Formation and Function of Physiological Gels

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The investigators will use mathematical analysis and computations to explore the mechanical and chemical dynamics of physiological gels. The fact that there are many polymer networks with gel-like properties in biological systems has been largely overlooked by experimentalists and theorists. Indeed, quantitative studies of biogels are scant in comparison with those of other physiological structures and processes. One aim of this project, therefore, is to bring to bear the tools of applied mathematics to several closely related problems of biogel growth and dynamic behavior. More specifically, the goal of this proposal is to study the processes of gel formation, secretion, and degradation; their regulation; and the relationship between these and function in dynamic physiological biogels. The investigators will study these issues by examining three specific problems: i) The growth of fibrin gel networks during blood clotting. ii) Vesicular exocytosis of mucin gel. iii) The growth and regulation of the mucin layer in the stomach and its role in gastric protection. The studies will involve multiple spatial and temporal scales, and will examine how microscopic properties and events affect macroscopic function. Mathematical models will be developed to understand how physical properties such as the viscoelastic constitutive properties and the gel morphology are determined and controlled, and how these properties affect the physiological function of the biogel. At the same time, the investigators will look for general principles of biogel dynamics that have consequences in other systems.Polymer networks with gel-like properties arise in a wide range of physiological settings and processes. Better insight into how such gels are formed and how their properties are regulated is critical to understanding these important processes and how they can be manipulated to improve human health. Because the formation and regulation of biogels is governed by physical and chemical properties and because these properties can be expressed mathematically, mathematical tools can be brought to bear on these problems. Through mathematical analysis and computational simulations of biogels, a wealth of detailed data can be obtained that complements the data obtainable from traditional laboratory experiments. Hence the combination of mathematical and experimental investigators brought together in this project is expected to lead to important new insights about biogel behavior in important physiological and pathological situations including blood clotting, mucin secretion, and protection of the stomach lining.