title: Critical jump sizes in DNA-protein interactions.
abstract: Interaction of a protein molecule with a specific-site on the DNA lattice can be modeled as an unbiased random jump process. Here we show that there exists a critical jump size (kc) beyond which site-specific association of a protein molecule with a DNA lattice cannot be facilitated. The maximum achievable association rate is predicted to be approximately 10(10) mol-1 s-1. This critical jump size scales with the total length of DNA lattice (N) as kc proportional, variantN2/3. Beyond kc the mean first passage time MFPT (denoted as T) required for the protein molecule to target the specific-site follows a linear scaling law as T proportional, variantN rather than the usual T proportional, variantN2 scaling law. On the basis of these results we argue that the evolution of the super coiled structures of the genomic DNA must be a consequence of the existence of this critical jump sizes. We finally show that the random jump method of searching for the specific-site by the protein molecule on the DNA lattice itself introduce an abstract linear type potential favoring the site-specific association rate.
authors.affiliation: Department of Chemical Sciences, Tata Institute of Fundamental Research Homi Bhabha Road, Colaba, Mumbai, India, 400005. muruga@tifr.res.in
authors.forename: R
authors.initials: R
authors.lastname: Murugan
mesh_terms: D001665:Binding Sites; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry*; D004268:DNA-Binding Proteins / Q000737:chemistry*; D008962:Models, Theoretical; D011485:Protein Binding
chemical_list: D004268:DNA-Binding Proteins; D004247:DNA