Cycle Representations of Receptor Complex Signal Transduction

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The border of living cells is covered with sentry molecules that sense the presence of chemical signals, assess the current situation, and initiate decision processes that determine a cell’s response to its environment. These “cell surface receptors” function like a car ignition switch: they accept a specific chemical signal (the key) and then communicate the presence of this chemical key to the interior of the cell. Because receptors have a profound influence on cell behavior, it is crucial to understand the details of how they function. The most important types of receptors are made up of several component parts that work together as complex molecular machines. Because of this complexity, mathematical models of cell surface receptors are integral to understanding both natural signaling mechanisms of cells and the mode of action of man-made therapeutic drugs. Mathematical and biophysical theory being developed by the PI is revealing how receptor function may be understood in terms of the properties of their parts (protein subunits) and the energetic interactions between these parts (conformational coupling). This fundamental scientific knowledge is the launching point for numerous applied endeavors that directly impact human wellbeing, such as scientifically informed drug development. In more technical terms, the PI’s recent mathematical work on cycle bases of product graphs provides a formalism for the efficient enumeration the possible modes of conformational coupling in a receptor dimer or high-order oligomer, beginning with arbitrary hypothesized monomeric state-transition diagram. This novel quantitative pharmacology modeling technique automatically satisfies the emergent thermodynamic constraints that arise in the receptor oligomer, and provides an unambiguous physical interpretation of each allosteric parameter. The PI is developing a general mathematical formalism, based on product graphs, for analysis of receptor complexes, with specific focus on dimeric G-protein-coupled receptors and receptor tyrosine kinases. The formalism will be extended to accommodate non-equilibrium phenomena mediated by nucleotide exchange. Software for the analysis of receptor oligomers will be developed and shared with life scientists. Because few mathematicians have the requisite biological background to be of help to medical scientists, and few medical scientists have the quantitative skills necessary to reverse engineer living cells, the PI is committed to training Ph.D. scientists who will have an interdisciplinary outlook, to exposing pre-medical undergraduates to the sophisticated mathematics, and to pedagogical writing that clarifies how mathematics is essential to progress in the life sciences. This award is co-funded with the Cellular Dynamics and Function program in Division of Molecular and Cellular Biosciences, and the Life Science Venture Fund in DMS.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.