Faithful segregation of replicated chromosomes is essential for efficient proliferation of cells. Accordingly, many bacteria are equipped with active chromosome and plasmid partition systems belonging to the ParABS family (Baxter and Funnell, 2014; Lutkenhaus, 2012; Vecchiarelli et al., 2012). Basic ParABS systems comprise two proteins, ParA and ParB, and a centromere-like, cis-acting DNA element called parS. The ParA proteins of this family are ATPases with a characteristic deviant Walker-A motif (Motallebi-Veshareh et al., 1990) and bind non-specific DNA (nsDNA) in an ATP-dependent manner by forming a DNA binding-competent dimer (Davey and Funnell, 1994; Leonard et al., 2005; Vecchiarelli et al., 2010). Accordingly, ParA proteins localize to the bacterial chromosome (the nucleoid) in vivo (Ebersbach and Gerdes, 2004; Hatano et al., 2007; Lim et al., 2014).

ParB is typically a dimeric sequence-specific DNA binding protein that binds tightly to the parS consensus sequences that mark the DNA cargo to be partitioned (Bouet et al., 2000; Mori et al., 1989; Pillet et al., 2011; Taylor et al., 2015). Most ParABS systems have multiple copies of a ParB dimer binding consensus sequence that collectively constitute a parS site. F-plasmid has a parS sequence cluster (parS_F, also called sopC) composed of 12 repeats of a 16 bp consensus sequence, each separated by 27 base-pair spacer sequences (Helsberg and Eichenlaub, 1986). The ParBs of known chromosomal and plasmid Par systems such as P1 and F bind to parS via a helix-turn-helix motif (Schumacher and Funnell, 2005; Schumacher et al., 2010). These HTH–ParB proteins also associate with several kilobases of DNA surrounding a parS site in vivo in a proximity-dependent manner without obvious sequence specificity (Breier and Grossman, 2007; Murray et al., 2006; Rodionov et al., 1999; Sanchez et al., 2015). This activity, known as ParB spreading, is believed to be essential for proper function of these systems (Breier and Grossman, 2007; Graham et al., 2014) and results in the formation of a large nucleo-protein complex (the partition complex) around the parS site on the DNA to be partitioned. Mutations in the B. subtilis parB gene blocking spreading and causing partition deficiency have been identified within the Box II region (GXRR) of the N-terminal domain (Breier and Grossman, 2007; Graham et al., 2014), a highly conserved motif among HTH–ParB homologues (Yamaichi and Niki, 2000). Recently, several groups reported that HTH–ParB proteins have CTPase activity and the Box II residues play key roles in CTP binding and hydrolysis, suggesting that ParB spreading is driven by an active process dependent on energy derived from CTP hydrolysis (Jalal et al., 2020; Osorio-Valeriano et al., 2019; Soh et al., 2019).

ParB interacts with ParA via its N-terminal region (Ravin et al., 2003) and activates nsDNA-bound ParA dimer’s ATPase, releasing it from DNA (Ah-Seng et al., 2009; Davis et al., 1992; Scholefield et al., 2011; Watanabe et al., 1992). In the absence of ParB stimulation, the ATP turnover of ParA is low, typically around one ATP per hour (Ah-Seng et al., 2009; Davis et al., 1992; Fung et al., 2001; Scholefield et al., 2011). Because of this slow basal ATPase rate, and since the majority of cellular ParB molecules is concentrated at the partition complexes due to ParB spreading, ATP hydrolysis by ParA and dissociation from the nucleoid is expected to occur principally in the vicinity of partition complexes. Biochemical studies of P1 ParA ATPase showed a significant time delay before activation of ParA for DNA binding after ATP binding, predicting a significant free bulk-diffusion period for ParA before reactivation for nsDNA binding (Vecchiarelli et al., 2010). This, along with in vivo imaging observations (Hatano et al., 2007; Ringgaard et al., 2009), led to a prediction that the nucleoid proximal to a partition complex would become depleted of ParA (the ParA depletion zone) and the proposal of a diffusion-ratchet model for plasmid segregation by the ParABS system (Vecchiarelli et al., 2010).

The diffusion-ratchet model is based on the premise that the nucleoid-bound ParA-ATPase activation by plasmid-bound ParB generates a local ParA depletion zone on the nucleoid, forming a nucleoid-bound ParA concentration gradient around the partition complex (Hu et al., 2017; Vecchiarelli et al., 2010). The interaction of plasmid-bound ParB with the ParA gradient on the nucleoid results in a cargo position-dependent free-energy difference (Sugawara and Kaneko, 2011). Binding of ParB to ParA reduces the system free-energy, therefore moving the cargo to a higher ParA concentration lowers the system free-energy. This cargo position-dependent free-energy difference translates to a directional motive force on the ParB bound cargo. The generation of sufficient cargo motive force to overcome thermal diffusion was demonstrated in cell-free reconstitution experiments showing that a bead coated with parS_F-containing DNA is driven across an nsDNA-coated flow cell surface in the presence of ParA_F, ParB_F, and ATP (Vecchiarelli et al., 2014). In some in vivo time-lapse imaging experiments, ParA has been observed to undergo pole-to-pole oscillations along the length of a nucleoid with a partition complex chasing the receding edge of a ParA distribution zone on the nucleoid, further supporting the diffusion-ratchet model (Hatano et al., 2007; Ringgaard et al., 2009). Variations of this model have also been proposed (Le Gall et al., 2016; Lim et al., 2014; McLeod et al., 2017).

Generating persistent directional motion by the diffusion-ratchet model requires a balance between the ParA–ParB association/dissociation dynamics prior to ATP hydrolysis and the steps and kinetic parameters that govern ATP hydrolysis. For example, if every ParA–ParB association resulted in instantaneous ATP hydrolysis and dissolution of the ParA–ParB bonds linking the partition complex (cargo) and the nucleoid, no cargo driving force would result. Conversely, if each bond persisted too long, the cargo would remain immobile on the nucleoid (Hu et al., 2017). However, the detailed biochemical reaction steps leading to ParB activation of DNA-bound ParA-ATPase and the subsequent release of ParA have not been determined.

In order to advance our quantitative understanding of the ParABS system mechanism, we investigated the assembly and disassembly kinetics of ParA_F–ParB_F complexes that form prior to ATP hydrolysis using F-plasmid ParA_FB_FS_F (also called SopA/B/C) as a model system. Employing a TIRF microscopy-based nsDNA-carpet assay (Vecchiarelli et al., 2013), we first examined the stoichiometry of the nsDNA-bound ParA_F–ParB_F complexes that accumulate in the absence of ATP hydrolysis. We investigated impacts of different ParB_F-cofactors (parS_F and CTP) or ParB_F mutations that hinder ParB_F dimerization, parS_F-binding, CTPase activity, or ParA_F ATPase activation. We then studied how the same set of cofactors or ParB_F mutations influenced ParA_F-ATPase activation by ParB_F. Our results showed that ParB_F formed complexes with nsDNA-bound ParA_F in which both ParB_F-interacting faces of the ParA_F dimers were occupied by the N-terminal ParA_F-activation domain of ParB_F. All such complexes observed in the presence of ATPγS exhibited similar, slow dissociation kinetics from nsDNA compared to ParA_F dimers in the absence of ParB_F so long as both ParB_F-interacting faces of the ParA_F dimers were occupied by ParB_F N-terminal domains. Binding of ParB_F N-terminal domains at both ParB_F interaction faces is also necessary for efficient ATPase activation of nsDNA-bound ParA_F dimers. Strikingly, the ParB_F cofactors, CTP and parS_F, acted synergistically to accelerate the assembly of pre-ATP hydrolysis ParB_F–ParA_F complexes on nsDNA. In addition, a magnetic tweezers-based DNA condensation assay revealed that stable DNA condensation by ParB_F required both CTP and parS_F. These observations suggested that CTP and parS_F promote both ParA_F–ParB_F and ParB_F–ParB_F interactions. The compaction of parS_F-containing DNA by ParB_F in the presence of CTP recapitulated the salient features of the condensed ParB spreading partition complex observed in vivo, suggesting that ParB_F in the presence of parS_F and CTP closely reflects the functional state of ParB_F in the partition complexes in vivo. Interestingly, ParB_F in these conditions accelerated ATP turnover by the nsDNA-bound ParA_F no more than twofold compared to ParB_F without parS_F and CTP, to a modest ~80 h⁻¹. These findings have important implications for the diffusion-ratchet model of F-plasmid partition by the ParABS system.

Here, we investigated the ParA–ParB interactions that lead to accelerated ATP hydrolysis by ParA and how they are impacted by parS_F and CTP. First, we addressed the nature of nsDNA-bound ParA_F–ParB_F complexes. In the presence of ATP, ParA_F forms DNA binding-competent dimers and binds the nsDNA-carpet without ParB_F. Upon forming a complex with ParB_F, ParA_F becomes activated for ATP hydrolysis and the complex rapidly disassembles (Vecchiarelli et al., 2013), impeding characterization of the complex. Therefore, we studied DNA-bound ParA_F–ParB_F complexes that accumulate prior to ATP hydrolysis by using non-hydrolysable ATPγS. ParA_F is not expected to form DNA binding competent dimers efficiently in the presence of ATPγS based on the study of the closely related ParA_P1 ATPase (Vecchiarelli et al., 2010). However, we found ParB_F promotes conversion of ParA_F to a DNA binding competent state in the presence of ATPγS (see below). Hence, in this study, we infused ParA_F-eGFP and ParB_F-Alexa647, or other fluorescent-labeled ParB_F variants, preincubated at room temperature for 10 min with ATPγS into an nsDNA-carpeted flow cell and quantified the densities of the two DNA-associated proteins by imaging the flow cell surface with TIRF microscopy (Figure 1). ParA_F alone at the concentration used here (1 μM, all protein concentrations are expressed as monomer concentrations) does not efficiently bind DNA in the presence of ATPγS as expected, and only low-level steady state density (less than ~200 monomers per μm²) of ParA_F-eGFP was detected on the DNA-carpet (Figure 2A,B). The observed DNA dissociation rate constant of ParA_F-ATPγS (~6 min⁻¹) is similar to that of ParA_F-ATP estimated by FRAP or by washing the flow-cell with nsDNA-containing buffer (~4.5–6 min⁻¹, Vecchiarelli et al., 2013). ParB_F-Alexa647 (2 μM) did not bind the DNA-carpet to a significant level in the 300 mM K-glutamate buffer used in this experiment.

Figure 1

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ParB_F^{1-42 R36A} forms a rapidly disassembling complex with ParA_F on the DNA carpet

An R36A mutation was reported to significantly compromise ParB_F’s ability to activate ParA_F’s ATPase (Ah-Seng et al., 2009). To test whether this mutation affected ParB_F’s ability to form a complex with ParA_F we repeated the experiments shown in Figure 2C–E using ParB_F^{1-42 R36A}- mCherry. ParB_F^1-42R36A- mCherry and ParA_F-eGFP bound with an approximately 1:1 stoichiometry, similar to ParB_F^1-42- mCherry but reached a steady-state density on the DNA-carpet of less than 10% of the density observed with ParB_F^1-42- mCherry (Figure 3A). When washed with buffer containing ATPγS, ParB_F^{1-42 R36A}- mCherry dissociated first followed by ParA_F, similar to the results obtained with ParB_F^1-42- mCherry but ParB_F^{1-42 R36A}-mCherry dissociated ~10-fold faster, followed by dissociation of ParA_F-eGFP within a few seconds (Figure 3B). When the wash buffer also contained 10 μM ParB_F^{1-42 R36A}-mCherry the two proteins dissociated in parallel maintaining ~1:1 stoichiometry (Figure 3C). Together these observations indicate that ParB_F^R36A interacts with ParA_F, but with a much faster dissociation rate constant compared to wild-type ParB_F. ParB_F^{1-42 R36A} could activate ParA_F-ATPase with an increased half-saturation concentration of 108 µM, approximately 100-fold higher than ParB_F^1-42 (Figure 3D). These results explain the puzzling report that while the R36A mutation severely compromised activation of ParA_F-ATPase by ParB_F, it did not impede oscillation of ParA_F on the nucleoid, and only mildly reduced plasmid stability (Ah-Seng et al., 2013). At the interface between the ParA_F-bound nucleoid and partition complexes containing many ParB_F dimers, the local ParB_F concentration is expected to be sufficiently high for this mutant protein to activate ParA_F-ATPase to effectively generate a ParA_F depletion zone and motive force driving the partition complex as indicated by the repeated oscillation of the nucleoid-bound ParA_F distribution.

Figure 3

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ParA_F and ParB_F bind to and dissociate from nsDNA together in the presence of ATPγS with ~1:1 stoichiometry

When ParA_F-eGFP and full-length ParB_F-Alexa647 were incubated together at 1 µM and 2 µM, respectively, in the presence of ATPγS, they bound to the DNA-carpet in parallel maintaining ~1:1 stoichiometry up to a density of ~5000 monomers/μm² (Figure 4A). They also dissociated from the DNA-carpet in parallel, maintaining ~1:1 stoichiometry, when washed with a buffer containing ATPγS, with an apparent dissociation rate constant of approximately ~1 min⁻¹ (Figure 4B). These results show that ParA_F and ParB_F form a hetero-tetramer containing two monomers each of ParA_F and ParB_F (A₂B₂), or larger oligomers composed of the hetero-tetramers, that binds as a unit on nsDNA in the presence of ATPγS.

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Full-length ParB_F, which forms dimer with apparent K_D of ~ 19 nM (Figure 4—figure supplement 1), activated ParA_F-ATPase in the presence of nsDNA to ~50 hr⁻¹ without significant sigmoidal concentration dependence (Figure 4E). Based on the results of experiments with monomeric ParB_F^1-42 proteins described earlier, we conclude that a single dimer of full-length ParB_F can straddle an nsDNA-bound ParA_F dimer, permitting the two N-termini to interact with both of the ParB_F-binding faces of the ParA_F dimer to activate the ATPase.

CTP alters the complex formed between ParA_F and ParB_F in a manner similar to parS_F and accelerates complex formation in the presence of parS_F

ParB proteins have recently been reported to have CTPase activity that is coupled with changes in their DNA binding properties and refolding of the CTPase domains into a globular dimeric structure in the presence of CTP (Soh et al., 2019; Osorio-Valeriano et al., 2019) from the more extended and poly-dispersed structure in the absence of nucleotide (Chen et al., 2015). We therefore decided to test whether the addition of CTP influences the ParA_F–ParB_F complex formed on the DNA-carpet in the presence of ATPγS. When ParA_F-eGFP and ParB_F-Alexa647 were incubated together in the presence of ATPγS (1 mM) and CTP (2 mM), they bound to and dissociated from the nsDNA-carpet with a stoichiometry of ~1:2 (Figure 5A, Figure 5—figure supplement 1A). The assembly kinetics of the carpet-bound complex was roughly the same as in the absence of CTP; however, the apparent dissociation rate constant during buffer wash was slightly but reproducibly slower by a factor of roughly two at ~0.6 min⁻¹. When parS_F was included together with CTP, the rate of A₂B₄ complex assembly on the DNA-carpet increased several-fold, the binding density of the complex on the DNA-carpet reached a correspondingly higher level, and the two proteins dissociated from the DNA-carpet maintaining a ~1:2 stoichiometry with apparent dissociation rate constant similar to that in the absence of parS_F (Figure 5B, Figure 5—figure supplement 1B). When CTP was replaced by CDP in the presence of parS_F, although the ParB_F/ParA_F ratio remained above 2, unlike in the presence of CTP, the complex assembly rate did not increase (Figure 5C, Figure 5—figure supplement 1C), thus behaving similarly to the reaction in the presence of parS_F alone.

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Next, we asked if the parS_F DNA fragment was incorporated in the A₂B₄ complexes assembled in its presence. The experiments in the presence of parS_F were repeated in the presence or absence of CTP with ParA_F (1 μM), ParB_F-Alexa647 (2 μM) and Alexa488-parS_F (1.1 μM), and the nsDNA-carpet-bound ratio of parS_F and ParB_F after 240 s sample infusion was measured (Figure 5D). The observed parS_F/(ParB_F)₂ ratio in the absence of CTP was ~0.2, while in the presence of CTP, the ratio was only ~0.04. Thus, whereas the assembly of the A₂B₄ complex involving CTP-ParB_F was accelerated by parS_F, a very small fraction of the resulting complex contained the parS_F-DNA fragment, indicating that parS_F plays a catalytic role in the activation of CTP-ParB_F and accelerated assembly of the A₂B₄ complex. This parallels the observation that a much lower concentration of parS_F fully activated the CTPase activity of ParB_F (Figure 5—figure supplement 2C) as has also been shown for ParB_Bsu (Soh et al., 2019).

In the presence of CTP, ParB_F condenses DNA carrying parS_F in cis

The recently discovered CTP and parS-dependent ParB conformational change appears to promote ParB parS-DNA binding and spreading (Soh et al., 2019), impacting ParB-DNA partition complex assembly. In vivo, spreading ParB forms condensed foci around parS sites indicating that parS-driven ParB spreading likely occurs in cis. Nonetheless, the possibility that parS can trigger ParB spreading in trans has not been tested in vitro. Previous studies reported DNA condensation by B. subtilis ParB via ParB–ParB interactions, but these studies were conducted in the absence of CTP and did not observe a strong effect of parS in cis (Graham et al., 2014; Song et al., 2017; Taylor et al., 2015). To see if parS_F can act in trans and to characterize how parS_F and CTP influence ParB_F–DNA interactions in vitro, we conducted single-molecule DNA pulling experiments employing magnetic tweezers. ParB_F at various concentrations was infused into a flow cell containing ~5 kbp DNA tethers that anchored magnetic beads to the coverslip surface (Figure 6A). The tethers contained either 12 parS_F consensus sequence repeats at their midpoints (parS_F-DNA), or no parS_F sequence (nsDNA). The protein sample was infused while the DNA tethers were stretched at 5 pN force, preventing DNA condensation. To allow DNA condensation by bound ParB_F molecules, the force was dropped to 0.05 pN and the tether extension was monitored for 30 s. To assess the stability of DNA condensation by ParB_F dimers, tether extension was monitored after increasing the force to 5 pN. In the absence of CTP, we only observed condensation at very high concentrations of ParB_F (>5 µM) and did not see a significant difference between parS_F-containing and non-specific tethers (Figure 6B inset). However, in the presence of CTP, 50 nM ParB_F robustly condensed parS_F-containing DNA tethers (Figure 6B purple). These condensed protein-DNA complexes resisted 5 pN extension force, requiring many minutes at 5 pN tension to de-condense (Figure 6—figure supplement 1A). The slow de-condensation took place through a series of abrupt steps, which we interpret as stepwise opening of large DNA loops held by multiple ParB_F–ParB_F interactions (Figure 6—figure supplement 1A). Condensation was comparable for DNA molecules that were topologically constrained, i.e., could be supercoiled, or unconstrained (nicked), suggesting that condensation is not a consequence of topological changes in the DNA caused by ParB_F translocating away from parS_F sites (Figure 6—figure supplement 2). We observed some condensation events with parS_F containing tethers in the presence of CDP, but these events were rarer, required higher ParB_F concentrations, and were almost completely de-condensed within 5 s of raising the force to 5 pN, in stark contrast to condensation in the presence of CTP (Figure 6B, light blue, Figure 6—figure supplement 1B). Since this experiment was also carried out using CDP that contained a compound hydrolysable by ParB_F, contribution of this compound to the limited tether condensation cannot be ruled out. In contrast, ParB_F was unable to substantially condense DNA tethers lacking parS_F sequences, even in the presence of CTP, and rare condensation events were quickly reversed by the application of 5 pN force (Figure 6B, dark blue). Addition of parS_F-containing DNA fragments together with ParB_F and CTP did not rescue the inability to condense tethers lacking parS_F, indicating that parS_F cannot act in trans to promote ParB spreading and condensation of DNA molecules (Figure 6—figure supplement 3). Together these results indicate that parS_F mediates loading of multiple CTP-bound ParB_F dimers in cis onto the DNA-tethers and these ParB_F dimers are capable of forming DNA looping bridges likely via inter-dimer interactions to form a condensed partition complex-like structure. As expected, ParB_F^R121A bearing a mutation at the critical Box II residue in the CTPase domain was unable to condense DNA to a significant degree even with parS_F containing tethers (Figure 6B, red). We propose that stable DNA condensation by ParB_F is mediated by CTPase domain dimerization and requires both parS_F and CTP at moderate ParB_F concentrations (~100 nM) (Figure 6C).

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In this report, we characterized facets of the ParA_F–ParB_F interaction leading to the assembly of the nsDNA-bound ParA_F–ParB_F complex that is required to activate ParA_F for ATP hydrolysis and dissociation from nsDNA under the influences of parS_F and CTP (summarized in Figure 7). Our results indicate that both ParB_F binding faces of the nsDNA-bound ParA_F dimers must be occupied by a ParB_F N-terminal domain for ATPase activation (Figures 2C–G and 7B). In principle, two copies of the ParB_F N-terminal domain activating a ParA_F dimer could belong to one ParB_F dimer as seen in the absence of CTP or parS_F (Figures 4A,B and 7B, middle). However, most ParB_F dimers in partition complexes in vivo are likely in the CTP- and parS_F-activated state, spreading over a parS_F-proximal DNA region. CTP or parS_F binding alters the ParB_F dimer structure to prevent a single ParB_F dimer from providing both copies of the N-terminal domain to occupy both binding faces of a ParA_F dimer, necessitating two ParB_F dimers, each providing one N-terminal domain to a ParA_F dimer (Figures 4C,D, 5, and 7B, bottom). Strikingly, parS_F together with CTP significantly increased the A₂B₄ complex assembly rate on nsDNA without strongly affecting its disassembly rate. Although we have not analyzed the full kinetic details of the process that leads to ATPase activation by ParB_F, we propose that a moderately slow transition separates formation of the ATPase-activated A₂B₄ complex from the rapidly reversible ParA_F–ParB_F interaction processes. Such a local slow step would partially decouple the reversible ParA_F–ParB_F interaction dynamics from the irreversible ATP hydrolysis, thereby promoting dynamic interactions between the nucleoid and partition complex that facilitate partitioning via the diffusion-ratchet mechanism as elaborated below.

Figure 7

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The clearest indication that both ParB_F-interacting faces of the nsDNA-bound ParA_F dimer must be occupied by the N-terminal domain of ParB_F for ATPase activation came from experiments using artificial ParB_F constructs. We showed that monomeric ParB_F^1-42 stimulates ParA_F ATPase with a clear sigmoidal concentration dependence, indicating that one molecule of ParB_F^1-42 binding to one side of a ParA_F dimer cannot fully activate the ParA_F ATPase (Figure 2F). When ATP hydrolysis was blocked by using non-hydrolysable ATPγS, ParB_F^1-42-mCherry formed an equimolar complex with ParA_F (Figure 2C–E). Thus, the ParA_F forms a complex with ParB_F^1-42-mCherry bound at both ParB_F-interacting faces of the ParA_F dimer prior to ATP hydrolysis (Figure 7B; top). Consistently, an artificially dimeric ParB_F^1-42 construct, ParB_F^1-42-mCherry-EcoRI^E111Q, efficiently activated ParA_F-ATPase with hyperbolic concentration dependence (Figure 2G).

In the absence of CTP or parS_F, the ParB_F dimer is held together by the C-terminal self-dimerization domain (Figure 7A, bottom) with dimerization K_D of ~19 nM (Figure 4—figure supplement 1). In this state, the N-terminal halves of the monomers are thought to be separate from each other according to the SAXS envelope of the structure (Chen et al., 2015; also see Figure 2—figure supplement 3B). Thus, one dimer could straddle a ParA_F dimer with each N-terminal ParA_F-interaction domain interacting with one of the two faces of a ParA_F dimer (Figure 7B, middle).

In contrast, when bound by CTP the CTPase domains in a ParB_F dimer fold to form a single globular domain (Figure 7A, bottom) (Soh et al., 2019; see Figure 2—figure supplement 3C). The two ParA_F-interaction domains emanating from this dimeric domain are unlikely to reach both sides of a ParA_F dimer, necessitating an A₂B₄ complex for ATPase activation (Figure 7B, bottom). In theory, it is possible that a chain of (A₂B₂)_n might form, but the 1:2 protein stoichiometry observed in the presence of ATPγS indicates such a configuration is unfavored. A₂B₄ complexes formed in the presence of CTP and parS_F DNA fragments contained almost no parS_F DNA fragments (Figure 5D). This is consistent with the notion that after binding parS_F, CTP-ParB_F dimers convert to a low parS_F-affinity state while remaining topologically bound to the DNA and spreading to surrounding DNA regions (Soh et al., 2019). The A₂B₄ complex formed in the presence of parS_F DNA fragments, even without CTP, contained significantly less than a stoichiometric amount of parS_F fragment (Figure 5D). This suggests that association with nsDNA-bound ParA_F dimer lowers the affinity of ParB_F for parS_F, perhaps shifting the structure closer toward parS_F-activated ParB_F-CTP.

The ParB:ParA stoichiometry change from 1:1 to 2:1 caused by parS_F (Figure 4C,D) did not occur with the Box II mutant ParB_F^R121A (Figure 4—figure supplement 2). It is possible that when a ParB_F dimer binds parS_F, the adjacent CTPase domains of the two monomers adopt a mutually interacting folded state akin to the CTP-bound state even without CTP, promoting a Box II dependent dimerized domain structure. This may disfavor formation of the A₂B₂ complex, favoring the A₂B₄ complex that was observed.

All the A₂B₂ and A₂B₄ complexes we observed in the presence of ATPγS dissociated from nsDNA more slowly (k_off = 0.5–1 min⁻¹; Source data 1) compared to ParA_F in the absence of ParB_F (~6 min⁻¹; Figure 2B). For the case of monomeric ParB_F^1-42, which dissociated from ParA_F more rapidly, the presence of 10 μM ParB_F^1-42 in the wash buffer restored the low apparent nsDNA dissociation rate constant of the complex (Figure 2E). Nevertheless, ParA_F dimers in these complexes appear to be primed for further conformational change toward less stably DNA-associated state. Upon dissociation of ParB_F^1-42 from the A₂B^1-42₂ complex, ParA_F dissociated from the DNA-carpet within a second or so, much faster than the ATPγS-ParA_F-dimer that has not yet formed a A₂B₂ or A₂B₄ complex (Figures 2D and 3B).

Our single-molecule DNA condensation measurements indicate that CTP-bound ParB_F dimers are activated by contacting parS_F to load in cis onto the parS_F-carrying DNA in numbers exceeding the copy number of the parS_F-consensus sequence (ParB spreading) as shown by others for chromosomal ParBs (Jalal et al., 2020; Soh et al., 2019), and condense the DNA forming an in vivo partition complex-like structure (Figure 6). Although the magnetic tweezers instrument used in this study did not allow direct measurement of the number of ParB_F molecules contained in the condensed DNA, the large number of de-condensation steps observed when high tension was applied is consistent with the presence of a large number of ParB_F dimers in the condensed DNA (Figure 6, Figure 6—figure supplement 1A). CDP failed to support efficient condensation of parS_F-carrying DNA by ParB_F and the limited condensation observed, which could be due to the contaminating material in the CDP used, was disrupted far more readily than CTP-supported condensates (Figure 6, Figure 6—figure supplement 1B). Our results show that DNA-condensation is caused by ParB_F–ParB_F interactions forming DNA-looping bridges without requiring other protein factors. Combined with evidence indicating that parS_F-activated ParB_F–CTP adopts a unique conformational state (Soh et al., 2019), we favor the view that DNA-bridging capability, mediated by inter-dimer ParB_F interaction, is another attribute of this ParB_F state.

Our observation indicates that the state of ParB_F discussed above is maintained after release from parS_F-containing DNA. ParB_F associates with nsDNA-bound ParA_F dimers forming the A₂B₄ complex with a faster apparent assembly rate in the presence of parS_F and CTP together than with either CTP or parS_F alone. This observation is consistent with the decreased half-saturation concentration in the ATPase activation assay (Figure 5F, Table 2). According to the sliding clamp model of spreading ParB–CTP dimers proposed by Soh et al., 2019, ParB_F–CTP dimers loaded onto a short parS_F DNA fragments would quickly slide off the DNA as shown by Jalal et al., 2020. Since our ATPase activation assay and the DNA-carpet-bound A₂B₄ complex assay in the presence of CTP and parS_F were done using a short linear parS_F DNA fragment, the parS_F-activated state of the ParB_F–CTP dimers we described in this study must remain in this ‘activated’ state for an extended period after sliding off the parS_F fragment. Accordingly, the A₂B₄ complexes bound to the DNA-carpet in the presence of CTP, ATPγS and parS_F fragments contained almost no parS_F fragments (Figure 5D). Thus, parS_F acts as a catalyst to convert ParB_F–CTP dimers from a pre-activation state to an activated state capable of faster A₂B₄ complex assembly. This notion is also consistent with the observation that significantly less than a stoichiometric concentration of parS DNA relative to ParB is sufficient for full activation of the ParB CTPase (Figure 5—figure supplement 2C; Soh et al., 2019). Although the ParB_F dimers in this activated state failed to load efficiently onto DNA lacking parS_F sequences in trans (Figure 6—figure supplement 3), in the absence of contrary evidence, the parsimonious assumption is that this ParB_F dimer retains the conformation of spreading ParB_F dimers that remain loaded on the parS_F-containing DNA in cis. Thus, we propose that the functional properties of ParB_F we observed in the presence of CTP and parS_F, both in facilitating assembly of A₂B₄ complexes and in activating ParA_F-ATPase, reflect those of the majority of ParB_F dimers in partition complexes in vivo.

Our study, together with previous studies, indicates that the ATP turnover rates of ParABS systems are slow because of multiple, slow kinetic steps. These slow steps are strategically placed in the reaction pathway in order to tune the system and drive the motion of the partition complex through the diffusion-ratchet mechanism (Sugawara and Kaneko, 2011; Vecchiarelli et al., 2010). Even at saturating concentrations of ParB_F in the parS_F-activated CTP-bound state, the maximum ATP turnover rate of ParA_F remained modest (~80 ATP/ParA_F-monomer/hour; Figure 5). The slow reactivation of ParA nucleoid binding after ATP hydrolysis likely dominates the overall ATPase cycle time (Vecchiarelli et al., 2010). The presence of a large fraction of ParA_F in the DNA-unbound state during the steady-state ATPase assay was evidenced by the fact that the half-saturation concentration of ParB_F (in the presence of CTP and parS_F) forming the A₂B₄ complex was ~0.2 μM, while the total ParA_F concentration was 1 μM, suggesting less than ~20% of ParA_F was in the nsDNA-bound state ready to interact with ParB_F. In vivo the reactivation rate is likely lower since nucleoid-bound ParA is only fully activated on encountering the partition complex, which lowers the concentration of ParA in the cytosol waiting to be reactivated. The lower precursor concentration slows the nucleoid rebinding rate of ParA non-linearly because reactivation involves a relatively fast nucleotide-dependent reversible ParA dimerization with apparent K_D of ~2 μM, followed by a slow conformational step. This makes the process dimerization-limited at lower precursor ParA concentrations according to the study of ParA_P1 (Vecchiarelli et al., 2010). Whereas this slow ParA reactivation and rebinding process, which allows the maintenance of the nucleoid-bound ParA concentration gradient (Hu et al., 2017), is a critical element of chemophoresis driven motility, the rate of ParA-ATPase activation by ParB is another important factor. In particular, efficient chemophoresis force generation relies on ParA_F–ParB_F interactions achieving a local quasi-equilibrium prior to ATP hydrolysis (Sugawara and Kaneko, 2011). Therefore, we speculate that there is a significant energy barrier associated with the conformational transition of a ParA_F–ParB_F complex to achieve ATPase activation (Figure 7C). The resulting local time delay, in addition to the fact that two ParB dimers are required to bind a ParA dimer to activate its ATPase, would partially decouple the pre-ATP hydrolysis ParA_F–ParB_F reversible interaction steps from the ATP hydrolysis step. This delay would in turn permit ParB–ParA binding to approach local quasi-equilibrium, increasing the efficiency of ParA distribution gradient sensing and motive force generation by the partition complex. In addition, this slow activation step would prevent possible over-depletion of the local nucleoid-bound ParA_F as the partition complex establishes the ParA_F depletion zone.

Disassembly of the ATP-bound A₂B₄ complex might be slow prior to ATP hydrolysis considering the stability of the complexes in the presence of ATPγS. Thus, we propose the energy barrier postulated above is positioned immediately prior to formation of this complex rather than between this complex assembly and ATP hydrolysis. A slow step after formation of the stable complex would prolong the lifetime of the link between the nucleoid and the partition complex impeding partition complex motion without permitting the reversible ParA_F–ParB_F interaction to approach equilibrium. We consider this conformational transition is likely the step synergistically accelerated by CTP and parS_F. We note that CTP-activated ParB_F stimulates ParA_F ATPase with sigmoidal concentration dependence (Figure 5E,F, Table 2), suggesting two ParB_F dimers separately bind a ParA_F dimer during a pre-equilibrium binding phase, forming a transient B₂A₂B₂ complex. We imagine the slow conformational step proposed here might be assisted by the property of the CTP/parS_F-activated ParB_F dimers that promotes inter-dimer interactions as suggested by the magnetic-tweezers experiments, stabilizing the interaction between the two ParB_F dimers within a complex, depicted as conversion of B₂A₂B₂ complex to A₂B₄ complex in Figure 7C. This might explain the higher assembly rate and stability of the complex formed with parS_F-activated ParB_F-CTP. Yet, CTP and parS_F DNA do not significantly increase the ATP turnover rate of ~80 h⁻¹, indicating that the proposed kinetic delay time must be a small fraction of the ATPase cycle time (~45 s), for which we believe the rate limiting step resides in the reactivation process of ParA for nsDNA binding after ATP hydrolysis (Vecchiarelli et al., 2010). Assembly of the A₂B^1-42₂ complex perhaps does not experience this time delay due to fewer steric constraints, but ParB_F^1-42 dissociates more readily compared to full-length ParB_F. If two CTP-bound and parS_F-activated ParB_F dimers independently associating with a nucleoid-bound ParA_F-ATP dimer is important for efficient partition complex motive force generation by the chemophoretic principle as proposed above, one might be able to design a mutant ParB_F that can activate ParA_F-ATPase by forming an A₂B₂ complex even in the presence of CTP, which would significantly affect plasmid partition efficiency. Efforts to generate such ParB_F mutants are currently under way.

This study demonstrates how parS_F, along with CTP, has wide-reaching roles in the F-plasmid ParABS system; not only in ParB_F’s ability to spread from parS_F and promote ParB_F–ParB_F interactions for partition complex compaction, but also in ParB_F dimer interactions with ParA_F. However, we still need to investigate how the ParB_F CTPase activity is impacted by parS_F in different states of the ParB_F–parS_F complex and its interaction with the ParA_F-DNA complex. More generally, in order to understand how the system is orchestrated to achieve system dynamics that result in robust plasmid segregation, improved understanding of the microscopic kinetic parameters is essential. Many details of the system dynamics still remain to be addressed to understand the full picture of the ParABS partition mechanism.

All data generated or analysed during this study are included in the manuscript and supporting files. Source data files have been provided for all relevant figures.

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Author details

1. James A Taylor

   Laboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, United States

   Present address

   Alzheimer’s Research UK Oxford Drug Discovery Institute, University of Oxford, Oxford, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

2. Yeonee Seol

   Biochemistry and Biophysics Center, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, United States

   Contribution

   Data curation, Formal analysis, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

3. Jagat Budhathoki

   Laboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, United States

   Contribution

   Data curation, Formal analysis

   Competing interests

   No competing interests declared

4. Keir C Neuman

   Biochemistry and Biophysics Center, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, United States

   Contribution

   Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0863-5671

5. Kiyoshi Mizuuchi

   Laboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, United States

   Contribution

   Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Writing - review and editing

   For correspondence

   kiyoshimi@niddk.nih.gov

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8193-9244

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