Research

2025

1. 

   Seasonal timing and interindividual differences in shiftwork adaptation

   Ruby Kim, Yu Fang, Minki Lee, and 4 more authors

   npj Digital Medicine, 2025

   Abs DOI

   Millions of shift workers in the U.S. face an increased risk of depression, cancer, and metabolic disease, yet individual responses to shift work vary widely. We find that a conserved biological system of morning and evening oscillators, which evolved for seasonal timing, may contribute to these interindividual differences. In this study, we analyze seasonality in medical interns working shifts, revealing that summer-winter variation correlates with increased circadian misalignment after shift work. Mathematical modeling suggests that seasonal timing influences the rate of adaptation to new schedules, predicting differential effects on morning and evening oscillators. Additionally, we examine genetic polymorphisms linked to seasonality in animals and find that human variants can impact how quickly circadian rhythms respond to schedule changes. Based on our findings, we hypothesize that the vast interindividual differences in shift work adaptation—critical for shift worker health—can in part be explained by biological mechanisms for seasonal timing.

2024

1. 

   A Survey of Mathematical Modeling of Hormonal Contraception and the Menstrual Cycle

   Lihong Zhao^*, Ruby Kim^*, Lucy S Oremland, and 3 more authors

   In Mathematical Modeling for Women’s Health: Collaborative Workshop for Women in Mathematical Biology, 2024

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2. 

   A mathematical model of melatonin synthesis and interactions with the circadian clock

   Janet Best, Ruby Kim, Michael Reed, and 1 more author

   Mathematical Biosciences, 2024

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3. 

   The real-world association between digital markers of circadian disruption and mental health risks

   Minki P Lee, Dae Wook Kim, Yu Fang, and 4 more authors

   npj Digital Medicine, 2024

   DOI

2023

1. 

   Mathematical insights into the role of dopamine signaling in circadian entrainment

   Ruby Kim, H. Frederik Nijhout, and Michael C. Reed

   Mathematical Biosciences, 2023

   Abs DOI

   The circadian clock in the mammalian brain comprises interlocked molecular feedback loops that have downstream effects on important physiological functions such as the sleep-wake cycle and hormone regulation. Experiments have shown that the circadian clock also modulates the synthesis and breakdown of the neurotransmitter dopamine. Imbalances in dopamine are linked to a host of neurological conditions including Parkinson’s disease, attention-deficit/hyperactivity disorder, and mood disorders, and these conditions are often accompanied by circadian disruptions. We have previously created a mathematical model using nonlinear ordinary differential equations to describe the influences of the circadian clock on dopamine at the molecular level. Recent experiments suggest that dopamine reciprocally influences the circadian clock. Dopamine receptor D1 (DRD1) signaling has been shown to aid in the entrainment of the clock to the 24-hour light-dark cycle, but the underlying mechanisms are not well understood. In this paper, we use our mathematical model to support the experimental hypothesis that DRD1 signaling promotes circadian entrainment by modulating the clock’s response to light. We model the effects of a phase advance or delay, as well as the therapeutic potential of a REV-ERB agonist. In addition to phase shifts, we study the influences of photoperiod, or day length, in the mathematical model, connect our findings with the experimental and clinical literature, and determine the parameter that affects the critical photoperiod that signals seasonal changes to physiology.

2022

1. 

   Uncovering the dynamics of a circadian-dopamine model influenced by the light-dark cycle

   Ruby Kim, and Thomas P. Witelski

   Mathematical Biosciences, 2022

   Abs DOI PDF

   The neurotransmitter dopamine (DA) is known to be influenced by the circadian timekeeping system in the mammalian brain. We have previously created a single-cell differential equations model to understand the mechanisms behind circadian rhythms of extracellular DA. In this paper, we investigate the dynamics in our model and study different behaviors such as entrainment to the 24-hour light–dark cycle and robust periodicity versus decoupling, quasiperiodicity, and chaos. Imbalances in DA are often accompanied by disrupted circadian rhythms, such as in Parkinson’s disease, hyperactivity, and mood disorders. Our model provides new insights into the links between the circadian clock and DA. We show that the daily rhythmicity of DA can be disrupted by decoupling between interlocked loops of the clock circuitry or by quasiperiodic clock behaviors caused by misalignment with the light–dark cycle. The model can be used to further study how the circadian clock affects the dopaminergic system, and to help develop therapeutic strategies for disrupted DA rhythms.

2021

1. 

   One-carbon metabolism during the menstrual cycle and pregnancy

   Ruby Kim, H. Frederik Nijhout, and Michael C. Reed

   PLoS Computational Biology, 2021

   Abs DOI

   Many enzymes in one-carbon metabolism (OCM) are up- or down-regulated by the sex hormones which vary diurnally and throughout the menstrual cycle. During pregnancy, estradiol and progesterone levels increase tremendously to modulate physiological changes in the reproductive system. In this work, we extend and improve an existing mathematical model of hepatic OCM to understand the dynamic metabolic changes that happen during the menstrual cycle and pregnancy due to estradiol variation. In particular, we add the polyamine drain on S-adenosyl methionine and the direct effects of estradiol on the enzymes cystathionine beta-synthase (CBS), thymidylate synthase (TS), and dihydrofolate reductase (DHFR). We show that the homocysteine concentration varies inversely with estradiol concentration, discuss the fluctuations in 14 other one-carbon metabolites and velocities throughout the menstrual cycle, and draw comparisons with the literature. We then use the model to study the effects of vitamin B12, vitamin B6, and folate deficiencies and explain why homocysteine is not a good biomarker for vitamin deficiencies. Additionally, we compute homocysteine throughout pregnancy, and compare the results with experimental data. Our mathematical model explains how numerous homeostatic mechanisms in OCM function and provides new insights into how homocysteine and its deleterious effects are influenced by estradiol. The mathematical model can be used by others for further in silico experiments on changes in one-carbon metabolism during the menstrual cycle and pregnancy.

2. 

   A mathematical model of circadian rhythms and dopamine

   Ruby Kim, and Michael C. Reed

   Theoretical Biology and Medical Modelling, 2021

   Abs HTML

   The suprachiasmatic nucleus (SCN) serves as the primary circadian (24hr) clock in mammals and is known to control important physiological functions such as the sleep-wake cycle, hormonal rhythms, and neurotransmitter regulation. Experimental results suggest that some of these functions reciprocally influence circadian rhythms, creating a highly complex network. Among the clock’s downstream products, orphan nuclear receptors REV-ERB and ROR are particularly interesting because they coordinately modulate the core clock circuitry. Recent experimental evidence shows that REV-ERB and ROR are not only crucial for lipid metabolism but are also involved in dopamine (DA) synthesis and degradation, which could have meaningful clinical implications for conditions such as Parkinson’s disease and mood disorders.