Effects of Long-Range Electrostatics on Time-Dependent Stokes Shift Calculations

Molecular dynamics simulations are essential to the correct interpretation of the response measured in time-dependent Stokes shift (TDSS) experiments of fluorescent probe molecules in biological environments. Within linear response theory, the TDSS response is the time correlation function of the fluctuations of Delta E(t), the difference between the solute environment interaction energy with the probe, modeled in both its electronically excited and ground states. Delta E(t) is dominated by electrostatic interactions between the environment and the ground- and excited-state charge distributions of the probe. The treatment of the long-ranged electrostatics in the calculation of the TDSS response in MD simulations is systematically investigated for three probes in aqueous solution: a model diatomic, coumarin 102, and Hoechst 33258. Nine different protocols for the treatment of the electrostatics were compared to particle mesh Ewald (PME), which was utilized as a reference standard. A computationally efficient pairwise alternative to PME, the damped shifted force method, was shown to reproduce the TDSS response calculated with PME for all three systems. In contrast, neglecting the role of the long-ranged electrostatics in the calculation of the TDSS response results in artifacts.