Much of biological inquiry has focused on the chemically-active parts of proteins that have a stable, rigid shape. However, over 30% of our proteins have regions that are not rigid, but rather are floppy tethers that connect the chemically-active regions. Two examples of tethers are: immunoreceptors, the proteins involved in how immune cells receive signals from other cells; and formins, proteins that maintain the cell's architectural skeleton and are hijacked by invading bacteria including cholera. Tethers are easy to overlook. In part, this is because the mathematical descriptions that allow understanding of rigid proteins do not work for tethers. Therefore, mathematically characterizing tethers may lead to novel avenues of research in biology and medicine that were missed by focusing only of the rigid regions of proteins. This project will develop a mathematical description of tethers. The mathematics will be used to, first, develop a rapid computational algorithm to simulate the first few steps of how immune cells respond to external signals, including how they respond to off-switch signals through the protein PD-1, signals that is exploited by cancers to evade immune detection. Second, the mathematics will be used to study the tethers in formins. The resulting mathematics will create new connections between two separate fields of mathematics: stochastic process theory, and polymer physics. The project will also result in the training of graduate students with skills in immunology, cell biology, applied mathematics, computational science, and biophysics. Open-access resources for enabling computational science researchers will also be developed. These will have a special focus on creating tools for research in the remote era, including tutorials for high school and undergraduate students.
Many proteins (around 30% in humans) have regions that lack well-defined structure, but rather fluctuate through an ensemble of configurations characterized by high intrinsic disorder. Many of these act as tethers that connect chemical reaction sites. Examples include immunoreceptors like the T Cell Receptor, PD1 and CD28, and formins, which regulate cytoskeleton assembly. Tethered reactions are ubiquitous; they have properties that are fundamentally distinct from standard solution reactions, requiring novel mathematical characterization; they are exploited by biology; and, in some cases, they provide novel avenues for therapeutics. This project exploits and extends a long-known mathematical correspondence between stochastic process theory and polymer physics to study tethered reactions. The mathematical theory aims to resolve biological mysteries, first, concerning the formin tethers and their ability to assemble the cytoskeleton even when bound at both termini, in a force-responsive manner. Second, the project addresses experimental data on immunoreceptor tethered signaling that cannot be explained by models that omit volume exclusion (crowding). The project will also develop 3 online resources that will help the Mathematical Biology community thrive in a future dominated by online interaction, including tutorials for high school and undergraduate students.
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.
