Parameter values for a kinetic model of the nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.

DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak & Tyson. In a recent publication, we showed that a gradient-based optimisation algorithm finds a locally optimal parameter set quite close to the 'Marlovits' estimates. In this paper, we combine global and local optimisation strategies to show that the 'refined Marlovits' parameter set, with one minor but significant modification to the Novak & Tyson equations, is the unique, best-fitting solution to the parameter estimation problem.

ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and many more features. The foundation for the algorithm is a stable and efficient trust region Levenberg-Marquardt minimizer that exploits the structure of the orthogonal distance regression problem. ODRPACK95 was created to extend the functionality and usability of ODRPACK. ODRPACK95 adds bound constraints, uses the newer Fortran 95 language, and simplifies the interface to the user called subroutine.

The life of a cell is governed by the physicochemical properties of a complex network of interacting macromolecules (primarily genes and proteins). Hence, a full scientific understanding of and rational engineering approach to cell physiology require accurate mathematical models of the spatial and temporal dynamics of these macromolecular assemblies, especially the networks involved in integrating signals and regulating cellular responses. The Virginia Tech Consortium is involved in three specific goals of DARPA's computational biology program (Bio-COMP): to create effective software tools for modeling gene-proteinmetabolite networks, to employ these tools in creating a new generation of realistic models, and to test and refine these models by well-conceived experimental studies. The special emphasis of this group is to understand the mechanisms of cell cycle control in eukaryotes (yeast cells and frog eggs). The software tools developed at Virginia Tech are designed to meet general requirements of modeling regulatory networks and are collected in a problem-solving environment called JigCell.

Abstract-This paper presents a sophisticated and efficient parallel scheme for the DIRECT global optimization algorithm of Jones et al. (1993). Although several sequential implementations for this algorithm have been successfully applied to large scale MDO problems, few parallel versions of the DIRECT algorithm have addressed well algorithm characteristics such as a single starting point, an unpredictable workload, and a strong data dependency. These challenges engender many interesting design issues including domain decomposition, data access and management, and workload balancing. In the present work, a hierarchical parallel scheme has been developed to address these challenges at three levels. Each level is supported by parallel and distributed data structures to access shared data sets, distribute workload, or exchange messages. Parameter estimation problems in systems biology provide an ideal application context for the present work. Global nonlinear parameter estimation results obtained on a 200 node Linux cluster are given for a cell cycle model for frog eggs.