Membrane affinity difference between MinD monomer and dimer is not crucial for MinD gradient formation in Bacillus subtilis

  1. Laura C Bohorquez
  2. Henrik Strahl
  3. Davide Marenduzzo
  4. Martin J Thiele
  5. Frank Bürmann
  6. Leendert W Hamoen

  • Curated by eLife

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    In the gram-positive model organism Bacillus subtilis, the membrane associated ParA family member MinD, concentrates the division inhibitor MinC at cell poles where it prevents aberrant division events. This important study presents compelling data suggesting that polar localization of MinCD is largely due to differences in diffusion rates between monomeric and dimeric MinD. This finding is exciting as it negates the necessity for a third, localization determinant, in this system as has been proposed by previous investigations.

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Abstract

Proteins can diffuse micrometers in seconds, yet bacterial cells are able to maintain stable protein gradients. The best studied bacterial protein gradient is the Min system of Escherichia coli. In rod-shaped bacteria the MinCD proteins prevent formation of minicells by inhibiting FtsZ polymerization close to the cell poles. In E. coli these proteins oscillate between cell poles within a minute, resulting in an increased MinCD concentration at the poles. This oscillation is caused by the interaction between MinD and the protein MinE, which form an ATP-driven reaction-diffusion system, whereby the ATPase MinD cycles between a monomeric cytosolic and a dimeric membrane attached states. Bacillus subtilis also has MinCD, but lacks MinE. In this case MinCD form a static gradient that requires the transmembrane protein MinJ, located at cell poles and cell division sites. A recent reaction-diffusion model was successful in recreating the MinD gradient in B. subtilis, assuming that MinD cycles between cytosol and membrane, like in E. coli. Here we show that the monomeric and dimeric states of B. subtilis MinD have comparable membrane affinities, that MinD interacts with MinJ as a dimer, and that MinJ is not required for membrane localization of MinD. Based on these new findings we tested different models, using kinetic Monte Carlo simulations, and found that a difference in diffusion rate between the monomer and dimer, rather than a difference in membrane affinity, is important for B. subtilis MinCD gradient formation.

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  1. eLife

    eLife Assessment

    In the gram-positive model organism Bacillus subtilis, the membrane associated ParA family member MinD, concentrates the division inhibitor MinC at cell poles where it prevents aberrant division events. This important study presents compelling data suggesting that polar localization of MinCD is largely due to differences in diffusion rates between monomeric and dimeric MinD. This finding is exciting as it negates the necessity for a third, localization determinant, in this system as has been proposed by previous investigations.

  2. eLife

    Reviewer #1 (Public review):

    The authors used fluorescence microscopy, image analysis, and mathematical modeling to study the effects of membrane affinity and diffusion rates of MinD monomer and dimer states on MinD gradient formation in B. subtilis. To test these effects, the authors experimentally examined MinD mutants that lock the protein in specific states, including Apo monomer (K16A), ATP-bound monomer (G12V) and ATP-bound dimer (D40A, hydrolysis defective), and compared to wild-type MinD. Overall, the experimental results support the conclusions that reversible membrane binding of MinD is critical for the formation of the MinD gradient, but the binding affinities between monomers and dimers are similar.

    The modeling part is a new attempt to use the Monte Carlo method to test the conditions for the formation of the MinD gradient in B. subtilis. The modeling results provide good support for the observations and find that the MinD gradient is sensitive to different diffusion rates between monomers and dimers. This simulation is based on several assumptions and predictions, which raises new questions that need to be addressed experimentally in the future.

  3. eLife

    Reviewer #3 (Public review):

    This important study by Bohorquez et al examines the determinants necessary for concentrating the spatial modulator of cell division, MinD, at the future site of division and the cell poles. Proper localization of MinD is necessary to bring the division inhibitor, MinC, in proximity to the cell membrane and cell poles where it prevents aberrant assembly of the division machinery. In contrast to E. coli, in which MinD oscillates from pole-to-pole courtesy of a third protein MinE, how MinD localization is achieved in B. subtilis-which does not encode a MinE analog-has remained largely a mystery. The authors present compelling data indicating that MinD dimerization is dispensable for membrane localization but required for concentration at the cell poles. Dimerization is also important for interactions between MinD and MinC, leading to the formation of large protein complexes. Computational modeling, specifically a Monte Carlo simulation, supports a model in which differences in diffusion rates between MinD monomers and dimers lead to concentration of MinD at cell poles. Once there, interaction with MinC increases the size of the complex, further reinforcing diffusion differences. Notably, interactions with MinJ-which has previously been implicated in MinCD localization, are dispensable for concentrating MinD at cell poles although MinJ may help stabilize the MinCD complex at those locations.

    Comments on revisions:

    I believe the authors put respectable effort into revisions and addressing reviewer comments, particularly those that focused on the strengths of the original conclusions. The language in the current version of the manuscript is more precise and the overall product is stronger.

  4. eLife

    Author response:

    The following is the authors’ response to the original reviews.

    Reviewer #1 (Public review):

    The authors used fluorescence microscopy, image analysis, and mathematical modeling to study the effects of membrane affinity and diffusion rates of MinD monomer and dimer states on MinD gradient formation in B. subtilis. To test these effects, the authors experimentally examined MinD mutants that lock the protein in specific states, including Apo monomer (K16A), ATP-bound monomer (G12V), and ATPbound dimer (D40A, hydrolysis defective), and compared to wild-type MinD. Overall, the experimental results support the conclusion that reversible membrane binding of MinD is critical for the formation of the MinD gradient, but that the binding affinities between monomers and dimers are similar.

    The modeling part is a new attempt to use the Monte Carlo method to test the conditions for the formation of the MinD gradient in B. subtilis. The modeling results provide good support for the observations and find that the MinD gradient is sensitive to different diffusion rates between monomers and dimers. This simulation is based on several assumptions and predictions, which raises new questions that need to be addressed experimentally in the future. However, the current story is sufficient without testing these assumptions or predictions.

    Reviewer #2 (Public review):

    Summary:

    Bohorquez et al. investigate the molecular determinants of intracellular gradient formation in the B. subtilis Min system. To this end, they generate B. subtilis strains that express MinD mutants that are locked in the monomeric or dimeric states, and also MinD mutants with amphipathic helices of varying membrane affinity. They then assess the mutants' ability to bind to the membrane and form gradients using fluorescence microscopy in different genetic backgrounds. They find that, unlike in the E. coli Min system, the monomeric form of MinD is already capable of membrane binding. They also show that MinJ is not required for MinD membrane binding and only interacts with the dimeric form of MinD. Using kinetic

    Monte Carlo simulations, the authors then test different models for gradient formation, and find that a MinD gradient along the cell axis is only formed when the polarly localized protein MinJ stimulates dimerization of MinD, and when the diffusion rate of monomeric and dimeric MinD differs. They also show that differences in the membrane affinity of MinD monomers and dimers are not required for gradient formation.

    Strengths:

    The paper offers a comprehensive collection of the subcellular localization and gradient formation of various MinD mutants in different genetic backgrounds. In particular, the comparison of the localization of these mutants in a delta MinC and MinJ background offers valuable additional insights. For example, they find that only dimeric MinD can interact with MinJ. They also provide evidence that MinD locked in a dimer state may co-polymerize with MinC, resulting in a speckled appearance.

    The authors introduce and verify a useful measure of membrane affinity in vivo.

    The modulation of the membrane affinity by using distinct amphipathic helices highlights the robustness of the B. subtilis MinD system, which can form gradients even when the membrane affinity of MinD is increased or decreased.

    Weaknesses:

    The main claim of the paper, that differences in the membrane affinity between MinD monomers and dimers are not required for gradient formation, does not seem to be supported by the data. The only measure of membrane affinity presented is extracted from the transverse fluorescence intensity profile of cells expressing the mGFP-tagged MinD mutants. The authors measure the valley-to-peak ratio of the profile, which is lower than 1 for proteins binding to the membrane and higher than 1 for cytosolic proteins. To verify this measure of membrane affinity, they use a membrane dye and a soluble GFP, which results in values of ~0.75 and ~1.25, respectively. They then show that all MinD mutants have a value - roughly in the range of 0.8-0.9 - and they use this to claim that there are no differences in membrane affinity between monomeric and dimeric versions.

    While this way to measure membrane affinity is useful to distinguish between binders and non-binders, it is unclear how sensitive this assay is, and whether it can resolve more subtle differences in membrane affinity, beyond the classification into binders and non-binders. A dimer with two amphipathic helices should have a higher membrane affinity than a monomer with only one such copy. Thus, the data does not seem to support the claim that "the different monomeric mutants have the same membrane affinity as the wildtype MinD". The data only supports the claim that B. subtilis MinD monomers already have a measurable membrane affinity, which is indeed a difference from the E. coli Min system.

    While their data does show that a stark difference between monomer and dimer membrane affinity may not be required for gradient formation in the B. subtilis case, it is also not prevented if the monomer is unable to bind to the membrane. They show this by replacing the native MinD amphipathic helix with the weak amphipathic helix NS4AB-AH. According to their membrane affinity assay, NS4AB-AH does not bind to the membrane as a monomer (Figure 4D), but when this helix is fused to MinD, MinD is still capable of forming a gradient (albeit a weaker one). Since the authors make a direct comparison to the E. coli MinDE systems, they could have used the E. coli MinD MTS instead or in addition to the NS4AB-AH amphipathic helix. The reviewer suspects that a fusion of the E. coli MinD MTS to B. subtilis MinD may also support gradient formation.

    The paper contains insufficient data to support the many claims about cell filamentation and minicell formation. In many cases, statements like "did not result in cell filamentation" or "restored cell division" are only supported by a single fluorescence image instead of a quantitative analysis of cell length distribution and minicell frequency, as the one reported for a subset of the data in Figure 5.

    The paper would also benefit from a quantitative measure of gradient formation of the distinct MinD mutants, instead of relying on individual fluorescent intensity profiles.

    The authors compare their experimental results with the oscillating E. coli MinDE system and use it to define some of the rules of their Monte Carlo simulation. However, the description of the E. coli Min system is sometimes misleading or based on outdated findings.

    The Monte Carlo simulation of the gradient formation in B. subtilis could benefit from a more comprehensive approach:

    (1) While most of the initial rules underlying the simulation are well justified, the authors do not implement or test two key conditions:

    (a) Cooperative membrane binding, which is a key component of mathematical models for the oscillating E. coli Min system. This cooperative membrane binding has recently been attributed to MinD or MinCD oligomerization on the membrane and has been experimentally observed in various instances; in fact, the authors themselves show data supporting the formation of MinCD copolymers.

    (2) Local stimulation of the ATPase activity of MinD which triggers the dimer-to-monomer transition; E. coli MinD ATP hydrolysis is stimulated by the membrane and by MinE, so B. subtilis MinD may also be stimulated by the membrane and/or other components like MinJ. Instead, the authors claim that (a) would only increase differences in diffusion between the monomer and different oligomeric species, and that a 2-fold increase in dimerization on the membrane could not induce gradient formation in their simulation, in the absence of MinJ stimulating gradient formation. However, a 2-fold increase in dimerization is likely way too low to explain any cooperative membrane binding observed for the E. coli Min system. Regarding (b), they also claim that implementing stimulation of ATP hydrolysis on the membrane (dimer-to-monomer transition) would not change the outcome, but no simulation result for this condition is actually shown.

    (3) To generate any gradient formation, the authors claim that they would need to implement stimulation of dimer formation by MinJ, but they themselves acknowledge the lack of any experimental evidence for this assertion. They then test all other conditions (e.g., differences in membrane affinity, diffusion, etc.) in addition to the requirement that MinJ stimulates dimer formation. It is unclear whether the authors tested all other conditions independently of the "MinJ induces dimerization" condition, and whether either of those alone or in combination could also lead to gradient formation. This would be an important test to establish the validity of their claims.

    Reviewer #3 (Public review):

    This important study by Bohorquez et al examines the determinants necessary for concentrating the spatial modulator of cell division, MinD, at the future site of division and the cell poles. Proper localization of MinD is necessary to bring the division inhibitor, MinC, in proximity to the cell membrane and cell poles where it prevents aberrant assembly of the division machinery. In contrast to E. coli, in which MinD oscillates from pole to pole courtesy of a third protein MinE, how MinD localization is achieved in B. subtilis - which does not encode a MinE analog - has remained largely a mystery. The authors present compelling data indicating that MinD dimerization is dispensable for membrane localization but required for concentration at the cell poles. Dimerization is also important for interactions between MinD and MinC, leading to the formation of large protein complexes. Computational modeling, specifically a Monte Carlo simulation, supports a model in which differences in diffusion rates between MinD monomers and dimers lead to the concentration of MinD at cell poles. Once there, interaction with MinC increases the size of the complex, further reinforcing diffusion differences. Notably, interactions with MinJ-which has previously been implicated in MinCD localization, are dispensable for concentrating MinD at cell poles although MinJ may help stabilize the MinCD complex at those locations.

    Reviewer #1 (Recommendations for the authors):

    (1) The title could be modified to better reflect the emphasis on MinD monomer and dimer diffusion rather than the fact that membrane affinity is not important in MinD gradient formation. In addition, because membrane association requires affinity for the membrane, this title seems inconsistent with statements in the main text, such as Lines 246-247: a reversible membrane association is important for the formation of a MinD gradient along the cell axis.

    We agree with the reviewer that the title can be more accurate, and we have now changed it to “Membrane affinity difference between MinD monomer and dimer is not crucial to MinD gradient formation in Bacillus subtilis”

    (2) This paper reports that the difference in diffusion rates between MinD monomers and dimers is an important factor in the formation of Bs MinD gradients. However, one can argue for the importance of MinD monomers in the cellular context. Since the abundance of ATP in cells often far exceeds the abundance of MinD protein molecules under experimental conditions, MinD can easily form dimers in the cytoplasm. How does the author address this problem?

    It is a good point that ATP concentration in the cell likely favours dimers in the cytoplasm. However, what is important in our model is that there is cycling between monomer and dimer, rather than where exactly this happen. In fact, the gradients works essentially equally well if dimers can become monomers only whilst they are at the membrane, as we have mentioned in the manuscript (lines 324-326 in the original manuscript). However, in the original manuscript this simulation was not shown, and now we have included this in the new Fig. 8D & E.

    (3)The claim "This oscillating gradient requires cycling of MinD between a monomeric cytosolic and a dimeric membrane attached state." (Lines 46, 47) is not well supported by most current studies and needs to be revised since to my knowledge, most proposed models do not consider the monomer state. The basic reaction steps of Ec Min oscillations include ATP-bound MinD dimers attaching to the membrane that subsequently recruit more MinD dimers and MinE dimers to the membrane; MinE interactions stimulate ATP hydrolysis in MinD, leading to dissociation of ADP-bound MinD dimers from the membrane; nucleotide exchange occurs in the cytoplasm.

    Here the reviewer refers to a sentence in a short “Importance” abstract that we have added. In fact, such abstract is not necessary, so we have removed it. Of note, the E. coli MinD oscillation, including the role of MinE, is described in detail in the Introduction.

    A recent reference is a paper by Heermann et al. (2020; doi: 10.1016/j.jmb.2020.03.012), which considers the MinD monomer state, which is not mentioned in this work. How do their observations compare to this work?

    The Heermann paper mentions that MinD bound to the membrane displays an interface for multimerization, and that this contributes to the local self-enhancement of MinD at the membrane. In our Discussion, we do mention that E. coli MinD can form polymers in vitro and that any multimerization of MinD dimers will further increase the diffusion difference between monomer and dimer, and might contribute to the formation of a protein gradient (lines 459-467). We have now included a reference to the Heermann paper (line 461).

    (4) Throughout the manuscript, errors in citing references were found in several places.

    We have corrected this where suggested.

    (5) The introduction may be somewhat misleading due to mixed information from experimental cellular results, in vitro reconstructions, and theoretical models in cells or in vitro environments. Some models consider space constraints, while others do not. Modifications are recommended to clarify differences.

    See below for responses

    (6) The citation for MinD monomers:

    The paper by Hu and Lutkenhaus (2003, doi: 10.1046/j.1365-2958.2003.03321.x.) contains experimental evidence showing monomer-dimer transition using purified proteins. Another paper by the same laboratory (Park et al. 2012, doi: 10.1111/j.1365-2958.2012.08110.x.) explained how ATP-induced dimerization, but this paper is not cited.

    The Park et al. 2012 paper focusses at the asymmetric activation of MinD ATPase by MinE, which goes beyond the scope of our work. However, we have cited several other papers from the Lutkenhaus lab, including the Wu et al. 2011 paper describing the structure of the MinD-ATP complex.

    Other evidence comes from structural studies of Archaea Pyrococcus furiosus (1G3R) and Pyrococcus horikoshii (1ION), and thermophilic Aquifex aeolicus (4V01, 4V02, 4V03). As they may function differently from Ec MinD, they are less relevant to this manuscript.

    We agree.

    (7) Lines 65, 66: Using the term 'a reaction-diffusion couple' to describe the biochemical facts by citing references of Hu and Lutkenhaus (1999) and Raskin and de Boer (1999) is not appropriate. The idea that the Min system behaves as a reaction-diffusion system was started by Howard et al. (2001), Meinhardt and de Boer (2001), and Huang et al. (2003) et al. In addition, references for MinE oscillation are missing.

    We have now corrected this (line 52).

    (8) Lines 77-79: Citations are incorrect.

    ATP-induced dimerization: Hu and Lutkenhaus (2003, DOI: 10.1046/j.1365-2958.2003.03321.x), Park et al. (2012). C-terminal amphipathic helix formation: Szeto et al. (2003), Hu and Lutkenhaus (2003, DOI: 10.1046/j.1365-2958.2003.03321.x).

    Citations have been corrected.

    (9) Line 78: The C-terminal amphipathic helix is not pre-formed and then exposed upon conformational change induced by ATP-binding. This alpha-helical structure is an induced fold upon interaction with membranes as experimentally demonstrated by Szeto et al. (2003).

    We have adjusted the text to correct this (lines 64-66).

    (10) Line 102: 'cycles between membrane association and dissociation of MinD' also requires MinE in addition to ATP.

    We believe that in the context of this sentence and following paragraph it is not necessary to again mention MinE, since it is focused on parallels between the E. coli and B. subtilis MinD membrane binding cycles.

    (11) In the introduction, could the author briefly explain to a general audience the difference between Monte Carlo and reaction-diffusion methods? How do different algorithms affect the results?

    The main difference between the kinetic Monte Carlo and typical reaction-diffusion methods which is relevant to our work is that the first is particle-based, and naturally includes statistical fluctuations (noise), whereas the second is field-based, and is in the normal implementation deterministic, so does not include noise. Whilst it should be noted that one can in principle include noise in the field-based reactiondiffusion methods, this is done rarely. Additionally, although we do not do this here, the kinetic MonteCarlo can also account, in principle, for particle shape (sphere versus rod), or for localized interactions (as sticky patches on the surface): therefore the kinetic Monte Carlo is more microscopic in nature. We have now shortly described the difference in lines 102-105.

    (12) Lines 126-128: The second part of the sentence uses the protein structure of Pyrococcus furiosus MinD (Ref 37) to support a protein sequence comparison between Ec and Bs MinD. However, the structure of the dimeric E. coli MinD-ATP complex (3Q9L) is available, which is Reference 38 that is more suited for direct comparison.

    To discuss monomeric MinD from P. furiosus, it will be useful to include it in the primary sequence alignment in Figure S1.

    We do not think that this detailed information is necessary to add to Figure S1, since the mutants have been described before (appropriate citations present in the text).

    (13) Lines 127, 166: Where Figure S1 is discussed, a structural model of MinD will be useful alongside with the primary sequence alignment.

    We do not think that this detailed information is necessary to understand the experiments since the mutants have been described before.

    (14) Lines 131-132: Reference is missing for the sentence of " the conserved..."; Reference 38. In Reference 38, there is no experimental evidence on G12 but inferred from structure analysis. Reference 26 discusses ATP and MinE regulation on the interactions between MinD and phospholipid bilyers; not about MinD dimerization.

    We have corrected this and added the proper references.

    For easy reading, the mutant MinD phenotypes can be indicated here instead of in the figure legends, including K16A (apo monomer), MinD G12V (ATP-bound monomer), and MinD D40A (ATP-bound dimer, ATP hydrolysis deficient).

    We have added the suggested descriptions of the mutants in the main text.

    (15) Lines 150-151: Unlike Ec MinD, which forms a clear gradient in one half of the cell, Bs MinD (wild type) mainly accumulates at the hemispheric poles. What percentage of a cell (or cell length) can be covered by the Bs MinD gradient? How does the shaded area in the longitudinal FIP compare to the area of the bacterial hemispherical pole? If possible, it might be interesting to compare with the range of nucleoid occlusion mechanisms that occur.

    Part of the MinD gradient covers the nucleoid area, since the fluorescence signal is still visible along the cell lengths, yet there is no sudden drop in fluorescence, suggesting that nucleoid exclusion does not play a role.

    (16) Line 160: In addition to summarizing the membrane-binding affinity, descriptions of the differences in the gradient distribution or formation will be useful.

    We have done this in lines 155-156 of the original manuscript: “The monomeric ATP binding G12V variant shows the same absence of a protein gradient as the K16A variant”.

    (17) Line 262: 'distribution' is not shown.

    We do not understand this remark. This information is shown in Fig. 5B (now Fig. 6B).

    (18) Line 287: Wrong citation for reference 31.

    Reference has been corrected.

    (19) Line 288 and lines 596 regarding the Monte Carlo simulation:

    (a) An illustration showing the reaction steps for MinD gradient formation will help understand the rationale and assumptions behind this simulation.

    We have added an illustration depicting the different modelling steps in the new Fig. 8.

    (b) Equations are missing.

    (c) A table summarizing the parameters used in the simulation and their values.

    (d) For general readers, it will be helpful to convert the simulation units to real units.

    (e) Indicate real experimental data with a citation or the reason for any speculative value.

    The Methods section provides a discussion of all parameters used in the potentials on which our kinetic Monte-Carlo algorithm is based. We have now also provided a Table in the SI (Table S1) with typical parameter values in both simulation units and real units. The experimental data and reasoning behind the values chosen are discussed in the Methods section (see “Kinetic Monte Carlo simulation”).

    (20) Lines 320-321: Reference missing.

    The interaction between MinJ and the dimer form of MinD is based on our findings shown in the original Fig. S4, and this information has not been published before. We have rephrased the sentence to make it more clear. Of note, Fig. S4 has been moved to the main manuscript, at the request of reviewer #2, and is now new Fig. 2.

    (21) Lines 355-359: Is the statement specifically made for the Bs Min system? Is there any reference for the statement? Isn't the differences in diffusion rates between molecules 'at different locations' in the system more important than reducing their diffusion rates alone? It is unclear about the meaning of the statement "the Min system uses attachment to the membrane to slow down diffusion". Is this an assumption in the simulation?

    The statement is generic, however the reviewer has a good point and we have made this statement more clear by changing “considerably reduced diffusion rate” to “locally reduced diffusion rate” (line 359).

    (22) Line 403: Citation format.

    We have corrected the text and citation.

    (23) Lines 442-444: The parameters are not defined anywhere in the manuscript.

    Discussed in the M&M and in the new Table S1.

    (24) Lines 464-465: Regarding the final sentence, what does 'this prediction' refer to? Hasn't the author started with experimental observations, predicted possible factors of membrane affinity and diffusion rates, and used the simulation approach to disapprove or support the prediction?

    We have changed “prediction” to “suggestion”, to make it clear that it is related to the suggestion in the previous sentence that “our modelling suggests that stimulation of MinD-dimerization at cell poles and cell division sites is needed.” (line 471).

    (25) Materials and Methods: Statistical methods for data analyses are missing.

    Added to “Microscopy” section.

    (26) References: References 34, 40, 51 are incomplete.

    References 34 and 40 have been corrected. Reference 51 is a book.

    (27) Figures: The legends (Figures 1-7) can be shortened by removing redundant details in Material and Methods. Make sure statistical information is provided. The specific mutant MinD states, including Apo monomer, ATP-bound dimer, ATP hydrolysis deficient, and non-membrane binding etc can be specified in the main text. They are repeated in the legends of Figures 1 and 2.

    We have removed redundant details from the legends and provided statistical information.

    (28) Supporting information:

    Table S1: Content of the acknowledgment statement may be moved to materials and methods and the acknowledgment section. Make sure statistical information is provided in the supporting figure legends.

    We are not sure what the reviewer means with the content acknowledgement in Table S1 (now Table S2). Statistical information has been added.

    Figure S1. Adding a MinD structure model will be useful.

    We do not think that a structural model will enlighten our results since our work is not focused at structural mutagenesis. The mutants that we use have been described in other papers that we have cited.

    Reviewer #2 (Recommendations for the authors):

    The authors should cite and relate their data to the preprint by Feddersen & Bramkamp, BioRxiv 2024. ATPase activity of B. subtilis MinD is activated solely by membrane binding.

    We have now discussed this paper in relation to our data in lines 407-409.

    I am not convinced the authors are able to make the statement in lines 160-161 based on their assay: "This confirmed that the different monomeric mutants have the same membrane affinity as wild-type MinD". It is unclear if measuring valley-to-peak ratios in their longitudinal profiles can resolve small differences in membrane affinity. Wildtype MinD should at least be dimeric, or (as the authors also note elsewhere) may even be present in higher-order structures and as such have a higher membrane affinity than a monomeric MinD mutant. The authors should rephrase the corresponding sections in the manuscript to state that the MinD monomer already has detectable membrane affinity, instead of stating that the monomer and dimer membrane affinity are the same.

    We agree that “the same affinity” is too strongly worded, and we have now rephrased this by saying that the different monomeric mutants have a comparable membrane affinity as wild type MinD (line 152).

    According to the authors' analysis, MinD-NS4B would not bind to the membrane as it has a valley-to-peak ratio higher than 1, similar to the soluble GFP. However, the protein is clearly forming a gradient, and as such probably binding to the membrane. The authors should discuss this as a limitation of their membrane binding measure.

    The ratio value of 1 is not a cutoff for membrane binding. As shown in Fig. 1F, GFP has a valley-topeak ratio close to 1.25, whereas the FM5-95 membrane dye has a ratio close to 0.75. In Fig. 3C (now Fig. 4C) we have shown that GFP fused with the NS4B membrane anchor has a lower ratio than free GFP, and we have shown the same in Fig. 4D (now Fig. 5D) for GFP-MinD-NS4B. The difference are small but clear, and not similar to GFP.

    The observation that MinD dimers are localized by MinJ is interesting and key to the rule of the Monte Carlo simulation that dimers attach to MinJ. However, the data is hidden in the supplementary information and is not analysed as comprehensively, e.g., it lacks the analysis of the membrane binding. The paper would benefit from moving the fluorescence images and accompanying analysis into the main text.

    We have moved this figure to the main text and added an analysis of the fluorescence intensities (new Fig. 2).

    The authors should show the data for cell length and minicell formation, not only for the MinDamphipathic helix versions (Fig. 5), but also for the GFP-MinD, and all the MinD mutants. They do refer to some of this data in lines 145-148 but do not show it anywhere. They also refer to "did not result in cell filamentation" in line 213 and to "resulted in highly filamentous cells" and "Introduction of a minC deletion restored cell division" in lines 167-160 without showing the cell length and minicell data, but instead refer to the fluorescence image of the respective strain. I would suggest the authors include this data either in a subpanel in the respective figure or in the supplementary information.

    The effect of uncontrolled MinC activity is very apparent and leads to long filamentous cells. Also the occurrence of minicells is apparent. Cell lengths distribution of wild type cells is shown in Fig. 6B, and minicell formation is negligibly small in wild type cells.

    The transverse fluorescence intensity profiles used as a measure for membrane binding are an average profile from ~30 cells. In the case of the longitudinal profiles that display the gradient, only individual profiles are displayed. I understand that because of distinct cell length, the longitudinal profiles cannot simply be averaged. However, it is possible to project the profiles onto a unit length for averaging (see for example the projection of profiles in McNamara. et al., BioRxiv (2023)). It would be more convincing to average these profiles, which would allow the authors to also quantify the gradients in more detail. If that is impossible, the authors may at least quantify individual valley-to-peak ratios of the longitudinal fluorescence profiles as a measure of the gradient.

    We agree that in future work it would be better to average the profiles as suggested. However, due to limited time and resources, we cannot do this for the current manuscript.

    Regarding the rules and parameters used for the Monte Carlo simulation (see also the corresponding sections in the public review):

    (1) The authors mention that they have not included multimerization of MinD in their simulation but argue in the discussion that it would only strengthen the differences in the diffusion between monomers and multimers. This is correct, but it may also change the membrane residence time and membrane affinity drastically.

    Simulation of multimerization is difficult, but we have now included a simulation whereby MinD dimers can also form tetramers (lines 341-348), shown in the new Fig. 8K. This did not alter the MinD gradient much.

    (2) The authors implement a dimer-to-monomer transition rate that they equate with the stochastic ATP hydrolysis rate occurring with a half-life of approximately 1/s (line 305). They claim that this rate is based on information from E. coli and cite Huang and Wingreen. However, the Huang paper only mentions the nucleotide exchange rate from ADP to ATP at 1/s. Later that paper cites their use of an ATP hydrolysis rate of 0.7/s to match the E. coli MinDE oscillation rate of 40s. From the authors' statement, it is unclear to me whether they refer to the actual ATP hydrolysis rate in Huang and Wingreen or something else. For E. coli MinD, both the membrane and MinE stimulate ATPase activity. Even if B. subtilis lacks MinE, ATP hydrolysis may still be stimulated by the membrane, which has also been reported in another preprint (Feddersen & Bramkamp, BioRxiv 2024). It may also be stimulated by other components of the Min system like MinJ. The authors should include in the manuscript the Monte Carlo simulation implementing dimer to monomer transition on the membrane only, which is currently referred to only as "(data not shown)".

    The exact value of the ATP hydrolysis rate is not so important here, so 1/s only gives the order of magnitude (in line with 0.7/s above), which we have now clarified in lines 631-632. We have now also added the “(data not shown” results to Fig. 8, i.e. simulations where dimer to monomer transitions (i.e. ATPase activity) only occurs at the membrane (Fig. 8D & E, and lines 319-322).

    (3) How long did the authors simulate for? How many steps? What timesteps does the average pictured in Figure 7 correspond to?

    We simulated 10^7time steps (corresponding to 100 s in real time). We have checked that the simulation steps for which we average are in steady state. Typical snapshots are recorded after 10^610^7time steps, when the system is in steady state. We have added this information in lines 299-300.

    There are several misconceptions about the (oscillating E. coli) Min system in the main text:

    (1) Lines 77-78: "In case of the E. coli MinD, ATP binding leads to dimerization of MinD, which induces a conformational change in the C-terminal region, thereby exposing an amphiathic helix that functions as a membrane binding domain" and "This shows a clear difference with the E. coli situation, where dimerization of MinD causes a conformational change of the C-terminal region enabling the amphipathic helix to insert into the lipid bilayer" in lines 400-403 are incorrect. There is no evidence that the amphipathic helix at the C-terminus of MinD changes conformation upon ATP binding; several studies have shown instead that a single copy of the amphipathic helix is too weak to confer efficient membrane binding but that the dimerization confers increased membrane binding as now two amphipathic helices are present leading to an avidity effect in membrane binding. Please refer to the following papers (Szeto et al., JBC (2003); Wu et al., Mol Microbiol (2011); Park et al., Cell (2011); Heermann et al., JMB (2020); Loose et al., Nat Struct Mol Biol (2011); Kretschmer et al., ACS Syn Biol (2021); Ramm et al., Nat Commun (2018) or for a better overview the following reviews on the topic of the E. coli Min system Wettmann and Kruse, Philos Trans R Soc B Biol (2018), Ramm et al., Cell and Mol Life Sci (2019); Halatek et al., Philos Trans R SocB Biol Sci (2018).

    This is indeed incorrectly formulated, and we have now amended this in lines 64-66 and lines 403406. Key papers are cited in the text.

    (2) The authors mention that E. coli MinD may multimerize, citing a study where purified MinD was found to polymerize, and then suggest that this is unlikely to be the case in B. subtilis as FRAP recovery of MinD is quick. However, cooperativity in membrane binding is essential to the mathematical models reproducing E. coli Min oscillations, and there is more recent experimental evidence that E. coli MinD forms smaller oligomers that differ in their membrane residence time and diffusion (e.g., Heermann et al., Nat Methods (2023); Heermann et al., JMB (2020);) I would suggest the authors revise the corresponding text sections and test the multimerization in their simulation (see above).

    As mentioned above, simulating oligomerization is difficult, but in order to approximate related cooperative effects, we have simulated a situation whereby MinD dimers can form tetramers. This simulation did not show a large change in MinD gradient formation. We have added the result of this simulation to Fig. 8 (Fig. 8K), and discuss this further in lines 341-348 and 459-467.

    (3) Lines 75-76 and lines 79-80: The sentences "MinC ... and needs to bind to the Walker A-type ATPase MinD for its activity" and "The MinD dimer recruits MinC ... and stimulates its activity" are misleading. MinC is localized by MinD, but MinD does not alter MinC activity, as MinC mislocalization or overexpression also prevents FtsZ ring formation leading to minicell or filamentous cells, as also later described by the authors (line 98). There is also no biochemical evidence that the presence of MinD somehow alters MinC activity towards FtsZ other than a local enrichment on the membrane. I would rephrase the sentence to emphasize that MinD is only localizing MinC but does not alter its activity.

    We have rephrased this sentence to prevent misinterpretation (lines 66-67).

    Minor points:

    (1) I am not quite sure what the experiment with the CCCP shows. The authors explain that MinD binding via the amphipathic helix requires the presence of membrane potential and that the addition of CCCP disturbs binding. They then show that the MinD with two amphipathic helices is not affected by CCCP but the wildtype MinD is. What is the conclusion of this experiment? Would that mean that the MinD with two amphipathic helices binds more strongly, very differently, perhaps non-physiologically?

    This experiment was “To confirm that the tandem amphipathic helix increased the membrane affinity of MinD”, as mentioned in the beginning of the paragraph (line 224).

    (2) Lines 456-457: Please cite the FRAP experiment that shows a quick recovery rate of MinD.

    Reference has been added.

    (3) Figure 4D: It is unclear to me to which condition the p-value brackets point.

    This is related to a statistical t-test. We have added this information to the legend of the figure.

    (4) Line 111, "in the membrane affinity of the MinD". I think that the "the" before MinD should be removed.

    Corrected

    (5) Typo in line 199 "indicting" instead of indicating.

    Corrected

    (6) Typo in line 220 "reversable" instead of reversible.

    Corrected

    (7) Lines 279, 284, 905: "Monte-Carlo" should read Monte Carlo.

    Corrected

    Reviewer #3 (Recommendations for the authors):

    Introduction: As written, the introduction does not provide sufficient background for the uninitiated reader to understand the function of the MinCD complex in the context of assembly and activation of cell division in B. subtilis. The introduction is also quite long and would benefit from condensing the description of the Min oscillation mechanism in E. coli to one or two sentences. While highlighting the role of MinE in this system is important for understanding how it works, it is only needed as a counterpoint to the situation in B. subtilis.

    Since the Min system of E. coli is by far the best understood Min system, we feel that it is important to provide detailed information on this system. However, we have added an introductory sentence to explain the key function of the Min system (line 46-48).

    Line 248: Increasing MinD membrane affinity increases the frequency of minicells - however it is unclear if cells are dividing too much or if it is just a Min mutant (i.e. occasionally dividing at the cell pole vs the middle)? Cell length measurements should be included to clarify this point (Figures 4 and 5).

    This information is presented in Fig. 5B (Cell length distribution), which is now Fig. 6B, indicating that the average cell length increases in the tandem alpha helix mutant, a phenotype that is comparable to a MinD knockout.

    Figure 5: I am a bit confused as to whether increasing MinD affinity doesn't lead to a general block in division by MinCD rather than phenocopying a minD null mutant.

    Although the tandem alpha helix mutant has a cell length distribution comparable to a minD knockout, the tandem mutant produces much less minicells then the minD knockout, indicating that there is still some cell division regulation.

  5. Version published to 10.7554/elife.101520.2 on eLife
  6. Version published to 10.7554/elife.101520 on eLife
  7. Version published to 10.7554/elife.101520.1 on eLife
  8. eLife

    eLife assessment

    This important study provides solid mechanistic and modeling data suggesting that the polar localization of MinCD in Bacillus subtilis is largely due to differences in diffusion rates between monomeric and dimeric MinD. This finding is exciting as it negates the necessity for a third, localization determinant, in this system as has been previously proposed. The work is generally strong but is incomplete without some additional quantitative analysis, as well as clarification of the underlying assumptions and details used for the modeling experiments.

  9. eLife

    Reviewer #1 (Public review):

    The authors used fluorescence microscopy, image analysis, and mathematical modeling to study the effects of membrane affinity and diffusion rates of MinD monomer and dimer states on MinD gradient formation in B. subtilis. To test these effects, the authors experimentally examined MinD mutants that lock the protein in specific states, including Apo monomer (K16A), ATP-bound monomer (G12V), and ATP-bound dimer (D40A, hydrolysis defective), and compared to wild-type MinD. Overall, the experimental results support the conclusion that reversible membrane binding of MinD is critical for the formation of the MinD gradient, but that the binding affinities between monomers and dimers are similar.

    The modeling part is a new attempt to use the Monte Carlo method to test the conditions for the formation of the MinD gradient in B. subtilis. The modeling results provide good support for the observations and find that the MinD gradient is sensitive to different diffusion rates between monomers and dimers. This simulation is based on several assumptions and predictions, which raises new questions that need to be addressed experimentally in the future. However, the current story is sufficient without testing these assumptions or predictions.

  10. eLife

    Reviewer #2 (Public review):

    Summary:

    Bohorquez et al. investigate the molecular determinants of intracellular gradient formation in the B. subtilis Min system. To this end, they generate B. subtilis strains that express MinD mutants that are locked in the monomeric or dimeric states, and also MinD mutants with amphipathic helices of varying membrane affinity. They then assess the mutants' ability to bind to the membrane and form gradients using fluorescence microscopy in different genetic backgrounds. They find that, unlike in the E. coli Min system, the monomeric form of MinD is already capable of membrane binding. They also show that MinJ is not required for MinD membrane binding and only interacts with the dimeric form of MinD. Using kinetic Monte Carlo simulations, the authors then test different models for gradient formation, and find that a MinD gradient along the cell axis is only formed when the polarly localized protein MinJ stimulates dimerization of MinD, and when the diffusion rate of monomeric and dimeric MinD differs. They also show that differences in the membrane affinity of MinD monomers and dimers are not required for gradient formation.

    Strengths:

    The paper offers a comprehensive collection of the subcellular localization and gradient formation of various MinD mutants in different genetic backgrounds. In particular, the comparison of the localization of these mutants in a delta MinC and MinJ background offers valuable additional insights. For example, they find that only dimeric MinD can interact with MinJ. They also provide evidence that MinD locked in a dimer state may co-polymerize with MinC, resulting in a speckled appearance.

    The authors introduce and verify a useful measure of membrane affinity in vivo.

    The modulation of the membrane affinity by using distinct amphipathic helices highlights the robustness of the B. subtilis MinD system, which can form gradients even when the membrane affinity of MinD is increased or decreased.

    Weaknesses:

    The main claim of the paper, that differences in the membrane affinity between MinD monomers and dimers are not required for gradient formation, does not seem to be supported by the data. The only measure of membrane affinity presented is extracted from the transverse fluorescence intensity profile of cells expressing the mGFP-tagged MinD mutants. The authors measure the valley-to-peak ratio of the profile, which is lower than 1 for proteins binding to the membrane and higher than 1 for cytosolic proteins. To verify this measure of membrane affinity, they use a membrane dye and a soluble GFP, which results in values of ~0.75 and ~1.25, respectively. They then show that all MinD mutants have a value - roughly in the range of 0.8-0.9 - and they use this to claim that there are no differences in membrane affinity between monomeric and dimeric versions.

    While this way to measure membrane affinity is useful to distinguish between binders and non-binders, it is unclear how sensitive this assay is, and whether it can resolve more subtle differences in membrane affinity, beyond the classification into binders and non-binders. A dimer with two amphipathic helices should have a higher membrane affinity than a monomer with only one such copy. Thus, the data does not seem to support the claim that "the different monomeric mutants have the same membrane affinity as the wildtype MinD". The data only supports the claim that B. subtilis MinD monomers already have a measurable membrane affinity, which is indeed a difference from the E. coli Min system.

    While their data does show that a stark difference between monomer and dimer membrane affinity may not be required for gradient formation in the B. subtilis case, it is also not prevented if the monomer is unable to bind to the membrane. They show this by replacing the native MinD amphipathic helix with the weak amphipathic helix NS4AB-AH. According to their membrane affinity assay, NS4AB-AH does not bind to the membrane as a monomer (Figure 4D), but when this helix is fused to MinD, MinD is still capable of forming a gradient (albeit a weaker one). Since the authors make a direct comparison to the E. coli MinDE systems, they could have used the E. coli MinD MTS instead or in addition to the NS4AB-AH amphipathic helix. The reviewer suspects that a fusion of the E. coli MinD MTS to B. subtilis MinD may also support gradient formation.

    The paper contains insufficient data to support the many claims about cell filamentation and minicell formation. In many cases, statements like "did not result in cell filamentation" or "restored cell division" are only supported by a single fluorescence image instead of a quantitative analysis of cell length distribution and minicell frequency, as the one reported for a subset of the data in Figure 5.

    The paper would also benefit from a quantitative measure of gradient formation of the distinct MinD mutants, instead of relying on individual fluorescent intensity profiles.

    The authors compare their experimental results with the oscillating E. coli MinDE system and use it to define some of the rules of their Monte Carlo simulation. However, the description of the E. coli Min system is sometimes misleading or based on outdated findings.

    The Monte Carlo simulation of the gradient formation in B. subtilis could benefit from a more comprehensive approach:

    (1) While most of the initial rules underlying the simulation are well justified, the authors do not implement or test two key conditions:
    (a) Cooperative membrane binding, which is a key component of mathematical models for the oscillating E. coli Min system. This cooperative membrane binding has recently been attributed to MinD or MinCD oligomerization on the membrane and has been experimentally observed in various instances; in fact, the authors themselves show data supporting the formation of MinCD copolymers.

    (2) Local stimulation of the ATPase activity of MinD which triggers the dimer-to-monomer transition; E. coli MinD ATP hydrolysis is stimulated by the membrane and by MinE, so B. subtilis MinD may also be stimulated by the membrane and/or other components like MinJ. Instead, the authors claim that (a) would only increase differences in diffusion between the monomer and different oligomeric species, and that a 2-fold increase in dimerization on the membrane could not induce gradient formation in their simulation, in the absence of MinJ stimulating gradient formation. However, a 2-fold increase in dimerization is likely way too low to explain any cooperative membrane binding observed for the E. coli Min system. Regarding (b), they also claim that implementing stimulation of ATP hydrolysis on the membrane (dimer-to-monomer transition) would not change the outcome, but no simulation result for this condition is actually shown.

    (3) To generate any gradient formation, the authors claim that they would need to implement stimulation of dimer formation by MinJ, but they themselves acknowledge the lack of any experimental evidence for this assertion. They then test all other conditions (e.g., differences in membrane affinity, diffusion, etc.) in addition to the requirement that MinJ stimulates dimer formation. It is unclear whether the authors tested all other conditions independently of the "MinJ induces dimerization" condition, and whether either of those alone or in combination could also lead to gradient formation. This would be an important test to establish the validity of their claims.

  11. eLife

    Reviewer #3 (Public review):

    This important study by Bohorquez et al examines the determinants necessary for concentrating the spatial modulator of cell division, MinD, at the future site of division and the cell poles. Proper localization of MinD is necessary to bring the division inhibitor, MinC, in proximity to the cell membrane and cell poles where it prevents aberrant assembly of the division machinery. In contrast to E. coli, in which MinD oscillates from pole to pole courtesy of a third protein MinE, how MinD localization is achieved in B. subtilis - which does not encode a MinE analog - has remained largely a mystery. The authors present compelling data indicating that MinD dimerization is dispensable for membrane localization but required for concentration at the cell poles. Dimerization is also important for interactions between MinD and MinC, leading to the formation of large protein complexes. Computational modeling, specifically a Monte Carlo simulation, supports a model in which differences in diffusion rates between MinD monomers and dimers lead to the concentration of MinD at cell poles. Once there, interaction with MinC increases the size of the complex, further reinforcing diffusion differences. Notably, interactions with MinJ-which has previously been implicated in MinCD localization, are dispensable for concentrating MinD at cell poles although MinJ may help stabilize the MinCD complex at those locations.

  12. Version published to 10.1101/2024.06.11.598461 on bioRxiv