title: Template-Directed Copolymerization, Random Walks along Disordered Tracks, and Fractals.
abstract: In biology, template-directed copolymerization is the fundamental mechanism responsible for the synthesis of DNA, RNA, and proteins. More than 50 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of information processing in DNA replication, transcription, and translation remain poorly understood. Challenging issues are the facts that DNA or RNA sequences constitute disordered media for the motion of polymerases or ribosomes while errors occur in copying the template. Here, it is shown that these issues can be addressed and sequence heterogeneity effects can be quantitatively understood within a framework revealing universal aspects of information processing at the molecular scale. In steady growth regimes, the local velocities of polymerases or ribosomes along the template are distributed as the continuous or fractal invariant set of a so-called iterated function system, which determines the copying error probabilities. The growth may become sublinear in time with a scaling exponent that can also be deduced from the iterated function system.
authors.affiliation: Center for Nonlinear Phenomena and Complex Systems, Université libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
authors.forename: Pierre
authors.initials: P
authors.lastname: Gaspard
mesh_terms: D004247:DNA / Q000737:chemistry*; D004261:DNA Replication; D012321:DNA-Directed RNA Polymerases; D017709:Fractals; D007700:Kinetics; D058105:Polymerization; D012313:RNA; D013816:Thermodynamics
chemical_list: D012313:RNA; D004247:DNA; D012321:DNA-Directed RNA Polymerases