Explicit water

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

A til Stan cc-dcpM don 1 diolacLric con sLtiii L is com in on ly used to mimic ihe effect of solvent in moleciiltir mechanics ctilciikilioiis, in the absence ol explicit water molecules. 

A distance-dependent dielectric constant is commonly used to mimic the effect of solvent in molecular mechanics calculations, in the absence of explicit water molecules. 

There are cases in which one is interested in the motion of a biomolecule but wishes also to study the effect of different solvent environments on this motion. In other cases, one may be interested in studying the motion of one part of the protein (e.g., a side chain or a loop) as moving in a solvent bath provided by the remainder of the protein. One way to deal with these issues is, of course, to explicitly include all the additional components in the simulation (explicit water molecules, the whole protein, etc.). This solution is computationally very expensive, because much work is done on parts of the system that are of no direct interest to the study. 

Figure 1 Schematic representation of an atomic model of a biomolecular solute surrounded by explicit water molecules.

Consider an alchemical transformation of a particle in water, where the particle s charge is changed from 0 to i) (e.g., neon sodium q = ). Let the transformation be performed first with the particle in a spherical water droplet of radius R (formed of explicit water molecules), and let the droplet then be transferred into bulk continuum water. From dielectric continuum theory, the transfer free energy is just the Born free energy to transfer a spherical ion of charge q and radius R into a continuum with the dielectric constant e of water ... 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

Basis Set Choice The most relevant geometrical parameters of several stationary points, with and without an explicit water molecule, located using several... 

The effect of solvation on uracil and thymine photophysics has been studied by Gustavvson and coworkers, who have studied uracil with four explicit water molecules and PCM to study distorted geometries [92,93,149], The conical intersection connecting Si to the ground state that was found in the gas phase is also present in solution. The barrier connecting the Si minimum to the conical intersection is lower in solution, however, causing much shorter lifetimes. So the nanosecond lifetime which is observed in the gas phase is not observed in solution but a picosecond lifetime is observed. 

Variational electrostatic projection method. In some instances, the calculation of PMF profiles in multiple dimensions for complex chemical reactions might not be feasible using full periodic simulation with explicit waters and ions even with the linear-scaling QM/MM-Ewald method [67], To remedy this, we have developed a variational electrostatic projection (VEP) method [75] to use as a generalized solvent boundary potential in QM/MM simulations with stochastic boundaries. The method is similar in spirit to that of Roux and co-workers [76-78], which has been recently... 

A recent ab initio quantum mechanical study (Han et al, 1998) used B3LYP/6-31G density functional theory to examine the relative stabilities of eight conformers of AAMA with four explicit water... 

Higo, J., Galzitskaya, O. V., Ono, S., and Nakamura, H. (2001). Energy landscape of a /3-hairpin peptide in explicit water studied by multicanonical molecular dynamics. Chem. Phys. Lett. 337, 169-175. 

Zhou, F. X. Berne, B. J. Germain, R., The free energy landscape of f) hairpin folding in explicit water, Proc. Natl Acad. Sci. USA 2001,98, 14931-14936. 

Wu, X. Wang, S., Helix folding of an alanine-based peptide in explicit water, J. Phys. Chem. B 2001,105, 2227-2235. 

One should assume that at least 200 ps of equilibration+sampling will be required for any reliable simulation in explicit water solvent. Since each simulation should be run at least twice (or forwards and backwards) to ensure a reproducible result, this means a floor of 400 ps simulation time will be required. Note that 200 ps (400 ps) is a lower bound, and that many simulations will need to be run considerably longer. It is not unusual to run protein-based simulations for a nanosecond or more to achieve convergence. For a large (protein based) system, this requires a substantial investment of computer time on today s computers. 

The introduction of the external potential Vex, in Equation 4 is designed to mimic the effect of the surrounding (implicit) bulk solvent on the system by restricting the movement of any explicit water molecules.49 Thus, Vex[ is interpreted as arising from the force exerted on the explicit atoms by the implicit surrounding bulk solvent. This restraining potential has the simple harmonic form,49... 

The background theory that underlies the FEP method as well as the molecular mechanics force fields that relate molecular structure to energy are reviewed in section one of the book. Section two describes the use of free energy calculations for determining molecular properties of ligands, including solvation, as calculated using both implicit and explicit water... 

Daidone, I., Amadei, A., and Di Nola, A. (2005). Thermodynamic and kinetic characterization of a beta-hairpin peptide in solution An extended phase space sampling by molecular dynamics simulations in explicit water. Proteins 59, 510-518. 

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