General mechanism for inchworm nanoscale track walkers: Analytical theory and realistic simulation

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.

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.

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.

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.

Perspective: nanomotors without moving parts that propel themselves in solution

Self-propelled nanomotors use chemical energy to produce directed motion. Like many molecular motors they suffer strong perturbations from the environment in which they move as a result of thermal fluctuations and do not rely on inertia for their propulsion. Such tiny motors are the subject of considerable research because of their potential applications, and a variety of synthetic motors have been made and are being studied for this purpose. Chemically powered self-propelled nanomotors without moving parts that rely on asymmetric chemical reactions to effect directed motion are the focus of this article. The mechanisms they use for propulsion, how size and fuel sources influence their motion, how they cope with strong molecular fluctuations, and how they behave collectively are described. The practical applications of such nanomotors are largely unrealized and the subject of speculation. Since molecular motors are ubiquitous in biology and perform a myriad of complex tasks, the hope is that synthetic motors might be able to perform analogous tasks. They may have the potential to change our perspective on how chemical dynamics takes place in complex systems.

Dynamics of a polymer in a Brownian ratchet

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

Nonadiabatic simulation study of photoisomerization of azobenzene: detailed mechanism and load-resisting capacity

Nonadiabatic dynamical simulations were carried out to study cis-to-trans isomerization of azobenzene under laser irradiation and/or external mechanical loads. We used a semiclassical electron-radiation-ion dynamics method that is able to describe the coevolution of the structural dynamics and the underlying electronic dynamics in a real-time manner. It is found that azobenzene photoisomerization occurs predominantly by an out-of-plane rotation mechanism even under a nontrivial resisting force of several tens of piconewtons. We have repeated the simulations systematically for a broad range of parameters for laser pulses, but could not find any photoisomerization event by a previously suggested in-plane inversion mechanism. The simulations found that the photoisomerization process can be held back by an external resisting force of 90-200 pN depending on the frequency and intensity of the lasers. This study also found that a pure mechanical isomerization is possible from the cis-to-trans state if the azobenzene molecule is stretched by an external force of approximately 1250-1650 pN. Remarkably, the mechanical isomerization first proceeds through a mechanically activated inversion, and then is diverted to an ultrafast downhill rotation that accomplishes the isomerization. Implications of these findings to azobenzene-based nanomechanical devices are discussed.

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.