Conveners
Multiscaling methods and parameter inference in stochastic biochemical networks
- Grzegorz Rempała (The Ohio State University)
Description
A reaction network is a chemical system involving multiple reactions and chemical species. Mathematical models of such networks are important tools of modern biosciences with applications to rage of biological problems from molecular experiments to population level studies. The simplest stochastic models of such networks treat the biological system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. This minisymposium will discuss approaches to approximation of such models that take the multiscale nature of the systems into account. In particular, such approximations often allow for inference on specific components of the network on the scale of interest and for incorporation of species transition constraints. While some of the talks will focus on new ideas for MCMC-based statistical inference for multiscale systems others will consider newly found connections between multiscale limits for constrained reaction networks and the rapidly growing research area of stochastic models for social networks and communicable diseases.
Characterizing enzyme kinetics is critical to understand cellular systems and to utilize enzymes in industry. To estimate enzyme kinetics from reaction progress curves of substrates, the Michaelis-Menten equation has been widely used for a century. However, this canonical approach works in a limited condition such as a large excess of substrate over enzyme. Even when such condition is...
We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph nodes into two compartments, namely, S and I, denoting susceptible and infected nodes, respectively. In addition to the sizes of these two compartments, we study counts of SI-edges...
In this talk I will introduce several quasi steady-state approximations (QSSAs) applied to the stochastic enzyme kinetics models. Different assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in the literature in deterministic ordinary...
The inference for the reaction rates in chemical networks is often challenging due to intrinsic and extrinsic biological noise, missing data and lack of experimental reproducibility. The talk will provide an overview of some recent work on new efficient methods of rates estimation in stochastic biochemical networks both at molecular and population scales. Stochastic SIR and Michaelis...
