Splitting Strategy for Simulating Genetic Regulatory Networks

Abstract

The splitting approach is developed for the numerical simulation of genetic regulatory networks with a stable steady-state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network show that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general-purpose Runge-Kutta methods. The new methods have no restriction on the choice of stepsize due to their infinitely large stability regions.

Steady-State-Preserving Simulation of Genetic Regulatory Systems

“…(II) A Two-Gene System with Cross-Regulation . The second model is a two-gene activation-inhibition system with cross-regulation (studied by Polynikis et al [ 15 ], Widder et al [ 17 ], Chen et al [ 32 ], You [ 26 ], and You et al [ 27 ]) where, for i = 1,2, r i is the concentration of mRNA R i produced by gene g i , p i is the concentration of protein P i , m i is the maximal transcription rate of gene g i , κ i is the translation rate of mRNA R i , and γ i and μ i are the degradation rates of mRNA R i and protein P i , respectively. The functions are the Hill functions of activation and repression, respectively.…”

“…For the genetic regulatory system ( 1 ) with a limit-cycle structure, You [ 26 ] proposed a new class of phase-fitted and amplification-fitted Runge-Kutta type methods which were shown to be more effective and more efficient than the traditional Runge-Kutta methods of the same order. Very recently, You et al [ 27 ] developed a splitting approach for genetic regulatory systems with a stable steady state. In the numerical simulation, the new splitting methods constructed in that paper are shown to be remarkably more effective and more suitable for long-term computation with large steps than the general-purpose Runge-Kutta methods.…”

Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems

“…Very recently You [ 16 ] developed a new family of phase-fitted and amplification fitted methods of RK type which have been proved very effective for genetic regulatory systems with a limit-cycle structure. You et al [ 17 ] considered a splitting approach for the numerical simulation of genetic regulatory networks with a stable steady state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network showed that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general purpose Runge-Kutta methods.…”