Collaborative Research: Models and Mechanisms of Population Synchrony and Entrainment

Biological clocks regulate daily rhythms in many organisms, including humans, and disruption of these clocks can significantly impair health and performance. These timing mechanisms operate at the cellular level and are present in single-celled organisms, such as disease-causing parasites, as well as in every cell of multicellular organisms. For proper organismal function, cellular clocks must remain synchronized. While the molecular basis of individual clocks is well understood, the mechanisms by which clocks coordinate across cells and align with environmental rhythms remain largely unknown. Understanding how biological systems establish and maintain synchrony is essential for explaining how organisms keep time, with broad implications for human health and economic productivity. To address this challenge, this project will combine mathematical modeling with experimental approaches to investigate how cellular clocks communicate and coordinate their activity. More specifically, the project will integrate the development of mathematical models and methodology with biological experiments, with the aim of identifying the principles governing synchronization in rhythmic biological populations. This project will also train researchers at the interface of mathematics and biology through integrated graduate and undergraduate programs across four partner institutions. Principal investigators will provide mentorship in theory, computation, experimentation, and scientific communication. Existing frameworks for modeling periodic biological phenomena and entrainment observed in complex systems have several limitations: deterministic models omit randomness that leads to loss of synchrony, traditional stochastic models face scalability challenges, and differential equations do not naturally capture effects of replication. Moreover, available measures of population synchrony are often ad hoc, system-specific, and restricted to simple state spaces. This project will develop a unified, general mathematical framework to model dynamic populations and measure their synchrony and entrainment in complex state spaces through three main objectives. The first objective is to establish general mathematical measures of synchrony for one or more coupled populations occupying topologically complex state spaces. The second objective is to develop dynamical models based on discrete-time multi-type branching processes (DTMTBPs) that incorporate time-dependent, distribution-dependent, and coupled-population transition probabilities to represent unidirectional, population-dependent, and bi-directional entrainment mechanisms. The third objective is to establish provably correct algorithms for synchrony computations, advance error bounds and limit theorems for DTMTBP simulations, and deliver efficient open-source computational tools. The proposed mathematical framework will substantially advance the approaches needed to quantify synchrony and understand multiple mechanisms of entrainment by producing analytically tractable, high-utility mathematical models and methods. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.