Multi-scale genetic dynamic modelling II: application to synthetic biology

Abstract

We model in detail a simple synthetic genetic clock that was engineered in Atkinson et al. (Cell 113(5):597-607, 2003) using Escherichia coli as a host organism. Based on this engineered clock its theoretical description uses the modelling framework presented in Kirkilionis et al. (Theory Biosci. doi: 10.1007/s12064-011-0125-0 , 2011, this volume). The main goal of this accompanying article was to illustrate that parts of the modelling process can be algorithmically automatised once the model framework we called 'average dynamics' is accepted (Sbano and Kirkilionis, WMI Preprint 7/2007, 2008c; Kirkilionis and Sbano, Adv Complex Syst 13(3):293-326, 2010). The advantage of the 'average dynamics' framework is that system components (especially in genetics) can be easier represented in the model. In particular, if once discovered and characterised, specific molecular players together with their function can be incorporated. This means that, for example, the 'gene' concept becomes more clear, for example, in the way the genetic component would react under different regulatory conditions. Using the framework it has become a realistic aim to link mathematical modelling to novel tools of bioinformatics in the future, at least if the number of regulatory units can be estimated. This should hold in any case in synthetic environments due to the fact that the different synthetic genetic components are simply known (Elowitz and Leibler, Nature 403(6767):335-338, 2000; Gardner et al., Nature 403(6767):339-342, 2000; Hasty et al., Nature 420(6912):224-230, 2002). The paper illustrates therefore as a necessary first step how a detailed modelling of molecular interactions with known molecular components leads to a dynamic mathematical model that can be compared to experimental results on various levels or scales. The different genetic modules or components are represented in different detail by model variants. We explain how the framework can be used for investigating other more complex genetic systems in terms of regulation and feedback.

An Averaging Principle for Combined Interaction Graphs — Connectivity and Applications to Genetic Switches

“…Such models can be tested with data derived from measurements on different scales, and are therefore much better to test empirically. The framework described can also be interpreted as allowing to assign more or less automatically deterministic dynamics to given interaction diagrams, where the modeler can make choices whether a variable can have a continuous range, or a discrete range, [15,16].…”

“…The evidence of the rhythms for this model is shown numerically. The modeling techniques described in this paper give also rise to model existing synthetic genomes from a dynamical perspective, with the hope to achieve that in future in a semi-automatic way once a sequence is known, see [15,16].…”

Multiscale Analysis in Many-Body Systems

“…This paper is intended as a general introduction to an approach aimed at studying systems (like a cell) whose processes take place at very different spatial, time and size scales (see [19][20][21]) involving different type of molecular "players". Some relevant applications of this approach can be found in [8][9][10]. The author would like to thank one of the referee for drawing his attention to [2,4,13] where the multiscale analysis is addressed from a more probabilistic point of view.…”

“…are of mass-action type, the average dynamics is no longer of that type and usually presents non-linear terms able, for instance, to describe those dynamical features usually termed generically as "nonlinear cooperativity". Novel applications of this approach to the study of synthetic genetic clock can be found in [9,10]; furthermore, the construction of the average dynamics has many features that appears in the modelling of molecular motors, see [1].…”