DNA sliding and loop formation by E. coli SMC complex: MukBEF

SMC (structural maintenance of chromosomes) complexes share conserved architectures and function in chromosome maintenance via an unknown mechanism. Here we have used single-molecule techniques to study MukBEF, the SMC complex in Escherichia coli. Real-time movies show MukB alone can compact DNA and ATP inhibits DNA compaction by MukB. We observed that DNA unidirectionally slides through MukB, potentially by a ratchet mechanism, and the sliding speed depends on the elastic energy stored in the DNA. MukE, MukF and ATP binding stabilize MukB and DNA interaction, and ATP hydrolysis regulates the loading/unloading of MukBEF from DNA. Our data suggests a new model for how MukBEF organizes the bacterial chromosome in vivo; and this model will be relevant for other SMC proteins.


Introduction
The SMC (structural maintenance of chromosome) complexes share conserved architectures and function in chromosome maintenance throughout all kingdoms of life, including heterodimeric condensin, cohesin, and SMC5/6 in eukaryotes and homodimeric SMC complex in prokaryotes, such as MukBEF in E. coli [1][2][3]. SMC dimers adopt a large ring structure containing a ~50-nm antiparallel coiled-coil "arm" with a hinge dimerization domain and an ABC-type ATPase head domain [4]. The distinctive and conserved molecular architecture suggests a common principle of SMC complex function. One mechanism explaining the formation of DNA loops is provided by the loop extrusion model, which proposes SMC proteins to act as loop-generating motors during iterative cycles of ATP hydrolysis. Single molecule assays have demonstrated that SMC protein translocates along DNA in an ATP-dependent manner [5][6][7]; in contrast, other studies have reported that SMC protein slides along DNA in an ATP-independent manner [8,9]. Meanwhile, there are reports of real-time visualization of symmetric/asymmetric DNA loop extrusion by condensin and symmetric loop extrusion by cohesin, albeit under small external force [10][11][12][13].
However, the physical nature of DNA as a highly dynamic polymer with properties that may profoundly affect the function of SMC proteins. Overlap of two DNA polymers in cylindrical confinement significantly reduces their conformational entropy, and theoretical simulations suggest that entropic forces can drive chromosome segregation under the right physical condition [14][15][16][17][18][19]. Moreover, experimental studies have already well characterized the E. coli nucleoid dynamics in living cells [20,21]. Different simulation-based models have been proposed: one Brownian dynamics simulation suggested that chromatin loops can be efficiently formed by non-equilibrium dynamics of DNA on the diffusive sliding of molecular slip links [22]. In contrast, other simulation-based models predict DNA loops can be actively extruded by ATP powered SMC motor proteins [23][24][25][26][27].
Here, we generated fluorescently labelled MukB (Fig.1A) and exploited two complementary single-molecule assays with total internal reflection fluorescence (TIRF) microscopy to probe the function of the E. coli SMC complex, MukBEF, by either immobilizing DNA or MukB on the surface (Fig.1B).

Fabrication of flow cell
The glass slides and coverslips were super-cleaned with acetone, 1 M NaCl and MiliQ water solutions. The bottom coverslip was functionalized with an amino-group in the 2% 3-aminopropyltheithoxysilane (440140, Sigma) in acetone for 10 min. Then surfaces were PEGylated by applying a viscous mixture of PEG and biotin-PEG to one side of the coverslip at room temperature for 3 h and washed intensively with MiliQ water. Four 1.5 mm holes were drilled in the glass slide in the pattern show in Fig. 1B, and 1.5 mm diameter tubing was glued into each hole with epoxy resin glue. Afterwards, double-side tape was stack between coverslip and drilled glass slide to make a flow cell.
For DA mutation, 100 nM MukB DA was introduced in the flow cell.

Immobilization of His 6 -tagged MukB for single-molecule study
Flow cell was firstly incubated with 0.3 mg/ml neutravidin in T50 buffer (20 mM Tris-HCl, pH = 7.5, 50 mM NaCl) for 1 min and washed with 400 μl T50 buffer. Afterwards, 2 μg/ml Biotinylated Anti-His Antibody (Penta-His Biotin Conjugate; Qiagen; No. 34440) in T50 buffer was introduced into flow cells at 50 μl/min, then wash immediately with 300ul T50 buffer. 5 nM -10 nM MukB was incubated with 100 pM λDNA or 100 pM 44 kb plasmid (p412-insert95 mats, a gift from Jaco van der Torre in Cees Dekker group) in T50 buffer for 20 min at room temperature (22 • C), then introduced into the flow cell at 5-10 μl/min to immobilize His 6 -tagged MukB on the surface.

Single-molecule Imaging
Single-molecule TIRF experiments were performed on a custombuilt, objective-type TIRF microscope. A green laser (532-nm Cobolt Samba; Cobalt) and a red laser (635-nm CUBE; Coherent) were combined using a dichroic mirror and coupled into a fibre optic cable. The output of the fibre was focused into the back focal plane of the objective (magnification of 100×, oil immersion, N.A. = 1.4, f/26.5; UPlanSApo, Olympus) and displaced perpendicular to the optical axis such that laser light was incident at the slide/solution interface at greater than the critical angle, creating an evanescent excitation field. Illumination powers were set as low as possible to avoid the photo damage of DNA.
Fluorescence emission was collected by the objective and separated from the excitation light by a dichroic mirror (545 nm/650 nm; Semrock) and clean-up filters (545-nm long pass, Chroma; 633/25-nm notch filter, Semrock). The emission signal was focused on a rectangular slit to crop the image and then spectrally separated, using a dichroic mirror (630-nm long pass; Omega), into two emission channels that were focused side-by-side onto an electron multiplying charge coupled device (EMCCD) camera (iXon 897; Andor). The EMCCD was set to an EM gain of 300, corresponding to an approximate real gain of four counts per photon. Each pixel on the EMCCD corresponded to a 96 × 96 nm region in the imaging plane.

Image analysis and data processing
Fluorescence images were analysed by ImageJ software. The background of image was firstly subtracted, and a binary mask was generated by applying thresholding to select fluorescent molecules. Afterwards, identified ranges were generated by applying 'analyse particles' on the mask, that were between 9 and 300 pixels and with the circularity between 0.2 and 1. The intensity of selected ranges was calculated for number determination of MukB and MukB EQ .

Expression and purification of the MukBEF His 6 -tagged proteins
Wild-type MukB was His 6 -tagged at the C-terminus and was expressed from plasmid pET-21(+) (Novagen #69740) in C3013I cells (NEB). For Immobilized His 6 -tagged MukB, a flexible 10(glycine-serine) linker was introduced between His tag and MukB. 2L cultures were grown in LB with 100 μg/ml carbenicillin at 37 • C to OD600-0.6 and induced by adding IPTG at final concentration of 0.4 mM. After 4 h at 30 • C, cells were harvested by centrifugation, suspended in 30 ml lysis buffer (50 mM HEPES pH 7.5, 300 mM NaCl, 5% glycerol, 10 mM imidazole) supplemented with 1 tablet Complete mini-protease inhibitor cocktail (Roche) and sonicated. Cell debris was removed by centrifugation and target proteins were first purified by TALON Superflow resin. Then, the fractions from TALON were diluted to 100 mM NaCl buffer and injected to HiTrapTM Heparin HP column (GE Healthcare) pre-equilibrated with Buffer A (50 mM HEPES pH 7.5, 100 mM NaCl, 5% glycerol, 1 mM EDTA, 1 mM DTT), then the column was washed at 1 ml/ min flow rate with a gradient 100-1000 mM NaCl. The eluted fractions  [28] was mutated to unnatural amino acid (p-azido-L-phenylalanine, AZF) and labelled with Cy5 (marked as red balls) via click chemistry. (B) Sketch of single molecule study. Top slide is designed for injection along two perpendicular directions. The bottom slide is to immobilize either MukB or DNA on the surface. In assay 1, 48.5 kbp λDNA was doubly tethered to the PEG modified surface. In assay 2, MukB was immobilized by using a His 6 -tagged variant of MukB and biotinylated anti--His 6 -antibody on the PEG surface.
For the purification of His 6 -tagged MukE and MuF, fractions from TALON resin were diluted and injected into HiTrap DEAE FF column (GE healthcare) pre-equilibated in Buffer A, and then the column was washed at 1 ml/min flow rate with a gradient 100-1000 mM NaCl. The eluted fractions were collected and dialyzed with dialysis buffer. Protein concentration was estimated by UV absorption at 280 nm on Nanodrop and purity was confirmed by SDS-PAGE. Purified proteins were aliquoted, snap-frozen and stored at − 80 • C until use.

Expression, purification and fluorescent labeling of the MukB His 6tagged protein
To label MukB site-specifically, the unnatural amino acid p-azido-Lphenylalanine (AZP) was incorporated into the MukB [29]. The plasmid pBAD-MukB-S718TAG-10 GS-6×His was constructed as following: First, MukB gene was inserted into pBAD vector. MukB was 6×His-tagged at the C-terminus, and a flexible 10(glycine-serine) linker was introduced between His tag and MukB. Then an amber (TAG) codon was introduced at 718 position of the hinge domain of MukB by site-directed mutagenesis. To express MukB incorporated with AZP, pBAD-MukB--S718TAG-10 GS-6 × His plasmid and a pEvol plasmid containing the engineered Amber suppressor tRNA/synthetase system carrying a chloramphenicol resistance marker, were transformed into a derived strain (FW01) from C321ΔA strain, with chromosomal MukB tagged with 3XFlag.
2L cultures were grown in LB with 100 μg/ml carbenicillin, 25 μg/ml chloramphenicol and 1% glucose at 30 • C to OD600-0.6 with 1 mM pazido-L-phenylalanine, and then induced by adding of L-arabinose at final concentration of 0.4% (W/V). After 4 h at 30 • C, cells were harvested by centrifugation, suspended in 30 ml lysis buffer (50 mM HEPES pH 7.5, 300 mM NaCl, 5% glycerol, 10 mM imidazole) supplemented with 1 tablet Complete mini-protease inhibitor cocktail (Roche) and sonicated. Cell debris was removed by centrifugation and target proteins were first purified by TALON Superflow resin. Then, the fractions from TALON were diluted to 100 mM NaCl buffer and injected to HiTrapTM Heparin HP column (GE Healthcare) pre-equilibrated with Buffer A (50 mM HEPES pH 7.5, 100 mM NaCl, 5% glycerol, 1 mM EDTA, 1 mM DTT), then the column was washed at 1 ml/min flow rate with a gradient 100-1000 mM NaCl. The eluted fractions were collected and the chromosomal MukB was removed by adding ANTI-FLAG M2 Affinity gel (A2220, Sigma) into the eluted fractions. After incubation for 30 min at 4 • C, and the gel was discarded by centrifugation. The supernatant was collected and concentrated by ultrafiltration.
The purified protein was labelled via copper free click chemistry. The protein was incubated with ~20 × molar excess of Dibenzylcyclooctyne (DBCO)-Sulfo-Cy5 (Jena Bioscience) at 4 • C overnight in the dark. The Cy5 labelled MukB was purified by size-exclusion chromatography on a Superdex 200 10/300 GL column (GE Healthcare). Peak fractions were pooled and concentrated by ultrafiltration.
Labeling efficiency was estimated to be 65% based on the absorbance ratio of 280 and 650 nm, using the calculated molar extinction coefficient of MukB at 280 nm (335,670 M − 1 cm − 1 ), the molar extinction coefficient of the Cy5 dye at 650 nm (250,000 cm-1M-1.), and correct factor for the absorption at 280 nm by the dye (ε 280 nm/ ε650 nm = 0.05).
2L cultures were grown in LB at 37 • C to OD600~0.6 and induced by adding IPTG at final concentration of 1 mM. After 4 h at 30 • C, cells were harvested by centrifugation, suspended in lysis and binding buffer (50 mM HEPES pH 7.5, 150 mM NaCl, 10% glycerol, 1 mM EDTA) supplemented with 1 tablet Complete mini-protease inhibitor cocktail (Roche) and sonicated. Cell debris was removed by centrifugation and target proteins were incubated with 2 ml ANTI-FLAG M2 Affinity gel (A2220, Sigma) at 4 • C for 4 h. The Flag tagged proteins were eluted out with high salt buffer (50 mM HEPES pH 7.5, 500 mM NaCl, 10% glycerol, 1 mM EDTA). The eluted fractions were collected and dialyzed with dialysis buffer. Purified protein was snap-frozen and stored at − 80 • C until use.

ATP Hydrolysis assays
ATP hydrolysis was analysed in steady state reactions using an ENZCheck Phosphate Assay Kit (Life Technologies). 150 μL samples containing standard reaction buffer supplemented with 2 mM of ATP were assayed in 18 BMG Labtech PherAstar FS plate reader at room temperature. The results were computed using MARS data analysis software. Quantitation of phosphate release was determined using the extinction coefficient of 11,200 M − 1 cm − 1 for the phosphate-dependent reaction at 360 nm at pH 7.0.

Mutagenesis
Point mutations in all constructs were made by using Q5 site-directed mutagenesis kit (NEB). Primers were designed with NEBase Changer. 10 ng of the template was taken to the reaction. Plasmids were isolated and mutations confirmed by sequencing.

Complementation assay
The assay relied on the ability of MukB expressed from pET-21(+) in the absence of IPTG (leaky expression) to complement growth defect of ΔmukB (RRL149) cells at non-permissive temperature (37 • C). Cells were transformed with pET-21(+) carrying mukB or mukB variant and allowed to recover overnight post transformation at permissive temperature (22 • C) on LB plates containing Carbenicillin (100 μg/ml) along with positive (pET-21(+) carrying WT-MukB) and negative (empty pET-21(+) vector) controls. Then single colonies were streaked onto two fresh plates and incubated at the permissive or non-permissive temperature to assay their ability to complement the growth deficiency.
To examine the function of MukBEF carefully, we tested the MukBEF components sequentially. First, we incubated 10 nM MukB alone with DNA in the absence of flow, all slack λDNA molecules became tight (compaction) (Fig. 2A, video S3), and DNA 'bulbs' (locally compacted DNA) can be observed frequently (98.7%, 149/151 of DNAs, and Fig. 2F). DNA compaction is gradual over time ( Fig. 2A and 2B) and the compaction rate is MukB concentration dependent, with higher compaction rate at higher concentration of MukB. For example, 10 nM MukB takes ~1000 s to fully compact DNA, while 100 nM MukB takes ~150 s (video S3 & video S4). We noticed that there is a 'threshold' protein concentration and salt sensitivity required for DNA compaction. For example, at 50 mM NaCl, 1 nM MukB alone cannot compact DNA, and 'bulbs' are rarely observed even after 4 h (1.7%, 1/60 DNAs), while for concentrations larger than 10 nM, MukB can easily compact DNA and 'bulbs' are frequently observed (98.7%, 149/151 of DNAs). At 150 mM NaCl, even 100 nM MukB cannot compact DNA and 'bulbs' are rarely observed (0%, 0/58 DNAs, Fig. 2F). This compaction is not stable and can be easily destroyed by resuming high flow rates (>0.5 pN), and that DNA 'bulbs' cannot be expanded into loops at ~1 pN of applied force.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.
To test whether MukB has a sequence preference for prominent loading sites to form 'bulbs', we over-stretched the DNA (similar as DNA curtain) and added 10 nM MukB-Cy5; a fairly homogenous distribution of MukB along the DNA can be observed (Fig. 2C & video S5), consistent  Fig. 2A. The distance between two tethered ends is ~4 μm. We noticed that it was hard to quantify the compaction rate, as in TIRF microscope, the laser intensity decays exponentially with increasing distance from the interface; therefore, the intensity of entire λDNA is low at the beginning as most λDNA fragments are floating out of TIRF field. As time goes, more DNA is compacted coming close to the surface, and the increased intensity of 'DNA bulb' comes from two fractions: one from compacted DNA, and the other from the increased laser intensity close to the surface. with MukB loading randomly onto DNA. The bleaching curve of MukB-Cy5 indicates multiple MukB molecules binding to DNA (Fig. 2D).

ATP inhibits MukB-mediated DNA compaction in the absence of MukEF
We further tested the function of ATP during DNA compaction by MukB. Strikingly, DNA cannot be compacted by MukB incubation with ATP-Mg 2+ and no 'bulbs' can be seen on DNA (the fraction of DNA bulbs: 1.0%, (1/98 of DNAs) Fig. 2E & Fig. 2F). Meanwhile, the dwell time of MukB on DNA in the presence of ATP-Mg 2+ was very short and stable association of MukB with DNA cannot be observed (video S6).
Constructs with EQ mutation in the SMC ATPase domain, where the two catalytic domains remain in an ATP engaged condition, are deficient in ATP hydrolysis and exhibit abnormally stable binding to DNA [31][32][33]. In vivo studies suggest that an EQ mutation holds together newly replicated chromosomes and inhibits chromosomes segregation [34], or inhibits the relocation of SMC proteins (MukBEF and cohesin) [35,36]. We further studied the EQ MukB mutant (MukB EQ ), which can bind but cannot hydrolyse ATP. Strikingly, MukB EQ can fully compact DNA both in the presence and absence of ATP-Mg 2+ at a MukB concentration above 10 nM (fraction of DNA bulbs: 90.2%, (46/51 of DNAs) and 88.0%, (103/117 of DNAs) Fig. 2E & Fig. 2F, video S7). Another DA mutation (MukB DA ) which cannot bind ATP, can also fully compact DNA both in the presence and absence of ATP-Mg 2+ at a higher MukB concentration (100 nM) (fraction of DNA bulbs: 96.3%, (52/54 of DNAs) and 98.1%, (51/52 of DNAs) Fig. 2E & Fig. 2F). The EQ and DA mutation data suggest that ATP does not contribute directly to DNA compaction.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.

MukEF and ATP-Mg 2+ conditionally stabilize pre-incubated MukB and DNA complex
MukEF depleted strains show the same temperature-sensitive growth phenotype as the MukB-null strain, and MukEF is essential for stable association of MukB with chromosome in vivo [37]. Thus, we further investigated the function of MukEF and ATP-Mg 2+ , for which we first incubated 10 nM MukB with DNA at 50 mM NaCl until DNA is fully compacted, then flowed in MukEF with ATP-Mg 2+ . We observed that DNA just becomes slack, and stable 'bulbs' can be observed (Fig. 3A& video S8) under high flow. Occasionally, these 'bulbs' can be expanded into 'loops', however, these loops do not grow in size over time. (Fig.3B & video S9). Most MukB was just washed off, with some clusters remaining on DNA, and quantification shows that the numbers of MukB varies. 84.1% (Fig. 3D) measured MukB shows the number between 2 and 4, which indicates that the major population of MukBEF clusters are dimers of homodimeric MukB. These 'bulbs' are very stable and remain associated with DNA even under ~2.5 pN of applied force.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.

Stable loop formation by MukB EQ EF and ATP-Mg 2+
Because MukB EQ EF can form clusters in vivo [35], we wanted to test the behaviour of MukB EQ EF in vitro. Here, we observed that MukB EQ EF forms clusters on the DNA with MukB EQ EF and ATP-Mg 2+ , and these MukB EQ EF complexes are very stably associated on DNA with 150 mM NaCl buffer and at ~1 pN of applied force (Fig. 3E, Fig. S5A & video S10). DNA 'bulbs' can also be observed, and frequently these 'bulbs' can be expanded into 'loops' at ~1 pN of applied force, however, the loops don't grow in size over time even when applying ~1 pN force (Fig. 3E & video S11). Quantification shows that the number of MukB EQ EF varies (Fig. 3J), and higher-number clusters appear more frequently compared to the wt-MukBEF with ATP-Mg 2+ (Fig. 3D and Fig. 3J). When we decreased MukB EQ to 1 nM, stable association of MukB EQ with DNA was also observed, however, without DNA 'bulbs' (Fig. 3F). We speculate that these DNA 'bulbs' and 'loops' are formed by dimerization of MukF, because they are very stable against high flow rates, in contrast to DNA 'bulbs' formed by MukB alone and which are not stable under high flow rates. To test this, we flowed in MukB EQ with truncated MukF (Monomeric MukF, MonoMukF) which is monomeric in solution, being unable to form stable heads-engaged dimers [38]. Very stable protein complexes can be observed on DNA with MonoMukF with 150 mM NaCl buffer and at ~1 pN of applied force (Fig. S5B and video S12); however, DNA 'bulbs' or 'loops' were rarely observed. Quantification shows that 88.4% of cluster population contains less than 2 MukB EQ , indicates MukB EQ is a single dimer with MonoMukF (Fig. 3K).
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.

DNA can be stretched on immobilized MukB and slides through MukB
To further investigate the dynamics of DNA under action of MukBEF, in assay 2, MukB was immobilized on the surface, and the interaction of DNA with MukB(EF) was analysed (Fig. 1B). First, we pre-incubated circular DNA (44 kb plasmid) with surface-immobilized MukB-His, as well as MukE-Flag, MukF-Flag and ATP-Mg 2+ in solution; in this case, essentially no DNA spots were observed on the surface (Fig. 4A and video S13). However, upon incubation of MukB-His with plasmid DNA, many DNA spots can be observed on the surface (Fig. 4A & video S14). For the control, we barely observed any DNA spots on the biotinylated anti-His 6 -antibody functionalized PEG surface in the absence of MukB-His, which indicates that the imaged DNA molecules are specifically captured by MukB. Under flow, we observed stretched plasmids on the surface and breaking of DNA, with laser excitation commonly triggering DNA sliding off the surface (Fig. 4B & video S15).
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.
To test what happens to linear DNA, we first incubated MukB with λDNA at 50 mM NaCl, then flowed the mixture into the cell functionalized with biotinylated anti-His 6 -antibody on the surface. Strikingly, λDNA can be easily stretched on the surface with many tether points and two DNA ends spinning round the tether points (Fig. 4C). At low concentration of MukB, λDNA was stretched only with two tether points, and laser-induced breaking of DNA commonly triggers DNA sliding off the tether points (Fig. 4C, D & video S16). Stretching DNA normally requires modification of DNA extremities to anchor DNA to a functionalized substrate, e.g., via sticky ends or biotin functionalization, and the bond strength between biotin and streptavidin is far beyond the weak electrostatic interaction between MukB and DNA (Fig. S3). Why could naked λDNA be stretched on the surface? One possibility is that the DNA is topologically entrapped in the MukB ring (Fig. 4E), which inhibits DNA detachment from the surface even under strong flow.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.
For open λDNA, it is very difficult to estimate the DNA length and thus to calculate the sliding speed, as many DNA fragments are floating out of the TIRF region. We managed to get two circular λDNA. After DNA breakage, λDNA slides on immobilized MukB and sequentially detaches (Fig. 4F & video S17). We further calculated the sliding speed for λDNA, which was ~2kbp/s (Fig. 4G). For plasmids, the sliding speed was ~5kbp/s, faster than for linear λDNA (Fig. 4G)

MukE, MukF and ATP binding stabilizes MukB and DNA complex on the surface
To further investigate the function of MukEF and ATP-Mg 2+ , we then flowed in MukE-Flag, MukF-Flag and ATP-Mg 2+ in 150 mM NaCl buffer to investigate the behaviour of λDNA on tethered MukB; after these additions, most λDNA molecules were just washed off (Fig. 4H & video S18). When we flowed in MukE-Flag, MukF-Flag and ATP-Ca 2+ , which is supposed to inhibit ATP hydrolysis of the nucleotide-binding domains [39], strikingly, most λDNA remained on the surface. We then significantly increased the flow rate up to 100ul/min (~2.5 pN) with MukE-Flag, MukF-Flag and ATP-Ca 2+ in 150 mM NaCl, and all λDNA were over-stretched on the surface to linear conformations with a few tether points (Fig. 4I & video S19). We then increased the laser power to break DNA into pieces (Fig. 4I & video S19). Strikingly, λDNA does not slide off the surface, and the tether points remained on the surface. This suggests that without ATP hydrolysis, MukE, MukF and ATP stabilize the interaction between MukB and DNA, and this stabilized interaction can even resist high force (~2.5 pN).

Discussion and conclusions
Our results show that MukB alone can compact DNA under low salt conditions when MukB concentration is above a certain 'threshold' concentration. This is in agreement with previous studies that showed MukB alone can compact DNA [40][41][42]. As MukB dimers alone have negligible ATPase activity [43][44][45], the catalytic cycle of ATP hydrolysis may influence the dwell time of MukB on DNA by regulating MukB head opening/closing (Fig. 5A), when MukE and MukF are absent, and this could be the underlying reason why ATP inhibits MukB-mediated DNA compaction. This observation is in contrast to the previous in vitro study which suggests ATP induces DNA compaction by MukB [46].
There exists one core argument that MukBEF together with ATP-Mg 2+ all are required for normal chromosome organization and segregation in vivo; while our in vitro single-molecule data shows that MukBEF together with ATP-Mg 2+ seems to be incapable of remodelling DNA; only rare MukBEF clusters on DNA 'bulbs' were observed occasionally. Actually, this is in agreement with in vivo observations that even high concentrations of ~100 nM of (Muk4B:4E:2F) complexes at high density of DNA in E.coli (the density of DNA in E.coli is 10 5 times of DNA used in the single-molecule assay) result only in 48% loading on DNA with a dwell time of about ~60 s. The unloading rate (k off MukBEF ) is ~0.015 s − 1 (dwell time 65 s), and the loading rate in vivo (k on MukBEF ) is only ~3.9*10 − 6 s − 1 which would result in 48% occupancy of MukBEF on chromosome [35,47]. In the single-molecule assay, it requires 1/3.9*10 − 6 = 2.56*10 5 s (~3 days) to capture a loading event in pre-incubated MukBEF solution, and that is also the reason why in an in vitro biochemistry assay which shows a 'fake' inhibition of MukEF to loading of MukB on DNA. The extremely low loading rate does also reveal that most collisions of MukBEF with DNA do not lead to loading, and there is a small chance that ATP binding or hydrolysis can trigger distinct conformational changes within the two head regions of MukBEF that could act synergistically to open the MukB ring for DNA loading/unloading. ATP hydrolysis is required to regulate MukB head opening/closing, and therefore regulates MukBEF loading/unloading on/from DNA to balance the numbers of MukBEF on DNA, as too many loops generated by MukBEF lead to over-compacted chromatin which may block chromosome replication, gene expression and regulation, whereas too few generated loops lead over-spread chromatin.
Pre-incubated MukBEF complexes rarely undergo stable association with DNA, while sequential incubation of MukB with DNA, and then MukEF and ATP-Mg 2+ , can stabilize MukB/DNA interaction. Together with in vivo observations that MukEF is essential for stable association of MukB [37,48], these superficially conflicting observations may be reconciled by assuming that DNA binds MukB topologically (DNA wrapping around the head domains of MukB proposed model in Fig. 5B & video S20). Similar DNA wrapping mechanism has also been proposed by other studies [49][50][51]. Structural studies of wide-type SMC, instead of mutated SMC, would help to verify the DNA wrapping mechanism.
Supplementary data related to this article can be found online at http s://doi.org/10.1016/j.bbrep.2022.101297.
Hydrolysis of ATP does only yield about 20 to 25 k B T energy. Actually, it was shown that 80% of the input energy of ATP was dissipated into heat and did not contribute to power the motor protein kinesin [52]. The free energy released upon ATP hydrolysis is rapidly dissipated and it is the differential binding of ATP and its hydrolysis products ADP and Pi that leads to the slow conformational transitions of the motor protein [53]. Some studies also suggested that ATP hydrolysis is not involved in directional motion; rather, it drives SMC protein loading and unloading onto chromatin [54][55][56]. A relatively small force (entropic force) of k B T/P is required to align elastic units of dsDNA, and this entropic force is ~0. 1 pN, within the range of external forces that were applied in this work, and also published for single-molecule experiments that observed DNA compaction or looping induced by cohesion and condensin [10,12,30,57]. Moreover, in cells, DNA can move or slide by itself if considering the elastic energy that DNA contains, such as supercoiling [58][59][60][61].
Our DNA-sliding ratchet model (Fig. 5C) does explain how MukBEF can efficiently organize DNA while having only low ATPase activity, and the intrinsic ability to entrap DNA topologically. This DNA sliding model can also explain the different behaviours of other SMC proteins. For example, cohesion complexes act differently in the presence of linear and circular DNA (not supercoiled) attached to beads under high salt concentration, where a cohesion complex can slide off the free ends of linear DNA, but gets trapped on circular DNA [62]. Nucleosomes containing ~150 base pairs of tightly wrapped DNA are the basic structural elements of chromatin compaction and regulation, while SMC proteins contribute to the large-scale chromosome organization and regulation. Nucleosomes do show sliding and loop formation [63][64][65][66][67]. Perhaps, SMC proteins and nucleosomes share a common DNA sliding, loop formation, and ratchet mechanism. Other SMC proteins can also be (caption on next page) M. Zhou immobilized on the surface to test this DNA sliding and ratchet mechanism. How SMC complexes facilitate DNA chromosome organization and segregation touches fundamental biological and physical questions: What are the molecular mechanisms of motor proteins? What is the contribution of entropy in the living cells? Although we cannot rule out complete answers for these questions, our results suggest a possible molecular mechanism of SMC protein, which could rationalize all the single-molecule observations in this study.

Author contributions
Man Zhou (M.Z.) and David Sherratt conceived and directed the project. M.Z. undertook biochemical experiments, single molecule experiments and undertook quantitative imaging and analysis. M. Z. wrote the manuscript.

Declaration of competing interest
The other authors declare that no competing interests exist.

Data availability
Data will be made available on request.

Acknowledgement
We thank Florence Wagner for plasmid preparation and EMSA as-   Leeds) helped with crystal structure modelling. We thank David Sherratt and, members of the Sherratt group and members of Kim Nasmyth group for helpful discussions. We thank Achillefs Kapanidis and Jörg Enderlein (Third Institute of Physics, University of Göttingen) for insightful discussion and constructive criticism of the manuscript. This work was supported by a Wellcome Investigator Award [200782/Z/16/Z to David Sherratt].