Cooperative effects enhance the transport properties of molecular spider teams

Molecular spiders are synthetic molecular motors based on DNA nanotechnology. While natural molecular motors have evolved towards very high efficiency, it remains a major challenge to develop efficient designs for man-made molecular motors. Inspired by biological motor proteins such as kinesin and myosin, molecular spiders comprise a body and several legs. The legs walk on a lattice that is coated with substrate which can be cleaved catalytically. We propose a molecular spider design in which n spiders form a team. Our theoretical considerations show that coupling several spiders together alters the dynamics of the resulting team significantly. Although spiders operate at a scale where diffusion is dominant, spider teams can be tuned to behave nearly ballistic, which results in fast and predictable motion. Based on the separation of time scales of substrate and product dwell times, we develop a theory which utilizes equivalence classes to coarse-grain the microstate space. In addition, we calculate diffusion coefficients of the spider teams, employing a mapping of an n-spider team to an n-dimensional random walker on a confined lattice. We validate these results with Monte Carlo simulations and predict optimal parameters of the molecular spider team architecture which makes their motion most directed and maximally predictable

Molecular Spiders in One Dimension

Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are established between various models of spiders and simple exclusion processes. For spiders with simple gait and varying number of legs we compute the diffusion coefficient; when the hopping is biased we also compute their velocity.Comment: 14 pages, 2 figure

Abstract Models of Molecular Walkers

Recent advances in single-molecule chemistry have led to designs for artificial multi-pedal walkers that follow tracks of chemicals. The walkers, called molecular spiders, consist of a rigid chemically inert body and several flexible enzymatic legs. The legs can reversibly bind to chemical substrates on a surface, and through their enzymatic action convert them to products. We study abstract models of molecular spiders to evaluate how efficiently they can perform two tasks: molecular transport of cargo over tracks and search for targets on finite surfaces. For the single-spider model our simulations show a transient behavior wherein certain spiders move superdiffusively over significant distances and times. This gives the spiders potential as a faster-than-diffusion transport mechanism. However, analysis shows that single-spider motion eventually decays into an ordinary diffusive motion, owing to the ever increasing size of the region of products. Inspired by cooperative behavior of natural molecular walkers, we propose a symmetric exclusion process (SEP) model for multiple walkers interacting as they move over a one-dimensional lattice. We show that when walkers are sequentially released from the origin, the collective effect is to prevent the leading walkers from moving too far backwards. Hence, there is an effective outward pressure on the leading walkers that keeps them moving superdiffusively for longer times. Despite this improvement the leading spider eventually slows down and moves diffusively, similarly to a single spider. The slowdown happens because all spiders behind the leading spiders never encounter substrates, and thus they are never biased. They cannot keep up with leading spiders, and cannot put enough pressure on them. Next, we investigate search properties of a single and multiple spiders moving over one- and two-dimensional surfaces with various absorbing and reflecting boundaries. For the single-spider model we evaluate by how much the slowdown on newly visited sites, owing to catalysis, can improve the mean first passage time of spiders and show that in one dimension, when both ends of the track are an absorbing boundary, the performance gain is lower than in two dimensions, when the absorbing boundary is a circle; this persists even when the absorbing boundary is a single site. Next, we study how multiple molecular spiders influence one another during the search. We show that when one spider reaches the trace of another spider it is more likely not to follow the trace and instead explore unvisited sites. This interaction between the spiders gives them an advantage over independent random walkers in a search for multiple targets. We also study how efficiently the spiders with various gaits are able to find specific targets. Spiders with gaits that allow more freedom of leg movement find their targets faster than spiders with more restrictive gaits. For every gait, there is an optimal detachment rate that minimizes the time to find all target sites

Multivalent Random Walkers:A computational model of superdiffusive transport at the nanoscale

We present a stochastic model and numerical simulation framework for a synthetic nanoscale walker that can be used to transport materials and information at superdiffusive rates in artificial molecular systems. Our \emph{multivalent random walker} model describes the motion of a walker with a rigid, inert body and flexible, enzymatic legs. A leg can bind to and irreversibly modify surface-bound chemical substrate sites arranged as nanoscale tracks. As the legs attach to, modify, and detach from the sites, the walker moves along these tracks. Walkers are symmetrical and the tracks they walk on are unoriented, yet we show that under appropriate kinetic constraints the walkers can transform the chemical free energy in the surface sites into directional motion, and can do ordered work against an external load force. This shows that multivalent random walkers are a new type of molecular motor, useful for directional transport in nanoscale systems. We model the motion of multivalent random walkers as a continuous-time discrete-state Markov process. States in the process correspond to the chemical state of the legs and surface sites, and transitions represent discrete chemical changes of legs binding to, unbinding from, and modifying the surface sites. The Markov property holds because we let the mechanical motion of the body and unattached legs come to equilibrium in between successive chemical steps, thus the transitions depend only on the current chemical state of the surface sites and attached legs. This coarse-grained model of walker motion allows us to use both equilibrium and non-equilibrium Markov chain Monte Carlo simulation techniques. The Metropolis-Hastings algorithm approximates the motion of a walker\u27s body and legs at a mechanical equilibrium, while the kinetic Monte Carlo algorithm simulates the transient chemical dynamics of the walker stepping across the surface sites. Using these numerical techniques, we find that MVRWs move superdiffusively in the direction of unmodified substrate sites when there is a residence time bias between modified and unmodified sites. This superdiffusive motion persists when opposed by external load forces, showing that multivalent random walkers are \emph{molecular motors} that can transform chemical free energy into ordered mechanical work. To produce these results we devised a distributed object-oriented framework for parallel simulation and analysis of the MVRW model. We use an object-relational mapping to persistently maintain all simulation-related objects as tuples in a relational database. We present a new object-relational mapping technique called the \emph{natural entity framework} which disambiguates the semantics of object identity and uniqueness in the relational and object-oriented programming models. Using the natural entity framework we are able to guarantee the uniqueness of mappings between data stored as objects in the relational database and external data stored in non-transactionally-secured HDF5 data files

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the non-interacting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.Comment: 19 pages, 22 figure

Spider walk in a random environment

ABSTRACT We analyze a random process in a random media modeling the motion of DNA nanomechanical walking devices. We consider a molecular spider restricted to a well-dened one-dimensional track and study its asymptotic behavior in an i. i. d. random environment. The spider walk is a continuous time motion of a finite ensemble of particles on the integer lattice with the jump rates determined by the environment. The particles mutual location must belong to a given finite set of congurations L; and the motion can be alternatively described as a random walk on the ladder graph Z x L in a stationary and ergodic environment. Our main result is an annealed central limit theorem for this process. We believe that the conditions of the theorem are close to necessary

Modelling and engineering artificial burnt-bridge ratchet molecular motors

Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridge ratchet (BBR) is one mechanism used to accomplish superdiffusive motion over long distances via the successive cleavage of surface-bound energy-rich substrate sites. The BBR mechanism is utilized throughout Nature: it can be found in bacteria, plants, mammals, arthropods (for example Crustaceans and Cheliceratans), as well as non-life forms such as influenza. Motivated to understand how fundamental engineering principles alter BBR kinetics, we have built both computer models and synthetic experimental systems to understand BBR kinetics. By exploring the dynamics of BBRs through simulation we find that their motor-like properties are highly dependent on the number of catalytic legs, the distance that the legs can reach from the central hub, and the hub topology. We further explore how design features in the underlying landscape affect BBR dynamics. We find that reducing the landscape from two- to one-dimensional increases superdiffusivity but leads to a loss in processivity. We also find that landscape elasticity affects all motor-like dynamical properties of BBRs: there are different optimal stiffnesses for distinct dynamical characteristics. For a spherical-hub BBR, speed, processivity, and persistence length are optimized at high, intermediate and soft stiffnesses, respectively, while rolling is also optimized at a high surface stiffness. Towards our development of a novel micron-sized protein-based BBR in the lab, we develop a new surface chemistry passivation technique and apply it to the surface of nanowires, turning an array of waveguiding nanowires into a high-throughput biosensing assay. In a separate assay, our protein-based BBR, which we call the lawnmower, is implemented in two dimensions on glass cover slips prepared with our surface chemistry (which serves as the lawn). We find the lawnmower dynamics reproduce key observations found in other similar systems, such as saltatory motion and broadly varying anomalously diffusive behaviour. The successful implementation of the lawnmower marks the first demonstration of an artificial protein-based molecular motor