Explicit Solvent Simulations

PCM when quantum mechanics is necessary, but explicit solvent simulations are too CPU-intensive. 

In an early work by Mertz and Pettitt, an open system was devised, in which an extended variable, representing the extent of protonation, was used to couple the system to a chemical potential reservoir [67], This method was demonstrated in the simulation of the acid-base reaction of acetic acid with water [67], Recently, PHMD methods based on continuous protonation states have been developed, in which a set of continuous titration coordinates, A, bound between 0 and 1, is propagated simultaneously with the conformational degrees of freedom in explicit or continuum solvent MD simulations. In the acidostat method developed by Borjesson and Hiinenberger for explicit solvent simulations [13], A. is relaxed towards the equilibrium value via a first-order coupling scheme in analogy to Berendsen s thermostat [10]. However, the theoretical basis for the equilibrium condition used in the derivation seems unclear [3], A test using the pKa calculation for several small amines did not yield HH titration behavior [13],... 

An alternative to the GB, COSMO, and Poisson electrostatic calculations is to model the solution to the Poisson equation in terms of pair potentials between solute atoms this procedure is based on the physical picture that the solvent screens the intra-solute Coulombic interactions of the solute, except for the critical descreening of one part of the solute from the solvent by another part of this solute. This descreening can be modeled in an average way to a certain level of accuracy by pairwise functions of atomic positions.18, M 65 One can obtain quite accurate solvation energies in this way, and it has recently been shown that this algorithm provides a satisfactory alternative to more expensive explicit-solvent simulations even for the demanding cases of 10-base-pair duplexes of DNA and RNA in water.66... 

Desolvation free energies are computed using either explicit solvent or an implicit solvent model. While explicit solvent simulations are usually considered more accurate or at least more representative of the true molecular environment, simulations using implicit solvent are often chosen... 

Zhang L, Gallicchio E, Levy RM (1999) Implicit Solvent Models for Protein-Ligand Binding, Insights Based on Explicit Solvent Simulations, (AIP Conference Proceedings, Simulation and Theory of Electrostatic Interactions in Solutions), 192 151 172... 

To further speed up this approach, one can replace the expensive explicit-solvent simulations with implicit ones. Statistical mechanical theory gives the Helmholtz free energy A, apart from the scaling constant of the classical partition function that cancels out in binding energy calculations, as... 

Scarsi M, Apostolakis J, Caflisch A. Comparison of a GB Solvation model with explicit solvent simulations potentials of mean force and conformational preferences of alanine dipeptide and 1,2-dichloroethane. J Phys Chem B 1998 102 3637-3641. 

In explicit solvent simulations, all the interactions in the system are described at the atomic level. Thus the expressions for the energy contain parameters characteristic of the atoms in the system. The nonbonded interaction energy (C/nb) between atoms in the system is usually given in terms of Coulomb (electrostatic) and van der Waals (vdW) contributions ... 

Zhang LY, Gallicchio E, Friesner RA, Levy RM. Solvent models for protein-ligand binding comparison of implicit solvent Poisson and surface generalized Born models with explicit solvent simulations. J Comput Chem 2001 22 591-607. 

As pointed out earlier if we are able to calculate this quantity with sufficient accuracy, it provides an attraaive alternative to performing computationally demanding, explicit solvent simulations. 

Because implicit solvent simulations are typically open, non-periodic systems, electrostatic interactions are calculated according to standard cutoff schemes that do not scale as well to large system sizes as the more efficient Ewald summation method [11,12] that is routinely used in explicit solvent simulations. 

More realistic kinetic behavior in implicit solvent simulations can be obtained with the Langevin thermostat [18] where stochastic collisions and friction forces provide kinetic energy transfer to and from the solute in an analogous fashion to explicit solute-solvent interactions. As a result, kinetic transition rates similar to rates from explicit solvent simulations can be recovered with an appropriate choice of the friction constant [2]. 

Formaneck, M.S., Cui, Q. The use of a Generalized Born model for the analysis of protein conformational transitions A comparative study with explicit solvent simulations for chemotaxis Y protein (CheY). J. Comput. Chem. 2006,27,1923M3. 

Raw computational speed has been considered one of the key advantages of the GB model. However, note that the cost of a calculation based directly on Eq. (3) is generally O(N ) for a system of N atoms, while the scaling is more favorable, N log(N), for Ewald-based methods used in explicit solvent simulations. For large systems, e.g. the nucleosome (25,000 atoms), the number of nanoseconds of MD per GPU hour may actually be less in a GB-based simulation (without additional approximations such as cut-offs) than in a comparable explicit solvent run [54], although the conformational search is still much faster in the implicit solvent. 

Within the scope of available ESMs, the explicit solvent simulations method is the most theoretically rigorous and most detailed approach to calculate AG, [7, 38,47, 48, 51,61-66]. The method is based on explicit simulation of a solute-solvent system... 

Regardless of the level of theory used (MM, QM, or QM/MM), within the scope of the explicit solvent simulations approach the hydration (solvation) free energy can be calculated by four main groups of methods [52] (1) thermodynamic integration, (2) free energy perturbation, (3) probabihty densities, and (4) nonequihbrium work methods. 

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