Bifurcation of velocity distributions in cooperative transport of filaments by fast and slow motors

Effective behavior of cooperative and nonidentical molecular motors

Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.

Force sharing and force generation by two teams of elastically coupled molecular motors

Many active cellular processes such as long-distance cargo transport, spindle organization, as well as flagellar and ciliary beating are driven by molecular motors. These motor proteins act collectively and typically work in small teams. One particularly interesting example is two teams of antagonistic motors that pull a common cargo into opposite directions, thereby generating mutual interaction forces. Important issues regarding such multiple motor systems are whether or not motors from the same team share their load equally, and how the collectively generated forces depend on the single motor properties. Here we address these questions by introducing a stochastic model for cargo transport by an arbitrary number of elastically coupled molecular motors. We determine the state space of this motor system and show that this space has a rather complex and nested structure, consisting of multiple activity states and a large number of elastic substates, even for the relatively small system of two identical motors working against one antagonistic motor. We focus on this latter case because it represents the simplest tug-of-war that involves force sharing between motors from the same team. We show that the most likely motor configuration is characterized by equal force sharing between identical motors and that the most likely separation of these motors corresponds to a single motor step. These likelihoods apply to different types of motors and to different elastic force potentials acting between the motors. Furthermore, these features are observed both in the steady state and during the initial build-up of elastic strains. The latter build-up is non-monotonic and exhibits a maximum at intermediate times, a striking consequence of mutual unbinding of the elastically coupled motors. Mutual strain-induced unbinding also reduces the magnitude of the collectively generated forces. Our computational approach is quite general and can be extended to other motor systems such as motor teams working against an optical trap or mixed teams of motors with different single motor properties.

Heterogeneity in kinesin function

The kinesin family proteins are often studied as prototypical molecular motors; a deeper understanding of them can illuminate regulation of intracellular transport. It is typically assumed that they function identically. Here we find that this assumption of homogeneous function appears incorrect: variation among motors' velocities in vivo and in vitro is larger than the stochastic variation expected for an ensemble of "identical" motors. When moving on microtubules, slow and fast motors are persistently slow, and fast, respectively. We develop theory that provides quantitative criteria to determine whether the observed single-molecule variation is too large to be generated from an ensemble of identical molecules. To analyze such heterogeneity, we group traces into homogeneous sub-ensembles. Motility studies varying the temperature, pH and glycerol concentration suggest at least 2 distinct functional states that are independently affected by external conditions. We end by investigating the functional ramifications of such heterogeneity through Monte-Carlo multi-motor simulations.

Dual-Color Herpesvirus Capsids Discriminate Inoculum from Progeny and Reveal Axonal Transport Dynamics

Alphaherpesviruses such as herpes simplex virus and pseudorabies virus (PRV) are neuroinvasive double-stranded DNA (dsDNA) viruses that establish lifelong latency in peripheral nervous system (PNS) neurons of their native hosts. Following reactivation, infection can spread back to the initial mucosal site of infection or, in rare cases, to the central nervous system, with usually serious outcomes. During entry and egress, viral capsids depend on microtubule-based molecular motors for efficient and fast transport. In axons of PNS neurons, cytoplasmic dynein provides force for retrograde movements toward the soma, and kinesins move cargo in the opposite, anterograde direction. The dynamic properties of virus particles in cells can be imaged by fluorescent protein fusions to the small capsid protein VP26, which are incorporated into capsids. However, single-color fluorescent protein tags fail to distinguish the virus inoculum from progeny. Therefore, we established a dual-color system by growing a recombinant PRV expressing a red fluorescent VP26 fusion (PRV180) on a stable cell line expressing a green VP26 fusion (PK15-mNG-VP26). The resulting dual-color virus preparation (PRV180G) contains capsids tagged with both red and green fluorescent proteins, and 97% of particles contain detectable levels of mNeonGreen (mNG)-tagged VP26. After replication in neuronal cells, all PRV180G progeny exclusively contain monomeric red fluorescent protein (mRFP)-VP26-tagged capsids. We used PRV180G for an analysis of axonal capsid transport dynamics in PNS neurons. Fast dual-color total internal reflection fluorescence (TIRF) microscopy, single-particle tracking, and motility analyses reveal robust, bidirectional capsid motility mediated by cytoplasmic dynein and kinesin during entry, whereas egressing progeny particles are transported exclusively by kinesins. IMPORTANCE Alphaherpesviruses are neuroinvasive viruses that infect the peripheral nervous system (PNS) of infected hosts as an integral part of their life cycle. Establishment of a quiescent or latent infection in PNS neurons is a hallmark of most alphaherpesviruses. Spread of infection to the central nervous system is surprisingly rare in natural hosts but can be fatal. Pseudorabies virus (PRV) is a broad-host-range swine alphaherpesvirus that enters neuronal cells and utilizes intracellular transport processes to establish infection and to spread between cells. By using a virus preparation with fluorescent viral capsids that change color depending on the stage of the infectious cycle, we find that during entry, axons of PNS neurons support robust, bidirectional capsid motility, similar to cellular cargo, toward the cell body. In contrast, progeny particles appear to be transported unidirectionally by kinesin motors toward distal egress sites.

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.

Multimotor transport in a system of active and inactive kinesin-1 motors

Long-range directional transport in cells is facilitated by microtubule-based motor proteins. One example is transport in a nerve cell, where small groups of motor proteins, such as kinesins and cytoplasmic dynein, work together to ensure the supply and clearance of cellular material along the axon. Defects in axonal transport have been linked to Alzheimer's and other neurodegenerative diseases. However, it is not known in detail how multimotor-based cargo transport is impaired if a fraction of the motors are defective. To mimic impaired multimotor transport in vitro, we performed gliding motility assays with varying fractions of active kinesin-1 motors and inactive kinesin-1 motor mutants. We found that impaired transport manifests in multiple motility regimes: 1), a fast-motility regime characterized by gliding at velocities close to the single-molecule velocity of the active motors; 2), a slow-motility regime characterized by gliding at close-to zero velocity or full stopping; and 3), a regime in which fast and slow motilities coexist. Notably, the transition from the fast to the slow regime occurred sharply at a threshold fraction of active motors. Based on single-motor parameters, we developed a stochastic model and a mean-field theoretical description that explain our experimental findings. Our results demonstrate that impaired multimotor transport mostly occurs in an either/or fashion: depending on the ratio of active to inactive motors, transport is either performed at close to full speed or is out of action.

Transport by populations of fast and slow kinesins uncovers novel family-dependent motor characteristics important for in vivo function

Intracellular cargo transport frequently involves multiple motor types, either having opposite directionality or having the same directionality but different speeds. Although significant progress has been made in characterizing kinesin motors at the single-molecule level, predicting their ensemble behavior is challenging and requires tight coupling between experiments and modeling to uncover the underlying motor behavior. To understand how diverse kinesins attached to the same cargo coordinate their movement, we carried out microtubule gliding assays using pairwise mixtures of motors from the kinesin-1, -2, -3, -5, and -7 families engineered to have identical run lengths and surface attachments. Uniform motor densities were used and microtubule gliding speeds were measured for varying proportions of fast and slow motors. A coarse-grained computational model of gliding assays was developed and found to recapitulate the experiments. Simulations incorporated published force-dependent velocities and run lengths, along with mechanical interactions between motors bound to the same microtubule. The simulations show that the force-dependence of detachment is the key parameter that determines gliding speed in multimotor assays, while motor compliance, surface density, and stall force all play minimal roles. Simulations also provide estimates for force-dependent dissociation rates, suggesting that kinesin-1 and the mitotic motors kinesin-5 and -7 maintain microtubule association against loads, whereas kinesin-2 and -3 readily detach. This work uncovers unexpected motor behavior in multimotor ensembles and clarifies functional differences between kinesins that carry out distinct mechanical tasks in cells.

The kinetics of mechanically coupled myosins exhibit group size-dependent regimes

Naturally occurring groups of muscle myosin behave differently from individual myosins or small groups commonly assayed in vitro. Here, we investigate the emergence of myosin group behavior with increasing myosin group size. Assuming the number of myosin binding sites (N) is proportional to actin length (L) (N = L/35.5 nm), we resolve in vitro motility of actin propelled by skeletal muscle myosin for L = 0.2-3 μm. Three distinct regimes were found: L < 0.3 μm, sliding arrest; 0.3 μm ≤ L ≤ 1 μm, alternation between arrest and continuous sliding; L > 1 μm, continuous sliding. We theoretically investigated the myosin group kinetics with mechanical coupling via actin. We find rapid actin sliding steps driven by power-stroke cascades supported by postpower-stroke myosins, and phases without actin sliding caused by prepower-stroke myosin buildup. The three regimes are explained: N = 8, rare cascades; N = 15, cascade bursts; N = 35, continuous cascading. Two saddle-node bifurcations occur for increasing N (mono → bi → mono-stability), with steady states corresponding to arrest and continuous cascading. The experimentally measured dependence of actin sliding statistics on L and myosin concentration is correctly predicted.

Kinesin-2: a family of heterotrimeric and homodimeric motors with diverse intracellular transport functions

Kinesin-2 was first purified as a heterotrimeric, anterograde, microtubule-based motor consisting of two distinct kinesin-related subunits and a novel associated protein (KAP) that is currently best known for its role in intraflagellar transport and ciliogenesis. Subsequent work, however, has revealed diversity in the oligomeric state of different kinesin-2 motors owing to the combinatorial heterodimerization of its subunits and the coexistence of both heterotrimeric and homodimeric kinesin-2 motors in some cells. Although the functional significance of the homo- versus heteromeric organization of kinesin-2 motor subunits and the role of KAP remain uncertain, functional studies suggest that cooperation between different types of kinesin-2 motors or between kinesin-2 and a member of a different motor family can generate diverse patterns of anterograde intracellular transport. Moreover, despite being restricted to ciliated eukaryotes, kinesin-2 motors are now known to drive diverse transport events outside cilia. Here, I review the organization, assembly, phylogeny, biological functions, and motility mechanism of this diverse family of intracellular transport motors.