Mathematics of Molecular and Cellular Biology

Three major areas of emphasis:
September-December 2007 - Nucleic Acid Structure and Function
January-March 2008 - Protein Structure and Function
April-June 2008 - Modeling Cellular Physiology

The interface between the mathematical sciences and biology has been growing steadily in importance in the last decade, but there is tremendous room for progress. Major advances are needed in mathematical, statistical and computational methods to generate significant impact on the prediction and control of spatio-temporal molecular and cellular behavior. This IMA program starts with nucleic acids, moves on to proteins, and ends with the modeling of cellular physiology. These areas have major interconnectedness, and the program will emphasize these relationships. In the Fall quarter we begin with nucleic acid (DNA and RNA) organization, structure, function, and the interaction between DNA and RNA in the production of proteins and the orchestration of cellular metabolism. In the Winter quarter we study protein structure and function. The new science of proteomics aims to understand how proteins are produced and how they function and malfunction. We need to understand how protein production is controlled, and the cascade of interaction among families of proteins. In the Spring quarter we study the mathematics of cellular physiology, a highly complex biological system, with structures from molecular to macroscopic scale, and processes with critical time scales from nanoseconds to hours. Modeling cellular behavior poses significant challenges to the mathematical sciences.

Progress at the interface will be enabled by developments in mathematics focused on biology at the molecular level. Accurate models of molecular forces appropriate to biological systems will be critically needed. These will have to work well even when (as during protein folding), molecules form, break and remake bonds, a far more difficult and nonlinear situation than found in crystalline substances. New and efficient methods will be needed to model the effect of solvents on important biological reactions. Purely stochastic methods are expected to be important, but, equally importantly, a theory will have to be built that supplies biologically meaningful probability distributions that are input to those methods. In addition, the mathematical models must be amenable to efficient computational algorithms that can analyze realistic biological reactions.

Molecular dynamics is a critical part of almost every quantitative study at the molecular level, and the time scales treatable by accurate MD methods, based on truly accurate molecular forces, are far too short to treat anything but the most simple biological reaction. At a higher but still relatively simple levels, there are simple organized structures in biology, e.g., such things as microtubules, mini-chromosomes, actin filaments, protein motors, viral capsids, membranes, that may be amenable to mesoscale (bridging the gap between microscopic and macroscopic) and macroscopic mathematical models. As emphasized by members of the Biological Advisory Committee it will be important to focus on sufficiently simple (but real) biological systems to maximize the value of the quantitative approach.