The Human Genome project and subsequent developments have given us unprecedented knowledge of the genes and proteins within us. There is much anticipation that this knowledge will translate into substantial improvements in human health and well-being. A central challenge, however, is the enormous complexity that we encounter at the molecular level. It is not merely that we have 20,000 genes but that the machinery that regulates each gene is itself extraordinarily complex with, in the case of some genes, billions of potential states. Moreover, when the gene is expressed as a protein, each protein may itself become modified so that it too can exist in many different states, which may have profoundly different consequences. This project will use two mathematical formalisms developed in previous work -- the "linear framework" and the method of "invariants" -- that have been shown to be capable of rising above the complexity and eliciting general principles. The investigators will use these formalisms to analyze two focus problems in which the underlying complexity has proved intractable: (1) "epigenetic" mechanisms in gene regulation, which play a central role in how the environment influences gene expression, and (2) decision-making switches based on protein modification states, which play a central role in controlling cellular behavior. A key aspect of the project is the involvement of undergraduate students from the mathematical and physical sciences, especially students from under-represented groups. The project will act as pipeline to motivate such students towards research in the biological and bio-medical sciences, a strategy that contributed substantially to the success of previous work.
The biochemical reactions within cells are generally assumed to follow the principle of mass action -- the rate of a reaction is the product of the concentrations of the reactants -- so that their behavior can be represented by a polynomial dynamical system. The steady states of a network of reactions are therefore solutions to a set of polynomial equations and form an algebraic variety. The investigators have pioneered the use of methods from algebraic geometry in the study of biochemical networks, leading to the introduction of the "linear framework" and the method of "invariants," both of which can distill biological principles in the face of molecular complexity. This project will further develop these approaches by attacking two major focus problems. First, the investigators will analyze the behavior of protein modification switches, which are central motifs in regulating cellular signaling pathways and cell behavior, and will characterize them in terms of their invariants. Second, the role of energy-dissipating, epigenetic mechanisms in gene regulation will be analyzed. In previous work, the investigators showed that energy dissipation leads to a profound increase in complexity through the phenomenon of history-dependence. Methods for interpreting that complexity and identifying how energy-dissipation contributes to environmental modulation of gene expression will be developed.
