A challenge to both understanding and modeling biochemical networks is integrating the effects of diffusion and stochasticity. Here, we use the theory of branching processes to give exact analytical expressions for the mean and variance of protein numbers as a function of time and position in a spatial version of an established model of gene expression. We show that both the mean and the magnitude of fluctuations are determined by the protein’s Kuramoto length—the typical distance a protein diffuses over its lifetime—and find that the covariance between local concentrations of proteins often increases if there are substantial bursts of synthesis during translation. Using high-throughput data, we estimate that the Kuramoto length of cytoplasmic proteins in budding yeast to be an order of magnitude larger than the cell diameter, implying that many such proteins should have an approximately uniform concentration. For constitutively expressed proteins that live substantially longer than their mRNA, we give an exact expression for the deviation of their local fluctuations from Poisson fluctuations. If the Kuramoto length of mRNA is sufficiently small, we predict that such local fluctuations become approximately Poisson in bacteria in much of the cell, unless translational bursting is exceptionally strong. Our results therefore demonstrate that diffusion can act to both increase and decrease the complexity of fluctuations in biochemical networks.
The time required to recover from cold-induced paralysis (chill-coma) is a common measure of insect cold tolerance used to test central questions in thermal biology and predict the effects of climate change on insect populations. The onset of chill-coma in the fall field cricket (Gryllus pe ... more
Influenza recurs seasonally in temperate regions of the world; however, our ability to predict the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited. Here we develop a framework for initializing real-time forecasts of seasonal influenza outbreaks, usin ... more
Undifferentiated nasopharyngeal carcinomas (NPCs) are commonly present with latent EBV infection. However, events regulating EBV infection at early stages of the disease and the role of EBV in disease pathogenesis are largely undefined. Genetic alterations leading to activation of cyclin D1 ... more