Explicit-solvent method

Explicit solvent methods. Monte Carlo methods are somewhat more popular than molecular dynamics methods. 

The main benefits of this approach are that (i) this is a molecular theory, and that (ii) due to the spherical symmetry of the correlation fnnctions in the ID RISM approach, the computational costs are significantly rednced compared to explicit solvent methods and high-dimensional molecular theories like 3D RISM [80-82, 93], MOZ [82, 83], and MDFT [69, 70]. For an average drug-like molecule a ID RISM calculation of solvation free energy takes less than a minute on a desktop PC [67, 71, 72, 92]. This time scale is already comparable with the compntational time scale for continuum methods (seconds). We note that an explicit solvent calculation for the same kind of molecules would take between honrs and days [38,47-58]. 

As mentioned above, (partial) cancelation of errors calculated for relative free energies in solution is also possible. Nevertheless, some studies have pointed out [13, 14] that the solute-solvent relative solvation free energy can differ by up to 1-2 kcal mol as determined on the basis of some continuum and explicit solvent methods. This uncertainty is very large when an equilibrium constant smaller than about 10 is to be determined. 

The primary problem with explicit solvent calculations is the significant amount of computer resources necessary. This may also require a significant amount of work for the researcher. One solution to this problem is to model the molecule of interest with quantum mechanics and the solvent with molecular mechanics as described in the previous chapter. Other ways to make the computational resource requirements tractable are to derive an analytic equation for the property of interest, use a group additivity method, or model the solvent as a continuum. 

Another way is to reduce the magnitude of the problem by eliminating the explicit solvent degrees of freedom from the calculation and representing them in another way. Methods of this nature, which retain the framework of molecular dynamics but replace the solvent by a variety of simplified models, are discussed in Chapters 7 and 19 of this book. An alternative approach is to move away from Newtonian molecular dynamics toward stochastic dynamics. 

The discrete protonation states methods have been tested in pKa calculations for several small molecules and peptides, including succinic acid [4, 25], acetic acid [93], a heptapeptide derived from ovomucoid third domain [27], and decalysine [61], However, these methods have sofar been tested on only one protein, the hen egg lysozyme [16, 61, 71], While the method using explicit solvent for both MD and MC sampling did not give quantitative agreement with experiment due to convergence difficulty [16], the results using a GB model [71] and the mixed PB/explicit... 

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],... 

Two remaining problems relating to the treatment of solvation include the slowness of Poisson-Boltzmann calculations, when these are used to treat electrostatic effects, and the difficulty of keeping buried, explicit solvent in equilibrium with the external solvent when, e.g., there are changes in nearby solute groups in an alchemical simulation. Faster methods for solving the Poisson-Boltzmann equation by means of parallel finite element techniques are becoming available, however.22 24... 

While the information has certainly advanced the understanding of the form of the transition structures, the issues of counterion and explicit solvent effects have yet to be addressed, largely as a result of limitations of the computational methods so far employed. 

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