Directional fidelity of nanoscale motors and particles is limited by the 2nd law of thermodynamics—Via a universal equality

Autonomous DNA molecular motor tailor-designed to navigate DNA origami surface for fast complex motion and advanced nanorobotics

Nanorobots powered by designed DNA molecular motors on DNA origami platforms are vigorously pursued but still short of fully autonomous and sustainable operation, as the reported systems rely on manually operated or autonomous but bridge-burning molecular motors. Expanding DNA nanorobotics requires origami-based autonomous non-bridge-burning motors, but such advanced artificial molecular motors are rare, and their integration with DNA origami remains a challenge. Here, we report an autonomous non-bridge-burning DNA motor tailor-designed for a triangle DNA origami substrate. This is a translational bipedal molecular motor but demonstrates effective translocation on both straight and curved segments of a self-closed circular track on the origami, including sharp ~90° turns by a single hand-over-hand step. The motor is highly directional and attains a record-high speed among the autonomous artificial molecular motors reported to date. The resultant DNA motor-origami system, with its complex translational-rotational motion and big nanorobotic capacity, potentially offers a self-contained "seed" nanorobotic platform to automate or scale up many applications.

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.

Analytical Decomposition of Transition Flux to Cycle Durations via Integration of Transition Times

Rigorous methods of decomposing kinetic networks to cycles are available, but the solutions usually contain entangled transition rates, which are difficult to analyze. This study proposes a new method of decomposing net transition flux to cycle durations, and the duration of each cycle is an integration of the transition times along the cycle. The method provides a series of neat dependences from the basic kinetic variables to the final flux, which support direct analysis based on the formulas. An assisting transformation diagram from symmetric conductivity to asymmetric conductivity is provided, which largely simplifies the application of the method. The method is likely a useful analytical tool for many studies relevant to kinetics and networks. Applications of the method shall provide new kinetic and thermodynamic information for the studied system.

A high-fidelity light-powered nanomotor from a chemically fueled counterpart via site-specific optomechanical fuel control

Optically powered nanomotors are advantageous for clean nanotechnology over chemically fuelled nanomotors. The two motor types are further bounded by different physical principles. Despite the gap, we show here that an optically powered DNA bipedal nanomotor is readily created from a high-performing chemically fuelled counterpart by subjecting its fuel to cyclic site-specific optomechanical control - as if the fuel is optically recharged. Optimizing azobenzene-based control of the original nucleotide fuel selects a light-responsive fuel analog that replicates the different binding affinity of the fuel and reaction products. The resultant motor largely retains high-performing features of the original chemical motor, and achieves the highest directional fidelity among reported light-driven DNA nanomotors. This study thus demonstrates a novel strategy for transforming chemical nanomotors to optical ones for clean nanotechnology. The strategy is potentially applicable to many chemical nanomotors with oligomeric fuels like nucleotides, peptides and synthetic polymers, leading to a new class of light-powered nanomotors that are akin to chemical nanomotors and benefit from their generally high efficiency mechanistically. The motor from this study also provides a rare model system for studying the subtle boundary between chemical and optical nanomotors - a topic pertinent to chemomechanical and optomechanical energy conversion at the single-molecule level.

Single-molecule mechanical study of an autonomous artificial translational molecular motor beyond bridge-burning design

A key capability of molecular motors is sustainable force generation by a single motor copy. Direct force characterization at the single-motor level is still missing for artificial molecular motors, though long reported for their biological counterparts. Here we report single-molecule detection of sustained force-generating motility for an artificial track-walking molecular motor capable of autonomous chemically fueled operation. A single motor plus its track (both made of deoxyribonucleic acids or DNA) is assembled, operated and detected under magnetic tweezers by a method designed to overcome difficulty from the motor's soft double-stranded track. The motor shows self-directed walking by ∼16 nm steps up to a distance of 120 nm (covering the entire track), yielding a stall force of ∼2-3 pN. These results imply a reasonably efficient chemomechanical conversion of the motor compared to a high-efficiency biomotor. The stall force is near the level of translational biomotors powering human muscles and allows similar force-demanding applications by their artificial counterparts. This single-motor study reveals fast subsecond steps, suggesting big room for improvement in the speed of DNA motors in general. Besides, the established single-molecule method is applicable to force measurements of many other DNA motors with soft tracks.

Thermodynamic marking of FOF1 ATP synthase

F_OF₁ 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 F_OF₁ machinery, its modeling from pure physical principles remains difficult and rare. Here we construct a thermodynamic model of F_OF₁ from experimentally accessible quantities plus a single entropy production that generally has vanishingly small values (<1k_B). Based on the physical inputs, this model captures F_OF₁ performance observed over an exhaustively wide range of proton-motive force and nucleotide concentrations. The model predicts a distinct 1/8k_BT 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 F_OF₁'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.

Generic maps of optimality reveal two chemomechanical coupling regimes for motor proteins: from F1-ATPase and kinesin to myosin and cytoplasmic dynein

Many motor proteins achieve high efficiency for chemomechanical conversion, and single-molecule force-resisting experiments are a major tool to detect the chemomechanical coupling of efficient motors. Here, we introduce several quantitative relations that involve only parameters extracted from force-resisting experiments and offer new benchmarks beyond mere efficiency to judge the chemomechanical optimality or deficit of evolutionary remote motors on the same footing. The relations are verified by the experimental data from F₁-ATPase, kinesin-1, myosin V and cytoplasmic dynein, which are representative members of four motor protein families. A double-fitting procedure yields the chemomechanical parameters that can be cross-checked for consistency. Using the extracted parameters, two generic maps of chemomechanical optimality are constructed on which motors across families can be quantitatively compared. The maps reveal two chemomechanical coupling regimes, one conducive to high efficiency and high directionality, and the other advantageous to force generation. Surprisingly, an F₁ rotor and a kinesin-1 walker belong to the first regime despite their obvious evolutionary gap, while myosin V and cytoplasmic dynein follow the second regime. This analysis also predicts the symmetries of directional biases and heat productions for the motors, which impose constraints on their chemomechanical coupling and are open to future experimental tests. The verified relations, six in total, present a unified fitting framework to analyze force-resisting experiments. The generic maps of optimality, to which many more motors can be added in future, provide a rigorous method for a systematic cross-family comparison of motors to expose their evolutionary connections and mechanistic similarities.

Inchworm bipedal nanowalker

Nanowalkers take either inchworm (IW) or hand-over-hand (HOH) gait. The IW nanowalkers are advantageous over HOH ones in force generation, processivity and high-density integration, though both gaits occur in intracellular nanowalkers from biology. Artificial IW nanowalkers have been realized or proposed, but all rely on different 'head' and 'tail' to gain an adventitious direction. Here we report an inherently unidirectional IW nanowalker that is a biped with two identical legs (i.e., indistinguishable 'head' and 'tail'). This walker is made of DNA, and driven by a light-powered G-quadruplex engine. The directional inchworm motion is confirmed by operating the walker on a DNA duplex track that is designed to show a distinctive fluorescence pattern for IW walkers as compared to HOH ones. Interestingly, this walker exhibits stride-controlled IW-to-HOH gait switch and direction reversal when the track's periodic binding sites have wider and wider separation. The results altogether present an integrated mechanism for implementing nanowalkers of different gaits and directions on molecular tracks, optical potentials or even solid-state surfaces.

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.

A DNA bipedal nanowalker with a piston-like expulsion stroke

Artificial molecular walkers beyond burn-bridge designs are important for nanotechnology, but their systematic development remains difficult. Herein, we have reported a new rationally designed DNA walker-track system and experimentally verified a previously proposed general expulsion regime for implementing non-burn-bridge nanowalkers. The DNA walker has an optically powered engine motif that reversibly extends and contracts the walker via a quadruplex-duplex conformational change. The walker's extension is an energy-absorbing and force-generating process, which drives the walker's leg dissociation off-track in a piston-like expulsion stroke. The unzipping-shearing asymmetry provides the expulsion stroke a bias, which decides the direction of the walker. Moreover, three candidate walkers of different sizes were fabricated. Fluorescence motility experiments indicated two of them as successful walkers and revealed a distinctive size dependence that was expected for these expulsive walkers, but was not observed in previously reported walkers. This study identifies unique technical requirements for expulsive nanowalkers. The present DNA design is readily adapted for making similar walkers from other molecules since the unzipping-shearing asymmetry is common.

Autonomous rotor heat engine

The triumph of heat engines is their ability to convert the disordered energy of thermal sources into useful mechanical motion. In recent years, much effort has been devoted to generalizing thermodynamic notions to the quantum regime, partly motivated by the promise of surpassing classical heat engines. Here, we instead adopt a bottom-up approach: we propose a realistic autonomous heat engine that can serve as a test bed for quantum effects in the context of thermodynamics. Our model draws inspiration from actual piston engines and is built from closed-system Hamiltonians and weak bath coupling terms. We analytically derive the performance of the engine in the classical regime via a set of nonlinear Langevin equations. In the quantum case, we perform numerical simulations of the master equation. Finally, we perform a dynamic and thermodynamic analysis of the engine's behavior for several parameter regimes in both the classical and quantum case and find that the latter exhibits a consistently lower efficiency due to additional noise.

Biomimetic Autonomous Enzymatic Nanowalker of High Fuel Efficiency

Replicating efficient chemical energy utilization of biological nanomotors is one ultimate goal of nanotechnology and energy technology. Here, we report a rationally designed autonomous bipedal nanowalker made of DNA that achieves a fuel efficiency of less than two fuel molecules decomposed per productive forward step, hence breaking a general threshold for chemically powered machines invented to date. As a genuine enzymatic nanomotor without changing itself nor the track, the walker demonstrates a sustained motion on an extended double-stranded track at a speed comparable to previous burn-bridge motors. Like its biological counterparts, this artificial nanowalker realizes multiple chemomechanical gatings, especially a bias-generating product control unique to chemically powered nanomotors. This study yields rich insights into how pure physical effects facilitate harvest of chemical energy at the single-molecule level and provides a rarely available motor system for future development toward replicating the efficient, repeatable, automatic, and mechanistically sophisticated transportation seen in biomotor-based intracellular transport but beyond the capacity of the current burn-bridge motors.

From bistate molecular switches to self-directed track-walking nanomotors

Track-walking nanomotors and larger systems integrating these motors are important for wide real-world applications of nanotechnology. However, inventing these nanomotors remains difficult, a sharp contrast to the widespread success of simpler switch-like nanodevices, even though the latter already encompasses basic elements of the former such as engine-like bistate contraction/extension or leg-like controllable binding. This conspicuous gap reflects an impeding bottleneck for the nanomotor development, namely, lack of a modularized construction by which spatially and functionally separable "engines" and "legs" are flexibly assembled into a self-directed motor. Indeed, all track-walking nanomotors reported to date combine the engine and leg functions in the same molecular part, which largely underpins the device-motor gap. Here we propose a general design principle allowing the modularized nanomotor construction from disentangled engine-like and leg-like motifs, and provide an experimental proof of concept by implementing a bipedal DNA nanomotor up to a best working regime of this versatile design principle. The motor uses a light-powered contraction-extension switch to drive a coordinated hand-over-hand directional walking on a DNA track. Systematic fluorescence experiments confirm the motor's directional motion and suggest that the motor possesses two directional biases, one for rear leg dissociation and one for forward leg binding. This study opens a viable route to develop track-walking nanomotors from numerous molecular switches and binding motifs available from nanodevice research and biology.

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.