MS01 - MFBM-1
Cartoon Room 1 (#3145) in The Ohio Union

Recent advances in the mathematics of biochemical reaction networks

Monday, July 17 at 10:30am

SMB2023 SMB2023 Follow Monday during the "MS01" time block.
Room assignment: Cartoon Room 1 (#3145) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS02-MFBM-1 (click here).

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Tung Nguyen, Matthew Johnson, Jiaxin Jin


Biochemical reaction networks are well known to be useful in modeling complex systems in biology and chemistry, such as gene regulatory networks and signaling cascades. This mini-symposium will showcase recent advancements in the field of reaction networks with a special focus on the connection between the underlying structure or topology of a reaction network and the possible dynamical behaviors that can emerge from it, including various notions of stability and robustness. The talks will feature applications of reaction networks to microbial interactions, insulin signaling, and synthetic gene circuits. We aim to foster a deeper understanding of the complex interplay between network structure and dynamics, and inspire new avenues of research in the field of mathematical biology.

Hyukpyo Hong

Institute for Basic Science (Biomedical Mathematics Group)
"Network translation allows for revealing long-term dynamics of stochastic reaction networks"
Long-term behaviors of biochemical systems are described by steady states in deterministic models and stationary distributions in stochastic models. Their analytic solutions can be obtained for limited cases, such as linear or finite-state systems. Interestingly, analytic solutions can be easily obtained when underlying networks have special topologies, called weak reversibility (WR) and zero deficiency (ZD). However, such desired topological conditions do not hold for the majority of cases. Thus, we propose a method of translating networks to have WR and ZD while preserving the original dynamics was proposed. Additionally, we prove necessary conditions for having WR and ZD after translation. Our method provides a valuable tool for analyzing and understanding the long-term behavior of biochemical systems, and we demonstrate its efficacy with several examples.
Additional authors: Jinsu Kim, Department of Mathematics, Pohang University of Science and Technology; Bryan S. Hernandez, Institute of Mathematics, University of the Philippines Diliman; Muhammad Ali Al-Radhawi, Departments of Bioengineering and of Electrical and Computer Engineering, Northeastern University; Eduardo D. Sontag, Departments of Bioengineering and of Electrical and Computer Engineering, Northeastern University; Jae Kyoung Kim, Biomedical Mathematics Group, Institute for Basic Science

Angelyn Lao

De La Salle University (Department of Mathematics and Statistics)
"A Reaction Network Analysis of Insulin Signaling"
The insulin signaling system is an important metabolic system that initiates the uptake of glucose into the cell. This reduced ability of cells to use available insulin for energy metabolism is viewed as a common factor in diseases such as obesity, type 2 diabetes, metabolic syndrome, and cancer, and more recently to brain insulin resistance in connection with mild cognitive impairment and Alzheimer’s disease (AD). The complexity of the insulin signaling system, both in terms of the number of molecular components involved as well as the intricate combination of positive and negative feedback loops, clearly warrants the application of mathematical modeling and computational tools. This talk presents the construction of the insulin signaling reaction network and the analysis of its robustness and stability using Chemical Reaction Network Theory.
Additional authors: Patrick Vincent N. Lubenia; Eduardo R. Mendoza

M. Ali Al-Radhawi

Northeastern University (Department of Electrical and Computer Engineering)
"Contraction and entrainment in reaction networks"
In previous work, we have developed an approach to understanding the long-term dynamics of classes of chemical reaction networks, based on “rate-dependent Lyapunov functions”, and developed an effective computational package. In this talk, we show that stronger notions of convergence can be established by proving contraction with respect to non-standard norms. This enables us to show that such networks entrain to periodic inputs. We illustrate our theory with examples from signalling pathways and genetic circuits.
Additional authors: David Angeli, Eduardo Sontag

Jinsu Kim

POSTECH (Mathematics / Mathematical biology)
"Recent studies about mixing times of stochastically modeled reaction networks"
Molecular counts of small-size biological systems can be modeled with continuous-time Markov chains on infinite positive integer grids with polynomial rates. In this talk, we will discuss recent studies about mixing times of continuous-time Markov chains modeling chemical reaction systems. The mixing time, which indicates the time for the distance between the distribution of the stochastic process and its stationary distribution, is typically investigated with the Lyapunov function method and canonical path method. Recently, we discovered examples that do not lend themselves easily to analysis via those two methods but are shown to have either fast mixing or slow mixing with our new technique.
Additional authors: Louis Fan; Chaojie Yuan;

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Annual Meeting for the Society for Mathematical Biology, 2023.