Stochastic Systems Biology: Theory and Simulation

Wednesday, June 16 at 04:15am (PDT)
Wednesday, June 16 at 12:15pm (BST)
Wednesday, June 16 08:15pm (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS12" time block.
Note: this minisymposia has multiple sessions. The second session is MS11-MFBM (click here).

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Jae Kyoung Kim (Department of Mathematical Sciences, KAIST, Republic of Korea), Ramon Grima (University of Edinburgh, United Kingdom)


Biological systems consist of a large number of species with reactions which occur in multiple spatio-temporal scales. Because performing stochastic simulations of such systems are computationally expensive and prohibitive, various strategies to reduce the computational cost have been investigated, e.g. quasi-state-state approximation or hybrid methods. Also it is of interest how the interaction between different scales, e.g. between cellular and tissue scales, affects noise at the single cell level. In this mini-symposium, the focus will be on recent research reporting on advances in this area. Furthermore, the application of these methods to investigate embryonic development, cell size homeostasis and cell movement will be presented.

Hyukpyo Hong

(Department of Mathematical Sciences, KAIST, Republic of Korea)
"Inference of stochastic dynamics in biochemical reaction networks by exploiting deterministic dynamics"
Biochemical reaction networks (BRNs) have a stochastic nature, so every reaction in BRNs display randomness. Inherent stochasticity can be captured only by stochastic models, but it is more challenging to analyze their dynamics while their deterministic counterparts are easier to be analyzed, in general. Thus, various methods exploiting deterministic dynamics to infer the stochastic one have been proposed. In particular, stochastic model reduction using deterministic quasi-steady-state approximations (QSSAs) of fast variables is widely used to efficiently simulate a stochastic model. For instance, Michaelis-Menten or Hill-type functions have been used for Gillespie stochastic simulation. In this talk, we provide a complete validity condition for stochastic model reduction using the deterministic QSSA to eliminate stochastic reversible binding, which is fundamental and ubiquitous in BRNs. Furthermore, we present a framework to analytically derive stationary distribution for a large class of BRNs using their deterministic steady states based on chemical reaction network theory.

Zhou Fang

(ETH Zurich, Switzerland)
" Stochastic filtering for multiscale stochastic reaction networks based on hybrid approximations"
The advance in fluorescent technologies and microscopy has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the associate filtering problem, i.e., how to estimate latent dynamic states of an intracellular reaction system from time-course measurements of fluorescent reporters. A straightforward approach to this filtering problem is to use a particle filter where samples are generated by simulation of the full model and weighted according to observations. However, the exact simulation of the full model usually takes an impractical amount of computational time and prevents this type of filters from being used for real-time applications. Inspired by the recent development of hybrid approximations to multiscale chemical reaction networks, we approach the filtering problem in an alternative way. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network and, therefore, can greatly reduce the computational effort required to simulate the dynamics. Consequently, we are able to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the efficacy and efficiency of our approach using several numerical examples.

Samuel Isaacson

(Boston University, Department of Mathematics and Statistics, USA)
"Stochastic Reaction-Drift-Diffusion Methods for Studying Cell Signaling"
Particle-based stochastic reaction-diffusion (PBSRD) models are one approach to study biological systems in which both the noisy diffusion of individual molecules, and stochastic reactions between pairs of molecules, may influence system behavior. They provide a more microscopic model than deterministic reaction-diffusion PDEs or stochastic reaction-diffusion SPDEs, which treat molecular populations as continuous fields. The reaction-diffusion master equation (RDME) and convergent RDME (CRDME) are lattice PBSRD models, with the latter providing a convergent approximation to the spatially-continuous volume-reactivity PBSRD model as the lattice spacing is taken to zero. In this talk I will present several generalizations of the RDME and CRDME to support spatial transport mechanisms needed for resolving membrane-bound signaling processes, including drift due to background potentials, interaction potentials between molecules, and continuous-time random walks to approximate molecular transport on surfaces.

Brian Munsky

(Colorado State University, USA)
"Designing Optimal Microscopy Experiments to Harvest Single-Cell Fluctuation Information while Rejecting Image Distortion Effects"
Modern fluorescence labeling techniques and optical microscopy approaches have made it possible to experimentally visualize every stage of basic gene regulatory processes, even at the level of single cells and individual DNA, RNA, and protein molecules, in living cells, and within fluctuating environments. To complement these observations, the mechanisms and parameters of discrete stochastic models can be rigorously inferred to reproduce and quantitatively predict every step of the central dogma of molecular biology. As single-cell experiments and stochastic models become increasingly more complex and more powerful, the number of possibilities for their integrated application increases combinatorially, requiring efficient approaches for optimized experiment design. In this presentation, we will introduce two model-driven experimental design approaches: one based on detailed mechanistic simulations of optical experiments, and the other on a new formulation of Fisher Information for discrete stochastic gene regulation models. Using different combinations of biological experiments and simulated data for single-gene transcription and single-RNA translation, we will demonstrate how these experiment design approaches can be extended to account for non-gaussian intrinsic and extrinsic process noise within individual cells as well as for non-trivial measurement noise effects due to optical distortions and image processing errors.

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Virtual conference of the Society for Mathematical Biology, 2021.