title: Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems.
abstract: Oscillation is one of the most important phenomena in the chemical reaction systems in living cells. The general purpose simulation algorithms fail to take into account this special character and produce unsatisfying results. In order to enhance the accuracy of the integrator, the second-order derivative is incorporated in the scheme. The oscillatory feature of the solution is captured by the integrators with an exponential fitting property. Three practical exponentially fitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRK methods, the two-gene system with cross-regulation and the circadian oscillation of the period protein in Drosophila are simulated. Each EFTDRK method has the best fitting frequency which minimizes the global error. The numerical results show that the new EFTDRK methods are more accurate and more efficient than their prototype TDRK methods or RK methods of the same order and the traditional exponentially fitted RK method in the literature.
authors.affiliation: Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China.
authors.forename: Zhaoxia
authors.initials: Z
authors.lastname: Chen
authors.affiliation: Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China.
authors.forename: Juan
authors.initials: J
authors.lastname: Li
authors.affiliation: Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China.
authors.forename: Ruqiang
authors.initials: R
authors.lastname: Zhang
authors.affiliation: Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China.
authors.forename: Xiong
authors.initials: X
authors.lastname: You
mesh_terms: D000465:Algorithms; D000818:Animals; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D004330:Drosophila / Q000235:genetics; D029721:Drosophila Proteins / Q000235:genetics; D053263:Gene Regulatory Networks; D008957:Models, Genetic; D056950:Period Circadian Proteins / Q000235:genetics
chemical_list: D029721:Drosophila Proteins; C539040:PER protein, Drosophila; D056950:Period Circadian Proteins