Downloaded by guest on September 25, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1716002114 a Pedaci Francesco and Nord L Ashley motor the flagellar in bacterial mechanosensitivity stator drives bond Catch 2) lhuhteecmlxsvr ieyi hi structure, their in widely life vary of complexes kingdoms three these all Although in (20). exist mechanosensitive complexes of protein variety membrane A (17–19). mechanosensors also are individual an 13), in (11, engage to motor observed the been in have of motor units speed 11 torque to rotational total up measured and the the increases thus unit (10). and stator membrane recruited inner the additional in Each away dynamically diffusing units eventually stator over, upon rotor, turn acts the motor around unit the anchored stator in Once stoichiometry bound varies. their prime each 12), (11, A while independently rotor dynamic; adequate. the is not stator BFM the is motors, the rotary of structure macroscopic to contrast BFM a in and the that example, for demonstrating model (8–10), constituents static molecular rotor BFM the ious of side cytosolic the 7). on (6, proteins 1A) common (Fig. FliG the units by upon stator acting formed the generation, force, ring torque motive for ion responsible the are the (PG) harnessing peptidoglycan By around rigid the (3–5). anchored to layer bound are and rotor units, the of stator perimeter to called embedded rotation complexes, transmem- is coupling Multiple brane filament. BFM membranes, flagellar the and cellular hook of extracellular the the chemo- rotor spans The swimming, and 2). enabling within (1, cell, swarming the and of taxis, flagellum each rotates T bond catch motor flagellar bacterial during surface-sensing environmental formation. in heterogeneous biofilm role and a a swarming play to ultimately adapt may to and adhe- viscosity cell stator the force-enhanced to sys- allows that respond of sion and propose sense list We to “molecu- stress. growing, mechanism this mechanical widespread but a that short, is suggesting strategy” a bonds, lar to catch BFM demonstrating complex. the tems motor add by flagellar evidence weakened results the of strong These its of instead provides to strengthened mechanosensitivity bond This drives applied (a force) wall. is bond force catch cell a higher the that a in when point the assem- increases an of anchoring of unit details lifetime stator the the that bled to indicate respect The model, torque. with adsorption magnetic robust applied external analysis obtained, via rates motor via the dynamically kinetic motors on while load individual speed, the motor and in varying of arrival units recordings of high-resolution stator kinetics of the the of measure directly departure we is Here, mechanosensitivity How- BFM vis- unknown. flagellum. driving the the mechanism through on molecular motor the dependent ever, the units by engaged experienced load of cous number the and mechanosen- with is assemble units, turnover sitive, This to stator BFM. known the by in channels dynamically provided disassemble ion is force-powered torque motive The ion swarming bacteria. and motile swimming many 2017) the of 11, powering rotates September that flagellum, review motor for bacterial rotary (received the each 2017 is 27, (BFM) motor October flagellar approved bacterial and The CA, Stanford, University, Stanford Block, M. Steven Kingdom by United Edited 2JD, OX1 Oxford Oxford, of University Laboratory, Kingdom; Clarendon United Physics, 6BT, WC1E London London, College eted icii tutrl CS,ISR,CR,Universit CNRS, INSERM, (CBS), Structurale Biochimie de Centre eety oe bevtosrvae httesao units stator the that revealed observations novel Recently, var- of exchange continuous the revealed have studies Several lxfudi ayseiso oiebcei hc actively which bacteria motile of species com- molecular many large in a found is plex (BFM) motor flagellar bacterial he shrci coli Escherichia | shrci coli Escherichia a mleGachon Emilie , | oeua motor molecular a,1 1,14–16). (10, a ue Perez-Carrasco Ruben , | mechanosensitivity c ipyisGaut ru,Uiest fClfri,Bree,C 42;and 94720; CA Berkeley, California, of University Group, Graduate Biophysics eMnplir 49 otele,France; Montpellier, 34090 Montpellier, de e ´ | b amn .Nirody A. Jasmine , 1073/pnas.1716002114/-/DCSupplemental at online information under supporting contains article This distributed is 1 article BY-NC-ND). (CC 4.0 access License NonCommercial-NoDerivatives open This Submission. Direct PNAS a is article This interest. of A.B., conflict paper. no J.A.N., the declare wrote F.P. R.P.-C., authors and The A.L.N., R.M.B., A.L.N., tools; and data; reagents/analytic analyzed F.P. and new R.M.B., contributed R.P.-C. research; of heart the at is (24–26) strength- force) by counterintuitively weakened, bond of (a instead that ened, mechanism suggests fol- analysis catch-bond Our and load. conditions external a in steady-state stator change rapid in initial a both lowing different various kinetics stoichiometry the a stator for characterize statistically imposes of to experiments which us allows these of This occupancy. perform each We loads, binding viscous release. unbind- stator stator quantify after and stimulate observe ing and We stall of stalling the BFM: period the reversibly probes during the directly by manipulation of motor load mechanosensitivity the external The by rotation. experienced sizes its load different the of exter- ulate individual microbeads an of hook magnetic Using the to and sin- stoichiometry. bound investigate field stator we magnetic quantify BFM, nal and the of motors consider- mechanosensitivity gle the into for fact ble novel this take now (12). The- ation must units. stator of models of measured composed number previously oretical changing likely that dynamically are a fact, with 21–23) in motors (11, implies, relationships gener- It torque BFM. torque–speed the the previous modeling of of successfully obstacles) ation for interpretation and ultimately the inhomogeneities and for data local consequences overcome important the to has upon relevant cell (likely placed mechanosensing the load of viscous for property the The 18). on (17, depends motor BFM recruit- stator the that directly in shown have is ment works protein recent surrounding Two the the membrane. by of cell mediated function, stress, mechanical the upon confor- thus dependent The and feature: key state, one mational share they sensitivity, and function, uhrcnrbtos ...adFP eindrsac;ALN n ..performed E.G. and A.L.N. research; designed F.P. and A.L.N. contributions: Author owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To tv yeo odta eoe togrudrforce. counterintu- under a stronger bond: becomes catch that a bond by of mechanosensi- governed type the itive is that BFM find the a and of as load tivity stators viscous the of the kinetics viscous of the the function measure on We motor. dependent the units on engaged load of mechanosensitive, number are units the stator with apply- The rotor. for the responsible to is torque ing that unit, channel stator ion the membrane-bound is the a with example accordance prime in A behavior environment. its surrounding optimize to compo- which cell property the the a dynamic, of allows are Many machine molecular bacteria. this of motile nents power- many motor of rotary swimming the is ing (BFM) motor flagellar bacterial The Significance ee obte lcdt h oeua ehns responsi- mechanism molecular the elucidate better to Here, c lsadoBarducci Alessandro , b eateto ahmtc,University Mathematics, of Department . .coli E. a www.pnas.org/lookup/suppl/doi:10. oos erpdymanip- rapidly we motors, ihr .Berry M. Richard , raieCmosAttribution- Commons Creative NSEryEdition Early PNAS d eatetof Department | d f6 of 1 ,

BIOPHYSICS AND COMPUTATIONAL BIOLOGY laser held at stall for 300 s. The magnets are then raised to the original A B bright field Hook height; the load is returned to that supplied by the bead in its vis- cous environment; and the rotation of the motor is recorded for L ring OM at least another 5 min. Each movement of the magnets occurs within 3 s. The load felt by the BFM is therefore quickly and P ring PG B dynamically manipulated twice during the measurement of an Mot B Mot A individual motor; an exemplification of this procedure is shown Rod in the torque–speed plane in Fig. 1D. The torque of individual MS ring IM motors is measured first at steady state before stall and then again immediately after stall. An example torque trace for the FliG flagellar motor viscous load γ500 is shown in Fig. 1 C, Upper (see also Fig. S1 FliM ref. bead C ring E.coli for a collection of individual traces at different viscous loads). FliN An increase in torque during stall is evident, followed by a step- 5 min C stall D wise relaxation to a torque value close to the original steady- state value.

release load line Viscous Load Dependency of Stator Assembly Dynamics. Under the assumption that torque traces represent noisy constant signals demarcated by discrete discontinuities due to stator association or dissociation, we use a recently developed step-detection algo- stall steady-state Torque rithm (30, 31) to fit the individual torque traces. By using this fit, a developed algorithm (Materials and Methods and SI Materials and Methods) is used to calculate stator stoichiometry, extracting stator number as a function of time, N (t), for each individual Speed trace. Contrary to previous works, this algorithm determines sta- tor stoichiometry based upon the discrete discontinuities of the Fig. 1. The experimental assay. (A) Schematic of the BFM showing rotor torque traces, not upon the absolute value of the torque; given and stator protein complexes. Stator units bind to the PG at the periph- the broad distributions of single-stator torque values (Fig. 2A), ery of the rotor, providing torque via an interaction with FliG. IM, inner this approach greatly reduces the error in stator stoichiometry membrane; OM, outer membrane. (B) Experimental setup. Bacterial cells estimation. Simulations (Fig. S2) suggest that, given the aver- are immobilized onto a coverslip, and a rotating superparamagnetic bead age noise in our torque measurements, the algorithms used here attached to the hook of a BFM is imaged and tracked. Two permanent mag- reconstructs the stator stoichiometry with an accuracy of 1.6 sta- nets (mounted on a vertical translation stage) create a magnetic field, capa- tor units and that the shortest states in stator stoichiometry, ble of generating sufficient torque τB on the bead to stall the motor. Ref., reference. (B, Inset) Tracked positions of a 1µm bead rotating one turn. which can be reliably resolved, last 3.5 s. (Scale bar: 100 nm.) (C) One experimental trace. Motor torque (C, Upper; In Fig. 2, we show distributions and average time courses of gray points) is measured before stall (t < 0), then again immediately upon the number of stator units N (t) in multiple repeats of the proce- release (t > 0). The output of the step detection algorithm (black line) is dure illustrated in Fig. 1. From the change in torque produced by used to determine stator stoichiometry (C, Lower). N., number. (D) The stator association and dissociation events, we quantify the distri- experimental assay shown in the torque speed plane, where stators may bution of torque produced by a single-stator unit (Fig. 2A). This associate during 5-min motor stall, subsequently dissociating back to steady- analysis shows that the torque generated by a single-stator unit state occupancy after stall (points in red not directly observed). increases with increasing viscous load (and decreasing speed), matching theoretical models of stator behavior (12, 32). This finding is in agreement with previous results based on sodium- BFM mechanosensitity, dynamically remodeling stator stoi- driven PomAB stator units (33), confirming that MotAB stator chiometry against changes in external resistance to rotation. units behave in a similar manner. Additionally, at steady state, we observe that the average stator occupancy increases with increas- Results ing applied viscous load (Fig. 2B and Fig. S3); this dependency is Torque Measurement and Load Manipulation. A nonswitching the fingerprint of stator mechanosensitivity. strain of E. coli lacking flagellar filaments and containing an In Fig. 2C, we show for each viscous load the average (col- endogenously biotinylated hook (27) is used for all experiments. ored line) and SD (shaded region) of the number of stator units Streptavidin-coated superparamagnetic beads are attached to N (t) obtained from different motors, before and after stall. For the hook of cells immobilized on a coverslip, and the rotation all of the viscous loads except for the highest (γ1300), the aver- of the beads is observed via wide-field holographic microscopy age stator number increases during stall. This is quantified in (28) (Fig. 1B). Tracking the position of the bead in time, we Fig. 2D: Stalling a viscous load γ1300 for 300 s does not yield calculate the velocity and torque, as described in Materials and a relevant change in stator number (−0.3 ± 1.1), while for the Methods. Data are acquired for motors driving five different vis- other viscous loads, mechanosensing causes the recruitment of cous loads, which are obtained by using beads of three different additional stator units during stall (1.0 ± 1.3 for γ500g , 1.7 ± 1.1 diameters and two buffer solutions of different viscosity, as indi- for γ500, 2.0 ± 1.4 for γ300g , and 2.3 ± 1.8 for γ300). After stall, cated in Table S1 (see SI Materials and Methods for details). Two as visible in Fig. 2C, N (t) decays back to the prestall, steady- permanent magnets are mounted, as shown in Fig. 1B. The mag- state value within ∼ 200 − 300 s. This implies that, on average, nets are attached to a motorized vertical translation stage which for all of the viscous loads except for the largest, additional controls the distance between the magnets and the sample, and stator units bind and engage with the BFM during the 300 s thus the magnitude of the magnetic field at the sample plane. the motor is stalled. Within minutes after the magnetic field is Both the BFM and the magnetic field exert a torque on the mag- removed and rotation resumed under the original viscous load, netic bead. For sufficiently large magnetic fields, the bead, and stator units dissociate, and their average number returns to the thus the motor, remain stalled in an equilibrium angular position, previous steady-state value, which depends on the viscous load where the magnetic torque and the motor torque cancel (29). experienced during rotation. This behavior is not observed at the For a given bead size, the steady-state rotation of individual highest viscous load γ1300, which shows, on average, the same motors is measured under a negligible magnetic field for 50– torque after stall as before, indicating that no statistically rele- 300 s before manipulation. The magnets are then lowered until vant change in stator number occurs during stall for this high the magnetic torque stalls the motor rotation, and the motor is viscous load.

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1716002114 Nord et al. Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 tihoer,rsetvl,a ucino xenlvsosla.(C load. viscous in external as of (color-coded function loads a as respectively, stoichiometry, N At considered events. is unbinding and state, units binding steady the stator by unbound unaffected and of constant concentration the Here, dynamics the rate lows a with site empty Hill– constant an to a bind can as constant unit stator written diffusing A be sites. rotor is could the by describes surrounded assembly model 34), as pre- This (35). stator kinetics, (10, model assembly adsorption of implicitly Langmuir stator model used of model a viously simplest rates, The unbinding required. Dynamics. and Assembly binding Stator Modeling the in break a by (indicated s 300 of period a for 2. Fig. h vrg n Do utpemtr.Tehrzna rydse ieidctsteaeaenme fsao nt esrdfor for 20 measured units stator to of entirely number time, average relaxation the characteristic indicates the Eq. line from dashed obtained gray fit the horizontal Eq. is The line motors. dashed multiple dark of The SD and average the ode al. et Nord ss E ( load. viscous external of function a as stall during recruited units stator of number the of KDE (D) 3. sdtrie by determined is , γ 1300 ttrsocimtybfr n fe tl.( A stall. after and before stoichiometry Stator k k k . on off off hl on ttrui a iegg iharate a with disengage can unit stator bound a while , h eutn vrg ttroccupancy stator average resulting The . sld,o pi qal between equally split or (solid), dN dN /dt dt N max = A, n h taysaesao occupancy, stator steady-state the and 0, = B, k needn n oitrcigbinding noninteracting and independent E D B AC on and D, (N max t c o oprsn rylnsso h rdcin fmdl,weetevrainin variation the where models, of predictions the show lines gray comparison, For . E .Sed-tt oaino h icu odcrepnst time to corresponds load viscous the of rotation Steady-state ). − N odtrietestator the determine To ) − k on k 3 x off for and xs.At axis). N t and k . > off 0. enldniyetmts(Ds ftesnl-ttrtru otiuinadtesteady-state the and contribution torque single-stator the of (KDEs) estimates density Kernel B) dte) ubro oosaaye a 4for 24 was analyzed motors of Number (dotted). N t SS = N and ,temtri eesdfo tl.Tetikclrcddln n h ooe einare region colored the and line color-coded thick The stall. from released is motor the 0, (t t ) eprleouino ttrsocimtyo oosdiigtedfeetviscous different the driving motors of stoichiometry stator of evolution Temporal ) c ntebto mg niaeteprmtr xrce yteepnnilfi using fit exponential the by extracted parameters the indicate image bottom the in fol- [1] ehnsnig(7 8,tevsosla-eedn distribu- load-dependent viscous of the tions 18), at (17, circle site. a mechanosensing lattice one of occupies form unit the each and takes rotor, lattice the of discrete (36, periphery the the models case, (RSA) analogous this adsorption is in model 37); sequential This random fluctuations. reversible against to num- units steady-state (10) stator the turnover of of reestablishment ber stator the by of explained be observations can previous conditions, state where osla.Rpdysaln oo seuvln osicigits switching N (γ to ing infinite equivalent is to motor load K a viscous stalling that Rapidly show load. 2B, cous Fig. in shown load nt fe tl,idctn ttrasml pna nraein increase an upon assembly stator indicating stall, after units nln ihpbihdeprmnsdmntaigstator demonstrating experiments published with line In γ ss 1300 K codnl,i u xeiet,ecp o h viscous the for except experiments, our in Accordingly, . N D (t eosreacerices ntenme fstator of number the in increase clear a observe we , = ) htw esr ne taysaeconditions, steady-state under measure we that k off /k t on < .Temtri hnsaldb h antcfield magnetic the by stalled then is motor The 0. stedsoito osat ne steady- Under constant. dissociation the is taysaestoichiometry, Steady-state ) N γ 300 ss n a h feto increas- of effect the has and ∞) → 8for 28 , = + 1 D γ γ γ γ γ N erae ihicesn vis- increasing with decreases max γ K K 300g D D sdeetrl to entirely due is 0for 40 , . NSEryEdition Early PNAS γ t 500 N < ss 0for 30 , tsed state. steady at 0 safnto of function a as , k on γ (dashed), 500g | f6 of 3 and , N [2] ss ,

BIOPHYSICS AND COMPUTATIONAL BIOLOGY applied load. A load-dependent KD indicates a load dependence in either or both of kon and koff . To investigate this further, we analyze the relaxation traces by comparing them with the analytical solution of Eq. 1, which predicts an exponential decay toward the steady-state occu- pancy Nss ,

−(kon +koff )t N (t) = Nss + (No − Nss )e , [3]

where No is the observed stator occupancy after the stall (t = 0). The experimental mean traces for N (t) after stall, shown in Fig. 2C, are well fit by a single exponential (dashed lines); this simple model of stator binding kinetics is thus compelling, and it allows the estimation of the binding and unbinding rates from the experimental traces using Eq. 1. Defining tc = 1/(kon + koff ) as the fitted decay time in figure Fig. 2C, in combination with Eq. 2, we find

Nss kon = , [4] tc Nmax

Nmax − Nss koff = . [5] tc Nmax

Fig. 2E plots experimental fits for Nss and tc against each other (circles) and compares predictions of models where the variation in KD is due entirely to kon (dashed line), entirely to koff (solid line), or split equally between kon and koff (dotted line). Fig. 3A shows kon and koff from Eqs. 4 and 5 vs. viscous load. It is evi- dent that the differences in relaxation after stall are mainly due to a change in koff with viscous load, while kon is relatively inde- pendent of load. For the highest viscous load γ1300, we find that N does not change during stall and the exponential relaxation is absent (Fig. 2C), so the rates cannot be extracted. This suggests Fig. 3. Stator kinetics. (A and B) The binding and unbinding rates of the that KD (γ1300) ∼ KD (γ = ∞), i.e., that the BFM mechanosen- stator units as a function of external viscous load on the motor (A) and sitivity saturates for high loads γ ≥ γ1300, and that there is no single-stator force (B). All rates are calculated by fitting Eq. 3 to traces in Fig. dynamical difference between rotating such a high viscous load 2C, with the exception of points outlined in cyan (SI Materials and Methods). and being stalled. To quantify the rates at γ1300, given the rel- (C and D) Dissociation constant, KD, and lifetime of an individual stator in atively constant value of kon for the smaller viscous loads, we the motor complex, respectively, as a function of the average local force make the assumption that kon (γ1300) is equal to the average of applied by a single stator to the rotor (and by symmetry to the PG layer). kon for the smaller loads. From the value of Nss (γ1300), we can Points and error bars give averages and standard deviations, respectively. then obtain koff (γ1300) from Eq. 2. While the proposed Hill–Langmuir adsorption model is suf- ficient to explain and fit our experimental data, we note that ment of stator association and dissociation rates as a function of there is no evidence for fixed binding sites at the periphery of external viscous load. the rotor in E. coli. Therefore, we also explore a more general- Stator unit mechanosensitivity must arise from a load depen- ized reversible RSA model which resembles the classic “car park- dence in one or both of the stator association and dissociation ing problem” (36, 37), where the stator binding is not restricted rates. It has been suggested that force upon the PG may cause to a discrete number of binding sites, but can occur continu- structural changes in stator binding sites which may affect sta- ously at any angular position on the ring (Fig. S4 A and B). In tor unit association rate (17). Additionally, crystal structures this model, a new stator unit cannot bind unless enough contigu- of MotBC of Salmonella and PomBC of Vibrio suggest that ous space is available in the ring (overlap is not allowed), which a drastic conformational change in the N-terminal portion of depends on the positions of the units currently bound. Hence, MotBC /PomBC is required for the stator to bind to the PG memory effects due to excluded volume arise, affecting the sta- (38, 39). Mutational studies suggest that this conformational tor occupancy dynamics, N (t). The details of this model are fur- change may be triggered by an interaction between the cytoplas- ther discussed in SI Materials and Methods. Numerical simula- mic domain of MotA and FliG (40), a process potentially com- tions of the model (Materials and Methods and SI Materials and plicated by the rotation of the rotor. Thus, one might imagine Methods) exhibit similar relaxation dynamics to the experiments that the rate of stator unit association could be dependent upon and the Hill–Langmuir model, and we conclude that both mod- the speed of the motor. However, we find that the rate of stator els can adequately fit our experimental observations. Strikingly, association is independent of viscous load, while the rate of sta- the extracted rates from fits of the experimental data are very tor dissociation is load-dependent, and it is in fact this property similar to those of the Hill–Langmuir model (Fig. S4C), confirm- that begets mechanosensitivity in the BFM. ing the viscous load-independent binding probability combined Fig. 2B shows our measurements of Nss as a function of viscous with an unbinding probability that decreases for increasing vis- load, confirming previous results (17, 18) that steady-state stator cous loads. number is proportional to viscous load. The saturation curve of this relationship (Fig. S3) is consistent with previous measure- Discussion ments of motor fluorescence as a function of viscous load (where In this study, we directly probe BFM mechanosensing behavior, the signal of fluorescent fusion stator units was a proxy for sta- providing an extensive quantification of stator stoichiometry as a tor number) (18). While this work provides evidence for a load- function of external viscous load, both at steady state and imme- dependent KD , it is unable to determine whether this depen- diately after a controlled change of load. By fitting measured sta- dence is governed by kon , koff , or both. A previous measurement tor kinetics to a reversible RSA model, we provide a measure- of koff (10), performed on immobilized cells where motors were

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1716002114 Nord et al. Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 iutnosyplsuo n tece t oncint the to unit connection the which its stant 3 with stretches Fig. force In We and the PG. 3B). also upon Fig. is onto pulls piconewtons; this unit few simultaneously reaction, of single by we range each that, (42)], the by note nm in applied (found [23 force rotor rotor local the the mean average of the the radius Considering quantify the 2A). by and (Fig. exerted rotor torque torque the single-unit higher on a unit stator into in each translates increase an load that viscous see for We external responsible BFM. the mechanism impor- in an molecular mechanosensitivity has stator the rates for dissociation consequence and tant association stator of dence in units stator wild-type motors. of unperturbed The dynamics dif- otherwise 41). the cause on (10, can reports counterparts study which wild-type present protein, their from fluorescent our behaviors a than ferent to faster fused magnitude units cover- of stator the orders to two flagella value measured of a attachment reported the slip, via stalled presumably ode al. et Nord require which forma- behaviors biofilm in and wild-type role motility The swarming a tion. as flagellar play envi- such during also prevailing surface-sensing, energy may the wasting and to avoid growth, cell adapt and the units, viscosity, allows stator ronmental potentially damaged feature mech- replace This catch-bond a to stator. by the explained be within mechanosen- also the anism may that BFM suggest the we of Here, sitivity myosin 50). motors, (49, molecular dynein other and two (48) for shown role been important already an have play bonds to Catch grows. bio- bonds demonstrating catch data logical experimental of prevalence the develop, to required be (47). MotB interaction will the describing pathway parameters relevant multidimensional unbinding physically or extract the structure of the landscape of energy knowledge further catch bonds, explain to and com- exist multidimensional BFM models multiple phenomenological the While one-dimensional within 4). further Fig. unit in stator to sketched the (as of lead plex lifetime of which strength the the and pocket increasing bond PG, PGB the the to the residues within binding of positional PGB exposure a the or of rearrangements shift catch-bond conformational possible either PG–MotB a the promote PG- across Membrane suggest tension the which facts Outer in in These mechanism related (46). hypothesized closely OmpA been the protein of also conformational a C-terminal has Recently, associated binding 39). (38, upon conformational PG large change the N- a reach domain The perform to (45). the must extension them MotB of unmask of accessible and flexibility portion readily mask terminal structural to not substantial necessary and considered a buried is of that are structure MotB and the been in of (44) has residues dimer PGB it PGB key discrimi- interestingly, the putative our cannot However, the While relevant that they detail. rotor. reported bonds structural the mechanism, the around any catch-bond on unit nate a impact stator indicate the an (MotB of data have MotB lifetime can of the force C-terminal for the the where at is located domain, (PGB) biologi- other 43). (25, in bonds observed catch as eventually cal will behavior, behavior slip-bond of catch-bond anchor into the the PG, transform maximum to the the applied to than be unit could greater stator unit the force single a a if by stator that generated the force predict of We region anchoring PG. the the in on suggest bond catch measure a we of rates existence kinetic mechanism. the the two molecular that are conclude nontrivial nonzero trap therefore this finger We a children’s of at a lifetime analogies and the macroscopic tension of under hook maximum it, A a across force. applied produces is bond tension catch if a decreases bond of slip lifetime canonical the conventional the While a (24–26). is behavior relationship catch-bond counterintuitive of fingerprint This force. this of neetnl,orqatfiaino h icu oddepen- load viscous the of quantification our Interestingly, ssnl-oeuesetocp ehiuscniu to continue techniques spectroscopy single-molecule As PG-binding MotB the and PG the between interface The K D n ieie(1/k lifetime and k off C (γ and 1300 .coli E. oee,ti td a efre with performed was study this However, ). eso h esrddsoito con- dissociation measured the show we D, off oo sbdrcinl n previous and bidirectional, is motor ftesao nt safunction a as units stator the of ) C nefc can interface C –PG C ), teghadlftm.Teaeaefrei ihrfralre icu load viscous bond larger the a for increase higher that is a pocket force or PGB average (Right stator the changes The the within lifetime. conformational and PGB stretches either strength the arrow) inducing of (blue PG, shift rotor the positional the at upon point stator anchoring the by produced 4. Fig. hsi oevatePtsa olo Vrin04)i alb(1 8.An 58). 1C (31, Fig. Matlab in shown in is 0.42) fit (Version its traces. toolbox and torque trace PottsLab motor torque the poststall example via the and prestall done of the is minimization both This a fit and to used signals, is constant functional piecewise noisy be to and (57), τ Fitting. and Calculation Torque (56). Motor plane sample the above motor Fig. linear in a onto shown mounted is are trajectory magnets posi- example bead An the positions. to angular fit 1 is the ellipse yield An to 55). tions (28, analysis cross-correlation using biotinylated by the 22 at to buffer motility attach in spontaneously performed are to Experiments allowed hooks. are superpara- Streptavidin beads slides. magnetic flow OD custom-made final in coverslip 33 a lysine–coated at to Broth rpm, Terrific delete in 200 genetically grown at are additionally cells we of and aliquots (27), Frozen hook biotinylated a has Configuration. Experimental and Bacteria in included are methods and materials Extended Methods and Materials be of to remains role mechanosensitivity potential stator’s discovered. The the to 52–54). respect (17, exact with defined its FliL although poorly rotor, still and is pro- stator to function the membrane prove with a may associates is which stator FliL tein the Finally, of bidirectional. symmetrically behavior be catch-bond direc- for asymmetrically the 18). or (51), load directional (17, tional often upon are motors dependent bonds clockwise-locked catch is While and assembly counterclockwise- stator both that show results inner IM, curves. torque–speed published previously membrane. with consistent and motor B, oaigbasaeiae noaCO aeaa ,0 zadlocalized and Hz 1,000 at camera CMOS a onto imaged are beads Rotating pe rcsaemda-lee yuigawno f05s Two s. 0.5 of window a using by median-filtered are traces Speed Inset. ,wt epc oalwvsosla (Left load viscous low a to respect with ), = ato fapooe ac-odmcaim h vrg force average The mechanism. catch-bond proposed a of Cartoon γω ω stemaue oainlvlct.Tru rcsaeassumed are traces Torque velocity. rotational measured the is where , γ sterttoa icu rgcefiin ftebead the of coefficient drag viscous rotational the is 600 f0506 el r moiie oapoly- a to immobilized are Cells 0.5–0.6. of h oqeo h F scluae as calculated is BFM the of torque The euse We NSEryEdition Early PNAS .coli E. IMtrasadMethods. and Materials SI . ,a hw nFg 2A, Fig. in shown as ), tanMB2 which MTB32, strain ◦ o ,shaking h, 5 for C ◦ C. L | 1 CheY. -Potts f6 of 5 L -

BIOPHYSICS AND COMPUTATIONAL BIOLOGY Stator Stoichiometry Calculation and Analysis. Stator stoichiometry is deter- ACKNOWLEDGMENTS. We thank H. J. E. Beaumont and D. Dulin for con- mined by preserving the discrete discontinuities from the step detection structive comments; D. Chamousset for technical help; and M. Storath and algorithm (see SI Materials and Methods for details and a test of both the A. Weinmann for step detection algorithms and support in implementa- step detection and stator stoichiometry determination algorithms). tion. Centre de Biochimie Stucturale is a member of the France-BioImaging and the French Infrastructure for Integrated Structural Biology, supported Numerical Simulations. In addition to the Hill–Langmuir adsorption model by Grants ANR-10-INBS-04-01 and ANR-10-INBS-05. R.P.-C. was supported by described by Eq. 3, we also consider a generalized reversible RSA model which Wellcome Trust Grant WT098325MA, and A.L.N., E.G., and F.P. were sup- incorporates a continuous binding ring around the rotor. As this model has no ported by the European Research Council under the European Union’s Sev- analytical solution, we determine stator binding and unbinding rates using enth Framework Program (FP/2007-2013)/ERC Grant 306475. A.B. acknowl- a genetic algorithm (differential evolution) to match simulated stator stoi- edges the support of the French Agence Nationale de la Recherche, under chiometry time trajectories to the average of the experimental trajectories. Grant ANR-14-ACHN-0016.

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