Research Interests

My research focuses on central problems in stochastic models for complex biological systems. For example, how do we efficiently analyze a model despite the huge number of parameters, variables, and equations? In order to answer this, I have studied efficient analysis of stochastic models (i.e., continuous-time Markov chain) for biochemical systems by developing the accurate stochastic model reduction method and the Bayesian method to infer parameters of reduced Markovian or non-Markovian models. Specifically, I provided a universally valid stochastic model reduction by investigating a rigorous validity condition for the reduction. In addition, I developed efficient and accurate Bayesian Markov chain Monte Carlo (MCMC) methods in various programming languages such as R, Matlab, or Julia. Moreover, I applied it to experimental data of prokaryotic cell responses to antibiotic drugs and found a key determinant of cell-to-cell heterogeneity in antibiotic responses: the number of slowest steps in a cell signaling pathway. The techniques I developed span the fields of probability, queueing theory, Bayesian inference, and dynamical systems. Beyond the mathematical and statistical topics, I work closely with biologists and medical doctors in order to address biological problems related to cognitive impairment or COVID-19.

Chemical Reaction Network Theory

A biological/biochemical system consists of biological/chemical species and reactions describing interactions among the species. Chemical reaction network theory (CRNT) is a discipline of applied mathematics in which we model a system using a directed graph representation and infer the dynamical property based on the strucural properties of the system. In the CRNT, a stochastic system is modeled by means of a continous-time Markov chain (CTMC). I am working on analytic derivation of stationary distributions for the CTMC, the steady-state solution of the Kolmogorov forward equation (i.e., chemical master equation), associated with a stochastic CRN. The analytic formula provides long-term information of the system such as sensitivity, robustness, and also a likelihood function for Bayesian Inference.

Bayesian Inference of parameters in non-Markovian systems

Not all reactions in a biochemical system can be experimentally measured simultaneously. To analyse such system, replacing unobserved reactions with a single random time delay has been widely adopted as it significantly reduce the number of variables and parameters. However, the resulting process is non-Markovian (i.e., state evolution depends on not only present but also past), making it difficult to infer kinetic and delay parameters. Based on the knowledge from stochastic process (e.g., queueing theory) I have developed Bayesian Markov-chain Monte Carlo (MCMC) method to inter the system parameters. These studies provide an effective tool to analyze a non-Markovian system.

Collaborative works

Beyond the mathematical and statistical topics, I am closely working with biologists and medical doctors to solve biological problems. Some of the problems that we want to address (or have addressed) are the followings. 

 (1) Which features of activity pattern of human measured by wearable devices are altered by cognitive impairment? Can we provide a prediagnosis for cognifive impairment using activity patterns? We are using fractal analysis based on the detrended fluctuation analysis to find such features. 

 (2) Back in 2020, we had no idea where the COVID-19 pandemic will go. During that time, most of mathematical models focused on the near-future prediction of the diseases, and it worked well; it provided an effecitve guide for non-pharmaceutical interventions. However, to meet the end of the disease, we had to know what the 'end' is. Thus, we modeled a COVID-19 extinction and endemicity based on two immunities with different longevities: long-lived severity-preventing immunity due to T-cell functioning and short-lived infection-preventing immunity due to antibody functioning. Our analysis demonstrates that high viral transmission unexpectedly reduces the rates of progression to severe COVID-19 during the course of endemic transition despite increased numbers of infection cases. It also shows that high viral transmission amongst populations with high vaccination coverages paradoxically accelerates the endemic transition of COVID-19 with reduced numbers of severe cases.