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

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.

A light-operated integrated DNA walker-origami system beyond bridge burning

Integrating rationally designed DNA molecular walkers and DNA origami platforms is a promising route towards advanced nano-robotics of diverse functions. Unleashing the full potential in this direction requires DNA walker-origami systems beyond the present simplistic bridge-burning designs for automated repeatable operation and scalable nano-robotic functions. Here we report such a DNA walker-origami system integrating an advanced light-powered DNA bipedal walker and a ∼170 nm-long rod-like DNA origami platform. This light-powered walker is fully qualified as a genuine translational molecular motor, and relies entirely on pure mechanical effects that are complicated by the origami surface but must be preserved for the walker's proper operation. This is made possible by tailor-designing the origami for optimal match with the walker to best preserve its core mechanics. A new fluorescence method is combined with site-controlled motility experiments to yield distinct and reliable signals for the walker's self-directed and processive motion despite origami-complicated fluorophore emission. The resultant integrated DNA walker-origami system provides a 'seed' system for future development of advanced light-powered DNA nano-robots (e.g., for scalable walker-automated chemical synthesis), and also truly bio-mimicking nano-muscles powered by genuine artificial translational molecular motors.

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.

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.

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.

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.

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.

How Well Can DNA Rupture DNA? Shearing and Unzipping Forces inside DNA Nanostructures

A purely DNA nanomachine must support internal stresses across short DNA segments with finite rigidity, producing effects that can be qualitatively very different from experimental observations of isolated DNA in fixed-force ensembles. In this article, computational simulations are used to study how well the rigidity of a driving DNA duplex can rupture a double-stranded DNA target into single-stranded segments and how well this stress can discriminate between unzipping or shearing geometries. This discrimination is found to be maximized at an optimal length but deteriorates as the driving duplex is either lengthened or shortened. This differs markedly from a fixed-force ensemble and has implications for the design parameters and limitations of dynamic DNA 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.

Comprehensive physical mechanism of two-headed biomotor myosin V

Two-headed biomotor myosin V autonomously coordinates its two identical heads in fuel consumption and mechanical stepping, so that the dimerized motor as a whole gains the capability of processive, unidirectional movement along cytoskeletal filament. How the dimer-level functions like sustained direction rectification and autonomous coordination emerge out of physical principles poses an outstanding question pertinent to motor protein biology as well as the nascent field of bioinspired nanomotors. Here the comprehensive physical mechanism for myosin V motor is identified by a dimer-level free-energy analysis that is methodologically calibrated against experimental data. A hallmark of the identified mechanism is a mechanically mediated symmetry breaking that occurs at the dimer level and prevails against ubiquitous thermal fluctuations. Another character is the onset of substantial free-energy gaps between major dimer-track binding configurations. The symmetry breaking is the basis for myosin V's directional rectification, and the energy gaps facilitate autonomous head-head coordination. The mechanism explains the experimental finding that myosin V makes ATP-independent consecutive steps under high opposing loads but not under pushing loads. Interestingly, myosin V and another major biomotor kinesin 1 are found to share essentially the same core mechanism but for distinctly different working regimes.

The intrinsic load-resisting capacity of kinesin

Conventional kinesin is a homodimeric motor protein that is capable of walking unidirectionally along a cytoskeletal filament. While previous experiments indicated unyielding unidirectionality against an opposing load up to the so-called stall force, recent experiments also observed limited processive backwalking under superstall loads. This theoretical study seeks to elucidate the molecular mechanical basis for kinesin's steps over the full range of external loads that can possibly be applied to the dimer. We found that kinesin's load-resisting capacity is largely determined by a synergic ratchet-and-pawl mechanism inherent in the dimer. Load susceptibility of this inner molecular mechanical mechanism underlies kinesin's response to various levels of external loads. Computational implementation of the mechanism enabled us to rationalize major trends observed experimentally in kinesin's stalemate and consecutive back steps. The study also predicts several distinct features of kinesin's load-affected motility, which are seemingly counterintuitive but readily verifiable by future experiment.