Towards the modeling of static electric field effects in rhodopsin photophysics using QM/MM calculations

A transmembrane voltage, arising from ion imbalance between the extracellular and cytoplasmic sides of a cell, can influence the biological function of transmembrane proteins. At the atomistic scale, transmembrane voltage can be modeled thanks to the application of an external electric field. Here, we introduce a new QM/MM model capable of efficiently describing the interaction of QM and MM atoms with a static electric field (SEF) thanks to ElectroStatic Potential Fitted (ESPF) operators. A simple decomposition of the full interaction energy is proposed in terms of electrostatic QM/MM interactions and interactions of QM and MM multipoles with the SEF. Having validated the method and tested its limitations in the case of a short protonated Schiff base model, it is applied to the case of the Gloeobacter Rhodopsin, a transmembrane photoactive protein with potential applications in optogenetics. In particular, we evidence that a weak electric field only perturb the local electric field, due to the protein amino-acids.