Dr. Francis Motta (Dept. of Mathematical Sciences, Florida Atlantic University)

4/25/2024  3:10pm

Abstract: 

Malaria in humans is a debilitating disease characterized by periodic fevers at 24, 48, or 72 hours depending on the species of Plasmodium infecting the host. The periodic fevers correspond to the highly synchronized bursting and reinvasion of host red blood cells, but the genetic, metabolic, and/or environmental factors allowing parasites to maintain synchronized, periodic developmental cycles is unknown.  High-resolution time-series gene expression data of Plasmodium falciparum in vitro and Plasmodium vivax ex vivo provided in recent studies are consistent with the hypothesis that population synchrony is controlled by a parasite intrinsic biological clock that maintains a precisely timed periodic developmental cycle, combined with phase coupling to host circadian rhythms. However, accurate quantification and analysis of the degree of population synchrony has been hampered by a lack of precise definitions and complicating biological mechanisms such as replication. Starting with this motivating application, we propose a general, quantified definition of population synchrony based on Fréchet variance of a distribution on a compact metric space. We justify this definition by establishing a variety of its desirable mathematical and computational properties. We discuss the measure's practical utility in modelling and analyzing a variety of population-level measurements, with an emphasis on the dynamics of the Plasmodium intraerythrocytic developmental cycle.