Molecular crowding creates traffic jamsof kinesin motors on microtubulesCécile Leduca,b,1, Kathrin Padberg-Gehlec,1, Vladimír Vargaa,d,1, Dirk Helbinge, Stefan Dieza,f,2, and Jonathon Howarda,2

aMax Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, 01307 Dresden, Germany; bLaboratoire Photonique, Numérique etNanosciences, Institut d’Optique Graduate School, Université de Bordeaux, Centre National de la Recherche Scientifique, 351 cours de la libération,33405 Talence, France; cTechnische Universität Dresden, Fachrichtung Mathematik, Institut für Wissenschaftliches Rechnen, 01062 Dresden, Germany;dWilliam Dunn School of Pathology, University of Oxford, South Parks Road, Oxford OX1 3RE, United Kingdom; eEidgenössische Technische HochschuleZürich, Clausiusstrasse 50, 8092 Zürich, Switzerland; and fTechnische Universität Dresden, B CUBE, Arnoldstrasse 18, 01307 Dresden, Germany

Edited by Yale E. Goldman, University of Pennsylvania/Pennsylvania Muscle Institute, Philadelphia, PA, and accepted by the Editorial Board February 3, 2012(received for review May 9, 2011)

Despite the crowdedness of the interior of cells, microtubule-basedmotor proteins are able to deliver cargoes rapidly and reliablythroughout the cytoplasm. We hypothesize that motor proteinsmay be adapted to operate in crowded environments by havingmolecular properties that prevent them from forming traffic jams.To test this hypothesis, we reconstituted high-density traffic of pur-ified kinesin-8 motor protein, a highly processive motor with longend-residency time, along microtubules in a total internal-reflec-tion fluorescence microscopy assay. We found that traffic jams,characterized by an abrupt increase in the density of motors withan associated abrupt decrease in motor speed, form even in theabsence of other obstructing proteins. To determine the molecularproperties that lead to jamming, we altered the concentrationof motors, their processivity, and their rate of dissociation frommicrotubule ends. Traffic jams occurred when the motor densityexceeded a critical value (density-induced jams) or when motordissociation from the microtubule ends was so slow that it resultedin a pileup (bottleneck-induced jams). Through comparison of ourexperimental results with theoretical models and stochastic simu-lations, we characterized in detail under which conditions density-and bottleneck-induced traffic jams form or do not form. Ourresults indicate that transport kinesins, such as kinesin-1, may beevolutionarily adapted to avoid the formation of traffic jams bymoving only with moderate processivity and dissociating rapidlyfrom microtubule ends.

Cells are crowded with macromolecules, polymers, and mem-branes. This crowding diminishes the diffusion of small

molecules and proteins (1), increases the oligomerization andaggregation of proteins (2), and strongly restricts the mobility oflarger particles and organelles (3). Despite this “congestion” inthe cytoplasm, it is remarkable how efficiently transport systemsdeliver cargoes inside cells. In healthy cells, transport of cargoesat net rates exceeding 1 μm∕s can be maintained over distancesup to tens of microns in cilia and flagella (4, 5), and up to severalmillimeters (or more) in the axons and dendrites of neurons (6,7). Do healthy cells have special mechanisms to avoid transportobstructions seen under pathological conditions (8, 9)?

There are several ways in which the molecular propertiesof motor proteins could be adapted to prevent traffic jams. Forexample, the robustness of intracellular transport may be due tothe high forces generated by motor proteins, which may clearobstructions (8). Or the affinity of motors for their tracks may below enough to prevent a sufficient buildup in density. Alterna-tively, motors may have mechanisms to sense molecular crowdingand to alter their behavior in order to prevent traffic jams. So far,however, little is understood about how motor proteins behave incrowded environments, and what physical mechanisms may causemotor proteins to form traffic jams in the first place.

On highways, traffic jams form if an increase in vehicle densityleads to a sufficiently large decrease in the vehicle velocity (10,11). In this case, increasing the density beyond a critical valueleads to a decrease in the vehicle flux (the velocity times the den-

sity), which reinforces the density buildup, leading to an abruptincrease in density and an associated abrupt decrease in velocity:a traffic jam. Do similar principles operate at the molecular level?Traffic jams of motor proteins on cytoskeletal filaments havebeen predicted theoretically (12–16), and experiments with pur-ified proteins indicate that motor proteins have properties thatmay predispose them to form traffic jams: In principle, almostall the motor-binding sites on a microtubule can be occupiedif the kinesin-1 (17, 18), kinesin-3 (15), or kinesin-8 (19) concen-tration is high enough. Moreover, abrupt local increases in kine-sin-1 density on a microtubule have been reported (15), butwhether these were associated with an abrupt decrease in speedwas not investigated in these experiments. Finally, a decrease inaverage kinesin-1 speed has been observed to occur as the motorconcentration is increased (20), though no abrupt speed or den-sity changes were detected. In this work, we have used two-colortotal internal-reflection fluorescence microscopy (19) to simulta-neously measure the speed of individual kinesin motors movingon microtubules while monitoring the local motor density. Usingthis strategy, we study whether motor proteins have the predis-position to form traffic jams on their own, and, if so, what are thekey motor properties responsible for jams.

ResultsTo understand how individual motors behave in crowded envir-onments, we used the motor protein Kip3 (in the kinesin-8family) as a model system to reconstitute high-density traffic onmicrotubules. Kip3 is an ideal motor for these studies. First, likeother members of the kinesin-8 family (21), it is highly processive,walking tens of microns along a microtubule toward its plus endbefore dissociating (22). Second, it pauses at the plus end beforedissociating. And third, its motor properties (e.g., processivity,end dissociation) can be tuned by altering the salt concentrationin solution (19) (SI Appendix, Fig. S1). One potential disadvan-tage of Kip3 for these studies is that it depolymerizes micro-tubules (22, 23); however, we circumvented this problem by usingmicrotubules that were grown in the presence of the slowly hydro-lyzing GTP analog, guanylyl-(α, β)-methylene-diphosphonate(GMPCPP), and additionally stabilized the microtubules with

Author contributions: C.L., K.P.-G., V.V., D.H., S.D., and J.H. designed research; C.L., K.P.-G.,and V.V. performed research; C.L., K.P.-G., V.V., and J.H. analyzed data; and C.L., K.P.-G.,V.V., D.H., S.D., and J.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. Y.E.G. is a guest editor invited by the EditorialBoard.

Freely available online through the PNAS open access option.

See Commentary on page 5911.1C.L., K.P.-G., and V.V. contributed equally to this work.2To whom correspondencemay be addressed. E-mail: diez@bcube-dresden.de or howard@mpi-cbg.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1107281109/-/DCSupplemental.

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taxol. Kip3 cannot depolymerize such “doubly stabilized”microtu-bules (19). To simultaneously measure individual motor speed andthe overall motor density, we added a low concentration of EGFP-labeled Kip3 (<0.05 nM) to variable amounts of mCherry-labeledKip3 (0–15 nM). Both fluorophores were excited with a 488-nmlaser and imaged by total internal-reflection fluorescence (TIRF)microscopy (Fig. 1A and SI Appendix, SI Methods).

Using this assay, we found that for sufficiently high total con-centrations of Kip3 (>1 nM), an abrupt increase in motor densityformed close to the microtubule plus end (red signal in Fig. 1B).This high-density (HD) region expanded toward the minus enduntil a steady state was reached. The density in the HD regionwas similar for all the microtubules present in a field of view(SI Appendix, Fig. S2). When a motor reached the HD region,it slowed down (green signal in Fig. 1B). The coexistence of aHD/low-speed region with a low-density (LD)/high-speed regionwas taken as the signature of a traffic jam (see Movie S1).

Our experimental observations could be simulated by themodel of Parmeggiani et al. (13). In this model, the microtubuleis represented as a one-dimensional lattice withN sites, each cor-responding to a tubulin dimer (see Fig. 1A, Lower). The latticecorresponds to a single protofilament of the microtubule; themodel therefore does not consider protofilament switching. Themotors are represented as particles, at most one occupying eachsite. At discrete time steps (Δt) the occupancy of the sites isupdated according to the following rules. (i) If the site is empty,then with probability k̄on the site becomes filled (proportional tothe concentration of motors in solution). (ii) If the site is occu-pied, the particle leaves the lattice with probability k̄off ; if it hasnot left, then it moves to the right (if the adjacent site to the rightis empty) or stays (if the next site is full). A special update ruleapplies at the right-hand end (the end toward which the motorswalk); if this site is occupied, there is a probability k̄end (not ne-cessarily equal to k̄off) that it becomes empty. In the stochasticsimulations, the sites are updated using a random-sequentialupdate; i.e., at each time step,N sites are chosen at random (withno restriction on how many times a site is chosen) and the sitesare updated one after the other. This update protocol mimicsmotor stepping as a random (Poisson) process (13). To relatethe simulation to the experimental results, the distance betweensites was set to d ¼ 8 nm and the discrete time step to Δt ¼d∕v0 ¼ 0.16 s where v0 ¼ 50 nm∕s is the motor speed at low den-sity. Within this time step, each motor advances on average onetubulin dimer per time step at low density, giving the correct aver-

age speed. The probabilities relate to the corresponding associa-tion and dissociation rates by k̄on ¼ kon · Δt · d, k̄off ¼ koff · Δt,and k̄end ¼ kend · Δt where kon is the association rate per tubulindimer, koff is the lattice-dissociation rate, and kend is the end-dissociation rate. The choice of time step ensures that the prob-abilities are <1.

The stochastic simulations reproduced many of the featuresof the experimental data (Fig. 1C). Using realistic parameters,there was a sharp transition in motor density between LD andHD regions, the motors abruptly slowed down when they crossedfrom the LD into the HD region, and the motor density distribu-tion approached a steady state with similar kinetics to the experi-mental data.

In order to better understand the mechanism of traffic jamformation, we measured the kinetics of jam growth. We madethe following observations. (i) The lengths of the traffic jamsincreased over time and approached steady state approximatelyexponentially (Fig. 2 A–C). (ii) The steady-state jam length in-creased linearly with the microtubule length with a slope equalto one (Fig. 2C, Inset). (iii) There was a critical microtubulelength necessary for jam formation (Fig. 2C, Inset). (iv) For agiven Kip3 concentration, the characteristic time associated withthe exponential approach to steady state was similar for all

Fig. 1. Experimental and simulation results of motor-protein traffic jams onmicrotubules. (A, Upper) Schematic of the dual-color in vitro assay. (Lower)Schematic of the simulation with lattice-association (k̄on), lattice-dissociation(k̄off), and end-dissociation (k̄end) probabilities.N is the number of sites on thelattice. (B) Dual-color kymograph showing the motor density in red (Kip3-mCherry, 3.2 nM) and the trajectories of individual motors in green (Kip3-EGFP, <0.05 nM) in the presence of 30 mM KCl. The top of the kymographcorresponds to the time when the motors were added to the microtubule.(C) Simulated kymograph using the following parameters (see text):k̄on ¼ 3.2 × 10−4 ¼ 0.24∕N with N ¼ 750, corresponding to an associationrate with 3.2 nM Kip3-mCherry in solution, ρ̄s ¼ k̄on∕ðk̄on þ k̄offÞ ¼ 0.91, andk̄end ¼ 0.2.

A D

B E

C F

Fig. 2. Kinetics of traffic jam growth. (A) Kymograph showing the distribu-tion of Kip3-mCherry (3.2 nM) motors along the microtubule lattice in thepresence of 30 mM KCl. The dynamics of the nonlinear growth of traffic jamswere well fit (red line) using our analytic model (SI Text, Eq. S11). (B) Motordensity profiles for different times corresponding to the dashed lines in A. (C)Traffic jam length as a function of time for five microtubules of differentlengths at 3.2 nM Kip3-mCherry. All the data were well fit (solid lines) by ouranalytic model (SI Text, Eq. S11). The red line corresponds to the data in A.(Inset) Steady-state jam lengths vs. microtubule (MT) lengths. (D) Simulatedkymograph of traffic jam with k̄on ¼ 4.4 × 10−4 ¼ 0.28∕N, N ¼ 625, ρ̄s ¼ 0.91,and k̄end ¼ 0.2. (E) Motor density profiles taken from the simulations in D atthe time points indicated by dashed lines. (F) Simulations of the traffic jamgrowth for different microtubule lengths. The red line corresponds to thesimulation in D. (Inset) Steady-state jam lengths vs. microtubule lengths.

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microtubule lengths (SI Appendix, Fig. S3). (v) When the motorconcentration was increased, the jam length approached its stea-dy-state value more quickly and the critical length depended onthe Kip3 concentration (SI Appendix, Fig. S4). All these proper-ties can be accounted for by an analytic model based on the as-sumption that the flux of motors is conserved at the boundarybetween LD and HD regions; the continuous curves in Fig. 2 Aand C are predictions based on the model (see SI Appendix). Oneway to understand these results is that a certain “antenna” length(19) or “capture” length of microtubule is required to raise thedensity sufficiently for jam formation. According to this picture,when the flux of motors to the microtubule plus end exceeds theflux off the end, the motors start to pile up, creating an HD regionat the end and a boundary between LD and HD regions. Thetraffic jam then grows toward the minus end. As the LD regionshrinks, the number of motors that enter the jam decreases, dueto the decrease in antenna length, until a steady state is reached(SI Appendix, Fig. S2); we call this a bottleneck-induced mechan-ism (14). The kinetics of traffic jam growth accorded with thestochastic simulations, including the slope of the steady-statejam length vs. microtubule length (Fig. 2 D–F), which shows thatthe Parmeggiani-Franosh-Frey model recapitulates many of thekinetic features of jam formation.

A molecular property crucial for understanding how trafficjams form is the relationship between motor speed and motordensity. To determine the dependence of speed on density, singleKip3-EGFP molecules, observed in the green channel (Fig. 3A),were tracked with subpixel resolution (24). The speed in the LDregion was similar to the speed in the absence of any other motors(v0 ¼ 56� 10 nm∕s, SD, n ¼ 15) (22). When the motors enteredthe HD region, the speed abruptly decreased. The simulationsrecapitulated this behavior (Fig. 3B). Results from several experi-ments showed that the observed motor densities and speeds clus-tered into two groups—LD/high speed and HD/low speed—withlittle overlap (Fig. 3C, blue points). To map out the full speed-density curve, we increased the salt concentration from 30 to110 mMKCl (SI Appendix, Fig. S5); the speed decreased approxi-mately linearly as the density increased (Fig. 3C, orange points).The slowing provides direct evidence for motor–motor interactionson the microtubule lattice. Further evidence for motor–motor in-teractions comes from the observed decrease in processivity withdensity. The run length decreased from 17� 5 μm (mean� SE) insingle-molecule conditions to 1.1� 0.4 μm in high-density assays(6.4 nM Kip3-mCherry). The run time, equal to the run lengthdivided by the speed, also decreased with density; accordingly, thelattice-dissociation rate, koff , the reciprocal of the run time, in-creased with density (Fig. 3C, Inset). Because the lattice-dissocia-tion rate saturated over a wide range of densities where jams form(Fig. 3C Inset), k̄off was kept constant in the simulations.

The stochastic simulations provide insight into the nature ofthe motor–motor interactions on the lattice. The simulations pre-dict a linear speed-density curve, both under conditions wheredistinct LD-HD regions formed (Fig. 3D, blue points) and underconditions exhibiting the full range of speeds and densities(Fig. 3D, orange points). This linear slowdown in the simulationsis due to steric interference: A particle cannot step forward if thespace in front is already occupied by another particle. The agree-ment between experiment and simulation suggests that Kip3slows down due to simple steric interference; this is unlike cartraffic, where a nonlinear dependence of velocity on density re-flects the complex interactions between the cars on highways (25).The slowdown also demonstrates that the motors do not fullysynchronize in a train-like motion in which the speed is indepen-dent of density (SI Appendix, Fig. S6).

To investigate experimentally how the end-dissociation rate(kend) and the lattice-dissociation rate (koff) affect traffic jam for-mation, we varied the salt concentration in our assays; both ratesincreased when the KCl concentration was increased. However,

interpreting these results was confounded by the large number ofexperimental parameters (four), which also included the motorconcentration (which influenced kon) and the microtubule length.We therefore used stochastic simulations and theory to facilitatethe interpretation of these data. We found that only three of thefour parameters are independent: There is a trade-off betweenthe association rate and the microtubule length in the sense thata lower association rate can be compensated for by a longermicrotubule length. This trade-off is a consequence of the anten-na mechanism mentioned above. In our simulations, we thereforechose three independent parameters to vary systematically andasked what ranges of values led to traffic jams and what werethe properties of the jams. The parameters we used were (i)the end-dissociation probability, k̄end, (ii) the Langmuir densityρ̄s ¼ k̄on∕ðk̄on þ k̄offÞ, which corresponds to the steady-state,fractional occupancy of the lattice in the absence of motility(also known as the Langmuir isotherm or equilibrium density,ref. 13), and (iii) k̄onN, which is proportional to the rate of motorbinding to the entire lattice. The propensity to form jams in-creased as the first parameter k̄end was decreased and the lattertwo parameters ρ̄s and k̄on were increased. To display our resultsin two-dimensional (as opposed to 3D) phase diagrams, we con-sidered two values for the third parameter: k̄onN ¼ 0.3, corre-sponding to a low total binding rate (Fig. 4, Center), and k̄onN ¼1, corresponding to a high total binding rate (Fig. 5, Center).In the simulations we took N ¼ 1;250, corresponding to a10-μm-long microtubule.

When the binding rate is low (k̄onN < 0.5), there are threesteady-state behaviors that the motor-filament system can dis-play. These behaviors are represented by different domains in the

A B

C D

Fig. 3. Dependence of motor speed on motor density. (A) Kymograph(inverted contrast) showing the movement of individual Kip3-EGFP mole-cules in the presence of Kip3-mCherry (3.2 nM, not shown). Tracked datapoints (green) were used to calculate the indicated velocities. Red dashedlines represent the traffic jam boundary (Left) and the end of themicrotubule(Right). (B) Simulated trajectories from Fig. 1C. (C) Experimental relationshipbetween motor speed and motor density in the presence of 30 mM KCl(blue points, 0 and 3.2 nM Kip3-mCherry) and 110 mM KCl (orange points,0 to 6.4 nM Kip3-mCherry). (Inset) Lattice-dissociation rate (s−1) vs. motordensity at 110 mM salt. (D) Simulated relationship between the normalizedmotor speed and density using the parameters: k̄on ¼ 2 × 10−4 ¼ 0.25∕Nwith N ¼ 1;250, ρ̄s ¼ 0.91, and k̄end ¼ 0.2 (equivalent to 2 nM Kip3) (bluepoints); k̄on ¼ 8 × 10−4 ¼ 1∕N with N ¼ 1;250, ρ̄s ¼ 0.5, and k̄end ¼ 0.2(equivalent to 8 nM Kip3) (orange points).

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phase diagram (Fig. 4, Center). At high end-dissociation rates, nojams occur (Fig. 4, domain a). At intermediate end-dissociationrates, there is a spike in motor density (with width below the op-tical resolution) restricted to the very end of the microtubule,which corresponds to motors pausing and being replaced by in-coming motors (Fig. 4, domain b). At low end-dissociation rates,there is a pileup of motors at the microtubule end because theflux to the end exceeds the flux from the end. An HD regionis initiated at the end and propagates to form a traffic jam of finitelength, a bottleneck-induced jam (Fig. 4, domain c). The bound-ary between domains b and c occurs when the flux to the micro-tubule end (by motor walking) can be just balanced by the flux offthe end (due to detachment from the last subunit). We observedall three behaviors experimentally by changing the KCl concen-tration in solution (Fig. 4 kymographs and density scans). Whenthe KCl concentration was increased, both the lattice-dissociationrate, koff , and the end-dissociation rate, kend, increased (SIAppendix, Fig. S1); this is equivalent to moving diagonally fromthe bottom right (30 mMKCl) to the top left (200 mMKCl) in thephase diagram. When the motor concentration was increased (at afixed salt concentration, e.g., 110 mM KCl), the lattice associationrate, kon, increased; this is equivalent to moving horizontally fromleft (low motor concentration) to right (high motor concentration)in the phase diagram. There was good qualitative agreement be-tween the experimental kymographs and the simulations (the loca-tions of the simulations are marked by x on the phase diagram).

When the binding rate is high (k̄onN > 0.5), two additional be-haviors are observed (Fig. 5). They occur when the critical densityfor jams is reached on the lattice, and not only at the microtubuleend. We call these jams density-induced jams. Density-induced

jams occur when the Langmuir density, ρ̄s, exceeds 0.5 (corre-sponding to the density at which the flux is a maximum, in thecase of a linear speed-density curve in Fig. 3 C and D; see SIAppendix, Fig. S7). Density-induced jams occur in domains dand e of Fig. 5, Center. If the end-dissociation probability islow (k̄end ≤ 0.5), jams are both bottleneck- and density-induced;they are formed both from the end and along the lattice (Fig. 5,domain d and SI Appendix, Fig. S8). If the end-dissociation prob-ability is high (k̄end ≥ 0.5), jams are only density-induced andform only along the lattice (Fig. 5, domain e). In the latter case,the density decreases all along the HD region of the microtubule,whereas in the former case, and when ρ̄s < ð1 − k̄endÞ, there is ahigher density at the end (compare simulations in domains d ande in Fig. 5), which is responsible for a decrease in motor speed.Below the critical Langmuir density (ρ̄s ≤ 0.5), the domains ofthe phase diagram are similar to those in Fig. 4: no jams at highend-dissociation probabilities (k̄end ≥ 0.5, Fig. 5, domain a), andeither a spike at the microtubule end for intermediate end dis-sociations (Fig. 5, domain b) or bottleneck-induced jams (Fig. 5,domain c) at low end-dissociation probabilities (k̄end ≤ 0.5). Theboundary between domains b and c is given by the equality offluxes at the plus end: ρ̄sð1 − ρ̄sÞ ¼ k̄endð1 − k̄endÞ and thereforek̄end ¼ ρ̄s , when k̄end ≤ 0.5 and ρ̄s ≤ 0.5. As in the case of lowbinding rates, there was good qualitative agreement betweenthe experimental kymographs and the simulations as the experi-mental parameters were varied by changing the KCl and motorconcentrations. Again, the locations of the simulations aremarked by x on the phase diagram.

Fig. 4. Simulated phase diagram for bottleneck-induced traffic jams at low motor concentration or for short microtubules. The central panel shows threedistinct behaviors that depend on the Langmuir density (ρ̄s, x axis) and the end-dissociation rate (k̄end, y axis). The association rate is fixed atk̄on ¼ 2.4 × 10−4 ¼ 0.3∕N, with N ¼ 1;250. (Domain a) Only the LD region is present—i.e., no jams occur. (Domain b) A density spike forms at the microtubuleend. (Domain c) LD and HD regions coexist and traffic jams are present. The surrounding panels depict examples of simulations (Right) and experimental data(Left) in the different domains of the phase diagram. Below each kymograph, a motor density profile at steady state is shown. The intensity scale bar of thesimulations is the same as in Fig. 1C. The experimental density varies from 0 to 3,000 arbitrary units (a.u.) [Scale bars: 2 μm (horizontal) and 2 min (vertical).]

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DiscussionWe defined a traffic jam on a microtubule as the coexistence of ahigh-density/low-speed region (the jam) and a low-density/high-speed region, with an abrupt change in the transition region. Wefound that the motor protein Kip3 can form traffic jams on itsown, in the absence of cargo or other microtubule-associated pro-teins (MAPs). This report shows that molecular motors can forma congested phase that slows transport. This behavior is a dra-matic example of macromolecular crowding (2), demonstratingjamming by active, energy-dissipating molecular interactions.

By varying the motor concentration in solution, the length ofthe microtubules, and the lattice- and end-dissociation rates, weobserved several qualitatively different behaviors: (i) no densitydiscontinuity (no jam), (ii) a density discontinuity that was loca-lized to the very end of the microtubule (a spike), (iii) a densitydiscontinuity that propagated from the microtubule end (bottle-neck-induced jam), and (iv) a density discontinuity that initiatedon the microtubule lattice (density-induced jam). These beha-viors are in good qualitative agreement with simulations basedon the Parmeggiani-Franosch-Frey model (13), indicating that thismodel captures many of the main principles underlying theformation of molecular traffic jams. We could not test the modelquantitatively, in the sense that all experimental parameters couldbe globally constrained, due, in part, to uncertainties in measuringthe protein concentrations. Whether quantitative agreementwould be possible is not certain because experiments show thattwo of the assumptions behind the Parmeggiani-Franosch-Freymodel—the independence of the lattice-dissociation rate and end-

dissociation rate on motor density—do not hold (see Fig. 3 andref. 19, respectively).

Although all our experiments were performed using Kip3,which is in the kinesin-8 family, the mechanisms that we have un-covered allow us to extrapolate to other kinesins. For example,based on our analysis, we predict that the transport motor kine-sin-1, under physiological buffer conditions, does not form jams.This prediction, which accords with the experimental results citedin the Introduction (17, 20), is based on the relatively low proces-sivity of kinesin-1 (<1 μm) (26) and its high end-dissociation rate(>3 s−1), which place it in the “no jam” region of the phase dia-gram. Thus we could describe these properties of kinesin-1 (andother transport motors such as kinesin-2, ref. 27, and kinesin-3,refs. 28 and 29, which also have comparatively low processivitiescompared to the kinesin-8s such as Kip3 studied here or Kif18A,ref. 21) as adaptations to avoid traffic jams.

Our experiments may give insight into another puzzling featureof intracellular transport. The microtubule-based transport ofcellular cargoes is often saltatory (30, 31), characterized by per-iods of directed transport along microtubules and diffusion in thecytoplasm. To understand the logic behind this behavior, considerthe following argument. If the cargo velocity decreases with den-sity, as in Fig. 3, a cargo traffic jam will form above a critical cargodensity (SI Appendix, Fig. S7). Then, a further increase in the fluxcannot be achieved by increasing the density, but paradoxically,the flux is rather increased by decreasing the density—a strikingexample of the principle “less is more.” Saltatory motion maytherefore be an adaptation to maximize cargo flux.

Fig. 5. Simulated phase diagram for traffic jams at highmotor concentration or for longmicrotubules. Central panel shows five distinct behaviors that dependon the Langmuir density (ρ̄s, x axis) and the end-dissociation rate (k̄end, y axis). The association rate is fixed at k̄on ¼ 8 × 10−4 ¼ 1∕N, with N ¼ 1;250. (Domain a)Only LD region is present—i.e. no jams form. (Domain b) There is only an LD region with a density spike at themicrotubule end. (Domains c, d, and e) LD and HDregions coexist and traffic jams are present. (Domain c) Jams are only bottleneck-induced (due to k̄end ≤ 0.5) and not density-induced (due to ρ̄s ≤ 0.5). Themotor-density profile reaches a plateau at the level ρ̄s in the LD region. (Domain d) Jams are both bottleneck- and density-induced due to k̄end ≤ 0.5 andρ̄s ≥ 0.5. The motor density in the HD region increases toward the microtubule plus end when ρ̄s < 1 − k̄end, and decreases when ρ̄s > 1 − k̄end. (Domain e) Jamsare density-induced due to ρ̄s ≥ 0.5 but not bottleneck-induced due to k̄end ≥ 0.5. The surrounding panels depict examples of simulations and experimentaldata in the different domains of the phase diagram. The intensity scale bar of the simulations is identical to the one in Fig. 1C. Below each kymograph, a motordensity profile at steady state is shown. The experimental density varies from 0 to 2,500 arbitrary units (a.u.) [Scale bars: 2 μm (horizontal), 2 min (vertical).]

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Why are kinesin-8s so processive? The answer is that kinesin-8sfunction to control microtubule length, and this control mechanismonly works provided the run length is longer than the microtubulelength (19). Do kinesin-8s form traffic jams in cells? First, it is pos-sible that some kinesin-8s, such as Kif18A, do indeed form trafficjams, based on the high motor density seen adjacent to the kine-tochore during mitosis (32, 33). Second, operating in cells on “non-stabilized”microtubules, Kip3, is a depolymerase which dissociatesrapidly as it removes tubulin dimers from the end; thus Kip3 clearsits own jams by preventing a bottleneck from forming at the end.

Cellular cargoes are expected to have a higher propensity forforming jams than the individual motor proteins studied here be-cause cargoes may be transported by several motors and in vitroexperiments show that transport by multiple motors is more pro-cessive than transport by a single motor (34). An elegant way toreduce cargo jams would be for the motors to sense the stericforces associated with crowding of their cargoes and, in response,to reduce their processivity, just as Kip3 motors increase theirdissociation rate as the density increases (Fig. 3C, Inset). Thusforce-dependent dissociation, thought to be responsible for mo-tor coordination in mitosis and axonemal motility (35–37), mayalso be important for maximizing cargo flux, not just in regulatingcargoes containing oppositely directed motors (38).

In pathological situations—mutations in motors or interfer-ence by MAPs such as tau—abnormal aggregations of cargoeswith associated decreases in speed are observed (6–9). Whetherthese aggregations are traffic jams, as defined here, is not clear.Furthermore, the circumstances in vivo that lead, for example, toneurodegeneration (39) are much more complex than our simpli-

fied in vitro model. Nevertheless, our simplified motor-microtu-bule model provides insight into the logistics of intracellulartransport and makes testable predictions, for example, that inter-fering with motor dissociation, by MAPs or by opposing motorspresent on the same cargo (20, 40–43), will increase the propen-sity for jamming.

Materials and MethodsThe 6xHis-Kip3-mCherry construct was created by exchanging the coding re-gion of EGFP in 6xHis-Kip3-EGFP by that of mCherry. Kip3 motors were ex-pressed and purified as described previously for 6xHis-Kip3-EGFP (22).Microtubules (ratio of biotinylated to nonbiotinylated tubulin 1∶30) werepolymerized in GMPCPP, further stabilized by 10 μM taxol (19), and boundto the surface of a flow chamber with antibiotin antibodies. Flow chamberswere constructed and assays were performed as described previously (19).Both mCherry and EGFP fluorophores were excited with a 488-nm laser (Ar-gon; Coherent) using TIRF microscopy. Images were recorded on an EM-CCD(iXon-DV 897; Andor) camera with image acquisition every 1–20 s. Kymo-graphs were generated and analyzed using Metamorph software (MolecularDevices Corporation). Single-molecules were tracked by FIESTA software (24)written in MATLAB.

ACKNOWLEDGMENTS. We thank Chris Gell for help with the TIRF setup; FelixRuhnow for the use of his tracking software; Corina Brauer, Regine Hartmann,and Heike Petzold for technical help with protein expression and assays; andVolker Bormuth, Louis Reese, Reik Donner, and Yannis Kalaidzidis for stimulat-ing discussions. C.L. and K.P.-G. were supported by the Gottlieb Daimler andKarl Benz Foundation and C.L. by the French Centre National de la RechercheScientifique. We acknowledge additional financial support by the EuropeanResearch Council starting Grant 242 933, the Deutsche Forschungsge-meinschaft Heisenberg program (both to S.D.), and the Max Planck Society.

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