Advertisement

The Bacterial Actin MamK

IN VITRO ASSEMBLY BEHAVIOR AND FILAMENT ARCHITECTURE*
Open AccessPublished:November 30, 2012DOI:https://doi.org/10.1074/jbc.M112.417030
      It is now recognized that actin-like proteins are widespread in bacteria and, in contrast to eukaryotic actins, are highly diverse in sequence and function. The bacterial actin, MamK, represents a clade, primarily found in magnetotactic bacteria, that is involved in the proper organization of subcellular organelles, termed magnetosomes. We have previously shown that MamK from Magnetospirillum magneticum AMB-1 (AMB-1) forms dynamic filaments in vivo. To gain further insights into the molecular mechanisms that underlie MamK dynamics and function, we have now studied the in vitro properties of MamK. We demonstrate that MamK is an ATPase that, in the presence of ATP, assembles rapidly into filaments that disassemble once ATP is depleted. The mutation of a conserved active site residue (E143A) abolishes ATPase activity of MamK but not its ability to form filaments. Filament disassembly depends on both ATPase activity and potassium levels, the latter of which results in the organization of MamK filaments into bundles. These data are consistent with observations indicating that accessory factors are required to promote filament disassembly and for spatial organization of filaments in vivo. We also used cryo-electron microscopy to obtain a high resolution structure of MamK filaments. MamK adopts a two-stranded helical filament architecture, but unlike eukaryotic actin and other actin-like filaments, subunits in MamK strands are unstaggered giving rise to a unique filament architecture. Beyond extending our knowledge of the properties and function of MamK in magnetotactic bacteria, this study emphasizes the functional and structural diversity of bacterial actins in general.
      Background: The bacterial actin MamK is involved in the organization of bacterial organelles called magnetosomes.
      Results: MamK is an ATPase and assembles into filaments with a unique architecture.
      Conclusion: MamK shares features of structure and assembly with other bacterial actin homologs, and it has some unique features of its own.
      Significance: This work will guide future studies to unravel molecular mechanisms underlying MamK function in vivo.

      Introduction

      Research over the last couple of decades has demonstrated that bacteria are not devoid of subcellular organization and that fine-tuned cellular processes govern their growth and development. Much of the appreciation for the level of complexity in bacteria has come with the discovery of homologs of the eukaryotic cytoskeletal proteins actin, tubulin, and intermediate filaments in bacteria (reviewed in Refs.
      • Cabeen M.T.
      • Jacobs-Wagner C.
      The bacterial cytoskeleton.
      ,
      • Ingerson-Mahar M.
      • Gitai Z.
      A growing family. The expanding universe of the bacterial cytoskeleton.
      ,
      • Shaevitz J.W.
      • Gitai Z.
      The structure and function of bacterial actin homologs.
      ). As in eukaryotes, these fulfill vital functions for cell growth, DNA segregation, and cell shape determination in bacteria.
      Actin, one of the most abundant proteins in eukaryotes, is critical for many cellular functions (
      • Dominguez R.
      • Holmes K.C.
      Actin structure and function.
      ,
      • Pollard T.D.
      • Cooper J.A.
      Actin, a central player in cell shape and movement.
      ). It shows a remarkable level of sequence conservation across eukaryotic species (
      • Galkin V.E.
      • VanLoock M.S.
      • Orlova A.
      • Egelman E.H.
      A new internal mode in F-actin helps explain the remarkable evolutionary conservation of actin's sequence and structure.
      ,
      • Sheterline P.
      • Clayton J.
      • Sparrow J.
      Actin.
      ). In contrast, bacterial actin sequences are highly divergent and share only little primary sequence similarity to actin. Recent bioinformatic analysis suggests that there are more than 40 different families of bacterial actins (
      • Derman A.I.
      • Becker E.C.
      • Truong B.D.
      • Fujioka A.
      • Tucey T.M.
      • Erb M.L.
      • Patterson P.C.
      • Pogliano J.
      Phylogenetic analysis identifies many uncharacterized actin-like proteins (Alps) in bacteria. Regulated polymerization, dynamic instability, and treadmilling in Alp7A.
      ). A unifying characteristic of actin and bacterial actins is the actin-fold, a conserved core structure that creates a nucleotide-binding and hydrolysis site (
      • Bork P.
      • Sander C.
      • Valencia A.
      An ATPase domain common to prokaryotic cell cycle proteins, sugar kinases, actin, and Hsp70 heat shock proteins.
      ,
      • Kabsch W.
      • Holmes K.C.
      The actin fold.
      ). One of the key features of actin is its ability to transition between monomeric and filamentous states. One of the main factors regulating this transition is the hydrolysis of nucleotides such as ATP by filamentous actin where hydrolysis provides an energy source for a conformational switch (
      • Dominguez R.
      • Holmes K.C.
      Actin structure and function.
      ,
      • Bork P.
      • Sander C.
      • Valencia A.
      An ATPase domain common to prokaryotic cell cycle proteins, sugar kinases, actin, and Hsp70 heat shock proteins.
      ,
      • Kabsch W.
      • Holmes K.C.
      The actin fold.
      ). In addition, a large number of accessory protein factors can influence this transition.
      Similar to actin, bacterial actins form filamentous structures, and the majority of studies thus far have concentrated on a few select groups, such as the functionally distinct MreB and ParM proteins (
      • Jensen R.B.
      • Gerdes K.
      Partitioning of plasmid R1. The ParM protein exhibits ATPase activity and interacts with the centromere-like ParR-parC complex.
      ,
      • Jones L.J.
      • Carballido-López R.
      • Errington J.
      Control of cell shape in bacteria: helical, actin-like filaments in Bacillus subtilis.
      ). MreB is widely conserved and functions in cell shape determination in rod-shaped bacteria. Through its interaction with cell membrane and cell wall-associated proteins, it influences new cell wall synthesis (
      • Salje J.
      • van den Ent F.
      • de Boer P.
      • Löwe J.
      Direct membrane binding by bacterial actin MreB.
      ). Recent in vivo studies suggest that MreB forms highly dynamic structures along the inner membrane of cells (
      • Domínguez-Escobar J.
      • Chastanet A.
      • Crevenna A.H.
      • Fromion V.
      • Wedlich-Söldner R.
      • Carballido-López R.
      Processive movement of MreB-associated cell wall biosynthetic complexes in bacteria.
      ,
      • Garner E.C.
      • Bernard R.
      • Wang W.
      • Zhuang X.
      • Rudner D.Z.
      • Mitchison T.
      Coupled, circumferential motions of the cell wall synthesis machinery and MreB filaments in B. subtilis.
      ,
      • van Teeffelen S.
      • Wang S.
      • Furchtgott L.
      • Huang K.C.
      • Wingreen N.S.
      • Shaevitz J.W.
      • Gitai Z.
      The bacterial actin MreB rotates, and rotation depends on cell-wall assembly.
      ). It is unclear to what level MreB filament assembly and disassembly is a factor in in vivo MreB dynamics. ParM functions in the efficient segregation of low copy plasmids between daughter cells. ParM filaments exhibit dynamic instability in vitro, i.e. assembly and rapid catastrophic disassembly, that is distinct from the behavior of actin and is more microtubule-like (
      • Garner E.C.
      • Campbell C.S.
      • Mullins R.D.
      Dynamic instability in a DNA-segregating prokaryotic actin homolog.
      ). This dynamic behavior is important for ParM function because it provides a mechanism to “scan” for the plasmid. Upon “finding” the plasmid, by binding the ParR-parC complex, ParM filaments are stabilized, and their behavior transitions from dynamic instability to steady filament growth, enabling active movement of the plasmid (
      • Salje J.
      • Gayathri P.
      • Löwe J.
      The ParMRC system. Molecular mechanisms of plasmid segregation by actin-like filaments.
      ). Although research on MreB and ParM has provided molecular and mechanistic insights into the function of these proteins, the function and properties of the majority of bacterial actins remain unexplored. However, it is becoming increasingly evident that the considerable sequence diversity within bacterial actins translates into functional, structural, and behavioral differences. Here, we performed a detailed analysis of the in vitro properties of the bacterial actin MamK from Magnetospirillum magneticum AMB-1, hereafter referred to as AMB-1.
      MamK proteins form their own phylogenetic group within the bacterial actins and have been implicated in the organization of subcellular organelles in magnetotactic bacteria (
      • Draper O.
      • Byrne M.E.
      • Li Z.
      • Keyhani S.
      • Barrozo J.C.
      • Jensen G.
      • Komeili A.
      MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
      ,
      • Komeili A.
      • Li Z.
      • Newman D.K.
      • Jensen G.J.
      Magnetosomes are cell membrane invaginations organized by the actin-like protein MamK.
      ). This phylogenetically diverse group of bacteria can form intracellular structures called magnetosomes, which are inner membrane invaginations that direct the formation of magnetic crystals. A single cell contains a number of magnetosomes that are aligned into one or multiple chains in the cytoplasm that together act as a compass needle. The possession of a magnetosome chain results in passive alignment of the bacteria to geo-magnetic field lines, which is thought to make the search for optimal growth conditions more efficient (
      • Bazylinski D.A.
      • Frankel R.B.
      Magnetosome formation in prokaryotes.
      ,
      • Jogler C.
      • Schüler D.
      Genomics, genetics, and cell biology of magnetosome formation.
      ,
      • Komeili A.
      Molecular mechanisms of compartmentalization and biomineralization in magnetotactic bacteria.
      ). The alignment of magnetosomes into well organized chains is dependent on MamK, and high resolution electron cryotomography studies have revealed that MamK likely forms filaments that flank magnetosomes in vivo (
      • Komeili A.
      • Li Z.
      • Newman D.K.
      • Jensen G.J.
      Magnetosomes are cell membrane invaginations organized by the actin-like protein MamK.
      ,
      • Katzmann E.
      • Müller F.D.
      • Lang C.
      • Messerer M.
      • Winklhofer M.
      • Plitzko J.M.
      • Schüler D.
      Magnetosome chains are recruited to cellular division sites and split by asymmetric septation.
      ). Although genetic evidence suggests a role for MamK in magnetosome alignment, it is yet unknown if MamK filaments function in the establishment or the maintenance of a proper magnetosome chain. A study in the related organism Magnetospirillum gryphiswaldense MSR-1 suggests a role for MamK in the active positioning of magnetosomes during cell division (
      • Katzmann E.
      • Müller F.D.
      • Lang C.
      • Messerer M.
      • Winklhofer M.
      • Plitzko J.M.
      • Schüler D.
      Magnetosome chains are recruited to cellular division sites and split by asymmetric septation.
      ). We recently demonstrated, using fluorescence recovery after photobleaching assays, that MamK-GFP forms dynamic filaments in vivo. Furthermore, an intact nucleotide-binding site and two redundant proteins, MamJ and LimJ, regulate filament dynamics in vivo (
      • Draper O.
      • Byrne M.E.
      • Li Z.
      • Keyhani S.
      • Barrozo J.C.
      • Jensen G.
      • Komeili A.
      MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
      ).
      To ultimately understand the role of MamK in cells, both in vivo and in vitro insights into MamK behavior is highly desirable. Several groups have previously studied the in vitro behavior of recombinantly expressed MamK. In an important first study, Taoka et al. (
      • Taoka A.
      • Asada R.
      • Wu L.F.
      • Fukumori Y.
      Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
      ) demonstrated that recombinant MamK can form filamentous structures in vitro. Filamentous bundles could be visualized by EM upon addition of ATPγS,
      The abbreviations used are: ATPγS
      adenosine 5′-O-(thiotriphosphate)
      TIRF
      total internal reflection fluorescence microscopy.
      a nonhydrolyzable ATP analog, but not upon addition ATP, suggesting that MamK filaments disassembled prior to visualization due to ATP hydrolysis. Similar observations were made by Sonkaria et al. (
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ). In contrast, Rioux et al. (
      • Rioux J.B.
      • Philippe N.
      • Pereira S.
      • Pignol D.
      • Wu L.F.
      • Ginet N.
      A second actin-like MamK protein in Magnetospirillum magneticum AMB-1 encoded outside the genomic magnetosome island.
      ) reported that MamK filament assembly occurred in the absence of ATP. These earlier studies presented valuable new insights; however, they provided only limited, and somewhat contradicting, information about assembly and filament dynamics and the role of nucleotides for MamK. Furthermore, these studies employed His-tagged derivatives of MamK that could exhibit different in vitro properties than the native untagged protein.
      Here, we concentrated our efforts toward a more complete understanding of the in vitro properties and behavior of MamK. This is the first in-depth analysis of the assembly and filament architecture of an untagged MamK protein. We show that MamK assembles into filaments in an ATP-dependent manner and that filament disassembly occurs with very slow kinetics in low salt conditions. Near physiological levels of potassium or mutations in the protein's ATPase active site of the protein abolish this disassembly behavior. These results substantiate a model in which MamK filaments, unlike the inherently unstable bacterial actin ParM, are stable in their default state and require accessory factors to become dynamic. Moreover, we show by cryoelectron microscopy (cryo-EM) that MamK assembles into filaments with unique features, further highlighting the structural diversity of bacterial actins.

      DISCUSSION

      As opposed to their eukaryotic counterparts, bacterial actin sequences are highly divergent and fulfill a wide range of cellular functions. This sequence and functional diversity are also accompanied by differences in dynamics and filament architecture. In this study, we characterized the in vitro properties of the bacterial actin MamK from M. magneticum AMB-1, which is involved in the organization and positioning of organelles in magnetotactic bacteria. The two major findings of our study are as follows: (i) MamK filaments, unlike ParM filaments, do not appear to disassemble catastrophically, and (ii) MamK filaments show a unique architecture in which interstrand monomers are in register and lack the staggered alignment typical of two-stranded actin filaments and most other characterized bacterial actins.
      The study of bacterial actin MamK and its role in magnetotactic bacteria is an active area of research, and several groups have contributed, through both in vivo and in vitro studies, to progress in the field. In a brief report, Taoka et al. (
      • Taoka A.
      • Asada R.
      • Wu L.F.
      • Fukumori Y.
      Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
      ) demonstrated, for the first time, that recombinant MamK-His can form filamentous structures in vitro. Similar to the study by Toaka et al. (
      • Taoka A.
      • Asada R.
      • Wu L.F.
      • Fukumori Y.
      Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
      ) and later studies (
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ,
      • Rioux J.B.
      • Philippe N.
      • Pereira S.
      • Pignol D.
      • Wu L.F.
      • Ginet N.
      A second actin-like MamK protein in Magnetospirillum magneticum AMB-1 encoded outside the genomic magnetosome island.
      ), we show that MamK polymerizes into filaments in vitro. Despite this similarity, important differences exist between our study and previous work. MamK-His filament bundles could be visualized by EM after addition of ATPγS, a nonhydrolyzable ATP analog but, interestingly, not after addition of ATP. This suggested that MamK-His filaments disassembled prior to visualization due to ATP hydrolysis (
      • Taoka A.
      • Asada R.
      • Wu L.F.
      • Fukumori Y.
      Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
      ,
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ). In stark contrast, Rioux et al. (
      • Rioux J.B.
      • Philippe N.
      • Pereira S.
      • Pignol D.
      • Wu L.F.
      • Ginet N.
      A second actin-like MamK protein in Magnetospirillum magneticum AMB-1 encoded outside the genomic magnetosome island.
      ) reported that MamK-His polymerization occurred in the absence of nucleotide. The authors included ATP during the purification procedure and suggested that ATP, as it does for actin, stabilized MamK against aggregation. In contrast to previous studies, we demonstrate that the untagged MamK polymerizes in an ATP-dependent manner and that MamK filaments can be visualized by EM in the presence of this nucleotide. In addition to the above mentioned differences, our study contradicts findings with regard to the role of K+ ions for MamK polymerization reported by Sonkaria et al. (
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ). The authors reported that MamK polymerization was inhibited in a K+ concentration-dependent manner, with complete absence of polymerization at 200 mm KCl. As discussed later, under our experimental conditions MamK clearly polymerizes at similarly high KCl concentrations.
      We can only speculate about the reasons for the different reported behaviors of MamK. A likely explanation is the use of slightly different MamK proteins in the different studies. Toaka et al. (
      • Taoka A.
      • Asada R.
      • Wu L.F.
      • Fukumori Y.
      Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
      ) and Sonkaria et al. (
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ) used MamK from the closely related organisms M. magnetotacticum MS-1 and M. gryphiswaldense MSR-1, respectively. However, the different MamK protein sequences are extremely similar, making it an unlikely reason for different in vitro properties. For instance, MamK from M. magnetotacticum MS-1 is 99% identical and 100% similar to its counterpart from AMB-1 studied here. It is important to note that Sonkaria et al. (
      • Sonkaria S.
      • Fuentes G.
      • Verma C.
      • Narang R.
      • Khare V.
      • Fischer A.
      • Faivre D.
      Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
      ) expressed a slightly longer version of the MamK protein. In addition to the His tag at the C terminus, another 13 residues were expressed at the N terminus of the protein. These additional 13 residues are present in database entries for MamK from M. gryphiswaldense MSR-1 but are lacking in other MamK proteins. This longer protein was reported not to express functionally in vivo and thus may not be the correct MamK sequence (
      • Katzmann E.
      • Müller F.D.
      • Lang C.
      • Messerer M.
      • Winklhofer M.
      • Plitzko J.M.
      • Schüler D.
      Magnetosome chains are recruited to cellular division sites and split by asymmetric septation.
      ). A further difference between our work and the previous studies is that we did not employ a His tag to purify MamK. Such tags could alter the protein's assembly and disassembly behavior. In fact, different properties have been reported for MreB from T. maritima purified either with or without a His tag (
      • Bean G.J.
      • Amann K.J.
      Polymerization properties of the Thermotoga maritima actin MreB. Roles of temperature, nucleotides, and ions.
      ,
      • Esue O.
      • Cordero M.
      • Wirtz D.
      • Tseng Y.
      The assembly of MreB, a prokaryotic homolog of actin.
      ).
      In vitro studies so far have only provided a static and limited picture of MamK assembly, and important questions about filament stability and architecture remain to be addressed. In this study, we investigated the dynamics of both MamK assembly and disassembly using light scattering assays. MamK filaments assemble rapidly in the presence of saturating levels of ATP. This is consistent with the behavior of other bacterial actins and may support the view that, in contrast to actin, bacterial actins do not require nucleation factors to promote efficient and rapid filament assembly. This filament assembly is not dependent on ATP hydrolysis as MamKE143A, with its greatly reduced activity, still formed filaments. The MamKE143A data are consistent with the behavior of the well characterized bacterial actin ParM. Garner et al. (
      • Garner E.C.
      • Campbell C.S.
      • Mullins R.D.
      Dynamic instability in a DNA-segregating prokaryotic actin homolog.
      ) demonstrated that ParM with the equivalent mutation E148A is able to assemble into filaments but fails to exhibit any detectable ATPase activity. Although the ParME148A protein assembles into filaments, the mutation renders these filaments stable as demonstrated in bulk by light scattering assays and at the single filament level using TIRF microscopy. The behavior of MamKE143A in light scattering experiments is consistent with the failure of filaments to disassemble and indicates that ATP hydrolysis is also important for MamK filament disassembly. Moreover, this is in line with our previous work showing that MamK-GFP filament turnover in an in vivo fluorescence recovery after photobleaching assay is dependent on an intact nucleotide-binding site (
      • Draper O.
      • Byrne M.E.
      • Li Z.
      • Keyhani S.
      • Barrozo J.C.
      • Jensen G.
      • Komeili A.
      MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
      ).
      Our data also show that wild type MamK filament bulk disassembly occurs, at least in the presence of low potassium levels, relatively slowly. This disassembly behavior is different from ParM for which filament dynamics is best understood. ParM filaments exhibit dynamic instability where disassembly occurs rapidly and catastrophically. It is worth noting that MamK's ATPase activity, with 0.2 μm min−1m protein, is significantly lower than for ParM (∼3–6 μm min−1m protein (
      • Garner E.C.
      • Campbell C.S.
      • Mullins R.D.
      Dynamic instability in a DNA-segregating prokaryotic actin homolog.
      ,
      • Rivera C.R.
      • Kollman J.M.
      • Polka J.K.
      • Agard D.A.
      • Mullins R.D.
      Architecture and assembly of a divergent member of the ParM family of bacterial actin-like proteins.
      ), perhaps accounting for some aspects of the different time scales of filament dynamics. A direct comparison of MamK filament disassembly to that of ParM is difficult and requires the assessment of molecular events at the single MamK filament level. For instance, it is unknown if MamK filaments have a polarity to their growth and disassembly. It is possible that MamK filaments grow bidirectionally similar to ParM or that growth occurs preferentially from one end. Considering that MamK polymerizes readily with ATP but not ADP, it is conceptually possible that MamK filaments undergo a process of treadmilling similar to actin. Our attempts to analyze single MamK filaments using TIRF have proven difficult. This is mainly because labeling of MamK with biotin, required for immobilization of filaments on streptavidin functionalized glass slides when performing TIRF, is inefficient, and association of the labeled protein with the glass surface is poor. Furthermore, the length of fluorescently labeled (Alexa 488) MamK filaments is short and at the resolution limit for this type of microscopy. More intensive efforts are required to study MamK at the single filament level to ultimately understand MamK dynamics in vivo.
      Studies with AMB-1 cells suggest that MamK filaments are intrinsically stable in vivo and rely on regulators for their dynamic behavior. Specifically, two redundant proteins encoded by genes of the so-called magnetosome gene island (MAI), namely MamJ and LimJ, appear to play a role in MamK dynamics in vivo. However, in the absence of other MAI genes, MamJ or LimJ is not sufficient to reconstitute MamK filament dynamics suggesting the presence of other factors (
      • Draper O.
      • Byrne M.E.
      • Li Z.
      • Keyhani S.
      • Barrozo J.C.
      • Jensen G.
      • Komeili A.
      MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
      ). In addition to proteins that influence MamK dynamics, an interesting question concerns physico-chemical conditions, such as the concentration of various ions, inside the AMB-1 cells that might affect the in vivo behavior of MamK. K+ ions play important roles in bacteria, where they are involved in cell turgor pressure maintenance (
      • Epstein W.
      • Schultz S.G.
      Cation transport in Escherichia coli: V. Regulation of cation content.
      ,
      • Whatmore A.M.
      • Reed R.H.
      Determination of turgor pressure in Bacillus subtilis. A possible role for K+ in turgor regulation.
      ), enzyme activation (
      ,
      • Suelter C.H.
      Enzymes activated by monovalent cations.
      ), and regulation of cytoplasmic pH (
      • Booth I.R.
      Regulation of cytoplasmic pH in bacteria.
      ,
      • Kroll R.G.
      • Booth I.R.
      The relationship between intracellular pH, the pH gradient and potassium transport in Escherichia coli.
      ). For instance, in E. coli and Bacillus sp. cells K+ is the major cytoplasmic cation with K+ concentrations ranging roughly from 150 mm and reaching up to 650 mm depending on growth conditions and availability (
      • Epstein W.
      • Schultz S.G.
      Cation transport in Escherichia coli: V. Regulation of cation content.
      ,
      • Jahns T.
      Ammonium-stimulated, sodium-dependent uptake of glutamine in Bacillus pasteurii.
      ,
      • McLaggan D.
      • Naprstek J.
      • Buurman E.T.
      • Epstein W.
      Interdependence of K+ and glutamate accumulation during osmotic adaptation of Escherichia coli.
      ,
      • Michels M.
      • Bakker E.P.
      Low-affinity potassium uptake system in Bacillus acidocaldarius.
      ,
      • Roe A.J.
      • McLaggan D.
      • O'Byrne C.P.
      • Booth I.R.
      Rapid inactivation of the Escherichia coli Kdp K+ uptake system by high potassium concentrations.
      ,
      • López D.
      • Fischbach M.A.
      • Chu F.
      • Losick R.
      • Kolter R.
      Structurally diverse natural products that cause potassium leakage trigger multicellularity in Bacillus subtilis.
      ). Our in vitro experiments show that increased K+ concentrations result in the formation of tight MamK filament bundles that display little to no disassembly under ATP-limiting conditions. This high level of stability is not due to modulation of the protein's ATPase activity because similar amounts of Pi were released with high or low K+ concentrations. Interestingly, the plasmid-segregating bacterial actin AlfA also shows filament bundling in vitro, but unlike MamK, high KCl concentrations are required to dissociate AlfA bundles, indicating that filament interactions occur through electrostatic interactions (
      • Polka J.K.
      • Kollman J.M.
      • Agard D.A.
      • Mullins R.D.
      The structure and assembly dynamics of plasmid actin AlfA imply a novel mechanism of DNA segregation.
      ).
      Interestingly, we also observed that Mg2+ ions can alter MamK filament stability by a mechanism that appears to be distinct from the K+ effect mentioned above. In the presence of excess Mg2+, we did not observe filament bundling. However, a reduction in ATPase activity, partially explaining the Mg2+-dependent effect on filament stabilization, was seen. It is possible that MamK possesses a low affinity binding site for divalent cations that, when saturated, alters the filament in such a way that the off rate of MamK monomers is reduced. In E. coli free cytoplasmic Mg2+ levels have been estimated to be in the range of 2–4 mm (
      • Alatossava T.
      • Jütte H.
      • Kuhn A.
      • Kellenberger E.
      Manipulation of intracellular magnesium content in polymyxin B nonapeptide-sensitized Escherichia coli by ionophore A23187.
      ,
      • Lusk J.E.
      • Williams R.J.
      • Kennedy E.P.
      Magnesium and the growth of Escherichia coli.
      ) making it plausible that the effects seen in these experiments may have physiological relevance.
      It is yet unknown what levels of cytoplasmic K+ AMB-1 cells maintain and how MamK filament bundling observed with increased K+ levels in vitro relates to in vivo conditions. High resolution imaging by electron cryotomography on intact AMB-1 cells rather suggests that MamK forms single filaments in vivo (
      • Komeili A.
      • Li Z.
      • Newman D.K.
      • Jensen G.J.
      Magnetosomes are cell membrane invaginations organized by the actin-like protein MamK.
      ). In wild type AMB-1 cells filaments of ∼6 nm width, similar to the width of single filaments in vitro, run alongside of magnetosomes in the cytoplasm. Although some level of interfilament interactions, in the form of local overlaps, is seen in vivo (
      • Komeili A.
      • Li Z.
      • Newman D.K.
      • Jensen G.J.
      Magnetosomes are cell membrane invaginations organized by the actin-like protein MamK.
      ), filament bundling to the extent that is seen under in vitro conditions is not observed. However, we previously observed in vivo bundling of putative MamK filaments between the gaps of the magnetosome chain that appear in mutant AMB-1 cells lacking the MamJ and LimJ proteins (
      • Draper O.
      • Byrne M.E.
      • Li Z.
      • Keyhani S.
      • Barrozo J.C.
      • Jensen G.
      • Komeili A.
      MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
      ). One interpretation of these results has been that MamJ and LimJ contribute to the dynamics of MamK filaments by directly or indirectly affecting its ATPase activity. However, in light of our in vitro results, one could alternatively suggest that the lack of in vivo filament dynamics in the absence of MamJ and LimJ is a result of pronounced interfilament interactions and bundling. In this model, the absence of MamJ, or the redundant protein LimJ, would impair the proper interaction of magnetosomes with MamK filaments that are then free to associate with each other. Further support for this model comes from the observation that in the complete absence of magnetosomes in an MAI deletion mutant, a strain without any putative MamK anchorage points, MamK-GFP fluorescence no longer shows a typical linear, pole-to-pole localization but rather shows shorter and much thicker filaments. Furthermore, in this mutant MamK filaments are no longer dynamic, and together with the change in MamK filament organization this may hint toward MamK filament bundling in these cells.
      Our structure of in vitro polymerized MamK reveals a novel architecture for an actin homolog. Although the surfaces of MamK involved in longitudinal contacts along each strand are similar to F-actin and other bacterial actin filaments, the cross-strand contacts are novel and lead to an unusual nonstaggered filament. Similar nonstaggered filament morphology has been observed for short filaments of MreB (
      • Salje J.
      • van den Ent F.
      • de Boer P.
      • Löwe J.
      Direct membrane binding by bacterial actin MreB.
      ). In that case, the shape of the subunits in averaged images and arguments about how subunits interact with membranes suggested an antiparallel arrangement of the two MreB strands. The two strands of MamK filaments, however, appear to be parallel to each other. The architecture of MamK filaments fits with a growing body of evidence that the broad diversity of bacterial actin filament morphologies arises primarily from variation in the cross-strand contacts, with similar surfaces utilized in forming longitudinal contacts along each strand (
      • Salje J.
      • van den Ent F.
      • de Boer P.
      • Löwe J.
      Direct membrane binding by bacterial actin MreB.
      ,
      • Polka J.K.
      • Kollman J.M.
      • Agard D.A.
      • Mullins R.D.
      The structure and assembly dynamics of plasmid actin AlfA imply a novel mechanism of DNA segregation.
      ,
      • Popp D.
      • Narita A.
      • Lee L.J.
      • Ghoshdastider U.
      • Xue B.
      • Srinivasan R.
      • Balasubramanian M.K.
      • Tanaka T.
      • Robinson R.C.
      Novel actin-like filament structure from Clostridium tetani.
      ,
      • Popp D.
      • Xu W.
      • Narita A.
      • Brzoska A.J.
      • Skurray R.A.
      • Firth N.
      • Ghoshdastider U.
      • Goshdastider U.
      • Maéda Y.
      • Robinson R.C.
      • Schumacher M.A.
      Structure and filament dynamics of the pSK41 actin-like ParM protein. Implications for plasmid DNA segregation.
      ,
      • Galkin V.E.
      • Orlova A.
      • Rivera C.
      • Mullins R.D.
      • Egelman E.H.
      Structural polymorphism of the ParM filament and dynamic instability.
      ,
      • Orlova A.
      • Garner E.C.
      • Galkin V.E.
      • Heuser J.
      • Mullins R.D.
      • Egelman E.H.
      The structure of bacterial ParM filaments.
      ,
      • Roeben A.
      • Kofler C.
      • Nagy I.
      • Nickell S.
      • Hartl F.U.
      • Bracher A.
      Crystal structure of an archaeal actin homolog.
      ,
      • Szwedziak P.
      • Wang Q.
      • Freund S.M.
      • Lowe J.
      FtsA forms actin-like protofilaments.
      ).
      MamK's unique filament architecture poses interesting questions about its assembly, particularly at early stages requiring a nucleus for filament assembly. In staggered filaments, such as actin or ParM, once a trimer is formed, each subsequent subunit addition forms a new high affinity “corner” site where an incoming subunit can make both longitudinal and cross-strand contacts. Our preliminary analysis, by applying the Nishida and Sakai formalism (
      • Nishida E.
      • Sakai H.
      Kinetic analysis of actin polymerization.
      ), estimates the MamK nucleus size to be a trimer. For MamK, with unstaggered strands, a model involving a trimer as nucleus would, however, cause a conceptual problem. For MamK, a high affinity site could potentially exist when three subunits are assembled, but addition of a fourth subunit would yield a closed structure with no available corner sites, to which subunits would be added (supplemental Fig. S4C). It has to be noted that the Nishida and Sakai formalism may not strictly apply to MamK. More extensive work, involving both experimental and theoretical approaches, is required to answer questions revolving around MamK nucleus size and filament assembly.
      Our study provides the first comprehensive view of MamK assembly behavior and filament architecture in vitro. As new regulators and interaction partners of MamK are discovered, this in vitro system will be an invaluable tool to decipher genetic and cell biological observations in a mechanistic light. The combination of these efforts should bring us closer to understanding the actual function of MamK in magnetosome alignment and division.

      Acknowledgments

      We thank Dyche Mullins and group members (University of California at San Francisco), in particular Jessica Polka and Scott Hansen, for providing guidance and access to equipment in the early stages of the project. We thank members of the Komeili laboratory for their critical reading of the manuscript. We extend our thanks to the Facility for Electron Microscopy Research at McGill University for the use of electron microscopes. We also thank Krishna Niyogi and Matthew Welch (University of California, Berkeley) for access to equipment.

      REFERENCES

        • Cabeen M.T.
        • Jacobs-Wagner C.
        The bacterial cytoskeleton.
        Annu. Rev. Genet. 2010; 44: 365-392
        • Ingerson-Mahar M.
        • Gitai Z.
        A growing family. The expanding universe of the bacterial cytoskeleton.
        FEMS Microbiol. Rev. 2012; 36: 256-266
        • Shaevitz J.W.
        • Gitai Z.
        The structure and function of bacterial actin homologs.
        Cold Spring Harbor Perspect. Biol. 2010; 2: a000364
        • Dominguez R.
        • Holmes K.C.
        Actin structure and function.
        Annu. Rev. Biophys. 2011; 40: 169-186
        • Pollard T.D.
        • Cooper J.A.
        Actin, a central player in cell shape and movement.
        Science. 2009; 326: 1208-1212
        • Galkin V.E.
        • VanLoock M.S.
        • Orlova A.
        • Egelman E.H.
        A new internal mode in F-actin helps explain the remarkable evolutionary conservation of actin's sequence and structure.
        Curr. Biol. 2002; 12: 570-575
        • Sheterline P.
        • Clayton J.
        • Sparrow J.
        Actin.
        Protein Profile. 1995; 2: 1-103
        • Derman A.I.
        • Becker E.C.
        • Truong B.D.
        • Fujioka A.
        • Tucey T.M.
        • Erb M.L.
        • Patterson P.C.
        • Pogliano J.
        Phylogenetic analysis identifies many uncharacterized actin-like proteins (Alps) in bacteria. Regulated polymerization, dynamic instability, and treadmilling in Alp7A.
        Mol. Microbiol. 2009; 73: 534-552
        • Bork P.
        • Sander C.
        • Valencia A.
        An ATPase domain common to prokaryotic cell cycle proteins, sugar kinases, actin, and Hsp70 heat shock proteins.
        Proc. Natl. Acad. Sci. U.S.A. 1992; 89: 7290-7294
        • Kabsch W.
        • Holmes K.C.
        The actin fold.
        FASEB J. 1995; 9: 167-174
        • Jensen R.B.
        • Gerdes K.
        Partitioning of plasmid R1. The ParM protein exhibits ATPase activity and interacts with the centromere-like ParR-parC complex.
        J. Mol. Biol. 1997; 269: 505-513
        • Jones L.J.
        • Carballido-López R.
        • Errington J.
        Control of cell shape in bacteria: helical, actin-like filaments in Bacillus subtilis.
        Cell. 2001; 104: 913-922
        • Salje J.
        • van den Ent F.
        • de Boer P.
        • Löwe J.
        Direct membrane binding by bacterial actin MreB.
        Mol. Cell. 2011; 43: 478-487
        • Domínguez-Escobar J.
        • Chastanet A.
        • Crevenna A.H.
        • Fromion V.
        • Wedlich-Söldner R.
        • Carballido-López R.
        Processive movement of MreB-associated cell wall biosynthetic complexes in bacteria.
        Science. 2011; 333: 225-228
        • Garner E.C.
        • Bernard R.
        • Wang W.
        • Zhuang X.
        • Rudner D.Z.
        • Mitchison T.
        Coupled, circumferential motions of the cell wall synthesis machinery and MreB filaments in B. subtilis.
        Science. 2011; 333: 222-225
        • van Teeffelen S.
        • Wang S.
        • Furchtgott L.
        • Huang K.C.
        • Wingreen N.S.
        • Shaevitz J.W.
        • Gitai Z.
        The bacterial actin MreB rotates, and rotation depends on cell-wall assembly.
        Proc. Natl. Acad. Sci. U.S.A. 2011; 108: 15822-15827
        • Garner E.C.
        • Campbell C.S.
        • Mullins R.D.
        Dynamic instability in a DNA-segregating prokaryotic actin homolog.
        Science. 2004; 306: 1021-1025
        • Salje J.
        • Gayathri P.
        • Löwe J.
        The ParMRC system. Molecular mechanisms of plasmid segregation by actin-like filaments.
        Nat. Rev. Microbiol. 2010; 8: 683-692
        • Draper O.
        • Byrne M.E.
        • Li Z.
        • Keyhani S.
        • Barrozo J.C.
        • Jensen G.
        • Komeili A.
        MamK, a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ.
        Mol. Microbiol. 2011; 82: 342-354
        • Komeili A.
        • Li Z.
        • Newman D.K.
        • Jensen G.J.
        Magnetosomes are cell membrane invaginations organized by the actin-like protein MamK.
        Science. 2006; 311: 242-245
        • Bazylinski D.A.
        • Frankel R.B.
        Magnetosome formation in prokaryotes.
        Nat. Rev. Microbiol. 2004; 2: 217-230
        • Jogler C.
        • Schüler D.
        Genomics, genetics, and cell biology of magnetosome formation.
        Annu. Rev. Microbiol. 2009; 63: 501-521
        • Komeili A.
        Molecular mechanisms of compartmentalization and biomineralization in magnetotactic bacteria.
        FEMS Microbiol. Rev. 2012; 36: 232-255
        • Katzmann E.
        • Müller F.D.
        • Lang C.
        • Messerer M.
        • Winklhofer M.
        • Plitzko J.M.
        • Schüler D.
        Magnetosome chains are recruited to cellular division sites and split by asymmetric septation.
        Mol. Microbiol. 2011; 82: 1316-1329
        • Taoka A.
        • Asada R.
        • Wu L.F.
        • Fukumori Y.
        Polymerization of the actin-like protein MamK, which is associated with magnetosomes.
        J. Bacteriol. 2007; 189: 8737-8740
        • Sonkaria S.
        • Fuentes G.
        • Verma C.
        • Narang R.
        • Khare V.
        • Fischer A.
        • Faivre D.
        Insight into the assembly properties and functional organisation of the magnetotactic bacterial actin-like homolog, MamK.
        PLoS ONE. 2012; 7: e34189
        • Rioux J.B.
        • Philippe N.
        • Pereira S.
        • Pignol D.
        • Wu L.F.
        • Ginet N.
        A second actin-like MamK protein in Magnetospirillum magneticum AMB-1 encoded outside the genomic magnetosome island.
        PLoS ONE. 2010; 5: e9151
        • Ohi M.
        • Li Y.
        • Cheng Y.
        • Walz T.
        Negative staining and image classification–Powerful tools in modern electron microscopy.
        Biol. Proced. Online. 2004; 6: 23-34
        • Mindell J.A.
        • Grigorieff N.
        Accurate determination of local defocus and specimen tilt in electron microscopy.
        J. Struct. Biol. 2003; 142: 334-347
        • Ludtke S.J.
        • Baldwin P.R.
        • Chiu W.
        EMAN. Semiautomated software for high resolution single-particle reconstructions.
        J. Struct. Biol. 1999; 128: 82-97
        • Egelman E.H.
        The iterative helical real space reconstruction method. Surmounting the problems posed by real polymers.
        J. Struct. Biol. 2007; 157: 83-94
        • Sachse C.
        • Chen J.Z.
        • Coureux P.D.
        • Stroupe M.E.
        • Fändrich M.
        • Grigorieff N.
        High-resolution electron microscopy of helical specimens: a fresh look at tobacco mosaic virus.
        J. Mol. Biol. 2007; 371: 812-835
      1. Frank J. Three-dimensional Electron Microscopy of Macromolecular Assemblies. Academic Press, Inc., San Diego1996: 1-342
        • Egelman E.H.
        A robust algorithm for the reconstruction of helical filaments using single-particle methods.
        Ultramicroscopy. 2000; 85: 225-234
        • Behrmann E.
        • Tao G.
        • Stokes D.L.
        • Egelman E.H.
        • Raunser S.
        • Penczek P.A.
        Real-space processing of helical filaments in SPARX.
        J. Struct. Biol. 2012; 177: 302-313
        • Pettersen E.F.
        • Goddard T.D.
        • Huang C.C.
        • Couch G.S.
        • Greenblatt D.M.
        • Meng E.C.
        • Ferrin T.E.
        UCSF Chimera–a visualization system for exploratory research and analysis.
        J. Comput. Chem. 2004; 25: 1605-1612
        • van den Ent F.
        • Amos L.A.
        • Löwe J.
        Prokaryotic origin of the actin cytoskeleton.
        Nature. 2001; 413: 39-44
        • Fiser A.
        • Sali A.
        Modeller: generation and refinement of homology-based protein structure models.
        Methods Enzymol. 2003; 374: 461-491
        • Altschul S.F.
        • Gish W.
        • Miller W.
        • Myers E.W.
        • Lipman D.J.
        Basic local alignment search tool.
        J. Mol. Biol. 1990; 215: 403-410
        • Katoh K.
        • Misawa K.
        • Kuma K.
        • Miyata T.
        MAFFT. A novel method for rapid multiple sequence alignment based on fast Fourier transform.
        Nucleic Acids Res. 2002; 30: 3059-3066
        • Rivera C.R.
        • Kollman J.M.
        • Polka J.K.
        • Agard D.A.
        • Mullins R.D.
        Architecture and assembly of a divergent member of the ParM family of bacterial actin-like proteins.
        J. Biol. Chem. 2011; 286: 14282-14290
        • Vorobiev S.
        • Strokopytov B.
        • Drubin D.G.
        • Frieden C.
        • Ono S.
        • Condeelis J.
        • Rubenstein P.A.
        • Almo S.C.
        The structure of nonvertebrate actin: implications for the ATP hydrolytic mechanism.
        Proc. Natl. Acad. Sci. U.S.A. 2003; 100: 5760-5765
        • Bean G.J.
        • Amann K.J.
        Polymerization properties of the Thermotoga maritima actin MreB. Roles of temperature, nucleotides, and ions.
        Biochemistry. 2008; 47: 826-835
        • Polka J.K.
        • Kollman J.M.
        • Agard D.A.
        • Mullins R.D.
        The structure and assembly dynamics of plasmid actin AlfA imply a novel mechanism of DNA segregation.
        J. Bacteriol. 2009; 191: 6219-6230
        • Popp D.
        • Narita A.
        • Lee L.J.
        • Ghoshdastider U.
        • Xue B.
        • Srinivasan R.
        • Balasubramanian M.K.
        • Tanaka T.
        • Robinson R.C.
        Novel actin-like filament structure from Clostridium tetani.
        J. Biol. Chem. 2012; 287: 21121-21129
        • Popp D.
        • Xu W.
        • Narita A.
        • Brzoska A.J.
        • Skurray R.A.
        • Firth N.
        • Ghoshdastider U.
        • Goshdastider U.
        • Maéda Y.
        • Robinson R.C.
        • Schumacher M.A.
        Structure and filament dynamics of the pSK41 actin-like ParM protein. Implications for plasmid DNA segregation.
        J. Biol. Chem. 2010; 285: 10130-10140
        • Esue O.
        • Wirtz D.
        • Tseng Y.
        GTPase activity, structure, and mechanical properties of filaments assembled from bacterial cytoskeleton protein MreB.
        J. Bacteriol. 2006; 188: 968-976
        • Wen K.K.
        • Yao X.
        • Rubenstein P.A.
        GTP-yeast actin.
        J. Biol. Chem. 2002; 277: 41101-41109
        • Epstein W.
        • Schultz S.G.
        Cation transport in Escherichia coli: V. Regulation of cation content.
        J. Gen. Physiol. 1965; 49: 221-234
        • Jahns T.
        Ammonium-stimulated, sodium-dependent uptake of glutamine in Bacillus pasteurii.
        Arch. Microbiol. 1994; 161: 207-214
        • McLaggan D.
        • Naprstek J.
        • Buurman E.T.
        • Epstein W.
        Interdependence of K+ and glutamate accumulation during osmotic adaptation of Escherichia coli.
        J. Biol. Chem. 1994; 269: 1911-1917
        • Michels M.
        • Bakker E.P.
        Low-affinity potassium uptake system in Bacillus acidocaldarius.
        J. Bacteriol. 1987; 169: 4335-4341
        • Roe A.J.
        • McLaggan D.
        • O'Byrne C.P.
        • Booth I.R.
        Rapid inactivation of the Escherichia coli Kdp K+ uptake system by high potassium concentrations.
        Mol. Microbiol. 2000; 35: 1235-1243
        • Galkin V.E.
        • Orlova A.
        • Schröder G.F.
        • Egelman E.H.
        Structural polymorphism in F-actin.
        Nat. Struct. Mol. Biol. 2010; 17: 1318-1323
        • Murakami K.
        • Yasunaga T.
        • Noguchi T.Q.
        • Gomibuchi Y.
        • Ngo K.X.
        • Uyeda T.Q.
        • Wakabayashi T.
        Structural basis for actin assembly, activation of ATP hydrolysis, and delayed phosphate release.
        Cell. 2010; 143: 275-287
        • Fujii T.
        • Iwane A.H.
        • Yanagida T.
        • Namba K.
        Direct visualization of secondary structures of F-actin by electron cryomicroscopy.
        Nature. 2010; 467: 724-728
        • Galkin V.E.
        • Orlova A.
        • Rivera C.
        • Mullins R.D.
        • Egelman E.H.
        Structural polymorphism of the ParM filament and dynamic instability.
        Structure. 2009; 17: 1253-1264
        • Esue O.
        • Cordero M.
        • Wirtz D.
        • Tseng Y.
        The assembly of MreB, a prokaryotic homolog of actin.
        J. Biol. Chem. 2005; 280: 2628-2635
        • Whatmore A.M.
        • Reed R.H.
        Determination of turgor pressure in Bacillus subtilis. A possible role for K+ in turgor regulation.
        J. Gen. Microbiol. 1990; 136: 2521-2526
      2. Rosen B.P. Silver S. Ion Transport in Prokaryotes. Academic Press, San Diego1987: 85-114
        • Suelter C.H.
        Enzymes activated by monovalent cations.
        Science. 1970; 168: 789-795
        • Booth I.R.
        Regulation of cytoplasmic pH in bacteria.
        Microbiol. Rev. 1985; 49: 359-378
        • Kroll R.G.
        • Booth I.R.
        The relationship between intracellular pH, the pH gradient and potassium transport in Escherichia coli.
        Biochem. J. 1983; 216: 709-716
        • López D.
        • Fischbach M.A.
        • Chu F.
        • Losick R.
        • Kolter R.
        Structurally diverse natural products that cause potassium leakage trigger multicellularity in Bacillus subtilis.
        Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 280-285
        • Alatossava T.
        • Jütte H.
        • Kuhn A.
        • Kellenberger E.
        Manipulation of intracellular magnesium content in polymyxin B nonapeptide-sensitized Escherichia coli by ionophore A23187.
        J. Bacteriol. 1985; 162: 413-419
        • Lusk J.E.
        • Williams R.J.
        • Kennedy E.P.
        Magnesium and the growth of Escherichia coli.
        J. Biol. Chem. 1968; 243: 2618-2624
        • Orlova A.
        • Garner E.C.
        • Galkin V.E.
        • Heuser J.
        • Mullins R.D.
        • Egelman E.H.
        The structure of bacterial ParM filaments.
        Nat. Struct. Mol. Biol. 2007; 14: 921-926
        • Roeben A.
        • Kofler C.
        • Nagy I.
        • Nickell S.
        • Hartl F.U.
        • Bracher A.
        Crystal structure of an archaeal actin homolog.
        J. Mol. Biol. 2006; 358: 145-156
        • Szwedziak P.
        • Wang Q.
        • Freund S.M.
        • Lowe J.
        FtsA forms actin-like protofilaments.
        EMBO J. 2012; 31: 2249-2260
        • Nishida E.
        • Sakai H.
        Kinetic analysis of actin polymerization.
        J. Biochem. 1983; 93: 1011-1020