A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids
2018; Springer Nature; Volume: 14; Issue: 11 Linguagem: Inglês
10.15252/msb.20188516
ISSN1744-4292
AutoresRoxanne E Debaugny, Aurore Sanchez, Jérôme Rech, Delphine Labourdette, Jérôme Dorignac, Frédéric Geniet, John Palmeri, Andrea Parmeggiani, François Boudsocq, Véronique Anton Leberre, Jean‐Charles Walter, Jean‐Yves Bouet,
Tópico(s)Escherichia coli research studies
ResumoArticle16 November 2018Open Access Transparent process A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids Roxanne E Debaugny Roxanne E Debaugny Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Aurore Sanchez Aurore Sanchez Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Jérôme Rech Jérôme Rech Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Delphine Labourdette Delphine Labourdette LISBP, CNRS, INRA, INSA, Université de Toulouse, Toulouse, France Search for more papers by this author Jérôme Dorignac Jérôme Dorignac Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Frédéric Geniet Frédéric Geniet Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author John Palmeri John Palmeri Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Andrea Parmeggiani Andrea Parmeggiani Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Dynamique des Interactions Membranaires Normales et Pathologiques, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author François Boudsocq François Boudsocq Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Véronique Anton Leberre Véronique Anton Leberre LISBP, CNRS, INRA, INSA, Université de Toulouse, Toulouse, France Search for more papers by this author Jean-Charles Walter Corresponding Author Jean-Charles Walter [email protected] Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Jean-Yves Bouet Corresponding Author Jean-Yves Bouet [email protected] orcid.org/0000-0003-1488-5455 Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Roxanne E Debaugny Roxanne E Debaugny Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Aurore Sanchez Aurore Sanchez Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Jérôme Rech Jérôme Rech Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Delphine Labourdette Delphine Labourdette LISBP, CNRS, INRA, INSA, Université de Toulouse, Toulouse, France Search for more papers by this author Jérôme Dorignac Jérôme Dorignac Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Frédéric Geniet Frédéric Geniet Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author John Palmeri John Palmeri Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Andrea Parmeggiani Andrea Parmeggiani Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Dynamique des Interactions Membranaires Normales et Pathologiques, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author François Boudsocq François Boudsocq Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Véronique Anton Leberre Véronique Anton Leberre LISBP, CNRS, INRA, INSA, Université de Toulouse, Toulouse, France Search for more papers by this author Jean-Charles Walter Corresponding Author Jean-Charles Walter [email protected] Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France Search for more papers by this author Jean-Yves Bouet Corresponding Author Jean-Yves Bouet [email protected] orcid.org/0000-0003-1488-5455 Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France Search for more papers by this author Author Information Roxanne E Debaugny1, Aurore Sanchez1,5, Jérôme Rech1, Delphine Labourdette2, Jérôme Dorignac3, Frédéric Geniet3, John Palmeri3, Andrea Parmeggiani3,4, François Boudsocq1, Véronique Anton Leberre2, Jean-Charles Walter *,3 and Jean-Yves Bouet *,1 1Laboratoire de Microbiologie et Génétique Moléculaires, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS), Université de Toulouse, UPS, Toulouse, France 2LISBP, CNRS, INRA, INSA, Université de Toulouse, Toulouse, France 3Laboratoire Charles Coulomb, CNRS-Université Montpellier, Montpellier, France 4Dynamique des Interactions Membranaires Normales et Pathologiques, CNRS-Université Montpellier, Montpellier, France 5Present address: Institut Curie, UMR 3664 CNRS-IC, Paris, France *Corresponding author. Tel: +33 467 143 146; E-mail: [email protected] *Corresponding author. Tel: +33 561 335 906; E-mail: [email protected] Molecular Systems Biology (2018)14:e8516https://doi.org/10.15252/msb.20188516 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS-bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico-mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that "Nucleation & caging" is the only coherent model recapitulating in vivo data. We also showed that the stochastic self-assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the "Nucleation & caging" model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self-assembly mechanism is widely conserved from plasmids to chromosomes. Synopsis High-resolution ChIP-seq and physico-mathematical modeling are used to analyze the in vivo ParB DNA-binding profiles. The "Nucleation and caging" self-assembly mechanism is widespread to ensure faithful bacterial DNA segregation by ParABS systems. ParBS partition complexes are highly dynamic nucleoprotein complexes. The robust ParB DNA binding profiles derived by ChIP-seq data are well-described by the "Nucleation and caging" model. The size of the partition complex is invariant to intracellular variation in ParB levels. This self-assembly mechanism is observed on Escherichia coli and V. cholerae chromosomes and on the F plasmid. Introduction The segregation of DNA is an essential process for the faithful inheritance of genetic material. Minimalistic active partition systems, termed Par, ensure this key cell cycle step in bacteria (Baxter & Funnell, 2014) and archaea (Schumacher et al, 2015). Three main types of bacterial partition systems have been identified and classified by their NTPase signatures. Of these, the type I, also called ParABS, is the only one present on chromosomes and the most widespread on low-copy-number plasmids (Gerdes et al, 2000). Each replicon encodes its own ParABS system and their proper intracellular positioning depends on the interactions of the three ParABS components: ParA, a Walker A ATPase; ParB, a dimer DNA binding protein; and parS, a centromere-like DNA sequence that ParB binds specifically. The ParA-driven mechanism that ensures the proper location and the directed segregation of replicons relies on the positioning of ParBS partition complexes within the nucleoid volume (Le Gall et al, 2016) and on a reaction diffusion-based mechanism (Hwang et al, 2013; Lim et al, 2014; Hu et al, 2017; Walter et al, 2017). The centromere-like parS sites are located close to the replication origin on chromosomes and plasmids, and are typically composed of 16-bp palindromic motifs (Mori et al, 1986; Lin & Grossman, 1998). ParB binds with high affinity to its cognate parS as dimers (Hanai et al, 1996; Bouet et al, 2000). This serves as a nucleation point for assembling high molecular weight ParB-parS partition complexes, as initially seen by the silencing of genes present in the vicinity of parS (Lynch & Wang, 1995; Lobocka & Yarmolinsky, 1996). ParB binds over 10 Kbp away from parS sites for all ParABS systems studied to date (Rodionov et al, 1999; Murray et al, 2006; Sanchez et al, 2015; Donczew et al, 2016; Lagage et al, 2016). This phenomenon, termed spreading, refers to the binding of ParB to centromere-flanking DNA regions in a non-specific manner. The propagation of ParB on DNA adjacent to parS is blocked by nucleoprotein complexes such as replication initiator complexes in the case of the P1 and F plasmids (Rodionov et al, 1999; Sanchez et al, 2015), or repressor–operator complexes on the bacterial chromosome (Murray et al, 2006). These "roadblock" effects led to the initial proposal that ParB propagates uni-dimensionally on both sides of the parS sites, in a so-called "1D-spreading" model (see Fig EV1A). However, this model was put into question as (i) the quantity of ParB dimers present in the cell was insufficient to continuously cover the observed spreading zone, and (ii) ParB binding to parS adjacent DNA resisted biochemical demonstration (reviewed in Funnell, 2016). Click here to expand this figure. Figure EV1. Physical predictions of the current ParB/parS assembly mechanisms Current models for ParB spreading and partition complex assembly. Schematic representation of the main currently proposed mechanisms for the assembly of partition complexes. ParB dimer (dark blue ovoids) binds specifically to the parS centromere sequence (black rectangle). (a) "1D spreading". ParB dimers propagate by nearest-neighbor interactions in 1D following the DNA track (black line) and form filaments away from parS in both directions. (b) "Spreading and bridging". ParB dimers form (short) 1D filaments on parS and on nsDNA by nearest-neighbor interactions. By bridging together these patches of ParB induce the formation of DNA loops. (c) "Nucleation and caging". The transient interactions of ParB with itself and with ParB-nsDNA provide a network of weaker interactions that nucleates the formation of a highly confined ParB zone. By preventing fast ParB diffusion away from the ParB/parS complex, these independent but synergistic interactions actively cluster most ParB around parS. Importantly, the DNA in the vicinity of parS would preferentially enter this high-density region of ParB. This results in the stochastic binding of ParB over the centromere-proximal DNA sequences which depend on the natural loops of the DNA, and leads to the observed power law decrease in ParB density occurring over large genomic distance. Modeling of the evolution of the DNA binding profiles in the vicinity of parS as a function of the ParB level. Schematics of ParB DNA binding profile as a function of ParB concentration from the predictions of the three main physico-mathematical models. Note that the intracellular concentration is a good estimate of the amount of ParB in clusters as over 90% of ParB are highly confined around parS. (Left) The "1D-spreading" model predicts a rapid decrease of the ParB density after the parS site (Broedersz et al, 2014). Most of the particles are homogeneously distributed at an average constant value along the DNA. This behavior is explained from general statistical physical ground: a 1D system of particles with nearest-neighbor interactions cannot display a phase transition leading to a global clustering. (Middle) The "Spreading & bridging" model, in the strong coupling limit, predicts a clustering of all ParBs along the DNA with the constraint of overlapping with parS site. This leads to a triangular profile with a 1/m slope depending on the number of particles m (Broedersz et al, 2014). (Right) With the "Nucleation and caging" model, the decay only depends on the geometry of the foci (discussed in the manuscript). Upon variation of ParB level, the profiles would remain unchanged at a fixed cluster size despite fluctuation in ParB density and would thus overlap after a rescaling of the amplitude. Only "Nucleation and Caging" describes the profiles observed experimentally using high-resolution ChIP-sequencing (Fig 2A). Download figure Download PowerPoint As an alternative to "1D-spreading", two other models for partition complex assembly have been proposed, namely "Spreading & bridging" (Broedersz et al, 2014) and "Nucleation & caging" (Sanchez et al, 2015). Both models (see Fig EV1A) rely on strong ParB clustering with over 90% of ParB confined around parS (Sanchez et al, 2015). The "Spreading & bridging" model proposes that nearest-neighbor interactions (1D-spreading) initiated at parS and non-parS DNA sites in combination with their subsequent interactions in space (3D-bridging), lead in one of the conditions tested (strong spreading and bridging) to the condensation of the ParB-bound DNA into a large 3D complex over a contiguous 1D DNA domain (Broedersz et al, 2014; Graham et al, 2014). The "Nucleation & caging" model rather proposes that the combination of dynamic but synergistic interactions, ParB-ParB and ParB-nsDNA (Sanchez et al, 2015; Fisher et al, 2017), clusters most of the ParB around parS nucleation sites where a few ParB dimers are stably bound (Fig 1A). The in vivo ParB binding pattern from high-resolution ChIP-sequencing data was described with an asymptotic decay as a characteristic power law with an exponent b = −3/2, corresponding to the decreasing probability of the DNA to interact with the ParB cluster as a function of the genomic distance from parS (Sanchez et al, 2015). This model therefore proposes that the DNA surrounding the parS site interacts stochastically with the sphere of high ParB concentration. Interestingly, these three different assembly mechanisms have been explicitly modeled (Broedersz et al, 2014; Sanchez et al, 2015), thus allowing their predictions to be experimentally tested. Figure 1. ParBF binding outside of parS centromere on plasmid and chromosome A. Schematic representation of the "Nucleation & caging" model. Most ParB dimers (green dots) are highly confined in a cluster (dotted circle) centered on the parS sites (black rectangles) onto which some ParBs are stably bound (red dots). The DNA entering the cluster is bound stochastically by ParB. Red and blue lines represent DNA present at small and large (or on a different molecule) genomic distance from parS, respectively. B. ParB clusters on F plasmid in vivo. Typical Escherichia coli cells (DLT3594) display foci of ParBF-mVenus protein (top) expressed from the endogenous genetic locus of the F plasmid (F1-10B-mVenus). The nucleoid is labeled with Hu-mCherry (central). The overlay (bottom) combines the two fluorescent channels. Over 99% of cells harbor ParBF foci. Scale bars: 1 μm. C. ParBF binding outside parSF on the F plasmid is compatible with a power law decay. High-resolution ChIP-seq performed on DLT3586 carrying the F plasmid (F1-10B). The ParB density, normalized to 1 at the first bp downstream the last parSF binding repeat after background subtraction, is displayed over 14 Kbp on the right side of parSF. Monte Carlo simulations and analytic formula are represented in red and dotted black lines, respectively. MC simulations were performed with a Freely Jointed Chain of linear length L = 15 Kbp and a cluster radius σ = 75 nm. The two other parameters, the Kuhn length a = 10 bp and the total number of proteins on the F plasmid Nt = 360 (related to the normalization constant of the protein concentration κ = 0.41), were fitted from the ChIP-seq data (see text and Box 1). As a benchmark for simulations, the analytics are obtained from equation 1 with the same parameters. Inset: The ParBF binding profile (black line) is represented as the number of nucleotide reads over 80 Kbp centered at parS. The number of reads in the input sample (gray line) is normalized to the total number of reads in the IP sample. D, E. Same as (B and C) with parSF inserted at the xylE locus on E. coli chromosome from DLT3584 and DLT2075, respectively. Cells were grown in the presence of 100 μM IPTG. The Kuhn length was adjusted to a = 22 bp in the simulations and analytics. The characteristics of the A–F genetic loci are presented in Appendix Fig S1A. Note that a highly similar ParBF DNA binding pattern is obtained when ParBF was expressed in trans from a plasmid (strain DLT3567; Appendix Fig S1D). Download figure Download PowerPoint To study the assembly mechanism of partition complexes, we used the archetypical type I partition system of the F plasmid from Escherichia coli. By varying several key parameters, we evaluated ParB binding patterns in vivo in relation to predictions of each model. We also investigated the chromosomal ParABS system of the main chromosome of Vibrio cholerae. In all tested conditions, our data indicate that ParB binding profiles robustly correlate only with the predictions of the "Nucleation & caging" model. Results ParBF distribution pattern around parSF is similar on chromosome and plasmid DNA The F plasmid partition complex assembles on a centromere sequence, parSF, composed of twelve 43-bp tandem repeats (Helsberg & Eichenlaub, 1986), which contain ten 16-bp inverted repeat motifs to which ParBF binds specifically in vitro (Pillet et al, 2011) and in vivo (Sanchez et al, 2015). Partition complex assembly has been investigated using small versions of the F plasmid, either ~10 or ~60 Kbp. To discriminate between the different partition complex assembly models, we used two larger DNA molecules: the native 100-Kbp F plasmid (F1-10B; Appendix Table S1) and the 4.6-Mbp E. coli chromosome with parSF inserted at the xylE locus, in strains either expressing (DLT1472) or not (DLT1215) ParBF from an IPTG-inducible promoter. We first verified the formation of ParBF clusters on these two different DNA molecules using the ParBF-mVenus fluorescent fusion protein. ParBF-mVenus, fully functional in plasmid partitioning (Appendix Table S2), was expressed from the endogenous locus on the F plasmid (F1-10B-BmV) or from a low-copy-number plasmid under the control of an IPTG-inducible promoter (pJYB294). In both cases, we observed bright and compact foci in nearly all cells (Fig 1B and D), indicating that the assembly of highly concentrated ParBF clusters on parSF from large DNA molecules, plasmid or chromosome, occurs similar to the smaller F plasmid counterparts (Sanchez et al, 2015). The number of foci from parSF inserted on the chromosome is half of what is observed with the F plasmid, as expected from the twofold difference in copy number (Collins & Pritchard, 1973). We then performed ChIP-sequencing using anti-ParB antibodies and compared the ParBF patterns from the 100-Kbp F1-10B plasmid and the xylE::parSF chromosome insertion (ChIP-seq data are summarized in Table EV1). For F1-10B, we observed a ParB binding pattern extending over 18 Kbp of parSF-flanking DNA nearly identical to the one previously observed on the 60-Kbp F plasmid (Sanchez et al, 2015), with the asymmetrical distribution arising from RepE nucleoprotein complexes formed on the left side of parSF on incC and ori2 iterons (Fig 1C). Besides the strong ParB binding enrichment in the vicinity of parSF, no other difference in the pattern between the input and IP samples was observed on the F plasmid and on the E. coli chromosome. When parSF is present on the chromosome, the ParBF binding pattern displays a comparable enrichment of xylE::parSF-flanking DNA over 15 Kbp (Fig 1E). The ParBF distribution extends ~9 and 6 Kbp on the right and left sides of parSF, respectively. The asymmetry does not depend on parSF orientation as an identical ParBF binding pattern was observed with parSF inserted in the reversed orientation (xylE::parSF-rev, Appendix Fig S1B and C). Similar patterns were also observed when ParBF or ParBF-mVenus were expressed in trans from a plasmid (Appendix Figs S1D and S3D). To the left side of parSF, ParBF binding ends near the yjbE locus that harbors two promoters (locus A; Fig 1E, inset and Appendix Fig S1A), and to the right, ParBF binding ends at the yjbI gene locus (locus E; Fig 1E and Appendix Fig S1A). A dip in the ParB binding intensity is also observed ~1 Kbp downstream from parSF spanning ~300 bp, corresponding to a promoter region (locus C; Fig 1E and Appendix Fig S1A). Dips and peaks in this ParBF binding pattern differ in terms of position and intensity when compared to the one present on the F plasmid. Overall, these data clearly indicate that the global ParBF binding distribution around parSF depends neither on the size nor the DNA molecule, plasmid or chromosome, and that the ParBF binding probability is dependent on the local constraints of each given locus. The "Nucleation & caging" binding model describes the partition complex assembly from the nucleation point to large genomic distance Based on a smaller version of the F plasmid, we previously proposed the "Nucleation & caging" model describing ParB stochastic binding at large distance (> 100 bp) from parS due to DNA looping back into the confined ParB cluster. The characteristic asymptotic decay is compatible with a power law with the exponent b = −3/2, a property that is also observed with 100-Kbp F plasmid (Fig 1C) and with parSF inserted on the E. coli chromosome (Fig 1E and Appendix Fig S1C). This property is thus an intrinsic parameter of the ParBF binding profile at distance > 100 bp from parSF. The abrupt initial drop in ParBF binding at a shorter genomic distance (< 100 bp) from parSF is explained by the difference of ParBF binding affinities between specific parSF sites (Kd ~2 nM) and non-specific DNA (Kd ~300 nM; Ah-Seng et al, 2009). We modeled the DNA molecule by a Freely Jointed Chain (FJC) constituted of N monomers of size a [Kuhn length about twice the persistence length of the corresponding Worm-like chain (Schiessel, 2013)]. One particle is always attached on parS whereas non-specific sites are in contact with a reservoir of particles displaying a Gaussian distribution centered on parS. The ParB density was normalized to 1 by the value on the right side of parS and captured for non-specific sites in the following phenomenological formula as the product of two probabilities integrated over the volume: (1)where is the probability for two DNA loci spaced by a genomic distance as to be at a distance r in space for a Gaussian polymer (de Gennes, 1979); is the equilibrium size of the section of DNA of linear length as; is the probability to find a protein ParB at a radial distance r from the centromere, with κ a normalization constant setting the total number Nt of ParB on the DNA molecule and σ the typical size of the cluster. Note that C(r) is the linearized form of the Langmuir model (Phillips et al, 2012) offering a more compact and intuitive expression for PNC(s). From 1, we easily calculate (see Box 1 for the details of the calculation): (2) Box 1: Analytic calculation of the linear probability of bound particles along DNA We model the DNA molecule by a Freely Jointed Chain (FJC) characterized by N freely rotating monomers of size a (total linear length L = aN). The probability distribution P(r, s) to have two monomers of a Gaussian polymer at a distance r and spaced by s monomers (linear distance as) along the polymer is given by de Gennes (1979): (3)where is the averaged radius occupied by a portion of polymer of size as. In the same way, we define the probability to find a particle ParB at the distance r from parS with a Gaussian repartition centered at parS and with a width σ corresponding to the averaged radius of the foci occupied by proteins: (4)where κ is an adimensional normalization constant setting the total number of ParB on the DNA. Thus, the occupation rate of a protein on DNA is given by: (5) The integration of equation 5 gives: (6) Note that PNC(0) = κ, thus κ is setting the height of the drop between specific and non-specific sites and can be estimated directly from the ChIP-seq data. When R2(s) ⪢ 3σ2, we recover a pure algebraic law PNC ~ s−3/2. The total number of particle Nt on the plasmid is: (7) The latter integral gives the expression of the parameter κ as a function of Nt: (8) The second term in equation 8 containing the total number N of monomers induces only corrections to the dominant behavior, we will thus restrict ourselves to the length enriched in ChIP-seq, i.e. 15 Kbp. Note that the limit N→∞ in equation 8 gives us a condition on the ratio a/σ in order to have proteins on DNA. As κ is the amplitude of a probability, it has to satisfy the condition 0 ≤ κ ≤ 1. Indeed, at a fixed σ, if the Kuhn length becomes too large the polymer does not return in the focus frequently enough in order to ensure Nt bound proteins onto the DNA. We note that the ParB proteins that bind to the DNA molecule targeted by ChIP-seq come from a bound state on competing non-spe DNA (see Fig 1A). Thus, the gain in energy is zero and the binding is solely governed by entropy. However, regarding the binding on specific DNA, there is a gain of energy corresponding to the difference between specific and non-specific binding energies Δε = εs − εns, respectively. This energy difference Δε is sufficiently large in E. coli to consider that parS sites are always occupied. Note that the decay versus the genomic distance as is asymptotically determined by a power law of exponent −3/2 modulated by an amplitude depending on the concentration of ParB. The model has only three parameters: σ = 75 nm is determined from superresolution microscopy (Lim et al, 2014; Sanchez et al, 2015). The two remaining parameters κ (a function of the total number of proteins Nt) and the Kuhn length a are readily obtained from a fit of ChIP-seq data (see Box 1 for the calculation and Materials and Methods for the fitting procedure). Note that the relation between κ and Nt depends on the bioinformatics analysis (Appendix Fig S1E). We obtained κ = 0.41 for both F plasmid or parSF-chromosomal insertions, leading to 360 and 120 ParB per DNA molecule, respectively, in good agreement with former estimate (Bouet et al, 2005). The last remaining free parameter is the Kuhn length a, estimated to 10 or 22 bp for the F plasmid or parSF-chromosomal insertions, respectively, to fully describe the ParBF DNA binding profiles (Fig 1C and E, and Appendix Fig S1D). These fitted values are lower than expected, likely due to the modeling that does not account for supercoiling and confinement. Nevertheless, using these defined parameters, the refined "Nucleation & caging" model provides a qualitative prediction of the experimental data over the whole range of genomic positions, from a few bp to more than 10 Kbp. ParBF DNA binding pattern over a wide range of ParB concentrations favors the "Nucleation & caging" model The physical modeling for each proposed model (Broedersz et al, 2014; Sanchez et al, 2015) predicts distinct and characteristic responses upon variation of the intracellular ParB concentration (see explanations in Fig EV1B). Briefly, (i) the "1-D filament" model predicts a rapid decrease of ParB binding followed by a constant binding profile dependent on ParB amount, (ii) the "Spreading & bridging" model predicts linear decays with slopes depending on the ParB amount, and (iii) the "Nucleation & caging" model predicts a binding profile which depends only on the size of the foci. The exponent b = −3/2 of the power law distribution would not change upon ParB amount variation resulting in an overall similar decay at a fixed focus size. In order to discriminate between these three model predictions, we performed ChIP-seq experiments over a large range of intracellular P
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