,
Exactly solvable models of molecular spiders
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Аннотация
Molecular spiders are synthetic bio-molecular systems with
``legs'' made of short single-stranded segments of
DNA. Spiders move on a surface covered by single-stranded DNA
segments complementary to the legs, and the legs can attach to them. When a leg detaches from a segment on the surface, it can attach to a neighboring segment, and the spider moves. The motion of the legs is modeled by particles hopping to nearest neighbor sites on a one or two dimensional lattice. In addition to particle exclusion, we consider two types of constraints: either any two neighboring legs (local rule), or any two legs (global rule) have to stay within a given distance to each other. In one dimension, the spiders can be mapped exactly to the Exclusion Process for both local and global constraints. These mappings lead to simple exact results for the speed and the diffusion coefficient of the spiders. In experiments, each site is altered when first visited by a leg, and the legs leave these sites faster at subsequent visits. Hence the proper description of the spider's motion requires the knowledge of its entire trajectory. Even in this non-Markovian case, for certain types of spiders we obtained exact results for the experimentally interesting number of visited sites as a function of time. Interesting phenomena associated with driven spiders, asymmetric gaits, interacting and two dimensional spiders will also be discussed.
