Mathematical Problems at the Interface between Materials Science and Biology: Polyelectrolyte gels, Devices and Physiological Applications

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This award will support interdisciplinary research in mathematics, condensed matter physics, continuum mechanics and biology. A main theme of the work is the study of forces in living systems. The PI will take the point of view of materials science, and analyze, first, semi-flexible, biopolymer systems. These are anisotropic polyelectrolyte gels and consist of directionally biased and electrically charged elastic networks holding fluid with ions. The project starts out woith the question how the combined elastic anisotropy (modeled as in the case of liquid crystal elastomers), electrostatic and short range Van-der-Waals interactions may explain phenomena such as the negative Poynting effect in semi-flexible polymers. The next stage of the research consists in modeling the interstitial tissue. This is a polyelectrolyte gel sustaining large, rod-like protein structures that make the network anisotropic. One main goal is the modeling of edema, in order to explain the large forces that confine the excess fluid in the interstitial tissue of patients. The mathematical problems are formulated as systems of partial differential equations stemming from mixture theory. Specifically, these consist of the time-dependent equations of liquid crystal elastomers coupled with Stokes problems for fluids, and with the Nernst-Planck equations for ions. The new research will partially follow previous work on isotropic polyelectrolyte gels by the PI and coauthors, but new mathematical and modeling tools have to be developed. These new tools will also be applied to modeling the dynamics of cancer cells on fiber tissue. The research will be collaborative, involving the PI and faculty members from mathematics, physics, bioscience and engineering, as well as industrial partners, together with postdocs and graduate and undergraduate students.This award will support research aimed at the study of forces that hold living structures together. The PI will focus on modeling interstitial tissue that connects organs, vessels and bone. In particular, the research will try to understand the physical principles underlying the trapping of unusually large amounts of liquid in the interstitial tissue, a condition known as edema. The work, jointly carried out with researchers at the Kidney Institute of the Medical School of the University of Minnesota and with a Minneapolis biosciences company, may help motivate the search for new therapies. These models will also support research on cancer cell dynamics, with the goal of modeling biomechanical aspects of the onset of tumor nucleation. The award will support collaborative research involving faculty members from mathematics, physics, bioscience and engineering, together with undergraduate students (math, physics and biosciences), postdocs and graduate students.