Cooperative Protofilament Switching Emerges from Inter-Motor Interference in Multiple-Motor Transport
CCooperative protofilament switchingemerges from inter-motor interference inmultiple-motor transport
David Ando , Michelle K. Mattson , Jing Xu & Ajay Gopinathan Department of Physics, University of California, Merced, CA, USA, Developmental and Cell Biology, University of California,Irvine, CA, USA.
Within living cells, the transport of cargo is accomplished by groups of molecular motors. Such collectivetransport could utilize mechanisms which emerge from inter-motor interactions in ways that are yet to befully understood. Here we combined experimental measurements of two-kinesin transport with atheoretical framework to investigate the functional ramifications of inter-motor interactions on individualmotor function and collective cargo transport. In contrast to kinesin’s low sidestepping frequency whenpresent as a single motor, with exactly two kinesins per cargo, we observed substantial motion perpendicularto the microtubule. Our model captures a surface-associated mode of kinesin, which is only accessible viainter-motor interference in groups, in which kinesin diffuses along the microtubule surface and rapidly‘‘hops’’ between protofilaments without dissociating from the microtubule. Critically, each kinesintransitions dynamically between the active stepping mode and this weak surface-associated mode enhancinglocal exploration of the microtubule surface, possibly enabling cellular cargos to overcome macromolecularcrowding and to navigate obstacles along microtubule tracks without sacrificing overall travel distance. C onventional kinesin (kinesin-1) is a microtubule-based motor that drives fast and long-range transport ofcellular material toward the cell periphery . On the single-molecule level, kinesin is a highly processivemotor that can take approximately 100 steps along a bare microtubule before disengaging. Each kinesinhas two identical microtubule-binding motor domains (‘‘heads’’), which the motor uses alternately to hydrolyzeATP and to step along the microtubule. Mechanisms behind the stepping and processive motion of individualkinesin motors have been studied extensively, with general agreement regarding a head over head mechanism formotors acting by themselves . Each kinesin motor has a low sidestepping frequency and typically tracks a singlemicrotubule protofilament during the course of its travel . Perhaps consequently, single kinesin-based transportis highly sensitive to macromolecular crowding on the microtubule surface .Intracellular kinesin-based transport is typically accomplished by groups of motors that must overcome ahighly crowded cellular environment and successfully navigate roadblocks along their microtubule tracks withoutprematurely dissociating . Defects in kinesin-based transport have been implicated in numerous diseases, espe-cially neurodegenerative diseases and quantitative understanding of kinesin’s group function is currently anarea of active research . Clearly, group behaviour can be governed by interactions between motors that are notrelated to single-motor functions, and these inter-motor interactions must be addressed in experiments employ-ing more than one kinesin per cargo. Recent theoretical and experimental investigations have uncovered evidencefor inter-motor interference, and demonstrated that two or more kinesins routinely function via the action of onemotor . The functional nature of such inter-motor interference is not clear, and has been thus far interpreted asnegative interference: when more than one motor is engaged in transport, each kinesin experiences an increasedprobability of detaching from the microtubule. Intuitively, this effect is negative for group function, sincepremature detachment of an individual kinesin substantially reduces the travel distance of the group.Typical efforts to understand function in groups of kinesin motors focus on characterizing experimentalmeasurements of the velocity and travel distance of multiple kinesin-based transport . However, inter-motorinteractions could lead to collective behaviour that manifests itself in other transport characteristics, such asmotion perpendicular to the microtubule axis, which requires a more explicit modeling of kinesin properties. Arecent study has directly demonstrated such inter-motor interaction, revealing that individual kinesin motorsexperience an increased likelihood to disengage in active transport while functioning in groups. Experimentallymeasurements of on axis and off-axis motion of cargo are regularly performed , yet our analysis and OPEN
SUBJECT AREAS:
KINESINBIOLOGICAL PHYSICSSINGLE-MOLECULE BIOPHYSICSCOMPUTATIONAL BIOPHYSICS
Received20 May 2014Accepted30 October 2014Published1 December 2014
Correspondence andrequests for materialsshould be addressed toJ.X. ([email protected]) or A.G.([email protected])
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REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 xperimental observations are unique in their focus on how inter-motor interactions can perturb off-axis motion as motor number andATP concentration are varied.In this paper, we address collective motor behavior in a controlledmanner by utilizing polystyrene beads as an in vitro cargo andemploying a single antibody to recruit exactly two kinesins onto eachbead. The resulting close proximity between kinesins on an identicalmicrotubule mimicked motor arrangements observed for cargos invivo . In contrast to single kinesin’s low sidestepping frequency ,our positional tracking data showed that cargo can be significantlyand frequently displaced transverse to the microtubule axis in a discrete fashion with no significant loss in processivity. To under-stand our measurements of group motor transport we used an expli-cit state-transition model with inter-motor interactions whichenabled us to extract the full spectrum of dynamics of individualmotors in a group setting, rather than just their average behaviour.Modeling the discrete transverse displacements required the intro-duction of a surface-associated mode of kinesin in which the motor isnot actively stepping, but remains in contact with the microtubuledue to the active engagement of other motors. We propose thatindividual motors in a group setting can utilize a radically differentform of stepping across the microtubule surface. Increasing the fre-quency of kinesin detachment in multiple motor configurations viainter-motor interference and a surface associated state may benefitgroup function in vivo by enabling a group of kinesins to avoidroadblocks along the microtubule, while the enhanced stochasticdissociation and rebinding of individual kinesins in a group canincrease the available microtubule landscape surrounding themotors . Results
Emergence of discrete transverse displacements (DTDs) in two-kinesin transport . To probe the functional interactions between twokinesin motors transporting the same cargo, we focused on thechanges in cargo position in the direction transverse to the microtubule between subsequent recording frames (33.3 ms tempo-ral resolution). We observed considerable changes in the transversedisplacement of two-motor cargos with reducing ATP concentra-tion, but not for single-motor cargos (Fig. 1A, SupplementaryDiscussion Fig. 1). Specifically, we observed symmetric transversedisplacement for both one- and two-motor cargos (Fig. 1, and repre-sentative traces in Supplementary Discussion Fig. 1), indicating thatcargo motion is not biased in either direction perpendicular to themicrotubule. However, with reducing ATP concentration (10 and20 m M), distinct peaks emerged within the cumulative distributionsof the two-motor transverse displacement due to what we termdiscrete transverse displacements (DTDs). The width and varianceof these DTD peaks were substantially smaller than those of the one-motor distribution ( . DTDs arise from simultaneous association of both kinesins withthe microtubule . At the lowest ATP concentration tested (10 m M),we observed two distinct classes of transverse displacement in two-kinesin transport at 10 m M ATP, one exhibiting pronounced DTDfeatures, and one exhibiting a broad distribution similar to thatobserved in single-kinesin transport (Fig. 1B). These two classes oftransverse displacement behaviour are well correlated with cargotravel and velocity along microtubules (Fig. 1C), and we observedDTDs only when the cargo also exhibited substantial travel distanceand somewhat slower velocity along microtubules (Fig. 1B,C).Observations at higher ATP concentrations followed a similarpattern (Supplementary Discussion 1), so further analysis of DTDsfocused on the least noisy 10 m M ATP data.The observed link between cargo travel distance and the form oftransverse displacement is perhaps not surprising; when the cargo islinked to the microtubule via only one kinesin, it experiences greater
Figure 1 | Single- and Two-kinesin motor transverse displacement measurements. (a) Histograms of the transverse displacement of cargos transportedby one (left) or two (right) kinesins at the indicated ATP concentrations. DTDs occur at 10 and 20 m M ATP for two-kinesin transport. (b) Top: Histogramof transverse cargo displacement at 10 m M ATP for two motor traces with travel distance . m m. Using a binning histogram density of 30 bins per 40 nm,the leftmost sidestep peak is located at -53.3 nm and the remaining sidestep peak on the left side is located at -29.8 nm. The rightmost sidestep peak islocated at 53.3 nm and the remaining right single sidestep is located at 26.6 nm. We find that ‘‘left’’ and ‘‘right’’ DTDs occur with roughly equal probability(49% vs 51%). Bottom: Same as (Top) except depicting traces with travel distances , m m. The sum of these two histograms is equal to the histogram ofDTDs of two-kinesin transport at 10 m M ATP. A sum of five gaussians approximates the two-motor ( . m m travel) transverse motion histogram well(Top), while the histogram of DTDs for the shorter traces (Bottom) was well approximated by a single gaussian. (c) Two-motor traces at 10 m M ATPseparate into two groups. One group (boxed in red) has a low standard deviation in its transverse displacement size of 46 nm on average, has a highprocessivity ( . m m), and a low velocity of 109 nm/s on average. Another group (boxed in blue) has traces with a travel distance of . m m, a highstandard deviation in its transverse displacement size of 62 nm on average, and a higher velocity of 187 nm/s on average. scientificreports SCIENTIFIC
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 hermal fluctuation (Fig. 1A, left) and an increased probability ofdissociating from the microtubule. Thus, we expected that the sin-gle-kinesin bound state dominates cargo trajectories in the groupwhich undergoes limited travel along the microtubule ( , m Mtraces). Similarly, as the dissociation rate for each bound kinesinmotor is increased at higher ATP concentrations, we expected anincreased probability of occurrence of the one-kinesin bound stateand an increased presence of the broad, single-motor-like transversedisplacement behaviour. These hypotheses were confirmed for two-kinesin transport at higher ATP concentrations (20 m M ATP isshown in Supplementary Fig. 9). On the other hand, at 10 m MATP, why is the single-kinesin bound state predominant for particu-lar traces during two-kinesin transport? Perhaps in certain cases it isnot possible for two motors to simultaneously engage the microtu-bule in the absence of load due to variations in motor-bead attach-ment geometry among specific beads. Regardless of the specificmechanism, at 10 m M ATP these single kinesin-like cargo traject-ories did not obscure the traces which displayed emergent DTDs anddid not significantly impact our quantitative modeling, as describedlater in the text.The histograms of the observed DTDs were well approximated bythe sum of five Gaussians (Fig. 1B, top, black lines) with the followingthree important features. First, the width of the central DTD peak(zero transverse displacement) was substantially smaller than that ofa single-motor distribution ( . DTD frequency reveals the presence of unbound, surface-associated(SA) motors . When present, the observed DTDs occurred quitefrequently relative to kinesin’s individual sidestepping rate. Thearea enclosed under the four gaussians in Fig. 1B (top, black lines)which have a non-zero mean relative to the total transverse fittedhistogram area is representative of the frequency of DTDs, a ratiowhich indicates that DTDs have a 71.5% probability of occurrence ineach two motor trace’s frame, or equivalently occur at a rate of at least 21.5 DTD/s (see Methods). First we rule out the possibility thatDTD events arise from transitions between two AE (activelyengaged) states and one AE state due to inter-motor strain. Asdemonstrated previously , in two-kinesin transport, the transitionrate from two-motor bound to one-motor bound states occurs at arate E ~ k off exp F = F d ð Þ , with k off the single motor off rate, F theinter-motor strain, and F d the detachment force estimated to be , . If DTDs occur due to transitions between two AE (activelyengaged) states and one AE state E is bounded by the DTDfrequency of 21.5/s, resulting in an inter-motor strain F of at least12 pN. This magnitude of inter-motor strain is not likely as it is morethan double the single motor force production of kinesin. Thus it isnot possible that DTD events arise from unbound motors rebindingduring two-kinesin transport.We further conclude that because DTD-containing traces have ahigh DTD rate that a mechanism other than AE motor sidewaysstepping is responsible for producing DTD events. Given that theDTD containing traces have an average velocity of 108.6 nm/s at10 m M ATP (corresponding to a forward-stepping rate of 13.6steps/s), if only one motor (either motor at anytime) is activelyengaged at all times with an unbound partner motor the engagedmotor would have to sidestep on average 158 sidesteps per 100 for-ward steps (21.5 DTD/s/13.6 steps/s) to generate the observed DTDrate of our cargo. If on the other hand both motors are always con-tinuously engaged, generating the observed average DTD rate fromonly AE motor sideways stepping would require that each kinesinmakes an average of 79 sidesteps per 100 forward steps (21.5 DTD/s/(2 * of approximately13 sidesteps per 100 steps (or 1.6 sidesteps/s at 10 m M ATP), bothassumptions require a significantly higher AE motor sideways step-ping rate for a single kinesin ( . to act as a tetherinfluencing the on/off rates of an individual motor dimer. In ourstudy, since we find that DTDs geometrically require only the shift-ing of a single motor head, as opposed to the entire functional dimer,to an adjacent protofilament (Supplement Discussion 1), we expli- scientificreports SCIENTIFIC
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 itly allow individual motor heads within each dimer to make contactacross different protofilaments in the weakly associated SA state.Assuming a rigid kinesin-bead complex, where motors are per-pendicular to the microtubule surface, the change in measured trans-verse position of a bead’s center of mass can be related to the changein the center of mass of the kinesin motor heads along the micro-tubule surface by a geometrical projection (Supplement Discussion1). The size of DTD events, which are measured relative to the changein center of mass of the transported bead , is constant within a giventrace at around 27 nm in the transverse direction and different tracesconsistently show this same magnitude for DTD events. Using ageometrical projection we calculate that DTD events with a 27 nmtransverse displacement correspond to a 1.4 nm shift in the center ofmass of the kinesin motor heads : The movement of a single kinesinhead (among 4 present in our double motor construct) to an adjacentmicrotubule protofilament 5.6 nm away would therefore result in thecenter of mass of all motor heads changing by 1.4 nm, i.e. 5.6 nm/4 m MATP), we observed substantially more transverse fluctuations in two-kinesin transport for the larger bead. The standard deviation in theobserved transverse fluctuation decreased from 41.7 nm to 23.4 nmwhen we reduced the bead diameter from 440 nm to 200 nm, inexcellent agreement with the value of 24.7 nm predicted by ourmodel (Supplementary Fig. 6). Thus, unbound, SA motors seem ableto contribute to the transport of intracellular cargos.
Stochastic state transition model with an SA state reproduces theobserved transverse motion and travel distance . The experimentaldata for processivity and transverse displacement rate (Fig. 1, Xu et al ) are replicated by a generic kinesin transition rate model thatincludes the SA state and interference between motors. We explicitlysimulate the two-motor system, dynamically modelling interferenceand the state of each motor throughout time; each motor can be inthe AE state, the SA state, or the off state (completely unbound fromthe microtubule) (Fig. 2). The motors were considered to bepermanently attached to the cargo bead but could change theirstate of attachment to the microtubule over time with seventransition rates and the state of the partner motor (Fig. 2B). Werecorded the transverse and axial positions of the motors duringthe simulation with the axial position set by active ATP stepping ofeither motor and transverse displacements determined by the AEsidestepping rate and SA hopping rate E (see Methods).The undetermined transition rates in our model were fitted by bestmatching simulated processivity values at all ATP concentrations toexperimentally measured processivity in two-kinesin transport andby simultaneously matching simulated transverse displacement his-tograms to experimental histograms at 10 m M ATP (see Methods).Using a brute-force search over a wide parameter space followed by aconjugate gradient search, a set of well performing rates which mini-mized the x error of the model to experiment were determined(Table 1). Optimal parameter values resulted in a model which clo-sely matched our experimental results (Fig. 3, Table 1) with a x fit of0.2.Using the optimal fitted transitions rates (Table 1), our modeldemonstrates that during two-motor travel, only a relatively smallfraction of travel consists of both motors being in the AE statesimultaneously: 26.3% of travel at 10 m M ATP, 25.6% of travel at20 m M ATP, and 13.5% of travel at 1 m M ATP. On the other hand,the SA state is able to capture a significant fraction of multi-motorbehavior, depending on the ATP concentration; 46.4% of travel at10 m M ATP, 32.4% of travel at 20 m M ATP, and 14.3% of travel at 1 m M ATP has one motor in a SA state and the partner motor in an AEstate. Although a relatively small fraction of two-motor steps mayconsist of simultaneously engaged AE motors, these steps may takelonger on average than single-motor steps due to inter-motor strainbetween AE motors, resulting in DTD-containing traces at 10 m MATP being slower than the non-DTD traces, as we observed. SAmotors may also provide some resistance in the axial direction ofmovement, which may also contribute to the reduced velocity ofthese DTD containing traces. Indeed, other experiments revealed
Figure 2 | Experimental and Model Arrangements. (a) Our experimental setup consists of a 440-nm diameter polystyrene bead as the cargo (green), withtwo recombinant K560 half-height kinesins (blue, AE kinesin; red, SA kinesin) connected through C-terminal histidine tags to a single monoclonalantibody (dark blue). Below the motors is shown a 13-protofilament right-handed A-lattice microtubule . The microtubule kinesin binding domainlattice is depicted; dark grey tubulins actively bind kinesin heads, while light grey tubulins interact through non-specific interactions. The transversedistance of 5.6 nm between microtubule protofilaments appears in red, and the axial spacing of 8 nm between kinesin binding locations appears in blue.(b) Transition rate variables and states in our dynamic two-motor state transition model. scientificreports SCIENTIFIC
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REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 eductions in velocity as motor numbers in kinesin-based transportincreased . Discussion
Our experiments were carried out in vitro , in the absence of externalload ; such that at any instant in time, the cargo is linked to themicrotubule via either a one- or two-kinesin bound state . Whenthermal motion is factored out, the transverse displacement of thecargo is dominated by the stochastic binding/unbinding of eachavailable kinesin to the microtubule, since each kinesin typicallytracks a single microtubule protofilament during transport . Inthe presence of thermal motion (our experiments were conductedat room temperature), the cargo’s transverse displacement alsoreflects the stiffness of the cargo’s linkage to the microtubule throughthe motors. Since two kinesins should stiffen this linkage, we pre-dicted that thermal motion would contribute less to the cargo’stransverse displacement when two motors were linked to the cargothan when a single motor provides the linkage. Since each kinesinassociates longer with the microtubule at lower ATP concentrations(e.g. 10 and 20 m M) , we interpret our experimental observation ofDTD peaks as resulting from a reduced ATP concentration whichincreases the duration of cargo binding in the two-kinesin or one-kinesin bound state. This yielded slow enough dynamics for us tocleanly probe the stochastic dynamics underlying cargo transport bytwo kinesins. Note that for single-kinesin transport, the cargo canonly be linked to the microtubule via a single motor at any instance, and thus we observe cargo transverse displacement that remainsunperturbed by varying the ATP concentration given that thermalmotion dominates observed transverse cargo displacement in thiscase.As sideways stepping by AE motors alone is unlikely to be respons-ible for the high DTD rate we observed, this rate is most likely due tointerference between motors and a mechanism in which motor headsare associated with the microtubule surface via non-specific interac-tions and diffuse along the surface. However other explanations arepossible such as a mechanism in which the motor-cargo recruitmentgeometry undergoes relatively rapid switching between conforma-tions. We feel that it is improbable that DTDs are due to conforma-tional changes because DTDs result in preferred absolute positionsfor the centre of mass of the cargo (Supplementary Fig. 8). While upto five peaks are visible in the histogram of per-frame cargo displace-ments at 10 m M ATP for two-kinesin transport, some of these tracesexhibit up to nine distinct peaks in the histogram of absolute trans-verse position of the cargo (Supplementary Fig. 8). Peaks in theabsolute transverse position histogram were spaced by approxi-mately 27 nm, close to the average transverse differential sidestepsize measured. It is unlikely that multiple conformational changes inthe kinesins-linker complex are of approximately the same mag-nitude, or that changes in motor conformation results in effects oncargo position that are identical to the effects of motors movingbetween protofilaments. Rather, peaks in the absolute transverseposition histogram likely correspond to different attachment geo-
Table 1 | Overview of model parameters, optimal model values, and experimental measurements of kinesin-based transport. Parametersare defined in Figure 2b
Parameter State transition rate Optimal model values [1 m M ATP], (Experimental value) b AE R OFF rate (if partner not AE) 0.32 s , (1 s ) c OFF R AE rate 6.4 s (5.0 s ) a AE R OFF rate (if partner AE) 23.1 s v SA R AE rate 45.6 s d AE R SA rate 17.3 s w SA R OFF rate 2.2 s y OFF R SA rate 2.2 s E SA protofilament switching rate 63.7 s Figure 3 | Model Results. (a) x error over the undetermined off rate and the AE-to-SA state transition rate phase space. Our model best fits experimentaldata at an AE to SA transition rate of 17.3/s and an off rate of 0.195/step when the partner motor is in the AE state. There appears to be a well behavedsingle global x error minimum. (b) Comparison of the histogram of transverse differential stepping for experimental traces at 10 m M ATP versusmodelled transverse motion at the best-fit model parameters. scientificreports
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REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 etries of the two kinesin motors to the microtubule surface(Supplementary Fig. 5). Furthermore, given the geometry of two-motor transport, each peak in the absolute transverse position his-togram corresponds to the projection of a single motor head movingto an adjacent protofilament (Supplementary Discussion 1), andDTDs which are 27 nm in size correspond to single motor headsmoving to adjacent protofilaments. This geometrical interpretationalso explains why only up to 9 peaks can be seen in the histogram ofabsolute transverse position (Supplementary Fig. 4,5).Alternatively, various types of interference between motors mayunderlie the frequent generation of DTDs. Inter-motor strain orsteric interactions between motors may result in greatly enhancedsidestepping rates for individual motors. However this type of inter-actions would increase the motor’s off rate and significantly decreaseprocessivity, which would be incompatible with our observations oflarge processivities for traces with frequent DTDs. For other types ofinterference which result in motors rapidly binding and unbindingfrom the microtubule, we would expect to frequently observe side-steps of the whole motors themselves, instead of the individual motorheads, as described in Supplementary Discussion 1. This scenario isruled out by the recruitment geometry in our experiments and by ourobservation that most DTDs corresponded to single motor headsmoving to an adjacent protofilament. Thus a form of interferencewhich reduces the likelihood that two partner motors can both beactively engaged at the same time, but allows one motor to be‘dragged’ along the microtubule is sufficient to model observedexperimental results. Such interference could physically result fromthe attachment geometry of the motors to the cargo or from themotor’s conformation. This type of negative interference betweenAE kinesins was previously demonstrated in vitro by Diehl , andis incorporated into our theoretical model.We assumed that motor heads in the SA state weakly interactwith the microtubule binding lattice via non specific interactions,which implies that AE and SA motors moving in the transversedirection are observationally indistinguishable in our experiment.This is because both situations can give rise to the same 27-nmcargo displacements via a geometrical projection driven by movingone kinesin motor head in the transverse direction by 5.6 nm, thetransverse distance between microtubule protofilaments. The dis-cordance between previous experimental measurements of AEsidestepping and the high frequency of sustained sidesteps weobserved in the two-motor case suggests that the vast majority ofDTDs are due to SA motor heads changing position from oneprotofilament to an adjacent one 5.6 nm away in the transversedirection. Direct measurement of the transverse displacement of anindividual motor head within a kinesin dimer (5.6 nm) would bechallenging. Here, single-head movement was resolved by project-ing the position of kinesin heads onto the position of the trans-ported cargo.Our experiments have yielded the first resolved measurements ofthe interactions of multiple motors with individual microtubule pro-tofilaments, revealing that the simplistic view of individual kinesinsas either in the AE state or completely off the microtubule is insuf-ficient to explain our observations. This is likely due to having twokinesin motors which are bound to the cargo in nearly identicallocations while sharing the same microtubule, which should max-imize interference between motors. Consideration of the off-axiscomponent of cargo motion uncovered a new SA state for motorswhich indicates that inter-motor interference during multiplemotor-based transport does not simply lead to premature dissoci-ation of motors, but may increase motor-cargo-track association byleading to a ‘tether’-like SA state, and that one motor can drive themajority of motion in multiple motor transport while maintaininghigh processivity. Thus, transverse displacement can be a powerfulexperimental tool for directly probing the underlying dynamics ofkinesins driving the same cargo. Enhanced transverse motion may contribute to the flexibilityneeded for multiple motors to navigate cargos through crowdedcellular environments (including obstacles along the microtubulesurface) without losses in travel distance. Increased transversemotion in multiple motor complexes may also increase the rate atwhich proteins bind cargos which are in the process of being trans-ported and facilitate the binding of kinesins which are bound to thesame cargo yet remain unattached to a microtubule. Further, thetether-like SA state may be functionally similar to the gliding beha-viour of the dynactin tail over the microtubule surface, which func-tionally increases the travel distance of dynein .Previous investigations have suggested that only one motor isactive for the majority of the time in multiple motor transport .Derr et al reported a linear increase in travel distance as the kinesincopy number increased, instead of the exponential increase expectedin models in which motors are either on or off in the conventionalmean field interpretation. Furuta et al determined that force pro-duction for multiple motors plateaued at two-motor force produc-tion irrespective of the number of engaged motors. Both of theseinvestigations indicated that multiple motors interfere with eachother and may frequently force each other into the SA state. TheSA state may also be important in reducing the number of motorsin the AE state in multiple-motor transport to minimize ATP hydro-lysis, as an energy efficiency or conservation mechanism.The specific geometry of the attachment of the motors to the cargobead enabled our observation of a high effective sidestepping rate forthe cargo. Different geometries could result in very different beha-viours, such as a small range of motion for the cargo (shorter distancefrom motor to cargo) and possibly no SA sidestepping. Thus, thelocation of the kinesin-binding domains on the cargo could consti-tute an important regulatory mechanism for transport, allowing thecell to fine-tune the type of motion and/or processivity required fortransporting a given cargo to its target.Given that conventional kinesin has functionally evolved to trans-port cargo in a multiple motor setting, it may be inappropriate toconsider kinesin stepping mechanisms devoid of the influence ofother motors, with new mechanisms and motor states possibly repre-senting a more fundamental way in which to understand kinesinfunction, rather than through the properties of single motor-cargoeswhich are rarely encountered in vivo . Methods
In vitro motility experiments . Protein purification and details of motilityexperiments are as described previously . Briefly, for two-kinesin motilityexperiments, histidine-tagged recombinant kinesin K560 was specifically recruitedto each polystyrene bead via penta-His-antibody (0.44 m m diameter, Qiagen ).Casein (5.55 mg/mL) was utilized to block antibody-independent, non-specificbinding of motors onto beads. The incubation ratio of penta-His antibody topolystyrene bead was titrated down to the single-antibody-per-bead range to ensurethat the maximum number of recruited kinesins per bead was two. Optical trap-mediated force measurements were employed to specifically select the population ofbeads carried by two active kinesins. For multiple-kinesin experiments where thenumber of kinesins was more than one but not well defined, kinesin was directlyadsorbed onto carboxlyated beads (200 nm diameter, Polysciences). The single-molecule range for both motor-cargo recruitment methods was determined viaPoisson statistics . For the stationary bead control experiment, bare beads(0.44 m m diameter, not coated with kinesin) were adsorbed non-specifically onto acoverslip in 35 mM PIPES. The optical trap was shut off for all motility measurementsto ensure measurements of bead travel without external load. Bead motility along themicrotubule was imaged via differential interference microscopy , with videorecorded at 30 fps (Basler), digitized using Lagarith lossless compression forsubsequent data analysis. Data analysis . Video recordings of bead motion were particle-tracked to within 10-nm resolution (1/3 pixel, see also Supplemental Fig. 7) using a previously describedtemplate matching algorithm . To decouple bead motion parallel to, and transverseto the microtubule, individual trajectories of bead motion were projected along themicrotubule lattice via least square regression analysis.DTD determination was performed by first histogramming the transverse differ-ential motion between all frames in traces which were over 8 m m long. This resultinghistogram was well matched by the sum of five gaussian curves, Fig. 1B, with non-zerocentered gaussians representing DTD events as typically the histogram of transverse scientificreports SCIENTIFIC
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255
REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 ifferentials consists of a single zero centered gaussian curve. The 21.5 DTD/s con-straint for two-motor transport at 10 m M ATP was calculated by first performing amulti-gaussian fit to the histogram of transverse differentials, calculating the ratio ofthe area under the four fitted gaussians which had non-zero mean relative to the totalhistogram area, and multiplying this ratio by the experimentally used observationframe rate to constrain the minimal rate of DTD events per second (21.5 DTD/s * Model . We explicitly modelled the two-motor system by allowing each motor to be inthe AE state, the SA state, or the off state during any given step and by recording thetransverse and axial positions of the motors during the simulation. For simplification,absolute transverse motion was allowed to remain unbounded in the simulation (onlydifferential transverse motion was compared between model and experiment). Thestepping rate for the motors (modelled motor velocity) was fixed by theexperimentally measured velocity at each modelled ATP concentration . The motorswere allowed to change their state of attachment to the microtubule once each step ofthe motors via transitions rates a , b , c , d , v , y , and w (Fig. 2B), while changes intransverse position were determined by rate E and a previously measured AEsidestepping rate . Specifically, we modelled the effect of the geometrical attachmentconstraints of the motors to cargo which result in intermotor interference by splittingthe off rate from the AE state to the off state into two different rates (Fig. 2B).Consistent with previous modelling efforts, these two off rates are assumed to occurdue to a per-step physical process, which implies that they will be sensitive to the ATPconcentration. We additionally assume that the partner of a SA motor is not allowedto transition to the SA state or to the off state because a SA motor does not hydrolyzeATP and thus cannot actively exert force or strain gate other motors during transport.Transitions from the AE state to the SA state, from the SA state to the off state, andfrom the off state to the SA state occur as a per-second diffusive search-like processesand are independent of the ATP concentration. Processivity histograms at all 3 ATPconcentrations were assumed to have the same percentage of DTD to non-DTDcontaining traces, a 44/56 ratio, as found at the 10 m M ATP concentration, with non-DTD traces modelled as having only one motor that contacts the microtubule. Cargobead trajectory simulations were terminated when both motors were in the off state.The histogram of modelled transverse displacement at 10 m M ATP and the pro-cessivity of model trajectories at 1 m M, 10 m M, and 20 m M ATP were compared totheir experimentally measured equivalents; optimal a , b , c , d , v , y , w , and E rateswhich minimized the x error of the model to experiment were determined by aconjugate gradient search (Table 1).1. Endres, N. F., Yoshioka, C., Milligan, R. A. & Vale, R. D. A lever-arm rotationdrives motility of the minus-end-directed kinesin ncd. Nature , 875–878(2005).2. Yildiz, A., Tomishige, M., Vale, R. D. & Selvin, P. R. Kinesin walks hand-over-hand.
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Acknowledgments
This work was partially supported by National Science Foundation (NSF) grantsEF-1038697 (to A.G.) and NSF-DBI-0960480 (to A.G.), by a James S. McDonnellFoundation Award (to A.G.), and by American Heart Association grant 825278F (to J.X.).The authors would like to thank Steve Gross, K.C. Huang and David Quint for valuableinput.
Author contributions
D.A., J.X. and A.G. conceived and designed the project. J.X. and M.K.M. performedexperiments. D.A. and J.X. analyzed data. D.A. performed the simulations. D.A., J.X. andA.G. wrote the main manuscript text and D.A. prepared figures. All authors reviewed themanuscript.
Additional information
Supplementary information
Competing financial interests:
The authors declare no competing financial interests.
How to cite this article:
Ando, D., Mattson, M.K., Xu, J. & Gopinathan, A. Cooperative scientificreports
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REPORTS | 4 : 7255 | DOI: 10.1038/srep07255| 4 : 7255 | DOI: 10.1038/srep07255 rotofilament switching emerges from inter-motor interference in multiple-motortransport. Sci. Rep. , 7255; DOI:10.1038/srep07255 (2014).This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.The images or other third party material in this article are included in the article’s Creative Commons license, unless indicatedotherwise in the credit line; if the material is not included under the CreativeCommons license, users will need to obtain permission from the license holderin order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ scientificreports SCIENTIFIC
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