two classes of proteins play important roles in dna segregation : topoisomerases and structural maintenance of chromosome ( smc ) complexes .
dna replication introduces positive ( + ) supercoiling ahead of the replication fork , and rotation of the forks leads to interlinking of the two sister chromosomes , generating ( pre)catenanes behind the replisomes throughout the chromosome . in escherichia coli , 225,000 catalytic events by the type ii topoisomerases dna gyrase and topoisomerase iv ( topoiv ) are required for each generation to unlink the 4.6-mb chromosome .
dna gyrase acts preferentially ahead of the replication fork to remove ( + ) supercoiling ( koster et  al . , 2010 , vos et  al . , 2011 ) .
topoiv removes the majority of links behind the replication forks ( joshi et  al . , 2013 ,
wang et  al . , 2008 ) , whereas the type i topoisomerase topoiii is able to remove links in single - stranded dna regions ( koster et  al . , 2010 , vos et  al . , 2011 ) and
ftsk - dependent xercd recombination at dif is able to remove catenation links in ter ( grainge et  al . , 2007 ) .
heterotetrameric topoiv consists of dimers of parc ( the dna binding and catalytic subunit ) and pare ( the regulatory atpase ) .
it changes dna topology by introducing a double - stranded break in dna and passing a second duplex segment of dna through the break before resealing it .
topoiv acts on topologically different substrates including ( + ) and negative (  ) supercoiled dna and knotted and catenated dna ( koster et  al .
its essential cellular role is in decatenation of newly replicated dna ( joshi et  al . , 2013 , wang et  al . , 2008 ) .
the mechanism of how topoiv recognizes and discriminates its substrates and which substrate is preferred in  vivo is not fully understood ( lee et  al .
2013a ) . a second class of proteins , smc complexes , play an equally important role in faithful dna segregation ( hirano , 2006 ) .
despite sharing little primary amino acid sequence homology with other smc complexes , the e.  coli complex mukbef retains much of the distinctive smc architecture ( nolivos and sherratt , 2014 , woo et  al . , 2009 ) , forming dimers joined at a hinge domain located at one end of an 50-nm - long intramolecular coiled coil with an atpase head domain at the other end of the coiled coil .
inactivation of the mukb protein or either of the two accessory proteins , muke and mukf , results in abnormal chromosome organization and segregation ( danilova et  al . , 2007 ,
the mukb dimerization hinge has been shown to physically interact in  vitro with parc , which stimulates topoiv - mediated relaxation of (  ) supercoils ( hayama and marians , 2010 , li et  al . , 2010 ) .
an enrichment of parc / e molecules in the vicinity of ori - associated mukbef clusters was observed in widefield imaging ( nicolas et  al . , 2014 ) .
here , we used super - resolution microscopy to characterize the behavior of single molecules of topoiv in live e.  coli . moreover , by perturbing the action of topoiv molecules using genetics , an inhibitor , and overexpression of competing protein domains , we are able to provide mechanistic insight into the function of topoiv and its interaction with mukbef clusters . using photoactivated - localization microscopy ( palm ) combined with single - particle tracking ( manley et  al . , 2008 )
, we show that 60 molecules of topoiv were present at any time , although sufficient parc and pare subunits were present for 105 topoiv molecules . impairing the interaction between functional topoiv and mukbef , by overexpressing a competing but non - functional parc c - terminal domain ,
resulted in an 2-fold reduction in the number of immobile topoiv molecules , consistent with the interaction between topoiv and mukbef directing the location and catalytic action of topoiv molecules toward ori - associated mukbef clusters .
we identified two populations of immobile topoiv molecules ; we propose that one with a dwell time of 1.8  s identifies catalytically active molecules , while the other , with a dwell time of 3070  ms , identifies molecules bound to mukbef clusters .
wide - field , palm , and 3d - structured illumination microscopy ( 3d - sim ) ( allen et  al . ,
2014 ) demonstrated that mukbef clusters were enriched along the long axis of the cell .
furthermore , we found that the mukb - parc interaction , although not essential for topoiv function , is crucial for timely segregation of newly replicated ori dna . impairing
this interaction caused delayed segregation of newly replicated sister oris , consistent with the mukbef - parc interaction enhancing decatenation of newly replicated dna .
to characterize the copy number and behavior of topoiv heterotetramers in live e.  coli cells , we labeled the parc or pare subunits by replacing the endogenous genes with functional c - terminal fusions to the photoactivable fluorophore , pamcherry .
the fusions were fully functional in in  vivo assays ( supplemental experimental procedures ; figure  s1a ; table s3 ) .
linking consecutive localizations into trajectories allowed us to follow the movement of individual parc / e molecules at 15-ms intervals until photobleaching ( figure  1a ) ( manley et  al . , 2008 , uphoff et  al . , 2013 ) .
289  34 photoactivatable molecules of parc and 210  46 photoactivatable molecules of pare , normalized to a 2.5-m - long cell , were counted .
since the photactivation efficiency of pamcherry was determined to be 50% in  vivo , the actual copy numbers are likely to be approximately two times higher than these values ( supplemental experimental procedures ) .
to measure the mobility of parc / e , we calculated an apparent diffusion coefficient ( d ) for each molecule from the one - step mean squared displacement ( msd ) of its trajectory using d  = msd/(4 t ) , where t is the frame time of 15  ms .
the different diffusing populations , which could not be described by a single diffusing species ( figure  s1b ) , were defined by fitting an analytical expression to the distribution of experimental d values ( stracy et  al . , 2015 ) .
we first established the mean d of immobile molecules . based on a localization error of 40  nm , we estimated mean d of immobile molecules to be 0.1  ms .
this was confirmed by fitting to the distribution d values for the previously characterized protein dna polymerase 1 ( where the immobile population was clearly resolvable ) , showing that dimm  = 0.11  0.01  ms ( uphoff et  al . , 2013 ,
the parc d distribution fitted well to a two - species model ( figure  1b ) : an immobile population ( 36%  1% ; constrained at dimm  = 0.11  ms ) and a second , unconstrained d distribution , corresponding to a slowly diffusing population ( 64%  1% ; dslow  = 0.35  0.01  ms ) .
molecules in the slow - diffusing population had a lower mobility than expected for free 3d diffusion , consistent with them undergoing transient interactions with dna , which parc does ( corbett et  al . , 2005 ) .
the spatial distribution of slowly diffusing parc molecules showed that they were associated with the nucleoid , consistent with them being transiently associated with dna ( figures s1 g and s3a ) .
in contrast , we propose that the immobile parc molecules are relatively stably bound to dna or dna - bound proteins .
the pare d distribution showed a third population of molecules with higher mobility in addition to the two populations similar to those observed for parc .
2013 ) , we propose that the fast - diffusing molecules represent free pare subunits , whereas the immobile and slow - diffusing molecules were in topoiv heterotetramers . to test this , we imaged pare - pamcherry molecules in cells in which unlabeled pare was overexpressed , outcompeting labeled pare in topoiv heterotetramers .
consistent with our hypothesis , 90% of pare - pamcherry molecules now diffused rapidly and were uniformly distributed throughout the cell , showing no bias toward the nucleoid region ( figures s1f and s1 g ) .
fitting a three - species model to this data ( with dimm and dslow constrained ) established that dfast  = 0.94  0.02  ms .
conversely , imaging pare - pamcherry molecules in a strain overexpressing unlabeled parc showed that the dfast population is completely lost ( figure  s1h ) , confirming that pare molecules in the dimm and dslow states are complexed with parc in topoiv heterotetramers .
the three - species model for the pare data , with constrained dimm , dslow , and dfast values , showed that 32%  1% were immobile , 24%  1% were slow diffusing , and 44%  1% were fast diffusing ( figure  1c ) .
as the copy - number estimates showed that there is no excess pare in the cell , the 44% of uncomplexed , fast - diffusing pare molecules must reflect a steady - state level of topoiv heterotetramer formation and dissociation , with 56% of pare subunits being present in 60 topoiv heterotetramers .
therefore , the 60 topoiv molecules present at any time form from a pool of parc and e molecules sufficient for 105 topoiv heterotetramers . by using the estimated copy numbers and the  1.1  m volume of cells 2.5  m long
, we estimated the in  vivo dissociation constant of topoiv heterotetramers to be 0.5  m ( supplemental experimental procedures ) . since parc interacts with the mukb dimerization hinge in  vitro ( hayama and marians , 2010 , li et  al .
, 2010 , vos et  al . , 2013b ) and shows an enrichment near mukbef clusters in  vivo ( nicolas et  al . , 2014 )
, we tested whether a fraction of the immobile parc and pare molecules result from their binding to immobile mukbef clusters on dna .
fitting a two - species model ( with the dimm and dslow populations established previously ) to the distribution of d values for parc molecules in mukb or mukb cells ; mukb is unable to bind atp and form ori - associated mukbef clusters ( badrinarayanan et  al . , 2012 ) , showed a 50% reduction in the immobile fraction of parc / pare consistent with these molecules being immobile as a consequence of their interaction with ori - associated mukbef clusters ( figure  2a ; figures s2a and s2b ) .
using a clustering algorithm to define parc clusters containing 25 localizations , we showed that parc formed a median of one cluster per cell and deletion of mukb removed most parc clustering ( figure  2a ) .
this was confirmed by the radial distribution analysis of all parc localizations that showed a strongly clustered distribution , which was reduced 4-fold in mukb cells ( figure  s2c ) . since mukb and mukb cells have disorganized chromosomes ( danilova et  al . , 2007 ) , we also considered whether the reduction in the fraction of immobile parc / e molecules in these cells was instead a consequence of global chromosome changes . to distinguish these possibilities
, we impaired the topoiv - mukb interaction by overexpressing an unlabeled parc c - terminal domain ( parc - ctd ) , which binds mukb ( vos et  al . , 2013b ) , thereby outcompeting topoiv binding .
overexpression of parc - ctd did not significantly affect growth rate , cell length , or formation of anucleate cells ( table s3 ) , consistent with unperturbed chromosome organization .
flow cytometry profiles showed a small increase in cells with multiple chromosomes ( figure  s1a ) . under these conditions ,
the immobile fraction of parc was reduced to the level in mukb cells ( figure  2a , bottom ) , and clustering of parc was lost , consistent with approximately half of immobile parc molecules being dependent on a direct interaction with immobile mukbef clusters . to demonstrate that parc clusters spatially associate with mukbef clusters , we imaged parc - pamcherry and mukb - mypet  in the same cells . calculating the radial distribution function of parc palm localizations with respect to the centroid of each mukbef focus showed that parc is enriched near mukbef foci , which moved very little during the observation period ( figure  2b ; figure  s2d ) , with 20% of parc localizations within 200  nm of mukbef centroids .
this result is consistent with the 16% of parc molecules that were immobile due to a direct interaction with mukb , as judged by the reduction in the fraction of immobile molecules in mukb cells ( figure  2a ) .
we noticed that while parc clusters were nearly always in close proximity to a mukbef focus , not all mukbef foci were associated with a parc cluster , a trend also evident in intensity projections from epifluorescent imaging ( figure  s3e ) .
imaging mukb - pamcherry  with palm showed that , despite having a similar copy number ( 195  57 copies / cell ; figure  s2f ) , mukbef formed approximately twice as many clusters per cell as parc ( figure  s2 g ) , thereby indicating an additional level of regulation governing the mukb - parc interaction . by using the fraction of immobile topoiv molecules dependent on mukb
( figures 1b , 1c , and 2a ) and , independently , the fraction of parc localizations close to mukb in the radial distribution analysis ( figure  2b ) , we estimated that 15 topoiv molecules were associated with mukbef clusters at any given time and determined the in  vivo dissociation constant of mukb - parc complexes to be 2  m ( supplemental experimental procedures ) , consistent with in  vitro measurements ( li et  al . , 2010 ) .
to understand further how mukbef clusters direct the organization of immobile parc molecules within the nucleoid , we determined the probability density of parc molecules across the short cell axis .
we segmented cell outlines from the bright - field images and determined the intracellular location of the tracks .
we then established a d threshold ( 0.16  ms ) , which preserved the ratio of immobile ( 36% ) to mobile ( 64% ) molecules , established from fitting , to classify each individual parc track as immobile or mobile .
the analysis showed that immobile parc molecules were preferentially located along the long axis of the cell ( figure  s3a ) .
similar intracellular positioning was observed for immobile mukb - pamcherry molecules , with an even stronger bias of immobile molecules along the long cell axis ( figure  s3a , right ) .
we found a similar pattern of mukbef cluster enrichment on the long cell axis when we analyzed the distribution of mukbef foci in epifluorescence images ( figure  s3b ) . in mukb cells
, immobile parc molecules showed a lower probability of locating to the cell long axis , consistent with mukbef clusters recruiting parc molecules to the long cell axis ( figure  s3a , middle ) . when we co - imaged mukb - mypet and dapi - stained dna with  3d structured illumination microscopy , we also observed mukbef clusters located along the long cell axis , close to regions of high nucleoid density ( figure  s3c ; movie s1 ; supplemental experimental procedures ) .
to dissect topoiv binding events , we analyzed long trajectories of ten or more localizations and sorted molecules into three categories : mobile molecules that remained above the d threshold for the observation period , immobile molecules that remained below the d threshold over the observation period , and molecules that exhibited transitions between these states ( figure  3a ) .
this analysis detected similar fractions of immobile molecules as  determined from fits to the d distributions ( compare figure  3b with figure  1b ) .
in addition , a fraction of the molecules underwent transitions , consistent with topoiv molecules being in a dynamic equilibrium between bound and mobile states ( figure  3a , right ) . in time - lapse experiments , using 15-ms exposures followed by 35-ms delays , we observed a reduction in the population of parc molecules that remained immobile over the course of the trajectory from 35% to 14% ( figure  3b ) .
molecules in the immobile category in the time - lapse experiments ( bound for ten or more localizations with a 50-ms frame time ) must remain bound for 0.5 s , compared to 0.15  s for the immobile molecules in normal 15-ms frame - time experiments ( bound for ten or more localizations ) .
the observed reduction in the fraction of immobile molecules shows that 21% of the binding events in muk cells lasted for 0.5 s. in contrast , when we performed the same analysis in mukb cells or in cells overexpressing parc - ctd , the fraction of immobile molecules remained unchanged in  normal and time - lapse palm experiments ( figure  3b ) .
this shows that in wild - type cells , a population of mukb - dependent transiently immobile ( 0.5 s ) topoiv molecules is present alongside molecules immobile for 0.5 s. because the underlying binding times are exponentially distributed , they can not be extracted intuitively from experiments .
we therefore used markov chain monte carlo simulations to gain a better estimate of the durations of the short - lived mukb - dependent binding events .
molecule trajectories were simulated undergoing brownian motion inside a confined cell volume ( bakshi et  al . , 2013 , persson et  al . , 2013 , uphoff et  al . , 2013 ) .
molecules were in one of two diffusive states : dfree and dimm , with transitions allowed between each state .
the free diffusion , dfree , of topoiv heterotetramers was calculated based on the free diffusion of pare ( dfast ) , correcting for their relative sizes ( supplemental experimental procedures ) .
molecule trajectories were simulated to generate localizations at either 15-ms intervals or 15-ms intervals with 35-ms delays to match normal and time - lapse experiments , respectively .
the simulated localizations were analyzed with the same tracking and categorizing algorithm as used for the experimental data .
we simulated interconverting molecules with different exponentially distributed binding durations from 0.1  ms to 150  ms ( keeping the fraction in each state equal ) . plotting the change in the fraction of molecules categorized as bound in time - lapse simulations compared to normal simulations showed that a binding duration of 3070  ms for mukb - dependent topoiv transient binding events recapitulated the experimentally observed decrease ( figure  3c ; figure  s4d ) .
furthermore , simulations with a binding time   exposure time showed that a transient ( 1  ms ) dna binding explains well the lower - than - expected mobility of slowly diffusing parc molecules ( figure  s4c ) .
finally , we characterized the molecules that remained immobile over the time - lapse experiment observation time ( binding time 0.5 s ) . because our ability to observe complete events was limited by photobleaching , we increased the observation time by using low excitation intensities , sparse photoactivation , and long ( 0.5 s ) exposure times , when mobile molecules are motion blurred , whereas immobile molecules appear as point sources , producing a diffraction - limited spot ( elf et  al . , 2007 , stracy et  al . ,
immobile molecules could therefore be distinguished by the width of the elliptical gaussian fits to the fluorescent spot .
we used thresholds established with pol1 ( with clearly resolvable immobile molecules ) of < 160  nm short axis width and < 200  nm long axis width to identify immobile molecules ( uphoff et  al .
the probability of observing a particular on - time is the product of the underlying binding - time probability and the bleaching probability .
the bleaching - time distributions were measured independently with the same acquisition and excitation conditions using mukb - pamcherry , which binds dna in clusters with a dwell time longer ( 50 s ) than the photobleaching lifetime ( badrinarayanan et  al . , 2012 ) .
we measured parc on - times at 0.5 s , 0.75 s , and 1  s exposure times and corrected for photobleaching ( uphoff et  al . , 2013 ) .
we found the mean binding time to be 1.8  0.4  s ( table s4 ) . in conclusion , we have shown that  immobile 
topoiv molecules display two different bound states : a 30- to 70-ms mukbef binding - dependent state and 1.8-s binding events , which we propose identify topoiv molecules undergoing a single catalytic cycle , since such a binding time is of the same order as measurements of a single topoiv catalytic cycle in  vitro ( crisona et  al .
, 2000 , neuman et  al . , 2009 , stone et  al . , 2003 ) .
based on analysis in  vitro of processive bursts on ( + ) supercoiled dna , they were expected to last tens of seconds ( crisona et  al . , 2000 , stone et  al . , 2003
) . to determine if the topoiv - mukb interaction directs topoiv catalytic activity close to mukbef clusters , we treated cells carrying a norfloxacin - resistant gyrase gene with norfloxacin , which blocks the topoiv catalytic cycle , resulting in parc molecules covalently bound to dna ( khodursky et  al . , 1995 )
we observed a 2-fold increase in the fraction of immobile parc / e molecules after 10-min norfloxacin treatment ( figure  4a ; figure  s5a ) , showing that most topoiv molecules had performed catalysis during this period ; however , we can not exclude the possibility that norfloxacin captures a fraction of nonproductive catalytic events that do  not result in topological changes .
longer incubation with norfloxacin did not increase the fraction of immobile molecules , showing that at 10  min , we had reached saturation and did therefore not have a quantitative measure of catalytic rate ; shorter exposure times were not experimentally tractable .
this result agrees with the fact that mukb cells can decatenate and segregate their chromosomes ( danilova et  al .
but it does not address the question of whether the mukb - parc interaction stimulates decatenation globally .
the enrichment of parc molecules close to mukbef clusters , as judged by radial distribution analysis , was retained after norfloxacin treatment ( figure  4b ) , showing that a fraction of topoiv molecules underwent catalysis close to mukbef clusters .
after norfloxacin treatment of wild - type cells , we observed a modest increase in the number of topoiv clusters per cell , whereas mukb cells showed a similar cluster distribution to wild - type cells ( figure  4a ) .
these data indicate that topoiv molecules undergo catalysis in defined clusters , some of which are close to mukbef clusters .
when we analyzed the distribution of catalytically active topoiv molecules across the short cell axis , we found that the previous bias toward the cell center was lost , presumably because the additional clusters were not associated with mukbef clusters ( figure  s5c ) .
mukbef clusters were retained after norfloxacin , and parc colocalized with them ( figure  s5b ) . in the absence of mukbef clusters , covalently linked dna - parc molecules were less likely to be located close to the long cell axis , similar to the situation in steady - state cells ( compare figure  s5c curve with figure  s3a middle curve ) . taken together , the results indicate that mukbef clusters direct the catalytic activity of some topoiv molecules to the cell long axis , whereas mukbef - independent catalysis occurs throughout the nucleoid . in these analyses
, we can not exclude the possibility that covalently bound topoiv reshapes the chromosome and thereby influences the spatial distribution of topoiv . nevertheless , the spatial distribution of mukbef clusters was retained , suggestive of normal chromosome organization being maintained .
furthermore , we note that topoiv - targeted strand breaks introduced by norfloxacin did not lead to chromosome fragmentation ( hsu et  al . , 2006 ) .
to address whether topoiv catalysis occurs in cells lacking ( pre)catenanes , we analyzed cells from a steady - state population that had not initiated dna replication , as assessed by a lack of mypet - dnan foci .
the reduction in the immobile fraction of parc from 36%  1% to 21%  2% in these cells , when compared to the whole population ( figure  4c ) , indicated that almost half of immobile topoiv molecules were dependent on replication .
the replication - independent molecules showed a similar cluster distribution to that in steady - state cells ( figure  s5d ) , consistent with a large fraction of them being bound to mukbef clusters .
norfloxacin treatment gave a similar proportion of immobile topoiv molecules as in steady - state cells , showing that topoiv catalysis occurs in the absence of ( pre)catenanes , but not addressing its frequency ( figure  s5e ) .
we conclude that even though the essential function of topoiv is in decatenation , its catalytic action is not restricted to ( pre)catenanes . to test whether the interaction between parc and ori - associated mukbef clusters influenced decatenation of newly replicated ori - sisters , we used two assays to assess the time of ori separation after replication , and we analyzed how this changed after impairment of the parc - mukbef interaction .
these assays have been validated previously and have shown that the time of locus separation is regulated by the activity / availability of topoiv , indicating that decatenation by topoiv directs the time of chromosome segregation ( joshi et  al . , 2013 , wang et  al . , 2008 ) .
in time - lapse experiments , we measured the time of ori1 locus separation after replication initiation , marked by the appearance of a fluorescent mypet - dnan focus ( figure  5a ) .
the ori1 locus replicates < 30  s after initiation at oric , and a sufficient amount of mypet - dnan loads at the forks to visualize it within < 2  min of initiation ( moolman et  al . , 2014 ) . cells in which the mukbef - parc interaction is normal had stably segregated 50% of the newly replicated ori1 loci by 17  min after the appearance of mypet - dnan .
in contrast , cells in which the mukbef - parc interaction was impaired by parc - ctd overexpression showed a 12  min increase in the time required for 50% of cells to exhibit ori1-segregation ( figures 5b and 5c ) .
we also compared the fraction of cells containing one or more ori1 foci in snapshots of steady - state populations ( figure  5d ) .
we observed a decrease in the fraction of cells containing two ori1 foci when the parc - mukbef interaction was impaired , consistent with delayed ori1 decatenation .
taken together , these results provide strong support for a mechanism in which the mukb - topoiv interaction plays a role in timely decatenation of newly replicated ori1 dna .
the in  vivo single - molecule approach exploited here provides a comprehensive understanding of the formation and behavior of topoiv molecules in their native unperturbed environment inside living cells .
we observed a dynamic equilibrium between free and complexed parc / e subunits , independently of replication , with 60 potentially functional topoiv heterotetramers at birth .
the observation that only 60% of subunits are in heterotetramers at any given time raises the possibility that more functional enzymes can be assembled if required . by combining in 
vivo super - resolution techniques with genetics , inhibitors , and overexpression of competing proteins , we have gained a molecular understanding of the interaction between topoiv and mukb and demonstrated the important functional significance of this interaction for dna segregation .
we are confident that the c - terminal fusions of parc and pare are fully functional , that the fluorescent protein domains themselves are not influencing the localization and diffusional properties of the fusion proteins and therefore that the observed behavior reflects the true properties of topoiv subunits ( supplemental experimental procedures ) .
we infer that individual topoiv molecules undergo multiple attempts to bind dna productively before undergoing catalysis .
this is reflected in the slow diffusion of parc / topoiv molecules , which simulations have indicated may result from transient ( 1  ms ) interactions with dna ( figure  1b ; figure  s4c ) .
we infer that this transient binding probably does not identify molecules undergoing catalysis , since a single topoiv catalytic cycle was measured to be 1  s in single - molecule and ensemble experiments in  vitro ( crisona et  al . , 2000 , neuman et  al . , 2009 , stone et  al . , 2003 )
our analysis is consistent with other data ( lee et  al . , 2013 , stone et  al . , 2003 , vos et  al . , 2013a
) that has led to the proposal that prior to catalysis , topoiv must first capture the g - dna segment that is to be cleaved and then capture a t - segment that is transported through the cleaved g - segment .
the transient dna binding we observed likely represents an initial interaction with dna proceeding g - segment capture or g - segment capture itself . assuming that long binding events , lasting 1.8  s ( tcatalysis , figure  3d ) , represent catalytically active molecules and that 14% ( fcatalysis ) of all molecules display this behavior ( figure  3b ) , we calculated the mean time for a given topoiv molecule to locate and productively bind to its substrate , tsearch , using fcatalysis  = tcatalysis/(tcatalysis  + tsearch ) ( uphoff et  al . , 2013 ) .
we calculated that ( tsearch  + tcatalysis )  = 13 s. therefore , for 11 s , topoiv molecules will diffuse slowly , presumably undergoing multiple transient interaction with dna , before initiating a catalytic cycle .
(  ) supercoils are relaxed distributively in  vitro , whereas ( + ) supercoils are relaxed processively ( crisona et  al . , 2000 , stone et  al . , 2003 )
given that processive events would be predicted to last tens of seconds , the inferred topoiv catalytic cycle of 1.8 s , derived from the long exposure analysis , suggests that topoiv predominantly acts distributively rather than processively in vivo .
this is consistent with rh (  ) supercoils and rh replicative catenanes being the preferred targets for topoiv .
our results provide a deeper understanding of the relative activity of topoiv on ( pre)catenanes behind replication forks and in maintaining global supercoiling homeostasis .
topoiv - mediated decatenation behind the fork is essential , and topoiv inactivation prevents decatenation and segregation of newly replicated sister loci without affecting replication or transcription ( wang et  al . , 2008 ) .
dna gyrase is thought to be largely responsible for removal of lh ( + ) supercoils ahead of replication forks and the transcription machinery ( vos et  al . , 2011 ) .
our results showing a reduction of immobile topoiv molecules in non - replicating cells , and a failure to detect processive relaxation of ( + ) supercoils in  vivo , are consistent with most topoiv activity being directed to decatenation of newly replicated dna .
consistent with this , covalent linking of topoiv to dna with norfloxacin does not block chromosomal or plasmid replication ( khodursky and cozzarelli , 1998 , khodursky et  al . ,
, topoiv could support replication at 30% of the wild - type rate ( khodursky et  al . , 2000 ) , indicating that topoiv may act ahead of the fork , although it could be that in the absence of gyrase accumulation of the ( + ) supercoiling ahead of the fork is converted intro precatenanes by replisome rotation , thereby allowing limited fork progression as a consequence of topoiv - mediated decatenation .
the presence of a similar proportion of topoiv heterotetramers in cells of all ages ( figures s5f  s5h ) and catalytically active topoiv molecules in cells that have not initiated replication , along with the demonstration that topoiv availability controls decatenation at ori ( figure  5 ) ( joshi et  al . , 2013 , wang et  al .
, 2008 , nicolas et  al . , 2014 ) , shows that topoiv activity is not directed exclusively to replication termination and is inconsistent with the hypothesis that active topoiv molecules form only at replication termination as a consequence of replisome disassembly ( espeli et  al . ,
our data lead us to propose that direct interaction between parc and mukb leads to a fraction of topoiv molecules being bound to mukbef clusters for 3070  ms , unless they undergo catalysis , in which case we propose that they will remain bound for 1.8 s. the mukbef cluster - parc interaction is important for timely segregation of newly replicated sister oris , consistent with the observation that topoiv availability determines ori1 locus separation time ( wang et  al . , 2008 ) .
furthermore , ablation of topoiv activity , prevents ori segregation and its reinstatement leads to resumed ori segregation ( nicolas et  al .
these observations strongly suggest that measurements of ori segregation time define decatenation efficiency . in the experiments here
, we have demonstrated an 12-min delay in ori1 segregation if the parc - mukb interaction is impaired , consistent with topoiv being less active in decatenation without this interaction .
we propose the topoiv interaction with mukbef clusters may favor ori decatenation partly because of an increased local concentration of topoiv and partly because of enhanced catalysis .
because the mukb - parc interaction stimulates relaxation of rh (  ) supercoils in  vitro , we would also expect this interaction to stimulate decatenation because of the identical chirality of replicative catenanes and negative supercoils ( nicolas et  al . , 2014 ) .
although in  vitro experiments designed to test whether the topoiv - mukb interaction stimulated decatenation showed little or no stimulation ( hayama et  al .
, 2013 , hayama and marians , 2010 , li et  al . , 2010 ) , the substrates used were different from those used in the supercoil relaxation experiments .
we propose , given our in  vivo results and the identical chirality of replicative catenanes and (  ) supercoils , that the topoiv - mukbef interaction will stimulate decatenation .
since the mukbef clusters are relatively stably associated with dna ( badrinarayanan et  al .
, 2012 ) , their interaction with topoiv may facilitate binding of the g- and/or t - segment by topoiv . alternatively
, this interaction might affect topoiv substrate specificity . since decatenation of newly replicated oris only occurs during a short period of the cell cycle
, we wonder also whether the mukbef cluster - topoiv interaction may stimulate (  ) supercoil relaxation in the region of the origin and thereby act to prevent premature ori firing , which requires that ori is highly negatively supercoiled ( donczew et  al . , 2014 ) .
consistent with this , we note that mukbef clusters tended to move away from ori prior to replication initiation ( nicolas et  al . , 2014 ) and that in cells in which the topoiv - mukb interaction is perturbed , we observed some replication initiation asynchrony ( figure  s1a ) .
we propose that the coordination of type ii topoisomerase activity by an smc complex revealed here is not limited to e.  coli .
other studies have implicated functional interactions between eukaryotic smcs and their topoiv counterpart , topoii ( baxter , 2015 , baxter and aragn , 2012 ) .
for example , condensin was shown to facilitate decatenation of yeast minichromosomes ( charbin et  al . , 2014 ) .
the sequential and coordinated action of topoiv and mukbef in the successive steps of decatenation and chromosome segregation revealed here provides a platform for future mechanistic studies that will reveal whether smc complexes provide dna - protein substrates that provide selectivity for topoisomerase action and precisely how topoisomerase action is coordinated with smc functions in chromosome processing .
single colonies were inoculated into m9 glycerol ( 0.2% ) and grown overnight at 37c to a600 0.40.6 , then diluted into fresh m9  and grown to a600 0.1 .
cells were centrifuged and immobilized on agarose  pads between two glass coverslips ( 0.17  mm thick , heated to 500c for 1  hr to remove any fluorescent background particles ) .
we prepared 1% agarose pads by mixing low - fluorescence 2% agarose ( bio - rad ) in dh2o 1:1 with 2 growth medium . for details , see supplemental experimental procedures .
live cell single - molecule - tracking palm used a custom - built total internal reflection fluorescence microscope .
bright - field cell images were recorded with an led source and condenser ( asi imaging ) .
palm single - molecule - tracking analysis used custom - written matlab software ( mathworks ) . we distinguished bound and diffusing proteins by calculating an apparent diffusion coefficient d  = msd/(4 t ) from the mean - squared displacement ( msd ) for each track with four steps .
note that d is an apparent diffusion coefficient because of cell confinement and motion blurring ( stracy et  al . , 2014 ) .
palm movies to measure long - duration binding events were recorded at low continuous 561-nm excitation intensities using long exposure times ( uphoff et  al . , 2013 ) .
at these exposure times , mobile parc - pamcherry molecules are motion blurred over a large fraction of the cell , whereas immobile parc - pamcherry molecules still appear as point sources , producing a diffraction limited spot .
the probability of observing a particular on - time is the product of the underlying binding - time probability and the bleaching probability .
the  bleaching - time distributions were measured independently using mukb - pamcherry ,  which binds dna in one to three large clusters per cell with a dwell time of 50  s ( badrinarayanan et  al . , 2012 ) , with the same acquisition and excitation conditions . on -
time and bleaching - time distributions were fitted with single - exponential functions to extract exponential - time constants ton and tbleach , and the binding - time constant was calculated by tbound  = ton  tbleach / ( tbleach  ton ) .
molecules were simulated undergoing brownian motion confined within a volume corresponding to the average size of cells imaged in experiments . the localization in each 15-ms frame determined from averaging the simulated molecule positions over 100 subframes and adding gaussian distributed localization error .
the list of simulated localizations , with their corresponding frame number , could then be analyzed in exactly the same way as the experimental data .
sister ori1 cohesion time in the strain kg52 containing plasmid pz68 ( overproducing a parc ctd domain ) was assessed in a 5-min time - lapse analysis .
a laco array was inserted 16 kb counterclockwise of oric ( ori1 ) ; laci - mcherry was expressed from the chromosomal leub locus , regulated by the lac promoter ( wang et  al . , 2008 ) .
a chromosomally encoded mypet - dnan fusion protein was used as a marker for the replisome ( moolman et  al . , 2014 , reyes - lamothe et  al . , 2010 ) .
cells were growing exponentially in minimal medium supplemented with glycerol , at 37c ( generation time 100  min ) .
ctd overproduction was induced by addition of l - arabinose ( final concentration , 0.2% ) 3  hr prior to the experiment . as a control ,
the strain with the empty plasmid pbad24 ( guzman et  al . , 1995 ) was used .
 summarythe type ii topoisomerase topoiv , which has an essential role in escherichia coli chromosome decatenation , interacts with mukbef , an smc ( structural maintenance of chromosomes ) complex that acts in  chromosome segregation . 
 we have characterized the intracellular dynamics of individual topoiv molecules and the consequences of their interaction with mukbef clusters by using photoactivated - localization microscopy . 
 we show that 15 topoiv molecules per cell are associated with mukbef clusters that are preferentially localized to the replication origin region ( ori ) , close to the long axis of the cell . a replication - dependent increase in the fraction of immobile molecules , together with a proposed catalytic cycle of 1.8 s , 
 is consistent with the majority of active topoiv molecules catalyzing decatenation , with a minority maintaining steady - state dna supercoiling . 
 finally , we show that the mukb - parc interaction is crucial for timely decatenation and segregation of newly replicated ori dna . 
Introduction
Results
Discussion
Experimental Procedures
Author Contributions