Stiff problems in numerical simulation of biochemical and gene regulatory networks
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With the sequence of genomes of many organisms now available, the major chal- lenge of functional genomics is 'reassembling the pieces'. A chemical reaction network is considered to be a very simple and e±cient view of a living system. The goal here is to be able to simulate an arbitrary ensemble of hypothesized biochemical and gene regulatory networks to predict what a cell is doing and compare them with the observed data. Any biological network can be modeled as a system of Ordinary Dif- ferential Equations (ODEs) mathematically. There are a number of standard ODE solvers, such as the Euler and Runge Kutta (RK) methods. But from time to time, these methods could be very ine±cient for some special systems, called sti® sys- tems. We consider other special ODE solvers, such as Livermore Solver for ODE with General Sparse Jacobian Matrices (LSODES). A simulator KINSOLVER with 4 integration options (Euler, Modi¯ed Euler, RK, Adaptive RK-Fehlberg) is now updated by adding LSODES. I also presented the theoretical and numerical work on the sti®ness of some biological circuits like qa gene cluster, lac operon and oregonator. Performance of di®erent methods including MATLAB ODE suite are compared too. The e±ciency of computation could be improved by a factor of 10 compared to the standard 4th order RK method.