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.
Molecular Motors, Simulation, Kinetic Monte Carlo
Level of Degree
Department of Computer Science
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Stojanovic, Milan N.
Fourth Committee Member
Krapivsky, Pavel L.
This work was generously supported by the National Science Foundation un- der grants 0533065, 0829896, and 1028238. I would also like to thank NVIDIA Corporation for a hardware gift that made possible some of the simulations.
Semenov, Oleg. "Abstract Models of Molecular Walkers." (2013). https://digitalrepository.unm.edu/cs_etds/35