Solvent water simulation

Force field calculations often truncate the non bonded potential energy of a molecular system at some finite distance. Truncation (nonbonded cutoff) saves computing resources. Also, periodic boxes and boundary conditions require it. However, this approximation is too crude for some calculations. For example, a molecular dynamic simulation with an abruptly truncated potential produces anomalous and nonphysical behavior. One symptom is that the solute (for example, a protein) cools and the solvent (water) heats rapidly. The temperatures of system components then slowly converge until the system appears to be in equilibrium, but it is not. 

HyperChem allows solvation of arbitrary solutes (including no solute) in water, to simulate aqueous systems. HyperChem uses only rectangular boxes and applies periodic boundary conditions to the central box to simulate a constant-density large system. The solvent water molecules come from a pre-equilibrated box of water. The solute is properly immersed and aligned in the box and then water molecules closer than some prescribed distance are omitted. You can also put a group of non-aqueous molecules into a periodic box. 

The fiuid-phase simulation approach with the longest tradition is the simulation of large numbers of the molecules in boxes with artificial periodic boundary conditions. Since quantum chemical calculations typically are unable to treat systems of the required size, the interactions of the molecules have to be represented by classical force fields as a prerequisite for such simulations. Such force fields have analytical expressions for all forces and energies, which depend on the distances, partial charges and types of atoms. Due to the overwhelming importance of the solvent water, an enormous amount of research effort has been spent in the development of good force field representations for water. Many of these water representations have additional interaction sites on the bonds, because the representation by atom-centered charges turned out to be insufficient. Unfortunately it is impossible to spend comparable parameterization work for every other solvent and... 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

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],... 

A solvated MD simulation is performed to determine an ensemble of conformations for the molecule of interest. This ensemble is then used to calculate the terms in this equation. Vm is the standard molecular mechanics energy for each member of the ensemble (calculated after removing the solvent water). G PB is the solvation free energy calculated by numerical integration of the Poisson-Boltzmann equation plus a simple surface energy term to estimate the nonpolar free energy contribution. T is the absolute temperature. S mm is the entropy, which is estimated using... 

Fig. 30.1. Volumes of minerals precipitated during a reaction model simulating the mixing at reservoir temperature of seawater into formation fluids from the Miller, Forties, and Amethyst oil fields in the North Sea. The reservoir temperatures and compositions of the formation fluids are given in Table 30.1. The initial extent of the system in each case is 1 kg of solvent water. Not shown for the Amethyst results are small volumes of strontianite, barite, and dolomite that form during mixing.

One aspect of MD simulations is that all molecules, including the solvent, are specified in full detail. As detailed above, much of the CPU time in such a simulation is used up by following all the solvent (water) molecules. An alternative to the MD simulations is Brownian dynamics (BD) simulation. In this method, the solvent molecules are removed from the simulations. The effects of the solvent molecules are then reintroduced into the problem in an approximate way. Firstly, of course, the interaction parameters are adjusted, because the interactions should now include the effect of the solvent molecules. Furthermore, it is necessary to include a fluctuating force acting on the beads (atoms). These fluctuations represent the stochastic forces that result from the collisions of solvent molecules with the atoms. We know of no results using this technique on lipid bilayers. 

In principle, it is a simple matter to include solvent water molecules directly in MD simulations, since appropriate intermolecular potential energy functions for water are available (1Z 37,38) one would just surround the solute molecules with a sufficient number of water molecules to approximate a bulk solution. Unfortunately, a "sufficient number of water molecules might be enormous, since many of the effects of aqueous solvation are long range or are due to entropic contributions arising from "structuring of the solvent, which may be cooperative in nature. 

In the following recent applications of the new ab initio simulation technique will be demonstrated, which would have posed serious difficulties to conventional QM/MM MD schemes, which need analytical solute-solvent interaction potentials and where some artifacts as outlined in the previous chapter would certainly cause errors in the results. These applications will be grouped to hydrated cations and anions, in another section also hydrated neutral molecules forming hydrogen bonds to the solvent water and hydrolysis processes will be discussed. In all cases structural and dynamical data of the solutions will be presented. 

That electrostatic forces could be crucial to vibrational energy relaxation was amply demonstrated by the liquid water simulations of Whitnell et al. (34). They noted that since the electrostatic portion of the force between their solvent and a dipolar solute was linear in the solute dipole moment, Equations (12) and (13) implied that the electrostatic part of the friction ought to scale as the dipole moment squared. When they then found that their entire relaxation rate scaled with the square of the solute dipole moment, it certainly seemed to be convincing evidence that electrostatics forces were indeed the primary ingredients generating ultrafast relaxation. Subsequent theoretical work on relaxation rates in such manifestly protic solvents as water and alcohols has largely served to reinforce this message (37,38,60,61). 

Fig. 11. Simulated and experimental two-pulse H20 (solvent water) ESEEM spectra. Theoretical ESEEM spectra for equatorial, axial, and ambient water are calculated as indicated. These can be compared to the experimental envelopes for the EetSp type 1 and type 2 Cu(II) sites (solid lines) and the simulations for these envelopes assuming for the type 1 copper, only ambient water, and for the type 2 copper, a combination of one equatorial, one axial, and ambient water (dotted lines) (Aznar et aL, 2002).

Self-Diffusion Coefficients of Ions and Solvent Water (Dj in a 2.2 molal Ltl Solution Obtained from MD Simulation and Experiments at 305... 

Clementi (1985) described ab initio computational chemistry as a global approach to simulations of complex chemical systems, derived directly from theory without recourse to empirical parametrizations. The intent is to break the computation into steps quantum mechanical computations for the elements of the system, construction of two-body potentials for the interactions between them, statistical mechanical simulations using the above potentials, and, finally, the treatment of higher levels of chemical complexity (e.g., dissipative behavior). This program has been followed for analysis of the hydration of DNA. Early work by Clementi et al. (1977) established intermolecular potentials for the interaction of lysozyme with water, given as maps of the energy of interaction of solvent water with the lysozyme surface. 

Furthermore, the explicit-water simulations do include the CDS terms to the extent that dispersion and hydrogen bonding are well represented by the force field. Finally, by virtue of the solvent being explicitly part of the system, it is possible to derive many useful non-entropy-based properties "" (radial distribution functions, average numbers of hydrogen bonds, size and stability of the first solvation shell, time-dependent correlation functions, etc.). Since many of these properties are experimentally observable, it is often possible to identify and correct at least some deficiencies in the simulation. Simulation is thus an extremely powerful tool for studying solvation, especially when focused on the response of the solvent to the solute. 

At the theoretical level, full quantum mechanical calculations on biologic macromolecules are not computationally feasible, nor would they be particularly helpful in understanding macro-molecular properties without proper inclusion of the solvent water or other biologic matrix on which these properties so intimately depend. However, ab initio quantum mechanical calculations on smaller systems that represent crucial steps in an enzymic reaction, for example, can be helpful in understanding specific processes within macromolecules or in estimating intermolecular forces and stereochemical effects in molecular mechanics simulations that are not experimentally accessible. 

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