamics with and without the Min system Two E. coli sister chromosomes were described as two self-avoiding ring polymers (Fritsche et al, 2012) that can move in an elongated rectangular parallelepiped of aspect ratio 1:8. For polymer rings of lengths N ¼ 80, the linear dimensions of the confining geometry were set up such that the radius of gyration R free gyr of the unconfined chain is larger than the linear square box sizes, leading to an 80 Â10 Â10 lattice size and volume fraction of a single chain of 10%. Overlapping configurations of two chains, whose centers of mass coincide with the middle of the cell's long axis, were created to initiate the segregation process. Independent Monte-Carlo trajectories (different initial conditions driven by different random number sequences) representing the dynamics of the segregation process were then sampled.
Chromosome tethering was implemented by temporarily fixing monomers that approach the border of the confinement (see Supplementary information). Simulations were performed using the bond-fluctuation method (BFM) (Carmesin and Kremer, 1988), which has been applied successfully to model the static and dynamic properties of polymer systems in previous studies (Binder and Heermann, 2002).

Supplementary information
Supplementary information is available at the Molecular Systems Biology website (www.nature.com/msb).