Reformulation of Maxwell's equations to incorporate near-solute solvent structure

Maxwell's equations, which treat electromagnetic interactions between macroscopic charged objects in materials, have explained many phenomena and contributed to many applications in our lives. Derived in 1861 when no methods were available to determine the atomic structure of macromolecules, Maxwell's equations assume the solvent to be a structureless continuum. However, near-solute solvent molecules are highly structured, unlike far-solute bulk solvent molecules. Current methods cannot treat both the near-solute solvent structure and time-dependent electromagnetic interactions in a macroscopic system. Here, we derive "microscopic" electrodynamics equations that can treat macroscopic time-dependent electromagnetic field problems like Maxwell's equations and reproduce the solvent molecular and dipole density distributions observed in molecular dynamics simulations. These equations greatly reduce computational expense by not having to include explicit solvent molecules, yet they treat the solvent electrostatic and van der Waals effects more accurately than continuum models. They provide a foundation to study electromagnetic interactions between molecules in a macroscopic system that are ubiquitous in biology, bioelectromagnetism, and nanotechnology. The general strategy presented herein to incorporate the near-solute solvent structure would enable studies on how complex cellular protein-ligand interactions are affected by electromagnetic radiation, which could help to prevent harmful electromagnetic spectra or find potential therapeutic applications.