Biological systems display heterogeneity at every level. Even cells that are genetically identical and exposed to the same environments can have different chemical composition. The fundamental reason is that molecules bounce around in an unpredictable way, much like dice do when thrown on a table, and react when they randomly collide. This project will describe the randomness mathematically. Specifically, it will explore the general connection between fluctuations and control, that is, how controlling some parts of a system creates heterogeneity in others, much as small variations in the weather must be translated into large variations in the temperature of radiators to keep the room temperature constant. Rather than model specific systems, it will take a more general approach to capture broad principles of complex systems. That makes the results widely applicable in other disciplines - whether in health and medicine, ecology, or infrastructure problems where conceptually similar challenges arise. The project will train students at the interface between scientific disciplines, as well as generate examples and principles that will be useful in undergraduate education.
Stochastic descriptions of cells have historically relied on detailed computer simulations that must guess many of the system details, or simplified toy models that only include a few reactions. This project will instead focus on the derivation of theorems of sufficient generality to hold for large families of processes, to rigorously understand broader design principles of biological systems. Specifically, the project will focus on deriving bounds on variances as a function of other system properties, to show, for example, how selection for maximal anabolic or enzymatic efficiency inevitably leads to large fluctuations. Similarly, the project will derive fluctuation trade-offs showing how suppressing noise in some components inevitably increases fluctuations in others. Mathematically this relies on both Markov and non-Markov processes, information theory, and fluctuation-dissipation relations, to derive statistical moments for open ended families of models.
