Reinitz 9618651 The investigator with Yuefan Deng of SUNY Stony Brook and their colleagues study large scale optimization methods applied to problems concerning gene networks and pattern formation in the fruit fly Drosophila. These optimization problems arise in a method known as "gene circuits", which was developed by one of the principal investigators and his coworkers. The essence of this method is the numerical inversion of a set of nonlinear ordinary differential equations by least squares fits of the trajectories of the equations to gene expression data obtained by fluorescence microscopy. In the past, these fits were performed by simulated annealing on serial computers using the Metropolis algorithm under the control of the Lam cooling schedule. They are computationally intensive, and the range of problems that can be considered was limited by the speed of available serial processors. The investigators are developing new computational methods for the solution of these problems on parallel processors. Importance sampling is the most efficient, or the most important, ingredient of an algorithm in treating complex continuum optimization problems such as the pattern formation analysis undertaken here. Simulated annealing is one method for importance sampling; the investigators are developing a general method for parallel simulated annealing on nonseparable problems. Other importance sampling methods are derived from methods that make use of the continuum properties of the problem at hand, such as Newton's method. The investigators develop a family of parallel importance sampling methods and then synergistically combine them. This family of methods includes genetic algorithms, continuum methods, a Lagrangian reformulation of the fitting problem, and simulated annealing. Networks of interacting genes lie at the heart of the problems that will face biologists and biotechnologists in the twenty first century. Processes ranging from embryonic d evelopment to cell division and cell death are controlled by networks of genes. In order to understand how these networks work, it is necessary to understand their internal "wiring diagrams". In particular, it is important to know how genes turn each other on and off. Modern molecular biology allows investigators to see which genes are on or off at a given moment, but in order to understand the "wiring" between genes, it is necessary to analyze changes in gene activity over time and analyze them by computer. The method of analysis can be reduced to an "optimization" problem, in which the smallest value of a complicated function is sought. In this project, the investigators are finding new ways to solve optimization problems on large scale parallel high-performance computers. Particular emphasis is placed on parallel methods for simulated annealing, an exceptionally powerful optimization method. This research is important to many areas beyond gene networks. Simulated annealing and related methods are used in structural biology and other biotechnology areas related to drug discovery. It is also used in the design of integrated circuits. These and other areas are likely to benefit from this work. Funding for the project is provided by the program of Computational Mathematics and the Office of Multidisciplinary Activities in MPS and by the Developmental Biology program in BIO.
