First-passage properties of molecular spiders

Adhesive Dynamics Simulations of Highly Polyvalent DNA Motors

Molecular motors, such as myosin and kinesin, perform diverse tasks ranging from vesical transport to bulk muscle contraction. Synthetic molecular motors may eventually be harnessed to perform similar tasks in versatile synthetic systems. The most promising type of synthetic molecular motor, the DNA walker, can undergo processive motion but generally exhibits low speeds and virtually no capacity for force generation. However, we recently showed that highly polyvalent DNA motors (HPDMs) can rival biological motors by translocating at micrometer per minute speeds and generating 100+ pN of force. Accordingly, DNA nanotechnology-based designs may hold promise for the creation of synthetic, force-generating nanomotors. However, the dependencies of HPDM speed and force on tunable design parameters are poorly understood and difficult to characterize experimentally. To overcome this challenge, we present RoloSim, an adhesive dynamics software package for fine-grained simulations of HPDM translocation. RoloSim uses biophysical models for DNA duplex formation and dissociation kinetics to explicitly model tens of thousands of molecular scale interactions. These molecular interactions are then used to calculate the nano- and microscale motions of the motor. We use RoloSim to uncover how motor force and speed scale with several tunable motor properties such as motor size and DNA duplex length. Our results support our previously defined hypothesis that force scales linearly with polyvalency. We also demonstrate that HPDMs can be steered with external force, and we provide design parameters for novel HPDM-based molecular sensor and nanomachine designs.

Burnt bridge ratchet motor force scales linearly with polyvalency: a computational study

Nano- and micro-scale burnt bridge ratchet motors, which translocate via "guide" molecules that bind to and degrade a field of "fuel" molecules, have recently emerged in several biological and engineering contexts. The capacity of these motors to generate mechanical forces remains an open question. Here, chemomechanical modeling suggests that BBR force scales linearly with the steady-state number of guide-fuel bonds.

Effect of polyvalency on tethered molecular walkers on independent one-dimensional tracks

We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers composed of coupled DNAzyme legs known as molecular spiders. The mechanism of the transient superdiffusion has been explained via the emergence of a boundary between the new and the previously visited sites, and the tendency of the multilegged walker to cling to this boundary, provided residence time for a first visit to a site is longer than for subsequent visits. Using both kinetic Monte Carlo simulation and an analytical approach, we model a system that consists of unipedal walkers, each on its own one-dimensional track, connected by a tether, i.e., a kinematic constraint that no two walkers can be more than a certain distance apart. Even though a single unipedal walker does not at all exhibit directional, superdiffusive motion, we find that a team of unipedal walkers on parallel tracks, connected by a flexible tether, does enjoy a superdiffusive transient. Furthermore, unipedal walker teams exhibit a greater expected number of steps per boundary period and are able to diffuse more quickly than bipedal walker teams, which leads to longer periods of superdiffusion.

RaTrav: a tool for calculating mean first-passage times on biochemical networks

BACKGROUND

The concept of mean first-passage times (MFPTs) occupies an important place in the theory of stochastic processes, with the methods of their calculation being equally important in theoretical physics, chemistry and biology. We present here a software tool designed to support computational biology studies where Markovian dynamics takes place and MFPTs between initial and single or multiple final states in network-like systems are used. Two methods are made available for which their efficiency is strongly dependent on the topology of the defined network: the combinatorial Hill technique and the Monte Carlo simulation method.

RESULTS

After a brief introduction to RaTrav, we highlight the utility of MFPT calculations by providing two examples (accompanied by Additional file 1) where they are deemed to be of importance: analysis of a protein-protein docking funnel and interpretation of the free energy transduction between two coupled enzymatic reactions controlled by the dynamics of transition between enzyme conformational states.

CONCLUSIONS

RaTrav is a versatile and easy to use software tool for calculating MFPTs across biochemical networks. The user simply prepares a text file with the structure of a given network, along with some additional basic parameters such as transition probabilities, waiting probabilities (if any) and local times (weights of edges), which define explicitly the stochastic dynamics on the network. The RaTrav tool can then be applied in order to compute desired MFPTs. For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme. However, the list of possible applications is much wider.