Forster Resonance Energy Transfer between Fluorescent Proteins: Efficient Transition Charge-Based Study

Toward a better understanding of the Forster resonance energy transfer (FRET) utilized in genetically encoded biosensors we theoretically examined the excitonic coupling between cyan fluorescent protein (CFP) and yellow FP (YFP) with time-dependent density functional theory (TD-DFT). Going beyond the dipole - dipole (dd) approximation in the original Forster theory, we adopted a transition charge from the electrostatic potential (TrESP) method that approximates the excitonic coupling as classical Coulomb interaction between the transition charges derived from the transition density for each FP fluorophore. From the TD-DFT calculations with embedded point charges for the trajectory generated by classical molecular dynamics (MD) simulations we found that the thermal fluctuation of the fluorophore geometry in FP and the protein electrostatic interactions do not significantly affect the Coulomb interaction between the FP pairs. The TrESP calculations utilizing the Poisson equation indicate that the screening and local field effects by solvent dielectric environment reduce the Coulomb interaction by an almost constant factor of 0.51. Based on these results, we developed a more efficient Frozen-TrESP method that calculates the structure-dependent Coulomb interaction using the reference transition charges preliminarily determined for the isolated fluorophore in the gas phase and confirmed its validity for the evaluation of the Coulomb interaction in the thermally fluctuating CFP-YFP dimer. Finally, we demonstrated the usefulness of the Frozen-TrESP to examine the dependence of the Coulomb interaction on the alignment of YFP with respect to CFP and provide the list of the reference transition charges for the other representative fluorophores of various FPs, which offers guidance on the optimal design of the FRET-based biosensors.