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The modeling and analysis of the complex interactions between genes and metabolites during development require computational approaches. However, existing methods cannot efficiently account for the large number of interacting players, the nonlinear nature of the interactions, or the disparate scales involved. The latter represents a challenge in modeling developmental systems since reaction rates and diffusion times can vary by several orders of magnitude (depending on the molecular system). Modeling processes of this type results in the pathology of stiffness. Numerically, stiffness occurs when, in order to prevent large amplification of errors, typical (non-stiff) algorithms require a step size much smaller than the scale at which the solution in changing. In this work, a new method to solve large stiff systems of equations in the non-linear power law form was developed. The power-law formatism is a proven powerful tool for biological systems modeling, and has many advantages over other formalisms used for this purpose. The advantages include the fact that it is canonical, and that it is an accurate local approximation to any type of interaction. Representative results are presented

osti oai (u.s. department of energy office of scientific and technical information)

Final Report, December, 1999. Sloan - US Department of Energy joint postdoctoral fellowship in computational molecular biology [Canonical nonlinear methods for modeling and analyzing gene circuits and spatial variations during pattern formation in embryonic development]