Parameter Estimation for a Mathematical Model of the Cell Cycle in Frog Eggs

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.

[1]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[2]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[3]  J. Tyson,et al.  Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. , 1993, Journal of cell science.

[4]  John J. Tyson,et al.  Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[5]  L. Petzold.  Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations , 1983 .

[6]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[7]  J. Tyson,et al.  Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA. , 1998, Biophysical chemistry.

[8]  T. Coleman,et al.  Two distinct mechanisms for negative regulation of the Wee1 protein kinase. , 1993, The EMBO journal.

[9]  Barbara M. Bakker,et al.  Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. , 2000, European journal of biochemistry.

[10]  Janet E. Rogers,et al.  User's reference guide for ODRPACK version 2.01:: software for weighted orthogonal distance regression , 1992 .

[11]  P. Boggs,et al.  A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression , 1987 .

[12]  A. Kumagai,et al.  Control of the Cdc2/cyclin B complex in Xenopus egg extracts arrested at a G2/M checkpoint with DNA synthesis inhibitors. , 1995, Molecular biology of the cell.

[13]  Alan C. Hindmarsh,et al.  Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations , 1993 .

[14]  F. Hynne,et al.  Full-scale model of glycolysis in Saccharomyces cerevisiae. , 2001, Biophysical chemistry.

[15]  G. Odell,et al.  The segment polarity network is a robust developmental module , 2000, Nature.

[16]  A. Kumagai,et al.  Regulation of the cdc25 protein during the cell cycle in Xenopus extracts , 1992, Cell.

[17]  Eduardo Sontag,et al.  Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 , 2003, Nature Cell Biology.

[18]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[19]  Stephen J. Wright,et al.  Optimization Software Guide , 1987 .

[20]  Kathy Chen,et al.  Network dynamics and cell physiology , 2001, Nature Reviews Molecular Cell Biology.

[21]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[22]  Marc W. Kirschner,et al.  Cyclin activation of p34 cdc2 , 1990, Cell.

[23]  L. Shampine,et al.  Computer solution of ordinary differential equations : the initial value problem , 1975 .

[24]  A. Hindmarsh.  LSODE and LSODI, two new initial value ordinary differential equation solvers , 1980, SGNM.

[25]  Katherine C. Chen,et al.  Kinetic analysis of a molecular model of the budding yeast cell cycle. , 2000, Molecular biology of the cell.

[26]  Richard H. Byrd,et al.  Algorithm 676: ODRPACK: software for weighted orthogonal distance regression , 1989, TOMS.

[27]  J. Tyson,et al.  Checkpoints in the cell cycle from a modeler's perspective. , 1995, Progress in cell cycle research.

[28]  S. Nash,et al.  Numerical methods and software , 1990 .

[29]  V. Hu.  The Cell Cycle , 1994, GWUMC Department of Biochemistry Annual Spring Symposia.

[30]  Lawrence F. Shampine,et al.  Numerical computing: An introduction , 1973 .