Proteins from the kinesin-8 family promote microtubule (MT) depolymerization, a process thought to be important for the control of microtubule length in living cells. In addition to this MT shortening activity, kinesin 8s are motors that show plus-end directed motility on MTs. Here we describe a simple model that incorporates directional motion and destabilization of the MT plus end by kinesin 8. Our model quantitatively reproduces the key features of length-vs-time traces for stabilized MTs in the presence of purified kinesin 8, including length-dependent depolymerization. Comparison of model predictions with experiments suggests that kinesin 8 depolymerizes processively, i.e., one motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in MT length as a function of time are related to depolymerization processivity. We have also determined the parameter regime in which the rate of MT depolymerization is length dependent: length-dependent depolymerization occurs only when MTs are sufficiently short; this crossover is sensitive to the bulk motor concentration.
Assembly and disassembly dynamics of microtubules (MTs) is tightly controlled by MT associated proteins. Here, we investigate how plus-end-directed depolymerases of the kinesin-8 family regulate MT depolymerization dynamics. Employing an individual-based model, we reproduce experimental findings. Moreover, crowding is identified as the key regulatory mechanism of depolymerization dynamics. Our analysis gives two qualitatively distinct regimes. For motor densities above a particular threshold, a macroscopic traffic jam emerges at the plus-end and the MT dynamics become independent of the motor …
Kinesin-5, also known as Eg5 in vertebrates is a processive motor with 4 heads, which moves on filamentous tracks called microtubules. The basic function of Kinesin-5 is to slide apart two anti-parallel microtubules by simultaneously walking on both the microtubules. We develop an analytical expression for the steady-state relative velocity of this sliding in terms of the rates of attachments and detachments of motor heads with the ATPase sites on the microtubules. We first analyse the motion of one pair of motor heads on one microtubule and then couple it to the motion of the other pair of mo…
The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. …
Gliding of microtubule filaments on surfaces coated with the motor protein kinesin has potential applications for nano-scale devices. The ability to guide the gliding direction in three dimensions allows the fabrication of tracks of arbitrary geometry in space. Here, we achieve this by using kinesin-coated glass wires of micrometer diameter range. Unlike previous methods in which the guiding tracks are fixed on flat two-dimensional surfaces, the flexibility of glass wires in shape and size facilitates building in-vitro devices that have deformable tracks.
Intracellular transport based on molecular motors and its regulation are crucial to the functioning of cells. Filamentary tracks of the cells are abundantly decorated with non-motile microtubule-associated proteins, such as tau. Motivated by experiments on kinesin-tau interactions [Dixit et al. Science 319, 1086 (2008)] we developed a stochastic model of interacting single-headed motor proteins KIF1A that also takes into account the interactions between motor proteins and tau molecules. Our model reproduce experimental observations and predicts significant effects of tau on bound time and run …
Kinesin-1 is an ATP-driven, two-headed motor protein that transports intracellular cargoes along microtubule. Based on recent experimental observations, we formulate a mechanochemical model for it, in which forward/backward/futile cycle of kinesin-1 can be realized through multiple biochemical pathways. Our results show that both forward and futile cycles consist of two biochemical pathways, while backward cycle may be realized through six possible pathways. Backward motion of kinesin-1 is mainly through backward sliding along microtubule when it is in semi-detach state, and usually coupled wi…
Molecular motors of the kinesin-1 family move in a directed and processive fashion along microtubules (MTs). It is generally accepted that steric hindrance of motors leads to crowding effects; however, little is known about the specific interactions involved. We employ an agent-based lattice gas model to study the impact of interactions which enhance the detachment of motors from crowded filaments on their collective dynamics. The predictions of our model quantitatively agree with the experimentally observed concentration dependence of key motor characteristics including their run length, dwel…
During the early developmental process of organisms, the formation of the left-right laterality requires a subtle mechanism, as it is associated with other principal body axes. Any inherent chiral feature in an egg cell can in principal trigger this spontaneous breaking of chiral symmetry. Individual microtubules, major cytoskeletal filaments, are known as chiral objects. However, to date there lacks convincing evidence of a hierarchical connection of the molecular nature of microtubules to large-scale chirality, particularly at the length scale of an entire cell. Here we assemble an in-vitro …
We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the hand-over-hand mechanism of the directed motion along the microtubule. The model gives the average directed velocity and the current of Kinesins along the microtubule. It is shown that beyond a certain density of Kinesins, the average velocity and current undergo notable decrease which is due to formation of traffic jams in the system.
Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion, resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simulta…
The microtubule (MT) motor Kip3p is very processive kinesin that promotes catastrophes and pausing in particular on cortical contact. These properties explain the role of Kip3p in positioning the mitotic spindle in budding yeast and potentially other processes controlled by kinesin-8 family members. We present a theoretical approach to positioning of a MT network in a cell. In order to explore the underlying mechanism we introduce an idealized system of two MTs connected by a microtubule organizing center (MTOC). The dynamics of Kip3p is modeled by interacting stochastic particles, which allow…
Regulating physical size is an essential problem that biological organisms must solve from the subcellular to the organismal scales, but it is not well understood what physical principles and mechanisms organisms use to sense and regulate their size. Any biophysical size-regulation scheme operates in a noisy environment and must be robust to other cellular dynamics and fluctuations. This work develops theory of filament length regulation inspired by recent experiments on kinesin-8 motor proteins, which move with directional bias on microtubule filaments and alter microtubule dynamics. Purified…
A microtubule (MT) is a hollow tube of approximately 25 nm diameter. The two ends of the tube are dissimilar and are designated as `plus' and `minus' ends. Motivated by the collective push and pull exerted by a bundle of MTs during chromosome segregation in a living cell, we have developed here a much simplified theoretical model of a bundle of parallel dynamic MTs. The plus-end of all the MTs in the bundle are permanently attached to a movable `wall' by a device whose detailed structure is not treated explicitly in our model. The only requirement is that the device allows polymerization and d…
Biomolecular motor proteins that generate forces by consuming chemical energy obtained from ATP hydrolysis are pivotal for organizing broad cytoskeletal structures in living cells. The control of such cytoskeletal structures benefits programmable protein patterning; however, our current knowledge is limited owing to the underdevelopment of an engineering approach for controlling pattern formation. Here, we demonstrate the tailoring of assembled patterns of microtubules (MTs) driven by kinesin motors by designing the boundary shape in fabricated microwells. We found an MT bundle structure along…
In living cells, motor proteins, such as kinesin and dynein can move processively along microtubule (MT), and also detach from or attach to MT stochastically. Experiments have found that, the traffic of motor might be jammed, and various theoretical models have been designed to understand this traffic jam phenomenon. But previous studies mainly focus on motor attachment/detachment rate dependent properties. Recent experiment of Leduc {\it et al.} found that the traffic jam formation of motor protein kinesin depends also on the length of MT [Proc. Natl. Acad. Sci. U.S.A. {\bf 109}, 6100-6105 (2…
Membrane tubes are important elements for living cells to organize many functions. Experiments have found that membrane tube can be extracted from giant lipid vesicles by a group of kinesin. How these motors cooperate in extracting the fluid-like membrane tube is still unclear. In this paper, we propose a new cooperation mechanism called two-track-dumbbell model, in which kinesin is regarded as a dumbbell with an end (tail domain) tightly bound onto the fluid-like membrane and the other end (head domain) stepping on or unbinding from the microtubule. Taking account of the elasticity of kinesin…
Kinesin and related motor proteins utilize ATP fuel to propel themselves along the external surface of microtubules in a processive and directional fashion. We show that the observed step-like motion is possible through time varying charge distributions furnished by the ATP hydrolysis circle while the static charge configuration on the microtuble provides the guide for motion. Thus, while the chemical hydrolysis energy induces appropriate local conformational changes, the motor translational energy is fundamentally electrostatic. Numerical simulations of the mechanical equations of motion show…
Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A [Phys. Rev. Lett. {\bf 95}, 118101 (2005)], in which each motor can bind strongly or weakly to its microtubule track, and each binding site of the track might be empty or occupied by one motor. As the usual two-state model, i.e. the totally asymmetric simple exclusion process (TASEP) with motor detachment and attachment, in steady state of the system, this three-state model also exhibits shock (or domain wall separating the high-density and low density phases) and bo…
Length-regulation of microtubules (MTs) is essential for many cellular processes. Molecular motors like kinesin 8, which move along MTs and also act as depolymerases, are known as key players in MT dynamics. However, the regulatory mechanisms of length control remain elusive. Here, we investigate a stochastic model accounting for the interplay between polymerization kinetics and motor-induced depolymerization. We determine the dependence of MT length and variance on rate constants and motor concentration. Moreover, our analyses reveal how collective phenomena lead to a well-defined MT length.
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and heavily crosslinked. Relating their large-scale dynamics to properties of their constituents remains an unsolved problem. Here we study an in vitro system made from microtubules and XCTK2 kinesin motors, which forms an aligned and active gel. Using photobleaching we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local polarity. This phenomenon is also obse…
Mixtures of microtubules and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. We map the non-equilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulent-like extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous non-equilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and …
Evaporation-Induced Pattern Formation and Wetting in Active Microtubule-Kinesin Droplets
Harvard University（哈佛大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Surrey（萨里大学）；Universität Konstanz（康斯坦茨大学）
In the presence of ATP, kinesin proceeds along the protofilament of microtubule by alternated binding of two motor domains on the tubulin binding sites. Since the processivity of kinesin is much higher than other motor proteins, it has been speculated that there exists a mechanism for allosteric regulation between the two monomers. Recent experiments suggest that ATP binding to the leading head domain in kinesin is regulated by the rearward strain built on the neck-linker. We test this hypothesis by explicitly modeling a $C_α$-based kinesin structure whose both motor domains are bound on the t…
Here we study a driven lattice gas model for microtubule depolymerizing molecular motors, where traffic jams of motors induce stochastic switching between microtubule growth and shrinkage. We term this phenomenon \enquote{traffic dynamic instability} because it is reminiscent of microtubule dynamic instability [T. Mitchison and M. Kirschner, Nature 312, 237 (1984)]. The intermittent dynamics of growth and shrinking emerges from the interplay between the arrival of motors at the microtubule tip, motor induced depolymerization, and motor detachment from the tip. The switching dynamics correlates…
In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentrati…
Kinesin is a molecular motor that transports cargo along microtubules. The results of many {\it in vitro} experiments on kinesin-1 are described by kinetic models \cite{Clancy11} in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a non-exponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the …
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization including the dynamic instability, growth of microtubules to saturation, time-localized periods of nucleation and depolymerization as well as…
We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo …
Active stresses, which are collectively generated by the motion of energy-consuming rod-like constituents, generate chaotic autonomous flows. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering, and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal pat…
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the …
Conventional kinesin is a dimeric motor protein that transports membranous organelles toward the plus-end of microtubules (MTs). Individual kinesin dimers show steadfast directionality and hundreds of consecutive steps, yetthe detailed physical mechanism remains unclear. Here we compute free energies for the entire dimer-MT system for all possible interacting configurations by taking full account of molecular details. Employing merely first principles and several measured binding and barrier energies, the system-level analysis reveals insurmountable energy gaps between configurations, asymmetr…
In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like jamming. Recently we reported ({\it Phys. Rev. Lett. {\bf 95}, 118101 (2005)}) a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing a novel interaction parameter $c$, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except $c$, from experimentally …
Self-organization of kinesin-driven, microtubule-based 3D active fluids relies on the collective dynamics of single microtubules. However, the connection between macroscopic fluid flows and microscopic motion of microtubules remains unclear. In this work, the motion of single microtubules was characterized by means of 2D gliding assays and compared with the flows of 3D active fluids. While the scales of the two systems differ by 1,000x, both were driven by processive, non-processive or an equal mixture of both molecular motor proteins. To search for the dynamic correlation between both systems…
We develop a stochastic kinetic model of a pre-formed attachment of a mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by a group of active motor proteins. Such an attachment is a particularly unique case of ligand-receptor bonds: The MT ligand changes its length (and thus binding sites) with time by polymerization-depolymerization kinetics, while multiple motor receptors tend to walk actively along the MT length. These processes, combined with force-mediated unbinding of the motors, result in an elaborate behavior of the MT connection to the cell cortex. We present…
Fueled by the hydrolysis of ATP, the motor protein kinesin literally walks on two legs along the biopolymer microtubule. The number of accidental backsteps that kinesin takes appears to be much larger than what one would expect given the amount of free energy that ATP hydrolysis makes available. This is puzzling as more than a billion years of natural selection should have optimized the motor protein for its speed and efficiency. But more backstepping allows for the production of more entropy. Such entropy production will make free energy available. With this additional free energy, the cataly…
Conventional analysis of in vitro assays of motor proteins rests on the assumption that all proteins with the same chemical composition function identically; however molecule-to-molecule variation is often seen even in well-controlled experiments. In an effort to obtain a statistically meaningful set of time traces that simultaneously avoid any experimental artifacts, we performed quantum-dot labeled kinesin experiments on both surface and levitated microtubules. Similar to glassy systems, we found that mean velocities of individual kinesin motors vary widely from one motor to another, the var…
Within cells, vesicles and proteins are actively transported several micrometers along the cytoskeletal filaments. The transport along microtubules is propelled by dynein and kinesin motors, which carry the cargo in opposite directions. Bidirectional intracellular transport is performed with great efficiency, even under strong confinement, as for example in the axon. For this kind of transport system, one would expect generically cluster formation. In this work, we discuss the effect of the recently observed self-enhanced binding-affinity along the kinesin trajectories on the MT. We introduce …
As a complementary tool to nanofluidics, biomolecular based transport is envisioned for nanotechnological devices. We report a new method for guiding microtubule shuttles on multi-walled carbon nanotube tracks, aligned by dielectrophoresis on a functionalized surface. In the absence of electric field and in fluid flow, alignment is maintained. The directed translocation of kinesin propelled microtubules has been investigated using fluorescence microscopy. To our knowledge, this is the first demonstration of microtubules gliding along carbon nanotubes.
Conventional kinesin is a homodimeric motor protein that unidirectionally transports organelles along filamentous microtubule (MT) by hydrolyzing ATP molecules. This study shows that the load modulations of ATP turnover and head diffusion are both essential in determining the performance of the dimer under loads. It is found that the consecutive run length of the dimer critically depends upon a few pathways, leading to the detachment of individual heads from MT. Modifying rates for these detachment pathways changes the run length but not the velocity of the dimer, consistent with mutant experi…
We have developed several distinct model systems of microtubule-based 3D active isotropic fluids and have compared their dynamical and structural properties. The non-equilibrium dynamics of these fluids is powered by three different types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. The fourth modification uses specific microtubule crosslinkers to induce bundle formation instead of a non-specific depletant. In comparison to the formerly developed systems, each new active fluid formulation has certain enhanced …
The fluctuation theorem is a representative theorem in non-equilibrium statistical physics actively studied in the 1990's. Relating to entropy production in non-equilibrium states, the theorem has been used to estimate the driving power of motor proteins from fluctuation in their motion. In this review, usage of the fluctuation theorem in experiments on motor proteins is illustrated for biologists, especially those who study mechanobiology, in which force measurement is a central issue. We first introduce the application of the fluctuation theorem in measuring the rotary torque of the rotary m…
In this work we study a microtubule (MT) model, whose length is regulated by the action of processive kinesin motors. We treat the case of infinite processivity, i.e. particle exchange in the bulk is neglected. The exact results can be obtained for model parameters which correspond to a finite length of the MT. In contrast to the model with particle exchange we find that the lengths of the MT are exponentially distributed in this parameter regime. The remaining parameter space of the model, which corresponds to diverging MT lengths, is analyzed by means of extensive Monte Carlo simulations and…
Intracellular bidirectional transport of cargo on microtubule filaments is achieved by the collective action of oppositely directed dynein and kinesin motors. Experiments have found that in certain cases, inhibiting the activity of one type of motor results in an overall decline in the motility of the cellular cargo in both directions. This counter-intuitive observation, referred to as {\em paradox of codependence} is inconsistent with the existing paradigm of a mechanistic tug-of-war between oppositely directed motors. Unlike kinesin, dynein motors exhibit catchbonding, wherein the unbinding …
KIF1A kinesins are single-headed motor proteins which move on cylindrical nano-tubes called microtubules (MT). A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. Does lane-changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}]. By carryi…
Intracellular transport along microtubules or actin filaments, powered by molecular motors such as kinesins, dyneins or myosins, has been recently modeled using one-dimensional driven lattice gases. We discuss some generalizations of these models, that include extended particles and defects. We investigate the feasibility of single molecule experiments aiming to measure the average motor density and to locate the position of traffic jams by mean of a tracer particle. Finally, we comment on preliminary single molecule experiments performed in living cells.
Traveling Waves Enhance Transport during Cytoplasmic Streaming in Drosophila Oogenesis
Lewis-Sigler Institute for Integrative Genomics, Princeton University（普林斯顿大学刘易斯-席格勒整合基因组学研究所）；Center for Computational Biology, Flatiron Institute（Flatiron研究所计算生物学中心）；Department of Molecular Biology, Princeton University（普林斯顿大学生物分子系）；Courant Institute, New York University（纽约大学库朗数学科学研究所）
Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully und…
