Mystery solved with math: Cytoplasmic traffic jam disrupts sleep-wake cycles

Human bodies adjust sleep schedules in accordance with the 'circadian rhythms', which are regulated by our time keeping system, the 'circadian clock'. This clock tells our body when to rest by generating the 24-hour rhythms of a protein called PERIOD (PER).

The amount of the PER protein increases for half of the day and then decreases for the remaining half. The principle is that the PER protein accumulating in the cytoplasm for several hours enters the cell nucleus all at once, hindering the transcription of PER genes and thereby reducing the amount of PER.

However, it has remained a mystery how thousands of PER molecules can simultaneously enter into the nucleus in a complex cell environment where a variety of materials co-exist and can interfere with the motion of PER. This would be like finding a way for thousands of employees from all over New York City to enter an office building at the same time every day.

A group of researchers led by Professor Jae Kyoung Kim from the KAIST Department of Mathematical Sciences solved the mystery by developing a spatiotemporal and probabilistic model that describes the motion of PER molecules in a cell environment.

This study was conducted in collaboration with Professor Choogon Lee's group from Florida State University, where the experiments were carried out, and the results were published in the Proceedings of the National Academy of Sciences (PNAS) last month.

The joint research team's spatial stochastic model described the motion of PER molecules in cells and demonstrated that the PER molecule should be sufficiently condensed around the cell nucleus to be phosphorylated simultaneously and enter the nucleus together. Thanks to this phosphorylation synchronization switch, thousands of PER molecules can enter the nucleus at the same time every day and maintain stable circadian rhythms.

However, when aging and/or diseases including dementia and obesity cause the cytoplasm to become congested with increased cytoplasmic obstacles such as protein aggregates and fat vacuoles, it hinders the timely condensation of PER molecules around the cell nucleus. As a result, the phosphorylation synchronization switch does not work and PER proteins enter into the nucleus at irregular times, making the circadian rhythms and sleep-wake cycles unstable, the study revealed.

Professor Kim said, "As a mathematician, I am excited to help enable the advancement of new treatment strategies that can improve the lives of so many patients who suffer from irregular sleep-wake cycles. Taking these findings as an opportunity, I hope to see more active interchanges of ideas and collaboration between mathematical and biological sciences."