Biomolecular electrostatics—I want your solvation (model)

We review the mathematical and computational foundations for implicit-solvent models in theoretical chemistry and molecular biophysics. These models are valuable theoretical tools for studying the influence of a solvent, often water or an aqueous electrolyte, on a molecular solute such as a protein. Detailed chemical and physical aspects of implicit-solvent models have been addressed in numerous exhaustive reviews, as have numerical algorithms for simulating the most popular models. This work highlights several important conceptual developments, focusing on selected works that spotlight the need for research at the intersections between chemical, biological, mathematical, and computational physics. To introduce the field to computational scientists, we begin by describing the basic theoretical ideas of implicit-solvent models and numerical implementations. We then address practical and philosophical challenges in parameterization, and major advances that speed up calculations (covering continuum theories based on Poisson as well as faster approximate theories such as generalized Born). We briefly describe the main shortcomings of existing models, and survey promising developments that deliver improved realism in a computationally tractable way, i.e. without increasing simulation time significantly. The review concludes with a discussion of ongoing modeling challenges and relevant trends in high-performance computing and computational science.