This grant has supported mathematical modeling and exploration of a number of important physiological gels.  A physiological gel is a mixture of water and polymer whose properties and behavior depend in complex ways on its individual components and on the interactions between them.  Such gels are widespread in biology and play a critical role in many physiological and disease processes.  For example, a gel made from the protein fibrin is formed as part of the blood's clotting response and this fibrin gel is a major component of clots that form to seal an injury as well as those that form, e.g.,  in the veins of the leg and cause serious health problems. Another gel made of mucin molecules normally protects the lining of the stomach from digestion by the highly acidic stomach juices; its dysfunction contributes to development of ulcers.  A related mucin gel lines the airways of the lungs; its properties are abnormal in patients with cystic fibrosis and prevent normal clearance of microbes from the lungs.  In fact, all of our cells are filled with cytoplasm which itself is a gel made up of several different protein polymer networks embedded in the cytosolic fluid.  The dynamics of cytoplasm are critical for many cell functions including the ability of the cell to move from one location to another, as must happen to maintain normal tissues and also happens when malignant tumor cells metastasize from the site of the original tumor.  In each of these situations, the movement and function of the gel is influenced by biochemical reactions.  Predicting the behavior of these gels and understanding them sufficiently to modulate their behavior for improved health are important but very challenging goals toward which this grant has allowed us to make substantial progress.

Under this grant, we have developed mathematical models describing the physics and chemistry of the particular physiological gels described above, developed new mathematical and computational tools with which to probe the models'  behavior, and used these tools to gain insights into the physiological function and dysfunction of the gels.  We have provided new understanding of the dynamics of both the formation and breakup of fibrin gels.  We have elucidated the mechanism underlying the explosive swelling of mucin gel as it is secreted into the extracellular space.  We have made significant progress in understanding the movement of cells through the mechanism of cellular blebbing.  In carrying out these projects, we have also developed a new modeling framework in which to describe other physiological and biological gels and provided powerful computational tools with which to study those gels.

The work of this grant has impact well beyond the mathematical community. The models and insights they provide to how specific biological gels function is important for basic biology as well as for medicine.  The modeling framework is important in other fields, e.g, chemical engineering, in which the behavior of complex gels is of great interest.  The computational tools are of widespread utility to researchers in many fields studying gels, whether in a biological or non-biological context.  The grant has also contributed to the development of a new generation of interdisciplinary mathematical scientists who, by taking positions in universities around the United States, will continue to work with scientists to use mathematics to study important biological questions, and will also educate young students about the exciting world of interdisciplinary mathematics.

Last Modified: 11/10/2013
Modified by: Aaron L Fogelson