The winch model can explain both coordinated and uncoordinated stepping of cytoplasmic dynein

Theoretical efficiency limits and speed-efficiency trade-off in myosin motors

Muscle myosin is a non-processive molecular motor generates mechanical work when cooperating in large ensembles. During its cyle, each individual motor keeps attaching and detaching from the actin filament. The random nature of attachment and detachment inevitably leads to losses and imposes theoretical limits on the energetic efficiency. Here, we numerically determine the theoretical efficiency limit of a classical myosin model with a given number of mechano-chemical states. All parameters that are not bounded by physical limits (like rate limiting steps) are determined by numerical efficiency optimization. We show that the efficiency is limited by the number of states, the stiffness and the rate-limiting kinetic steps. There is a trade-off between speed and efficiency. Slow motors are optimal when most of the available free energy is allocated to the working stroke and the stiffness of their elastic element is high. Fast motors, on the other hand, work better with a lower and asymmetric stiffness and allocate a larger fraction of free energy to the release of ADP. Overall, many features found in myosins coincide with the findings from the model optimization: there are at least 3 bound states, the largest part of the working stroke takes place during the first transition, the ADP affinity is adapted differently in slow and fast myosins and there is an asymmetry in elastic elements.

Three-color single-molecule imaging reveals conformational dynamics of dynein undergoing motility

Dynein, a dimeric motor protein, moves along microtubules through adenosine 5′-triphosphate- and thermal-driven motions of two large ring domains (AAA rings) and small microtubule-binding domains (MTBDs) separated by a long coiled-coil. Previous single-molecule studies have tracked the positions of the AAA rings during motility, but not the MTBDs. Here, we tracked the relative positions of both MTBDs and one AAA ring by three-color, nanometer-resolution imaging. The observation of both MTBDs provided a direct measurement of how dynein steps on the tubulin subunits, and the simultaneous observation of three fiducial markers revealed extraordinary flexibility and previously unknown conformational states of the motor during motility. The techniques presented here can be used to explore conformational dynamics of many other macromolecular complexes.

The motor protein dynein undergoes coordinated conformational changes of its domains during motility along microtubules. Previous single-molecule studies analyzed the motion of the AAA rings of the dynein homodimer, but not the distal microtubule-binding domains (MTBDs) that step along the track. Here, we simultaneously tracked with nanometer precision two MTBDs and one AAA ring of a single dynein as it underwent hundreds of steps using three-color imaging. We show that the AAA ring and the MTBDs do not always step simultaneously and can take differently sized steps. This variability in the movement between the AAA ring and MTBDs results in an unexpectedly large number of conformational states of dynein during motility. Extracting data on conformational transition biases, we could accurately model dynein stepping in silico. Our results reveal that the flexibility between major dynein domains is critical for dynein motility.

How Cytoplasmic Dynein Couples ATP Hydrolysis Cycle to Diverse Stepping Motions: Kinetic Modeling

Cytoplasmic dynein is a two-headed molecular motor that moves to the minus end of a microtubule by ATP hydrolysis free energy. By employing its two heads (motor domains), cytoplasmic dynein exhibits various bipedal stepping motions: inchworm and hand-over-hand motions, as well as nonalternating steps of one head. However, the molecular basis to achieve such diverse stepping manners remains unclear because of the lack of an experimental method to observe stepping and the ATPase reaction of dynein simultaneously. Here, we propose a kinetic model for bipedal motions of cytoplasmic dynein and perform Gillespie Monte Carlo simulations that qualitatively reproduce most experimental data obtained to date. The model represents the status of each motor domain as five states according to conformation and nucleotide- and microtubule-binding conditions of the domain. In addition, the relative positions of the two domains were approximated by three discrete states. Accompanied by ATP hydrolysis cycles, the model dynein stochastically and processively moved forward in multiple steps via diverse pathways, including inchworm and hand-over-hand motions, similarly to experimental data. The model reproduced key experimental motility-related properties, including velocity and run length, as functions of the ATP concentration and external force, therefore providing a plausible explanation of how dynein achieves various stepping manners with explicit characterization of nucleotide states. Our model highlights the uniqueness of dynein in the coupling of ATPase with its movement during both inchworm and hand-over-hand stepping.

Continuum mechanical parameterisation of cytoplasmic dynein from atomistic simulation

Cytoplasmic dynein is responsible for intra-cellular transport in eukaryotic cells. Using Fluctuating Finite Element Analysis (FFEA), a novel algorithm that represents proteins as continuum viscoelastic solids subject to thermal noise, we are building computational tools to study the mechanics of these molecular machines. Here we present a methodology for obtaining the material parameters required to represent the flexibility of cytoplasmic dynein within FFEA from atomistic molecular dynamics (MD) simulations, and show that this continuum representation is sufficient to capture the principal dynamic properties of the motor.

A model for the chemomechanical coupling of the mammalian cytoplasmic dynein molecular motor

Available single-molecule data have shown that some mammalian cytoplasmic dynein dimers move on microtubules with a constant step size of about 8.2 nm. Here, a model is presented for the chemomechanical coupling of these mammalian cytoplasmic dynein dimers. In contrast to the previous models, a peculiar feature of the current model is that the rate constants of ATPase activity are independent of the external force. Based on this model, analytical studies of the motor dynamics are presented. With only four adjustable parameters, the theoretical results reproduce quantitatively diverse available single-molecule data on the force dependence of stepping ratio, velocity, mean dwell time, and dwell-time distribution between two mechanical steps. Predicted results are also provided for the force dependence of the number of ATP molecules consumed per mechanical step, indicating that under no or low force the motors exhibit a tight chemomechanical coupling, and as the force increases the number of ATPs consumed per step increases greatly.

Molecular mechanisms of the interhead coordination by interhead tension in cytoplasmic dyneins

Cytoplasmic dyneins play a major role in retrograde cellular transport by moving vesicles and organelles along microtubule filaments. Dyneins are multidomain motor proteins with two heads that coordinate their motion via their interhead tension. Compared with the leading head, the trailing head has a higher detachment rate from microtubules, facilitating the movement. However, the molecular mechanism of such coordination is unknown. To elucidate this mechanism, we performed molecular dynamics simulations on a cytoplasmic dynein with a structure-based coarse-grained model that probes the effect of the interhead tension on the structure. The tension creates a torque that influences the head rotating about its stalk. The conformation of the stalk switches from the α registry to the β registry during the rotation, weakening the binding affinity to microtubules. The directions of the tension and the torque of the leading head are opposite to those of the trailing head, breaking the structural symmetry between the heads. The leading head transitions less often to the β registry than the trailing head. The former thus has a greater binding affinity to the microtubule than the latter. We measured the moment arm of the torque from a dynein structure in the simulations to develop a phenomenological model that captures the influence of the head rotating about its stalk on the differential detachment rates of the two heads. Our study provides a consistent molecular picture for interhead coordination via interhead tension.

A mathematical understanding of how cytoplasmic dynein walks on microtubules

Cytoplasmic dynein 1 (hereafter referred to simply as dynein) is a dimeric motor protein that walks and transports intracellular cargos towards the minus end of microtubules. In this article, we formulate, based on physical principles, a mechanical model to describe the stepping behaviour of cytoplasmic dynein walking on microtubules from the cell membrane towards the nucleus. Unlike previous studies on physical models of this nature, we base our formulation on the whole structure of dynein to include the temporal dynamics of the individual subunits such as the cargo (for example, an endosome, vesicle or bead), two rings of six ATPase domains associated with diverse cellular activities (AAA+ rings) and the microtubule-binding domains which allow dynein to bind to microtubules. This mathematical framework allows us to examine experimental observations on dynein across a wide range of different species, as well as being able to make predictions on the temporal behaviour of the individual components of dynein not currently experimentally measured. Furthermore, we extend the model framework to include backward stepping, variable step size and dwelling. The power of our model is in its predictive nature; first it reflects recent experimental observations that dynein walks on microtubules using a weakly coordinated stepping pattern with predominantly not passing steps. Second, the model predicts that interhead coordination in the ATP cycle of cytoplasmic dynein is important in order to obtain the alternating stepping patterns and long run lengths seen in experiments.

Energetic Costs, Precision, and Transport Efficiency of Molecular Motors

An efficient molecular motor would deliver cargo to the target site at a high speed and in a punctual manner while consuming a minimal amount of energy. According to a recently formulated thermodynamic principle, referred to as the thermodynamic uncertainty relation, the travel distance of a motor and its variance are, however, constrained by the free energy being consumed. Here we use the principle underlying the uncertainty relation to quantify the transport efficiency of molecular motors for varying ATP concentration ([ATP]) and applied load (f). Our analyses of experimental data find that transport efficiencies of the motors studied here are semioptimized under the cellular condition. The efficiency is significantly deteriorated for a kinesin-1 mutant that has a longer neck-linker, which underscores the importance of molecular structure. It is remarkable to recognize that, among many possible directions for optimization, biological motors have evolved to optimize the transport efficiency in particular.

Minimum requirements for motility of a processive motor protein

Motor proteins generally have a two-way coupling between the ATP hydrolysis site, the lever movement and the binding affinity for their track, which allows them to perform efficient stepping. Here we explore the minimal requirements for directed motility based on simpler schemes in which the binding/unbinding from the track is decoupled from the ATPase cycle. We show that a directed power stroke alone is not sufficient for motility, but combined with an asymmetry in force-induced unbinding rates it can generate stepping. The energetic efficiency of such stepping is limited to approximately 20%. We conclude that the allosteric coupling between the ATP hydrolysis and the track binding is not strictly necessary for motility, but it greatly improves its efficiency.

Angular measurements of the dynein ring reveal a stepping mechanism dependent on a flexible stalk

The force-generating mechanism of dynein differs from the force-generating mechanisms of other cytoskeletal motors. To examine the structural dynamics of dynein's stepping mechanism in real time, we used polarized total internal reflection fluorescence microscopy with nanometer accuracy localization to track the orientation and position of single motors. By measuring the polarized emission of individual quantum nanorods coupled to the dynein ring, we determined the angular position of the ring and found that it rotates relative to the microtubule (MT) while walking. Surprisingly, the observed rotations were small, averaging only 8.3°, and were only weakly correlated with steps. Measurements at two independent labeling positions on opposite sides of the ring showed similar small rotations. Our results are inconsistent with a classic power-stroke mechanism, and instead support a flexible stalk model in which interhead strain rotates the rings through bending and hinging of the stalk. Mechanical compliances of the stalk and hinge determined based on a 3.3-μs molecular dynamics simulation account for the degree of ring rotation observed experimentally. Together, these observations demonstrate that the stepping mechanism of dynein is fundamentally different from the stepping mechanisms of other well-studied MT motors, because it is characterized by constant small-scale fluctuations of a large but flexible structure fully consistent with the variable stepping pattern observed as dynein moves along the MT.

Modelling biomacromolecular assemblies with continuum mechanics

We have developed a continuum mechanical description of proteins using a finite element algorithm which has been generalized to include thermal fluctuations and which is therefore known as fluctuating finite element analysis (FFEA). Whereas conventional molecular dynamics (MD) simulations provide a trajectory in which each individual atomic position fluctuates, a FFEA trajectory shows how the overall shape of the protein changes due to thermal agitation. We describe the theoretical background to FFEA, its relationship to more established biomolecular modelling methods and provide examples of its application to the mesoscale biomolecular dynamics of the molecular motor dynein.