Abstract
Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus–response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules.
Highlights
The model reduction of multiscale biochemical systems is a step of fundamental importance towards the system-level understanding of gene regulation or of various signalling pathways
An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers
We demonstrate the applicability of this simple state space structure through three examples: isomerization, binding and dissociation of TFs to multiple copies of a gene and protein dimerization
Summary
The model reduction of multiscale biochemical systems is a step of fundamental importance towards the system-level understanding of gene regulation or of various signalling pathways. With the fine control of all these scaling parameters, the authors could approximate the different variables and reaction channels with diffusion approximations (SDEs) or continuous deterministic processes (integral equations), depending on the inherent scaling properties of the system They could not provide rules for the appropriate choice of scaling constants, which is a great hindrance to the application of this model reduction technique. 2 Equilibrium distributions have been observed to provide less information than transient measurements for network identification in metabolic networks [24] and for parameter identification in gene expression [25] An exception to this trend has been metabolic control analysis, which is interested in optimizing flows in steady state [26], but its modelling framework tends to be the deterministic reaction rate equation. This technique is relevant in situations where a marginal of a product-form equilibrium distribution must be computed in a system with conservation
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
