Extract Motive Energy from Single-Molecule Trajectories.

Single-molecule trajectories from nonequilibrium unfolding experiments are widely used to recover a biomolecule's intrinsic free-energy profile. Trajectories of molecular motors from similar single-molecule experiments may be mapped to biased diffusion over an inclined free-energy profile. Such an effective potential is not a static equilibrium property anymore, and how it can benefit molecular motor study is unclear. Here, we introduce a method to deduce this effective potential from motor trajectories with realistic temporal-spatial resolution and find that the potential yields a motor's stall force─a quantity that not only characterizes a motor's force-generating capacity but also largely determines its energy efficiency. Interestingly, this potential allows the extraction of a motor's stall force from trajectories recorded at a single resisting force or even zero force, as verified with trajectories from two molecular motor models and also experimental trajectories from a real artificial motor. This finding drastically reduces the difficulty of stall force measurement, making it accessible even to force-incapable optical tracking experiments (commonly regarded as irrelevant to stall force determination). This study further provides a method for experimentally measuring a second-law-decreed least energy price for submicroscopic directionality─a previously elusive but thermodynamically important quantity pertinent to efficient energy conversion of molecular motors.

Diffusion Biased by a Soft Neck Linker Regulates Kinesin Stepping.

Conventional kinesin is a high-performance motor that moves primarily toward the plus end of microtubules and occasionally toward the opposite direction. The physical mechanism of this directional stepping remains unclear. Here we develop a kinetic two-cycle model incorporating kinesin forward and backward stepping, in which the neck linker zippering and ATP catalysis process are conserved in backward steps. This model is quantitatively validated by a variety of experimental data, including load dependence of velocity, stepping ratio, and dwell time. The physical mechanism of kinesin stepping regulated by a biased diffusion process is identified by analyzing the load dependence and relevant thermodynamic properties of the model. Furthermore, the model suggests the kinesin directionality is optimized resulting from fulfilling a thermodynamic constraint. Our modeling provides a chemomechanical coupling mechanism that connects the flexibility of the neck linker zippering effect for direction rectification and the measured performance into a consistent frame.

Thermodynamic marking of FOF1 ATP synthase.

FOF1 ATP synthase is a ~100% efficient molecular machine for energy conversion in biology, and holds great lessons for man-made energy technology and nanotechnology. In light of formidable biocomplexity of the FOF1 machinery, its modeling from pure physical principles remains difficult and rare. Here we construct a thermodynamic model of FOF1 from experimentally accessible quantities plus a single entropy production that generally has vanishingly small values (<1kB). Based on the physical inputs, this model captures FOF1 performance observed over an exhaustively wide range of proton-motive force and nucleotide concentrations. The model predicts a distinct 1/8kBT slope for ATP synthesis rate versus proton-motive force, which is verified by experimental data and represents a profound thermodynamic marking of this amazingly efficient machine operating near a universal limit of the 2nd law of thermodynamics. The model further predicts two symmetries of heat productions, which are testable by available experimental techniques and offer quantitative constraints on FOF1's possible mechanisms behind its ~100% efficiency.

Track-walking molecular motors: a new generation beyond bridge-burning designs.

Track-walking molecular motors are the core bottom-up mechanism for nanometre-resolved translational movements - a fundamental technological capability at the root of numerous applications ranging from nanoscale assembly lines and chemical synthesis to molecular robots and shape-changing materials. Over the last 10 years, artificial molecular walkers (or nanowalkers) have evolved from the 1st generation of bridge-burning designs to the 2nd generation capable of truly sustainable movements. Invention of non-bridge-burning nanowalkers was slow at first, but has picked up speed since 2012, and is now close to breaking major barriers for wide-spread development. Here we review the 2nd generation of artificial nanowalkers, which are mostly made of DNA molecules and draw energy from light illumination or from chemical fuels for entirely autonomous operation. They are typically symmetric dimeric motors walking on entirely periodic tracks, yet the motors possess an inherent direction for large-scale amplification of the action of many motor copies. These translational motors encompass the function of rotational molecular motors on circular or linear tracks, and may involve molecular shuttles as 'engine' motifs. Some rules of thumb are provided to help readers design similar motors from DNA or other molecular building blocks. Opportunities and challenges for future development are discussed, especially in the areas of molecular robotics and active materials based on the advanced motors.

Mechanical transduction via a single soft polymer.

Molecular machines from biology and nanotechnology often depend on soft structures to perform mechanical functions, but the underlying mechanisms and advantages or disadvantages over rigid structures are not fully understood. We report here a rigorous study of mechanical transduction along a single soft polymer based on exact solutions to the realistic three-dimensional wormlike-chain model and augmented with analytical relations derived from simpler polymer models. The results reveal surprisingly that a soft polymer with vanishingly small persistence length below a single chemical bond still transduces biased displacement and mechanical work up to practically significant amounts. This "soft" approach possesses unique advantages over the conventional wisdom of rigidity-based transduction, and potentially leads to a unified mechanism for effective allosterylike transduction and relay of mechanical actions, information, control, and molecules from one position to another in molecular devices and motors. This study also identifies an entropy limit unique to the soft transduction, and thereby suggests a possibility of detecting higher efficiency for kinesin motor and mutants in future experiments.

Polymer-Based Accurate Positioning: An Exact Worm-like-Chain Study.

Precise positioning of molecular objects from one location to another is important for nanomanipulation and is also involved in molecular motors. Here, we study single-polymer-based positioning on the basis of the exact solution to the realistic three-dimensional worm-like-chain (WLC) model. The results suggest the possibility of a surprisingly accurate flyfishing-like positioning in which tilting one end of a flexible short polymer enables positioning of the other diffusing end to a distant location within an error of ∼1 nm. This offers a new mechanism for designing molecular positioning devices. The flyfishing effect (and reverse process) likely plays a role in biological molecular motors and may be used to improve speed of artificial counterparts. To facilitate these applications, a new force-extension formula is obtained from the exact WLC solution. This formula has an improved accuracy over the widely used Marko-Siggia formula for stretched polymers and is valid for compressed polymers too. The new formula is useful in analysis of single-molecule stretching experiments and in estimating intramolecular forces of molecular motors, especially those involving both stretched and compressed polymer components.

Autonomous synergic control of nanomotors.

Control is a hallmark of machines; effective control over a nanoscale system is necessary to turn it into a nanomachine. Nanomotors from biology often integrate a ratchet-like passive control and a power-stroke-like active control, and this synergic active-plus-passive control is critical to efficient utilization of energy. It remains a challenge to integrate the two differing types of control in rationally designed nanomotor systems. Recently a light-powered track-walking DNA nanomotor was developed from a bioinspired design principle that has the potential to integrate both controls. However, it is difficult to separate experimental signals for either control due to a tight coupling of both controls. Here we present a systematic study of the motor and new derivatives using different fluorescence labeling schemes and light operations. The experimental data suggest that the motor achieves the two controls autonomously through a mechanics-mediated symmetry breaking. This study presents an experimental validation for the bioinspired design principle of mechanical breaking of symmetry for synergic ratchet-plus-power stroke control. Augmented by mechanical and kinetic modeling, this experimental study provides mechanistic insights that may help advance molecular control in future nanotechnological systems.

Role of directional fidelity in multiple aspects of extreme performance of the F(1)-ATPase motor.

Quantitative understanding of the best possible performance of nanomotors allowed by physical laws pertains to the study of nanomotors from biology as well as nanotechnology. The biological nanomotor F(1) ATPase is the best available model system as it is the only nanomotor known for extreme energy conversion near the limit of energy conservation. Using a unified theoretical framework centered on a concept called directional fidelity, we analyze recent experiments in which the F(1) motor's performance was measured for controlled chemical potentials and expose from the experiments quantitative evidence for the motor's multiple extreme performances in directional fidelity, speed, and catalytic capability close to physical limits. Specifically, the motor nearly exhausts the available energy from the fuel to retain the highest possible directional fidelity for an arbitrary load, encompassing the motor's extreme energy conversion and beyond. The theory-experiment comparison implies a tight chemomechanical coupling up to stalemate as futile steps occur, but unlikely involve fuel consumption. The F(1)-motor data also help clarify the relation between directional fidelity and experimentally measured stepping ratio.

Directional fidelity of nanoscale motors and particles is limited by the 2nd law of thermodynamics--via a universal equality.

Directional motion of nanoscale motors and driven particles in an isothermal environment costs a finite amount of energy despite zero work as decreed by the 2nd law, but quantifying this general limit remains difficult. Here we derive a universal equality linking directional fidelity of an arbitrary nanoscale object to the least possible energy driving it. The fidelity-energy equality depends on the environmental temperature alone; any lower energy would violate the 2nd law in a thought experiment. Real experimental proof for the equality comes from force-induced motion of biological nanomotors by three independent groups - for translational as well as rotational motion. Interestingly, the natural self-propelled motion of a biological nanomotor (F1-ATPase) known to have nearly 100% energy efficiency evidently pays the 2nd law decreed least energy cost for direction production.

Bipedal nanowalker by pure physical mechanisms.

Artificial nanowalkers are inspired by biomolecular counterparts from living cells, but remain far from comparable to the latter in design principles. The walkers reported to date mostly rely on chemical mechanisms to gain a direction; they all produce chemical wastes. Here we report a light-powered DNA bipedal walker based on a design principle derived from cellular walkers. The walker has two identical feet and the track has equal binding sites; yet the walker gains a direction by pure physical mechanisms that autonomously amplify an intrasite asymmetry into a ratchet effect. The nanowalker is free of any chemical waste. It has a distinct thermodynamic feature that it possesses the same equilibrium before and after operation, but generates a truly nonequilibrium distribution during operation. The demonstrated design principle exploits mechanical effects and is adaptable for use in other nanomachines.

A coordinated molecular 'fishing' mechanism in heterodimeric kinesin.

Kar3 is a kinesin motor that facilitates chromosome segregation during cell division. Unlike many members of the kinesin superfamily, Kar3 forms a heterodimer with non-motor protein Vik1 or Cik1 in vivo. The heterodimers show ATP-driven minus-end directed motility along a microtubule (MT) lattice, and also serve as depolymerase at the MT ends. The molecular mechanisms behind this dual functionality remain mysterious. Here, a molecular mechanical model for the Kar3/Vik1 heterodimer based on structural, kinetic and motility data reveals a long-range chemomechanical transmission mechanism that resembles a familiar fishing tactic. By this molecular 'fishing', ATP-binding to Kar3 dissociates catalytically inactive Vik1 off MT to facilitate minus-end sliding of the dimer on the MT lattice. When the dimer binds the frayed ends of MT, the fishing channels ATP hydrolysis energy into MT depolymerization by a mechanochemical effect. The molecular fishing thus provides a unified mechanistic ground for Kar3's dual functionality. The fishing-promoted depolymerization differs from the depolymerase mechanisms found in homodimeric kinesins. The fishing also enables intermolecular coordination with a chemomechanical coupling feature different from the paradigmatic pattern of homodimeric motors. This study rationalizes some puzzling experimental observation, and suggests new experiments for further elucidation of the fishing mechanism.

Modeling motility of the kinesin dimer from molecular properties of individual monomers.

Conventional kinesin is a homodimeric motor protein that unidirectionally transports organelles along filamentous microtubule (MT) by hydrolyzing ATP molecules. There remain two central questions in biophysical studies of kinesin: (1) the molecular physical mechanism by which the kinesin dimer, made of two sequentially identical monomers, selects a unique direction (MT plus end) for long-range transport and (2) the detailed mechanisms by which local molecular properties of individual monomers affect the motility properties of the dimer motor as a whole. On the basis of a previously proposed molecular physical model for the unidirectionality of kinesin, this study investigates the synergic motor performance of the dimer from well-defined molecular properties of individual monomers. During cargo transportation and also in single-molecule mechanical measurements, a load is often applied to the coiled-coil dimerization domain linking the two motor domains ("heads"). In this study, the share of load directly born by each head is calculated, allowing for an unambiguous estimation of load effects on the ATP turnover and random diffusion of individual heads. The results show that the load modulations of ATP turnover and head diffusion are both essential in determining the performance of the dimer under loads. It is found that the consecutive run length of the dimer critically depends upon a few pathways, leading to the detachment of individual heads from MT. Modifying rates for these detachment pathways changes the run length but not the velocity of the dimer, consistent with mutant experiments. The run length may increase with or without the ATP concentration, depending upon a single rate for pure mechanical detachment. This finding provides an explanation to a previous controversy concerning ATP dependence of the run length, and related quantitative predictions of this study can be tested by a future experiment. This study also finds that the experimental observations for assisting loads can be quantitatively explained by load-biased head diffusion. We thus conclude that the dimer motility under resisting as well as assisting loads is governed by essentially the same mechanisms.