Stochastic methods for biochemical reaction networks

Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)

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

Ankit Gupta

(ETH Zurich, Switzerland)
"A deep learning approach for solving chemical master equations"
Stochastic reaction network models are a popular tool for studying the effects of dynamical randomness in biological systems. Such models are typically analysed by estimating the solution of the chemical master equation (CME) that describes the evolution of the probability distribution of the random state-vector representing molecular counts of the reacting species. The size of the CME system is typically very large or even infinite, and due to this high-dimensional nature accurate numerical solutions of the CME are very difficult to obtain. In this talk we will present a novel deep learning approach for estimating CME solutions and illustrate it with a number of examples. The proposed method only requires a handful of stochastic simulations and it yields not just the CME solution but also its sensitivities to all the model parameters.

Grzegorz Rempala

(The Ohio State University, United States)
"Approximating bio-chemical dynamics using survival models"
In a stochastic chemical network one can often use the notion of a reaction hazard in order to provide a simple statistical model for the system evolution. This approach is especially helpful if we want to consistently follow the fate of a single molecule of some special species through its different transformations, as is the case, for instance, for a single individual in the classical model of an SIR epidemic network. I will provide some general results on the usage of the method and its mathematical properties with particular attention given to stochastic epidemic models. This is joint work with Daniele Cappelletti from Politecnico di Torino.

Jinsu Kim

(University of California Irvine, USA)
"Mixing times for stochastically modeled biochemical reaction systems"
Mixing times of Markov chains play a significant role in studying stochastic systems as they indicate how fast the system will be stabilized. In this talk, I will introduce analytic approaches such as Lyapunov-Foster criteria and Spectral gap theory that can be used to find a class of reaction networks whose associated Markov process admits exponential ergodicity, which means the associated probability density function converges to its stationary distribution exponentially fast. Beyond the theoretical aspects, I will also talk about how exponential ergodicity can be applied in computational system biology.

Wasiur KhudaBukhsh

(The Ohio State University, United States)
"Chemical reaction networks with covariates"
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. We consider relaxing this assumption by incorporating age-dependent random time delays into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of Partial Differential Equations (PDEs) in the large-volume limit, as opposed to Ordinary Differential Equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms.

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