How the interplay between mechanical and nonmechanical interactions affects multiple kinesin dynamics

Collective intracellular cargo transport by multiple kinesins on multiple microtubules

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Transport of microtubules according to the number and spacing of kinesin motors on gold nano-pillars

Motor proteins function in in vivo ensembles to achieve cargo transport, flagellum motion, and mitotic cell division. Although the cooperativity of multiple motors is indispensable for physiological function, reconstituting the arrangement of motors in vitro is challenging, so detailed analysis of the functions of motor ensembles has not yet been achieved. Here, we developed an assay platform to study the motility of microtubules driven by a defined number of kinesin motors spaced in a definite manner. Gold (Au) nano-pillar arrays were fabricated on a silicon/silicon dioxide (Si/SiO₂) substrate with spacings of 100 nm to 500 nm. The thiol-polyethylene glycol (PEG)-biotin self-assembled monolayer (SAM) and silane-PEG-CH₃ SAM were then selectively formed on the pillars and SiO₂ surface, respectively. This allowed for both immobilization of kinesin molecules on Au nano-pillars in a precise manner and repulsion of kinesins from the SiO₂ surface. Using arrayed kinesin motors, we report that motor number and spacing do not influence the motility of microtubules driven by kinesin-1 motors. This assay platform is applicable to all kinds of biotinylated motors, allows the study of the effects of motor number and spacing, and is expected to reveal novel behaviors of motor proteins.

Dynamics of cooperative cargo transport by two elastically coupled kinesin motors

Intracellular transport is performed often by multiple motor proteins bound to the same cargo. Here, we study theoretically collective transport of the cargo by two kinesin motors. We propose that the motor has only the elastic interaction with the cargo via the linker connecting them and has no interaction with another motor. With parameters values for single motors from the available single-molecule data, we show that at linker's elastic strength [Formula: see text] pN/nm the theoretical data of both velocity and run length of the two-motor assembly under no load are identical to the available experimental data. The run length distribution is single exponential. The single-motor-bound state of the assembly dominates the transport. Both the force dependence of the velocity of the cargo driven by single load-bearing motor and that by two load-bearing motors in the assembly are consistent with the experimental data. The stall force of the assembly is larger than the sum of stall forces of two uncoupled motors. Moreover, we predict that the stall force increases with the increase of K and becomes saturated at large K, with the saturated value being 1.5-fold larger than the sum of stall forces of the two uncoupled motors.

A fluid membrane enhances the velocity of cargo transport by small teams of kinesin-1

Kinesin-1 (hereafter referred to as kinesin) is a major microtubule-based motor protein for plus-end-directed intracellular transport in live cells. While the single-molecule functions of kinesin are well characterized, the physiologically relevant transport of membranous cargos by small teams of kinesins remains poorly understood. A key experimental challenge remains in the quantitative control of the number of motors driving transport. Here we utilized "motile fraction" to overcome this challenge and experimentally accessed transport by a single kinesin through the physiologically relevant transport by a small team of kinesins. We used a fluid lipid bilayer to model the cellular membrane in vitro and employed optical trapping to quantify the transport of membrane-enclosed cargos versus traditional membrane-free cargos under identical conditions. We found that coupling motors via a fluid membrane significantly enhances the velocity of cargo transport by small teams of kinesins. Importantly, enclosing a cargo in a fluid lipid membrane did not impact single-kinesin transport, indicating that membrane-dependent velocity enhancement for team-based transport arises from altered interactions between kinesins. Our study demonstrates that membrane-based coupling between motors is a key determinant of kinesin-based transport. Enhanced velocity may be critical for fast delivery of cargos in live cells.

Velocity Fluctuations in Kinesin-1 Gliding Motility Assays Originate in Motor Attachment Geometry Variations

Motor proteins such as myosin and kinesin play a major role in cellular cargo transport, muscle contraction, cell division, and engineered nanodevices. Quantifying the collective behavior of coupled motors is critical to our understanding of these systems. An excellent model system is the gliding motility assay, where hundreds of surface-adhered motors propel one cytoskeletal filament such as an actin filament or a microtubule. The filament motion can be observed using fluorescence microscopy, revealing fluctuations in gliding velocity. These velocity fluctuations have been previously quantified by a motional diffusion coefficient, which Sekimoto and Tawada explained as arising from the addition and removal of motors from the linear array of motors propelling the filament as it advances, assuming that different motors are not equally efficient in their force generation. A computational model of kinesin head diffusion and binding to the microtubule allowed us to quantify the heterogeneity of motor efficiency arising from the combination of anharmonic tail stiffness and varying attachment geometries assuming random motor locations on the surface and an absence of coordination between motors. Knowledge of the heterogeneity allows the calculation of the proportionality constant between the motional diffusion coefficient and the motor density. The calculated value (0.3) is within a standard error of our measurements of the motional diffusion coefficient on surfaces with varying motor densities calibrated by landing rate experiments. This allowed us to quantify the loss in efficiency of coupled molecular motors arising from heterogeneity in the attachment geometry.

Elastic Anisotropy Scenario for Cooperative Binding of Kinesin-Coated Beads on Microtubules

Muto et al. reported in 2005 an observation called cooperative binding, according to which the initial binding of a bead covered with active kinesins on a microtubule filament was capable of favoring the subsequent binding of similar beads on the same filament up to distances of the order of a few microns. This positive bias is stronger ahead of the initially bound bead than behind. We explain this effect by combining the recently proposed notion of shear screening length with the notion of localized tubulin conformational transition induced by motor binding. Elastic terms linked to the polarity of protofilaments, up to now ignored, provide adequate description to the long-range elastic shear generated by motor binding. The subsequent binding is favored when and where the shear displacement of protofilaments meets the requirement for specific strong binding. We propose experimental tests of our model, which open the way to a new type of spectroscopy for biomolecular processes.

Collective dynamics of processive cytoskeletal motors

Major cellular processes are supported by various biomolecular motors that usually operate together as teams. We present an overview of the collective dynamics of processive cytokeletal motor proteins based on recent experimental and theoretical investigations. Experimental studies show that multiple motors function with different degrees of cooperativity, ranging from negative to positive. This effect depends on the mechanical properties of individual motors, the geometry of their connections, and the surrounding cellular environment. Theoretical models based on stochastic approaches underline the importance of intermolecular interactions, the properties of single motors, and couplings with cellular medium in predicting the collective dynamics. We discuss several features that specify the cooperativity in motor proteins. Based on this approach a general picture of collective dynamics of motor proteins is formulated, and the future directions and challenges are discussed.

Theoretical Analysis of Dynamic Processes for Interacting Molecular Motors

Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by analyzing a new class of totally asymmetric exclusion processes where interactions are accounted for in a thermodynamically consistent fashion. It allows us to connect explicitly microscopic features of motor proteins with their collective dynamic properties. Theoretical analysis that combines various mean-field calculations and computer simulations suggests that dynamic properties of molecular motors strongly depend on interactions, and correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maximal particle flux. It is also argued that molecular motors transport is more sensitive to attractive interactions. Applications of these results for kinesin motor proteins are discussed.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

Construction and analyses of elastically coupled multiple-motor systems

Precision analyses of the collective motor behaviors have become important to dissecting mechanisms underlying the trafficking of subcellular commodities in eukaryotic cells. Here, we describe a synthetic approach to create structurally defined multiple protein complexes containing two elastically coupled motor molecules. Motors are connected using a simple DNA-scaffolding molecule and DNA-conjugated, artificial protein polymers that function as tunable elastic linkers. The procedure to self-assemble these components produces complexes in high synthetic yield and allows individual multiple-motor systems to be interrogated at the single-complex level. Methods to evaluate cooperative motor responses in a static optical trap are also discussed. While enabling the average transport properties of single/noninteracting and coupled motors to be compared, these procedures can provide insight into the extent to which motors cooperate productively via load sharing as well as the roles loading-rate-dependent phenomena play in collective motor functions.

Motor proteins and molecular motors: how to operate machines at the nanoscale

Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environments, strongly supporting fundamental cellular processes such as the transfer of genetic information, transport, organization and functioning. In the past two decades motor proteins have become a subject of intense research efforts, aimed at uncovering the fundamental principles and mechanisms of molecular motor dynamics. In this review, we critically discuss recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized to explain the non-equilibrium nature and mechanisms of molecular motors.

Cargo transportation by two species of motor protein

The cargo motion in living cells transported by two species of motor protein with different intrinsic directionalities is discussed in this study. Similarly to single motor movement, the cargo steps forward and backward along a microtubule stochastically. Recent experiments found that cargo transportation by two motor species has a memory; it does not change its direction as frequently as expected, which means that its forward and backward step rates depend on its previous motion trajectory. By assuming that the cargo has only the least possible memory, i.e., its step direction depends only on the direction of its last step, two cases of cargo motion are analyzed in detail in this study: (I) cargo motion under constant external load, and (II) cargo motion in one fixed optical trap. Due to the existence of memory, in the first case, the cargo can keep moving in the same direction for a long distance. In the second case, the cargo will oscillate in the trap. The oscillation period decreases and the oscillation amplitude increases with increasing forward step rate of the motor, but both of them decrease with increasing trap stiffness. The most likely location of the cargo, where the probability of finding the oscillating cargo is maximum, may be the same as or may be different from the trap center, which depends on the step rates of the two motor species. Meanwhile, if the motors are robust, i.e., their forward to backward step rate ratios are high, there may be two such most likely locations, located one on each side of the trap center. The probability of finding the cargo in a given location, the probability of the cargo being in forward or backward motion, and various mean first passage times of the cargo to a given location or a given state are also analyzed.

Analysis of Cooperative Behavior in Multiple Kinesins Motor Protein Transport by Varying Structural and Chemical Properties

Intracellular transport is a fundamental biological process during which cellular materials are driven by enzymatic molecules called motor proteins. Recent optical trapping experiments and theoretical analysis have uncovered many features of cargo transport by multiple kinesin motor protein molecules under applied loads. These studies suggest that kinesins cooperate negatively under typical transport conditions, although some productive cooperation could be achieved under higher applied loads. However, the microscopic origins of this complex behavior are still not well understood. Using a discrete-state stochastic approach we analyze factors that affect the cooperativity among kinesin motors during cargo transport. Kinesin cooperation is shown to be largely unaffected by the structural and mechanical parameters of a multiple motor complex connected to a cargo, but much more sensitive to biochemical parameters affecting motor-filament affinities. While such behavior suggests the net negative cooperative responses of kinesins will persist across a relatively wide range of cargo types, it is also shown that the rates with which cargo velocities relax in time upon force perturbations are influenced by structural factors that affect the free energies of and load distributions within a multiple kinesin complex. The implications of these later results on transport phenomena where loads change temporally, as in the case of bidirectional transport, are discussed.

Functional asymmetry in kinesin and dynein dimers

Active transport along the microtubule lattice is a complex process that involves both the Kinesin and Dynein superfamily of motors. Transportation requires sophisticated regulation much of which occurs through the motor's tail domain. However, a significant portion of this regulation also occurs through structural changes that arise in the motor and the microtubule upon binding. The most obvious structural change being the manifestation of asymmetry. To a first approximation in solution, kinesin dimers exhibit twofold symmetry, and microtubules exhibit helical symmetry. The higher symmetries of both the kinesin dimers and microtubule lattice are lost on formation of the kinesin-microtubule complex. Loss of symmetry has functional consequences such as an asymmetric hand-over-hand mechanism in plus-end-directed kinesins, asymmetric microtubule binding in the Kinesin-14 family, spatially biased stepping in dynein and cooperative binding of additional motors to the microtubule. This review focusses on how the consequences of asymmetry affect regulation of motor heads within a dimer, dimers within an ensemble of motors, and suggests how these asymmetries may affect regulation of active transport within the cell.