Cargo transport by several motors

Cargo surface fluidity can reduce inter-motor mechanical interference, promote load-sharing and enhance processivity in teams of molecular motors

In cells, multiple molecular motors work together as teams to carry cargoes such as vesicles and organelles over long distances to their destinations by stepping along a network of cytoskeletal filaments. How motors that typically mechanically interfere with each other, work together as teams is unclear. Here we explored the possibility that purely physical mechanisms, such as cargo surface fluidity, may potentially enhance teamwork, both at the single motor and cargo level. To explore these mechanisms, we developed a three dimensional simulation of cargo transport along microtubules by teams of kinesin-1 motors. We accounted for cargo membrane fluidity by explicitly simulating the Brownian dynamics of motors on the cargo surface and considered both the load and ATP dependence of single motor functioning. Our simulations show that surface fluidity could lead to the reduction of negative mechanical interference between kinesins and enhanced load sharing thereby increasing the average duration of single motors on the filament. This, along with a cooperative increase in on-rates as more motors bind leads to enhanced collective processivity. At the cargo level, surface fluidity makes more motors available for binding, which can act synergistically with the above effects to further increase transport distances though this effect is significant only at low ATP or high motor density. Additionally, the fluid surface allows for the clustering of motors at a well defined location on the surface relative to the microtubule and the fluid-coupled motors can exert more collective force per motor against loads. Our work on understanding how teamwork arises in cargo-coupled motors allows us to connect single motor properties to overall transport, sheds new light on cellular processes, reconciles existing observations, encourages new experimental validation efforts and can also suggest new ways of improving the transport of artificial cargo powered by motor teams.

Synchronization of elastically coupled processive molecular motors and regulation of cargo transport

The collective work of motor proteins plays an important role in cellular transport processes. Since measuring intermotor coupling and hence a comparison to theoretical predictions is difficult, we introduce the synchronization as an alternative observable for motor cooperativity. This synchronization can be determined from the ratio of the mean times of motor resting and stepping. Results from a multistate Markov chain model and Brownian dynamics simulations, describing the elastically coupled motors, coincide well. Our model can explain the experimentally observed effect of strongly increased transport velocities and powers by the synchronization and coupling of myosin V and kinesin I.

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.

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.

Metrics for characterizing collective transport by multiple dimeric kinesins

Kinesin is a processive molecular motor which transports various cellular cargos by converting chemical energy into mechanical movements. Although the motion of a single molecule has been characterized in several studies, the dynamics of collective transport remains controversial. Since the chemical reactions fueling molecular motors are stochastic processes, the movements of coupled motors are not perfectly synchronized. The goal of this study is to develop metrics to analyze the level of synchronization of coupled (stochastic) motors. The correlation among movements of coupled motors, the slackness, the cooperativity, and the power loss of kinesins are explored using the developed metrics. These metrics can be extended to characterize collective work done by other molecular motors also.

Transport properties of melanosomes along microtubules interpreted by a tug-of-war model with loose mechanical coupling

In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent cargo-motor linkers and stepping motion for the motors. It has been recently proposed that the stiffness of the motor plays an important role when multiple motors collectively transport a cargo. Therefore, we considered in our model the recently reported values for the stiffness of the cargo-motor linker determined in living cells (∼0.01 pN/nm, [1]) which is significantly lower than the motor stiffness obtained in in vitro assays and used in previous studies. Our model could reproduce the multimodal velocity distributions and typical trajectory characteristics including the properties of the reversions in the overall direction of motion observed during melanosome transport along microtubules in Xenopus laevis melanophores. Moreover, we explored the contribution of the different motility states of the cargo-motor system to the different modes of the velocity distributions and could identify the microscopic mechanisms of transport leading to trajectories compatible with those observed in living cells. Finally, by changing the attachment and detachment rates, the model could reproduce the different velocity distributions observed during melanosome transport along microtubules in Xenopus laevis melanophores stimulated for aggregation and dispersion. Our analysis suggests that active tug-of-war processes with loose mechanical coupling can account for several aspects of cargo transport along microtubules in living cells.

Distinct transport regimes for two elastically coupled molecular motors

Cooperative cargo transport by two molecular motors involves an elastic motor-motor coupling, which can reduce the motors' velocity and/or enhance their unbinding from the filament. We show theoretically that these interference effects lead, in general, to four distinct transport regimes. In addition to a weak coupling regime, kinesin and dynein motors are found to exhibit a strong coupling and an enhanced unbinding regime, whereas myosin motors are predicted to attain a reduced velocity regime. All of these regimes, which we derive by explicit calculations and general time scale arguments, can be explored experimentally by varying the elastic coupling strength.

Tug of war of molecular motors: the effects of uneven load sharing

We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature: a quite widespread model which assumes equal force sharing, here referred to as the mean field model (MFM), and a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations, the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be the consequences of the load sharing assumptions and can be interpreted in terms of the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness, while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin-1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins.