Stochastic dynamics and denaturation of thermalized DNA.
In the first part of the paper, the stochastic dynamics of the Peyrard-Bishop-Dauxois (PBD) DNA model is studied. A one-dimensional averaged Itô stochastic differential equation governing the total energy of the system and the associated Fokker-Planck equation governing the transition probability density function of the total energy are derived from the Langevin equations for the base-pair (bp) separation of the PBD DNA model by using the stochastic averaging method for quasinonintegrable Hamiltonian systems. The stationary probability density function of the average energy and the mean square of the bp separation are obtained by solving the reduced Fokker-Planck equation. In the second part of the paper, the local denaturation of the thermalized PBD DNA model is studied as a first-passage-time problem in the energy. A backward Kolmogorov equation and a Pontryagin equation are derived from the averaged Itô equation and solved to yield the waiting-time distribution and the mean bp opening time. All the analytical results are confirmed with those from Monte Carlo simulation. It is pointed out that the proposed method may yield a reasonable mean bp opening time if the friction coefficient is fixed using experimental results.
Deng
Mao Lin
ML
Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, China.
Zhu
Wei Qiu
WQ
D003198:Computer Simulation; D004247:DNA / Q000737:chemistry* / Q000648:ultrastructure*; D006358:Hot Temperature; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D009690:Nucleic Acid Conformation; D009691:Nucleic Acid Denaturation; D013269:Stochastic Processes
D004247:DNA