MS04 - MFBM-1
Cartoon Room 1 (#3145) in The Ohio Union

Stochastic methods for biochemical reaction networks

Tuesday, July 18 at 04:00pm

SMB2023 Follow Tuesday during the "MS04" time block.
Room assignment: Cartoon Room 1 (#3145) in The Ohio Union.

Note: this minisymposia has multiple sessions. The other session is MS03-MFBM-1 (click here).

Wasiur KhudaBukhsh, Hye-Won Kang

Description:

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.

Wasiur R. KhudaBukhsh

University of Nottingham (School of Mathematical Sciences)

"Multiscale approximations for a simple transfection process"

The talk will focus on chemical reaction networks (CRNs) that describe creation, annihilation, combination or binding, and changes in the physical state of a collection of chemical species. Many prominent examples of intracellular dynamics, genetic switches, and dynamics of population interactions can be modelled by CRNs, where the interacting particles exhibit vastly different intrinsic scales in terms of abundance, or the reactions operate at different time scales varying over many orders of magnitude. The traditional deterministic approach to multiscale approximations used in such situations employs singular perturbation theory, often invoking Tikhonov’s theorem and Fenichel theory. In this talk, I will take a stochastic viewpoint and consider a probabilistic way to derive multiscale approximations. The talk will be fairly nontechnical, and no prior knowledge biology is required.
Additional authors: Joint work with Yajie Guo (University of Nottingham)

Ruth Baker

University of Oxford (Mathematical Institute)

"Efficient approaches for simulating and calibrating stochastic models of biological processes"

With the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of data now being generated. As such, increasingly larger and more complicated processes are now being explored, including large signalling or gene regulatory networks, and the development, dynamics and disease of entire cells and tissues. Detailed mathematical models of these processes have the potential to provide vital insights where data alone cannot, but to achieve this goal requires meeting significant mathematical challenges in efficiently simulating models and calibrating them to experimental data. In this talk, I will outline some methods we have developed that leverage both low- and high-fidelity models and variance-reducing Monte Carlo approaches to make progress.

Jae Kyoung Kim

KAIST (Mathematical Sciences)

"Inference of non-Markovian systems from cell signaling to infectious diseases"

The complex processes involved in cell signaling and infectious diseases often include multiple hidden intermediate steps. However, it is possible to simplify these systems by replacing them with a single time delay distribution, such as a gamma distribution. This simplification reduces the number of variables, making it easier to infer parameters based on limited observations. Although this approach offers advantages, it presents a challenge. Since the model is non-Markovian, traditional inference techniques based on the Markov property (where dynamics depend only on the current state, not the past) cannot be directly applied. In my presentation, I will introduce a Bayesian inference framework specifically designed for non-Markovian systems. This framework enables us to identify the properties of the cell signaling network that reduce cell-to-cell heterogeneity in response to antibiotics. Additionally, I will discuss how our framework can be used to infer both the reproduction number and the distribution of infectious periods solely from confirmed case time series. This resolves the biased estimation issues associated with the conventional SEIR ODE model.

Boseung Choi & Eunjin Eom

Korea University (Division of Big Data Science; Department of Economics Statistics)

"A Bayesian model for the relationship SARS-CoV-2 wastewater and community-wide seroprevalence with mutation and vaccination effect"

Since early in the COVID-19 pandemic, SARS-CoV-2 wastewater concentration has been measured as a surrogate for community prevalence. However, our knowledge remains limited regarding wastewater concentration and the effects of the COVID-19 vaccination on the overall disease burden as measured by hospitalization rates. We used weekly SARS-CoV-2 wastewater concentration, antibody test results, and spatially linked vaccination and hospitalization data, from April to August 2021. Our susceptible (S), vaccinated (V), variant-specific infected (I1 and I2), recovered (R), and seropositive (T) model (SVI2RT) tracked prevalence longitudinally. This was related to wastewater concentration for spatial analysis of strain mutation, vaccination effect, and overall hospitalization burden. To construct the SVI2RT compartment model, we utilized the dynamical survival analysis (DSA) framework for using survival analysis methods to build approximate models of individual-level ecological dynamics based on mean-field approximations and the Markov Chain Monte Carlo (MCMC) method based on the Bayesian approaches. We used the Bayesian linear regression model to identify the effect of the estimated prevalence according to the Alpha and Delta mutations on the community wastewater concentration and the hospitalization burden. We found strong linear association between wastewater concentration and estimated community prevalence. During the study period, the estimated effect of SARS-CoV-2 Delta variant emergence was seen as large as the increase in infection counts, corresponding to the increase in wastewater concentration. Hospitalization burden and wastewater concentration had the strongest correlation at 1 week lag time. Therefore, the wastewater samples can be used to estimate the effects of vaccination and hospitalization burden.
Additional authors: Grzegorz A. Rempala, Mathematical Biosciences Institute, Ohio State University, United States of America

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Annual Meeting for the Society for Mathematical Biology, 2023.