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.
[4] 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.
are usually determined by a least squares fit of the calculated and experimental transfer free energies for a series of organic compounds.
A number of numerical Poisson-Boltzmann equation solvers of varying generality and efficiency have been developed,[10][11][12] including one application with a specialized computer hardware platform.
It is based on modeling the solute as a set of spheres whose internal dielectric constant differs from the external solvent.
[16] The Generalized Born (GB) model augmented with the hydrophobic solvent accessible surface area (SA) term is GBSA.
Although this formulation has been shown to successfully identify the native states of short peptides with well-defined tertiary structure,[17] the conformational ensembles produced by GBSA models in other studies differ significantly from those produced by explicit solvent and do not identify the protein's native state.
[4] In particular, salt bridges are overstabilized, possibly due to insufficient electrostatic screening, and a higher-than-native alpha helix population was observed.
For each of group of atom types, a different parameter scales its contribution to solvation ("ASA-based model" described above).
[21] It is possible to include a layer or sphere of water molecules around the solute, and model the bulk with an implicit solvent.
[23] the bulk solvent is modeled with a Generalized Born approach and the multi-grid method used for Coulombic pairwise particle interactions.
It is reported to be faster than a full explicit solvent simulation with the particle mesh Ewald summation (PME) method of electrostatic calculation.
[25] Models like PB and GB allow estimation of the mean electrostatic free energy but do not account for the (mostly) entropic effects arising from solute-imposed constraints on the organization of the water or solvent molecules.
The most popular way to do this is by taking the solvent accessible surface area (SASA) as a proxy of the extent of the hydrophobic effect.
[26] Note that this surface area pertains to the solute, while the hydrophobic effect is mostly entropic in nature at physiological temperatures and occurs on the side of the solvent.
Implicit solvent models such as PB, GB, and SASA lack the viscosity that water molecules impart by randomly colliding and impeding the motion of solutes through their van der Waals repulsion.
Viscosity may be added back by using Langevin dynamics instead of Hamiltonian mechanics and choosing an appropriate damping constant for the particular solvent.
[27] In practical bimolecular simulations one can often speed-up conformational search significantly (up to 100 times in some cases) by using much lower collision frequency
The non-existent “hydrophobic” interactions of polar atoms are overridden by large electrostatic energy penalties in such models.
Strictly speaking, ASA-based models should only be applied to describe solvation, i.e., energetics of transfer between liquid or uniform media.
This was sometimes done for interpreting protein engineering and ligand binding energetics,[37] which leads to “solvation” parameter for aliphatic carbon of ~40 cal/(Å2 mol),[38] which is 2 times bigger than ~20 cal/(Å2 mol) obtained for transfer from water to liquid hydrocarbons, because the parameters derived by such fitting represent sum of the hydrophobic energy (i.e., 20 cal/Å2 mol) and energy of van der Waals attractions of aliphatic groups in the solid state, which corresponds to fusion enthalpy of alkanes.
[40] More testing is needed to evaluate the performance of different implicit solvation models and parameter sets.
They are often tested only for a small set of molecules with very simple structure, such as hydrophobic and amphiphilic alpha helixes (α).
The transfer of an ion from water to a nonpolar medium with dielectric constant of ~3 (lipid bilayer) or 4 to 10 (interior of proteins) costs significant energy, as follows from the Born equation and from experiments.
However, since the charged protein residues are ionizable, they simply lose their charges in the nonpolar environment, which costs relatively little at the neutral pH: ~4 to 7 kcal/mol for Asp, Glu, Lys, and Arg amino acid residues, according to the Henderson-Hasselbalch equation, ΔG = 2.3RT (pH - pK).
The low energetic costs of such ionization effects have indeed been observed for protein mutants with buried ionizable residues.
In the simplest accessible surface area-based models, this problem was treated using different solvation parameters for charged atoms or Henderson-Hasselbalch equation with some modifications.