Branching morphogenesis, the creation of a hollow tree of branched ducts from an initially simple structure, is a robust, important, and widely studied model system in developmental biology. There is a large body of experimental results on what is and is not required to generate the glandular structures, but there is as yet no single theory which ties together all that is known about branching morphogenesis. The two main existing theories hypothesize that the origin and direction of branching activity rest solely in, respectively, (1) the epithelium, and (2) the mesenchyme. This study proposes a new hypothesis, that activity in (3) both tissues is essential. This study will develop a mathematical model of the forces and deformations involved in branching morphogenesis, using a multiphase for mulation to track changes in the density of cells, extracellular matrix components, and interstitial fluid. The model will be analyzed, using asymptotics, perturbations, bifurcation analysis, parameter estimation, and numerical simulation. The first task will be to evaluate the agreement of the model with experimental facts, and the second will be to help answer some long-standing questions, specifically the relative mechanical roles of the epithelium and the mesenchyme. Specific predictions will be made, that others may test them experimentally. The primary goal of this project is to distinguish between the three major theories of branching morphogenesis mentioned above. It is very likely that the insights gained from this modeling study of branching morphogenesis will lead to a better under standing in general of the physical forces in confluent (epithelial) and sparse (mesenchymal) tissues, both in homeostasis and in development, with applications and insights in other contexts such as somitogenesis, tooth and hair formation, angiogenesis, healing, and tumor growth. The study will also lead to an improved understanding of the multiphase models of biological tissues which have been developed in other contexts, through extending these passive models to tissues which are actively growing and remodeling. The formation of branched tubular structures occurs throughout an organism, in many different tissues, and is essential to the very existence of large organisms which need to transport fluids more than a short distance. Branching morphogenesis is a widespread phenomenon in animal development, generating the form of such organs as the lung, mammary gland, salivary gland, and kidney. Although nearly every technique of cellular and developmental biology has been applied to it, and much has been learned from these experiments, there is still uncertainty as to the mechanism of branching. The overwhelming majority of experiments on branching have concentrated on biochemical aspects, following the dominant paradigm in biological research of the last few decades. Yet the essence of morphogenesis is that tissues grow and move and change shape, and this requires physical forces to emerge from the molecular biology. Hence the next logical step in morphogenesis research is study of the biomechanical aspects, which are what create and modify form. A mathematical model will be developed of the mechanical forces and resulting material deformations of the tissues involved in morphogenesis. Analysis of the model will (1) allow a comparison of the biomechanical aspects of the currently competing theories of branching morphogenesis, (2) lead to greater understanding of the relatively new modeling methodology itself, which is useful in many other biological applications, and (3) suggest new interpretations and experiments towards the goal of understanding one of the most important phenomena in developmental biology.
