Mathematics of Biological Charge Transport: Molecules and Beyond

One of the most important challenges in biology today is to link our ever increasing knowledge about the structure of biomolecules to its function. Genomic sequencing and advances in structural biology are starting to give us a detailed view of what biomolecules look like, but it is still a very challenging matter to infer functional characteristics from structural data. This is important, not only for its intrinsic scientific merit, but also for its potential impact on society, through rational drug design and discovery. This problem is in large part a mathematical challenge. One objective is to compute the current voltage relation of an ion channel or the binding constants of enzymes given structural data. Such is the goal of mathematical molecular biology, and this is the first focus of this workshop. A major barrier for mathematical scientists to work in this field is the lack of knowledge on molecular biology, while a major barrier for biologists is the lack of modern mathematical tools and techniques that have been developed in the past 20 years. This workshop is designed to help bridge gaps between molecular biologists and mathematical scientists.

Most, if not all, biomolecules are charged, and all biomolecular reactions take place in an ionic solvent. Thus, considerations of charge transport are central to any serious attempt to link structure to function in molecular biology. This brings us to the second and technical focus of our workshop, charge transport. The simplest model of charge transport is the Poisson-Nernst-Planck system, a classical model whose mathematical properties are still not well-understood and still poses difficult computational challenges. Charge transport has seen a resurgence in interest due partly to its central role in mathematical molecular biology and has seen emergent applications in other fields in biology and related areas, such as soft condensed matter physics. This workshop aims to bring together experts on mathematical biomolecular electrostatics with researchers working more broadly on charge transport.