Kinetic properties of bio-molecules by different noises in the two-dimensional free-energy model

Fluctuation characteristics of a migration rate constant can mainly dominate kinetic properties of bio-molecules, and these characteristics are usually submitted to surroundings and the configuration qualities of bio-molecules themselves. The two-dimensional (2D) free-energy landscape including the extension coordinate and conformational variable is needed to study the migration rate of bio-molecules in our work. We adopted the 2D generalized Langevin equation to reveal the key nature of the bio-molecules’ kinetic properties during the turnover processes by using fractional Gaussian noise (fGn) and white noise (WN). Specifically, the dependence of mean waiting time under external force on both intrinsic energy height and noise strength ratio has been extensively analyzed. Particular attention in this work is paid to distinguish the important discrepancies among the normal diffusion, sub-diffusion, and mixed kinetics. Our results suggest that the unsymmetrical kernel matrix formed by fGn and WN is a significant factor to reveal the key information of the bio-molecules in the complex system. Moreover, mixed kinetic behavior is also an important phenomenon, which cannot be neglected.