Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics

On the Control of Directionality of Myosin

The origin of the unique directionality of myosin has been a problem of fundamental and practical importance. This work establishes in a conclusive way that the directionality is controlled by tuning the barrier for the rate-determining step, namely, the ADP release step. This conclusion is based on exploring the molecular origin behind the reverse directionality of myosins V and VI and the determination of the origin of the change in the barriers of the ADP release for the forward and backward motions. Our investigation is performed by combining different simulation methods such as steer molecular dynamics (SMD), umbrella sampling, renormalization method, and automated path searching method. It is found that in the case of myosin V, the ADP release from the postrigor (trailing head) state overcomes a lower barrier than the prepowerstroke (leading head) state, which is also evident from experimental observation. In the case of myosin VI, we noticed a different trend when compared to myosin V. Since the directionality of myosins V and VI follows a reverse trend, we conclude that such differences in the directionality are controlled by the free energy barrier for the ADP release. Overall, the proof that the directionality of myosin is determined by the activation barrier of the rate-determining step in the cycle, rather than by some unspecified dynamical effects, has general importance.

Limits on the Precision of Catenane Molecular Motors: Insights from Thermodynamics and Molecular Dynamics Simulations

Thermodynamic uncertainty relations (TURs) relate precision to the dissipation rate, yet the inequalities can be far from saturation. Indeed, in catenane molecular motor simulations, we record precision far below the TUR limit. We further show that this inefficiency can be anticipated by four physical parameters: the thermodynamic driving force, fuel decomposition rate, coupling between fuel decomposition and motor motion, and rate of undriven motor motion. The physical insights might assist in designing molecular motors in the future.

Error-Controlled Coarse-Graining Dynamics with Mean-Field Randomization

In order to comprehend the stochastic behavior of biological systems, it is essential to accurately infer the dynamics of chemical reaction networks. However, computation of the likelihood remains a bottleneck. In this study, we propose the mean-field randomization procedure as a means of efficiently generating error-controlled coarse-graining dynamics. The error is measured by mutual information between the generated trajectories and the coarse-graining procedure. We demonstrate that the exact dynamics can be recovered by resampling, which eliminates the correlation between the dynamics and the procedure. We developed three algorithms to efficiently generate exact or coarse-graining trajectories within a specified error range. By subjecting our algorithms to testing on chemical reaction systems of varying complexities and scales, we observe that they outperform existing state-of-the-art algorithms, and the efficiency of coarse-graining trajectory generation is only weakly dependent on system scales.

Nonequilibrium design strategies for functional colloidal assemblies

We use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

Sterically driven current reversal in a molecular motor model

Simulations can help unravel the complicated ways in which molecular structure determines function. Here, we use molecular simulations to show how slight alterations of a molecular motor's structure can cause the motor's typical dynamical behavior to reverse directions. Inspired by autonomous synthetic catenane motors, we study the molecular dynamics of a minimal motor model, consisting of a shuttling ring that moves along a track containing interspersed binding sites and catalytic sites. The binding sites attract the shuttling ring while the catalytic sites speed up a reaction between molecular species, which can be thought of as fuel and waste. When that fuel and waste are held in nonequilibrium steady-state concentrations, the free energy from the reaction drives directed motion of the shuttling ring along the track. Using this model and nonequilibrium molecular dynamics, we show that the shuttling ring's direction can be reversed by simply adjusting the spacing between binding and catalytic sites on the track. We present a steric mechanism behind the current reversal, supported by kinetic measurements from the simulations. These results demonstrate how molecular simulation can guide future development of artificial molecular motors.

A [3]-catenane non-autonomous molecular motor model: Geometric phase, no-pumping theorem, and energy transduction

We study a model of a synthetic molecular motor-a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one-subjected to time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space, which corrects previous erroneous results. We also analyze the performance of the motor subjected to step-wise driving protocols in the absence and presence of an applied load. Optimization strategies for generating large currents and maximizing free energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization.

Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics - rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self-assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states' population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.

Chemical fuels for molecular machinery

Chemical reaction networks that transform out-of-equilibrium 'fuel' to 'waste' are the engines that power the biomolecular machinery of the cell. Inspired by such systems, autonomous artificial molecular machinery is being developed that functions by catalysing the decomposition of chemical fuels, exploiting kinetic asymmetry to harness energy released from the fuel-to-waste reaction to drive non-equilibrium structures and dynamics. Different aspects of chemical fuels profoundly influence their ability to power molecular machines. Here we consider the structure and properties of the fuels that biology has evolved and compare their features with those of the rudimentary synthetic chemical fuels that have so far been used to drive autonomous non-equilibrium molecular-level dynamics. We identify desirable, but context-specific, traits for chemical fuels together with challenges and opportunities for the design and invention of new chemical fuels to power synthetic molecular machinery and other dissipative nanoscale processes.

Sample size dependence of tagged molecule dynamics in steady-state networks with bimolecular reactions: Cycle times of a light-driven pump

Here, steady-state reaction networks are inspected from the viewpoint of individual tagged molecules jumping among their chemical states upon the occurrence of reactive events. Such an agent-based viewpoint is useful for selectively characterizing the behavior of functional molecules, especially in the presence of bimolecular processes. We present the tools for simulating the jump dynamics both in the macroscopic limit and in the small-volume sample where the numbers of reactive molecules are of the order of few units with an inherently stochastic kinetics. The focus is on how an ideal spatial "compartmentalization" may affect the dynamical features of the tagged molecule. Our general approach is applied to a synthetic light-driven supramolecular pump composed of ring-like and axle-like molecules that dynamically assemble and disassemble, originating an average ring-through-axle directed motion under constant irradiation. In such an example, the dynamical feature of interest is the completion time of direct/inverse cycles of tagged rings and axles. We find a surprisingly strong robustness of the average cycle times with respect to the system's size. This is explained in the presence of rate-determining unimolecular processes, which may, therefore, play a crucial role in stabilizing the behavior of small chemical systems against strong fluctuations in the number of molecules.