title: Multi-scale genetic dynamic modelling I : an algorithm to compute generators.
abstract: We present a new approach or framework to model dynamic regulatory genetic activity. The framework is using a multi-scale analysis based upon generic assumptions on the relative time scales attached to the different transitions of molecular states defining the genetic system. At micro-level such systems are regulated by the interaction of two kinds of molecular players: macro-molecules like DNA or polymerases, and smaller molecules acting as transcription factors. The proposed genetic model then represents the larger less abundant molecules with a finite discrete state space, for example describing different conformations of these molecules. This is in contrast to the representations of the transcription factors which are-like in classical reaction kinetics-represented by their particle number only. We illustrate the method by considering the genetic activity associated to certain configurations of interacting genes that are fundamental to modelling (synthetic) genetic clocks. A largely unknown question is how different molecular details incorporated via this more realistic modelling approach lead to different macroscopic regulatory genetic models which dynamical behaviour might-in general-be different for different model choices. The theory will be applied to a real synthetic clock in a second accompanying article (Kirkilioniset al., Theory Biosci, 2011).
authors.affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. mak@maths.warwick.ac.uk
authors.forename: Markus
authors.initials: M
authors.lastname: Kirkilionis
authors.forename: Ulrich
authors.initials: U
authors.lastname: Janus
authors.forename: Luca
authors.initials: L
authors.lastname: Sbano
mesh_terms: D000465:Algorithms; D005786:Gene Expression Regulation; D005796:Genes; D008390:Markov Chains; D008957:Models, Genetic; D013269:Stochastic Processes; D014158:Transcription, Genetic