Recent molecular dynamics simulations and experimental observations have shown that the dynamics of single-molecule protein can be described with hopping among energy basins caused by backbone motions and side-chain related processes. We formalize the dynamic evolution by combining a stochastic approach with a Lindblad equation. In our model, the open quantum system is comprised of the active center and an environment relating to the protein matrix. The effects of the protein matrix are separated into two categories: fast fluctuations with frequencies higher than the dynamics of the active center, and slow modulations that allow the active center to respond adiabatically. We describe the response of the active center to the fast environmental fluctuations with a memory kernel. The active center responds to the slow modulations with a dynamical evolution on an energy landscape, which can be properly described by a series of stochastic transition matrices. We applied this method to analyze the photon emission from photoactivated fluorescent protein KFP1 in viewing that the light emission behavior of KFP1 is highly sensitive to the hydrogen bonding between its chromophores and the neighboring amino acid groups. We found the conformation fluctuation of KFP1 can vary the hydrogen bonding, thus encodes the energy-landscape evolution of the chromophore into the photon emission traces. By dynamically adjusting the trapping strength and the number of traps locating between two basins on the energy landscape, the conformation fluctuation can vary the photon emission behavior of KFP1. The distribution of the trapping strength exhibits two peaks with one near the thermal energy and the other higher than the thermal energy by a factor of 1.8. Conformational changes of AK1 undergo mutual adjustment process responded to thermal-driven modulation.
