Research

My research interests are in mathematical biology studied using methods from dynamical systems, data science, and scientific computing. I am driven to investigate human health problems using advanced mathematical tools. My main areas of focus have been: (1) Development and analysis of mechanistic models of circadian phenomena, (2) Synchronization of neurons on a realistic network, (3) Analysis of large-scale wrist-wearable activity, heart rate, and sleep data, and (4) Mathematical models that advance women’s health.

Dynamics of the Circadian Timekeeping System

The circadian timekeeping system is regulated across multiple spatial and time scales that span many orders of magnitude. At the molecular level, each cell in the body has its very own clock–a transcription-translation feedback loop (TTFL) that drives periodic rhythms of gene expression. Mathematically, this “molecular clock” is a stable limit cycle that can be influenced by external forcing by the 24hr light-dark cycle, meal timing, and other environmental cues. At the network level, neurons synchronize with each other through both short- and long-range connections. They communicate with each other through synaptic transmission on the time scale of milliseconds to minutes as well as through other types of paracrine signaling on the time scale of minutes to hours. These coupled dynamical systems create a highly robust and flexible system of both mathematical and biological interest. The following papers are related to the dynamics of circadian timekeeping:

Analysis of Wrist-Wearable Data

We also use data analysis, statistics, and modeling to study wrist-wearable (Apple watch or fitbit) data from thousands of medical interns across the U.S., in collaboration with the Sen lab in the UM Department of Psychiatry. Most organisms have intrinsic circadian rhythms influenced by external cues such as light, food, and activity. When the circadian timekeeping system is disrupted, such as in shift work and jet lag in humans, individual responses can vary dramatically. While some individuals re-adjust quickly, others experience lasting health effects. We study measurements of circadian timekeeping based on wearable heart rate and step data in a genotyped cohort of medical interns. The following papers are related to wearable data analysis and modeling:

  • Kim R, Fang Y, Lee MP, Kim DW, Tang Z, Sen S, Forger DB (In preparation). Real-world associations between SLC20A2 polymorphisms and wrist-wearable data explain seasonal variation in sleep and circadian rhythms.
  • Lee MP, Kim DW, Fang Y, Kim R, Bohnert ASB, Sen S, Forger DB (Under review). The association between real-world behavior-induced circadian disruption and depression risks: A large-scale cohort study of training physicians.

Models of the Menstrual Cycle and Health Impacts

Sex hormones like estrogen and testosterone significantly affect our physiology, resulting in sex-related differences in disease outcomes and reactions to drugs. For example, there are major impacts of sex hormones on one-carbon metabolism (OCM), which is central to the synthesis of building blocks (DNA, proteins, etc.) for cells and tissues in the body. OCM disruptions are linked to cancer, cardiovascular disease, and neurological disorders, as well as deficiencies in nutrients such as B-vitamins and choline. However, women have been historically underrepresented in medical studies. See this 2024 article on “Why we know so little about women’s health.” Mathematical models can be used to help advance personalized health care approaches and allow for a more inclusive understanding of human health. The following papers are related to my work modeling the menstrual cycle:

  • Kim R, Nijhout HF, Reed MC. (2021). One-carbon metabolism during the menstrual cycle and pregnancy. PLoS Computational Biology. 17(12): e1009708. https://doi.org/10.1371/journal.pcbi.1009708
  • Zhao L*, Kim R*, Oremland LS, Chowkwale M, de Pillis LG, Brooks HZ. (2024). A Survey of Mathematical Modeling of Hormonal Contraception and the Menstrual Cycle. In: Ford Versypt, A.N., Segal, R.A., Sindi, S.S. (eds) Mathematical Modeling for Women’s Health. The IMA Volumes in Mathematics and its Applications, vol 166. Springer, Cham. https://doi.org/10.1007/978-3-031-58516-6_3