Implicit solvation

Implicit solvation (sometimes termed continuum solvation) is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of molecular mechanics. The method is often applied to estimate free energy of solute-solvent interactions in structural and chemical processes, such as folding or conformational transitions of proteins, DNA, RNA, and polysaccharides, association of biological macromolecules with ligands, or transport of drugs across biological membranes. Implicit solvation (sometimes termed continuum solvation) is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of molecular mechanics. The method is often applied to estimate free energy of solute-solvent interactions in structural and chemical processes, such as folding or conformational transitions of proteins, DNA, RNA, and polysaccharides, association of biological macromolecules with ligands, or transport of drugs across biological membranes. The implicit solvation model is justified in liquids, where the potential of mean force can be applied to approximate the averaged behavior of many highly dynamic solvent molecules. However, the interfaces and the interiors of biological membranes or proteins can also be considered as media with specific solvation or dielectric properties. These media are not necessarily uniform, since their properties can be described by different analytical functions, such as “polarity profiles” of lipid bilayers. There are two basic types of implicit solvent methods: models based on accessible surface areas (ASA) that were historically the first, and more recent continuum electrostatics models, although various modifications and combinations of the different methods are possible. The accessible surface area (ASA) method is based on experimental linear relations between Gibbs free energy of transfer and the surface area of a solute molecule. This method operates directly with free energy of solvation, unlike molecular mechanics or electrostatic methods that include only the enthalpic component of free energy. The continuum representation of solvent also significantly improves the computational speed and reduces errors in statistical averaging that arise from incomplete sampling of solvent conformations, so that the energy landscapes obtained with implicit and explicit solvent are different. Although the implicit solvent model is useful for simulations of biomolecules, this is an approximate method with certain limitations and problems related to parameterization and treatment of ionization effects. The free energy of solvation of a solute molecule in the simplest ASA-based method is given by: where A S A i {displaystyle ASA_{i}} is the accessible surface area of atom i, and σ i {displaystyle sigma _{i}} is solvation parameter of atom i, i.e., a contribution to the free energy of solvation of the particular atom i per surface unit area. The needed solvation parameters for different types of atoms (carbon (C), nitrogen (N), oxygen (O), sulfur (S), etc.) are usually determined by a least squares fit of the calculated and experimental transfer free energies for a series of organic compounds. The experimental energies are determined from partition coefficients of these compounds between different solutions or media using standard mole concentrations of the solutes. Notably, solvation energy is the free energy needed to transfer a solute molecule from a solvent to vacuum (gas phase). This energy can supplement the intramolecular energy in vacuum calculated in molecular mechanics. Thus, the needed atomic solvation parameters were initially derived from water-gas partition data. However, the dielectric properties of proteins and lipid bilayers are much more similar to those of nonpolar solvents than to vacuum. Newer parameters have thus been derived from water-1-octanol partition coefficients or other similar data. Such parameters actually describe transfer energy between two condensed media or the difference of two solvation energies. Although this equation has solid theoretical justification, it is computationally expensive to calculate without approximations. The Poisson-Boltzmann equation (PB) describes the electrostatic environment of a solute in a solvent containing ions. It can be written in cgs units as: or (in mks): where ϵ ( r → ) {displaystyle epsilon ({vec {r}})} represents the position-dependent dielectric, Ψ ( r → ) {displaystyle Psi ({vec {r}})} represents the electrostatic potential, ρ f ( r → ) {displaystyle ho ^{f}({vec {r}})} represents the charge density of the solute, c i ∞ {displaystyle c_{i}^{infty }} represents the concentration of the ion i at a distance of infinity from the solute, z i {displaystyle z_{i}} is the valence of the ion, q is the charge of a proton, k is the Boltzmann constant, T is the temperature, and λ ( r → ) {displaystyle lambda ({vec {r}})} is a factor for the position-dependent accessibility of position r to the ions in solution (often set to uniformly 1). If the potential is not large, the equation can be linearized to be solved more efficiently. A number of numerical Poisson-Boltzmann equation solvers of varying generality and efficiency have been developed, including one application with a specialized computer hardware platform. However, performance from PB solvers does not yet equal that from the more commonly used generalized Born approximation.