9501980 Bentil This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on a mechanical approach to biological pattern formation. This interdisciplinary modeling project will focus on studying and constructing realistic model mechanisms that capture key biological processes that may be involved in spatial patterning and showing how they are orchestrated. Model applications will include mechanisms for the generation of embryonic fingerprints. Particular emphasis will be placed on (i) development of analytical and numerical techniques for the solution of model equations, such as perturbation theory and the use of the level set approach for the solution of Hamilton-Jacobi-type equations coupled with parabolic equations, (ii) biological interpretation of the results in terms of insights and predictions, (iii) model comparisons based on currently known biology, and (iv) model refinements as they apply to specific biological patterning problems such as the development of fingerprints. It is expected that this work will result in a much better understanding, both mathematically and biologically, of the mechanical effects of cell traction on cell motion and cell aggregation within embryonic tissues, and should, therefore, provide significant insight into how this relatively new mechanical approach to modeling biological patterns could be used to address pattern formation problems in developmental biology. The education component will focus on an interdisciplinary mathematical modeling curriculum for undergraduate and beginning graduate students. It is proposed to design, develop, and implement a coordinated biomathematical modeling curriculum for life science students that will initially be adopted at the University of Massachusetts, Amherst and, therefore, available to the other four colleges (Amherst, Hampshire, Mount Holyoke, and Smith) in the Five Colleges Consor tium through the established student and faculty exchange. The curriculum will consist of two parts: the first part will be a bridge between calculus and its applications and it will involve technology in the classroom. It is expected that this course will provide the textual material necessary to support a substantial modeling course. The second part will be a sequence that will introduce students to contemporary biomathematical modeling. It is expected that this course will cover quantitative topics that will help life science students deal with the numerical and technical information they will encounter. Regular meetings with undergraduate course directors and other interdisciplinary faculty members will be an important part of this mission. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.
