MS03 - MFBM-1
Cartoon Room 1 (#3145) in The Ohio Union

Stochastic methods for biochemical reaction networks

Tuesday, July 18 at 10:30am

SMB2023 SMB2023 Follow Tuesday during the "MS03" time block.
Room assignment: Cartoon Room 1 (#3145) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS04-MFBM-1 (click here).

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Wasiur KhudaBukhsh, Hye-Won Kang


Stochastic modeling is becoming increasingly popular in biological sciences. The ability to account for intrinsic fluctuations and uncertainty in experimental outcomes has been an advantage of stochastic methods. The application of stochastic tools has proven to be tremendously useful in analyzing biological systems. The objective of this 2-part mini-symposium is to highlight recent advances in biochemical reaction networks -- both at the ecological and the molecular scales. The sessions will cover a wide range of themes (including applications and techniques) giving a general overview of the field. Specific topics include new asymptotic results/approximations, multiscale methods and statistical inference algorithms for those biological systems and applications to phylogenetics and epidemiology. Special focus will be on methods that can be translated into usable tools from a practical perspective.

Grzegorz A. Rempala

The Ohio State University (Biostatistics)
"Agent-based, aggregated dynamics for chemical reaction networks"
In this talk I will present a modeling framework for approximating stochastic dynamics of a single tagged molecule in a large biochemical network (CRN). This framework is based on approximating the dynamics of the CRN representing a biological system with hybrid dynamics combining the stochastic laws of individually-tagged molecules with the mean-field laws of the remaining species comprising the CRN. The approximation is well-defined over the entire process evolution time and leads to efficient and fully parallelizable simulation techniques. Moreover, it also allow for principled and efficient statistical inference for model parameters, which is difficult or even impossible in traditional agent-based models (ABM). As part of the development of the ABA approach, one could also consider how to incorporate different individual features (e.g., when molecules of the same species have individual characteristics or spatial features). I will present some molecular examples illustrating potential applications, including the HIV virus dendritic cell invasion models and models of multi-stage transcriptional bursting.

Hye-Won Kang

University of Maryland, Baltimore County (Department of Mathematics and Statistics)
"Stochastic oscillations in the enzyme-catalyzed chemical reaction network in glycolysis"
We consider a simple chemical reaction network in glycolysis. In a large volume limit of this system, species concentrations can exhibit a steady or an oscillatory behavior depending on the choice of the parameter values. To investigate how the inherent fluctuations affect the oscillatory behavior of the species copy numbers, we compare stochastic and deterministic dynamics of the system with selected parameter values near a separatrix. Due to the inherent fluctuations, a parameter region of the stochastic model cannot be separated clearly by the system behavior. We test several chemical reaction networks modified from the original system in glycolysis and investigate how the effects of the inherent fluctuations can be regulated. This is joint work with Luan Nguyen at UMBC.
Additional authors: Luan Nguyen (University of Maryland, Baltimore County)

Yi Fu

University of California, San Diego (Bioinformatics and Systems Biology PhD Program)
"Comparison Theorems for Stochastic Chemical Reaction Networks"
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. Our proof also yields a method for simultaneously simulating the sample paths of two comparable SCRNs. Our tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. We illustrate our results with applications to models of chromatin regulation and enzymatic kinetics.
Additional authors: Felipe Campos (UCSD); Simone Bruno (MIT); Domitilla Del Vecchio (MIT); Ruth Williams (UCSD)

Arnab Ganguly

Louisiana State University (Mathematics)
"Statistical inference of stochastic differential equations with applications to biochemical reactions"
Stochastic differential equations (SDES) are potent tools in modeling temporal evolution of a variety of systems. For the model to be accurate it is necessary to learn or estimate certain key parameters of the underlying SDE or sometimes the entire driving functions from the available data. Although computational methods for these types of learning problems have been studied in the literature, there is a critical lack of theoretical results on limiting behavior of the underlying estimators even for one-dimensional SDEs. The complexity of the SDE dynamics hinders usage of standard statistical tools in deriving the relevant properties. The goal of this talk is to partly fill this gap in theoretical understanding of these types of inference problems. In particular, we will discuss recent results on desirable asymptotic properties including consistency and central limit theorem of some of the estimators. We will specifically illustrate these results for SDEs that are used to model biochemical reaction systems.

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Annual Meeting for the Society for Mathematical Biology, 2023.