Stochastic methods for biochemical reaction networks

Thursday, June 17 at 09:30am (PDT)
Thursday, June 17 at 05:30pm (BST)
Friday, June 18 01:30am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS19" time block.
Note: this minisymposia has multiple sessions. The second session is MS18-CBBS (click here).

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Wasiur KhudaBukhsh (The Ohio State University, United States), Hye-Won Kang (University of Maryland at Baltimore County, United States)


Stochastic modelling is becoming increasingly popular in biological sciences. The ability to account for intrinsic fluctuations and uncertainty in experimental outcomes has been a crucial advantage of stochastic methods. The application of stochastic tools has proven to be useful in analysing biological data. In particular, stochastic methods have found usefulness in studying the spread of infectious diseases, in understanding the biophysics of enzyme kinetics, metabolism, immune-response mechanisms, and in constructing phylogenetic trees etc. The objective of this two-part mini-symposium is to highlight some of the recent advances in the field of stochastic biochemical reaction networks. Both sessions will cover a wide range of themes (including applications and techniques) giving a broad overview of the field. Specific topics include new asymptotic results/approximations, multi-scale methods, statistical inference algorithms and parameter identifiability issues. Special focus will be on methods that can be translated into usable tools from a practical perspective.

David Anderson

(University of Wisconsin Madison, USA)
"Time-dependent product-form Poisson distributions for reaction networks"
It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this talk, I will discuss the following related question: under what conditions will the time-dependent distribution of a reaction network be a product of Poissons for all time? I will provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical “complex-balancing” for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). This is joint work with Chaojie Yuan (Indiana) and David Schnoerr (Imperial College London).

Lea Popovic

(Concordia University, Canada)
"Stochastic reduction of spatially heterogeneous biochemical reaction networks"
We start from a measure valued process which models the full particle behaviour of chemical reaction networks in spatially heterogeneous systems. Scaling of such a process with a high abundance of some species types and large reaction rates of some reactions leads to a reaction-diffusion pde deterministic limit, or to a mixture of discrete-Markov-and-continuous-deterministic limit process. In this talk we consider a reduced stochastic description of the original measure-valued process by approximating its fluctuations around the limiting process.

Hye-Won Kang

(University of Maryland at Baltimore County, United States)
"Stochastic modeling of metabolic enzyme complexes"
Enzymes in purine biosynthesis and glucose metabolism have been shown to spatially organize into different types of multienzyme complexes. These multienzyme complexes regulate metabolic flux in living human cells. Metabolic pathways for purine biosynthesis and glucose metabolism are associated with each other, but their metabolic enzyme complexes are spatially independent in human cells. We hypothesize that these metabolic enzyme complexes communicate with each other when they are in close location. This talk will introduce a stochastic model for metabolic enzyme complexes using the Langevin dynamics to investigate their spatial communication.

Felipe Campos

(University of California, San Diego, USA)
"Error bounds for the one-dimensional constrained Langevin approximation for density-dependent Markov chains"
The Constrained Langevin Approximation (CLA) is a reflected diffusion approximation for stochastic chemical reaction networks proposed by Leite & Williams. In this work, we extend this approximation to (nearly) density dependent Markov chains, when the diffusion state space is one-dimensional. Then, we provide a bound for the error of the CLA in a strong approximation. Finally, we discuss some applications for chemical reaction networks and epidemic models, illustrating these with numerical examples. Joint work with Ruth Williams.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.