Doctoral Dissertation Defense: Luan Chip Nguyen

Chemical reaction networks are used to describe many biological processes including metabolic pathways. Due to interactions between different chemical species, we can see interesting dynamics of the chemical systems such as oscillations, spatial patterns, and self-assembly. In this dissertation, we investigate several chemical reaction networks in glucose metabolism and explore their interesting dynamic behaviors. First, we study the well-mixed glycolytic pathway involving two chemical species. The ODE model shows limit cycle behavior for some parameter values. We enlarge the glycolytic pathway so that we can control the limit cycle behavior. In addition, we also look at the stochastic dynamics of the enlarged network depending on the system volume. Next, we consider the spatially-distributed glycolytic pathway. The stochastic model for the glycolytic pathway shows interesting spatial patterns when the corresponding deterministic model exhibits the Turing instability. The compartment size in the stochastic model affects spatial pattern formation. Thus, we estimate the appropriate compartment size using the mean lifetime of chemical species. Last, we develop a stochastic model to describe the PFKL condensate formation using the Langevin dynamics. We find several key parameter values using numerical simulations of the stochastic model via LAMMPS.