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

Muscle myosin is a non-processive molecular motor that 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.

Oscillating external force as a tool to tune motility characteristics of molecular motors.

Molecular motors move in a dynamic environment of the cytoskeleton which generates fluctuations exceeding the thermal agitation. Their efficient motility and force generation are generally achieved via complex gating and coupling mechanisms between chemical steps, conformational changes, and mechanical steps in the working cycle. However, the motors display various force-velocity relations seemingly related (also) to the asymmetry of their unbinding from the track depending on the direction of the applied force. Here we study theoretically how the motility of molecular motors changes when they operate under an oscillating external force. We explore the roles of the shape of the force-velocity relation and the asymmetry of the force-induced unbinding. We find that a motor speeds up under force oscillations if its unbinding has a strong load dependence and a moderate asymmetry with respect to the direction of load. Motors whose unbinding is slowed down under hindering forces withstand average loads higher than the usual stall force. The relation between the function, unbinding properties, and predicted responses to the oscillating force supports the idea that the asymmetry of the load induced unbinding could serve as an adaptation of motors to their different physiological functions.

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.

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

Cytoplasmic dynein moves processively along microtubules, but the mechanism of how its heads use the energy from ATP hydrolysis, coupled to a linker swing, to achieve directed motion, is still unclear. In this article, we present a theoretical model based on the winch mechanism in which the principal direction of the linker stroke is toward the microtubule-binding domain. When mechanically coupling two identical heads (each with postulated elastic properties and a minimal ATPase cycle), the model reproduces stepping with 8-nm steps (even though the motor itself is much larger), interhead coordination, and processivity, as reported for mammalian dyneins. Furthermore, when we loosen the elastic connection between the heads, the model still shows processive directional stepping, but it becomes uncoordinated and the stepping pattern shows a greater variability, which reproduces the properties of yeast dyneins. Their slower chemical kinetics allows processive motility and a high stall force without the need for coordination.

Spin models for orientational ordering of colloidal molecular crystals.

Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred to as molecules. Using the strength of the potential and the filling fraction as control parameters, a phase transition to unconventional orientationally ordered states can be induced. We introduce an approach that focuses at the discrete set of orientational states relevant for the phase ordering. The orientationally ordered states are mapped to classical spin systems. We construct effective Hamiltonians for dimeric and trimeric molecules on triangular lattices suitable for a statistical mechanics discussion. A mean-field analysis produces a rich phase behavior which is substantiated by Monte Carlo simulations.