Empirical hydration models

Extensive literature has developed related to the preferential interaction of different solvents with proteins or peptides in bulk solution.156-5X1 Similar concepts can be incorporated into descriptions of the RPC behavior of peptides and employed as part of the selection criteria for optimizing the separation of a particular peptide mixture. As noted previously, the dependency of the equilibrium association constant, /CassoCji, of a peptide and the concentration of the solvent required for desorption in RPC can be empirically described1441 in terms of nonmechanistic, stoichiometric solvent displacement or preferential hydration models, whereby the mass distribution of a peptide P, with n nonpolar ligands, each of which is solvated with solvent molecules Da is given by the following ... 

Again in the case of the lyotropic number interpolation the accuracy is dependent on the accuracy of the measurement of the lyotropic number, though the sum of the hydration heats only changes slowly with lyotropic number. It must also be stressed that the lattice energies obtained in this way are not theoretical lattice energies in that they are not based on any model of the crystal. Rather they are empirical or experimental in that they are based on a combination of empirical hydration enthalpies and experimental enthalpies of solution. 

The empirical hydration free energy density is expressed by a linear combination of some physical properties calculated around the molecule with net atomic charges, polarizabilities, dispersion coefficients of the atoms in the molecule, and solvent accessible surface [Son, Han et al, 1999]. These physical properties are the result of the interaction of the molecule with its environment. To calculate the H F E D of a molecule a grid model was proposed a shell of critical thickness rc was defined around the solvent-accessible surface with a number of grid points inside (e.g., 8 points/A ). 

Elizalde, B. E., Pilosof, A. M. R., and Bartholomai, G. B. (1996). Empirical model for water uptake and hydration rate of food powders by sorption and Baumann methods. /. Food Sci. 61, 407-409. 

Richards, N., Williams, P. B., and Tute, M. (1991) Empirical methods for computing molecular partition coefficients. I. Upon the need to model the specific hydration of polar groups in fragment based approaches. Int. J. Quant. Chem. 18, 299-316. 

A more complete and much more rigorous description of bonding in complexes would be provided by a quantum mechanical treatment. Such a treatment is especially needed in the case of departures from the ionic model and increasing contribution of covalent bonding (ion pairs, soft donors and acceptors). However only a few studies have been reported. They are mainly concerned with cation hydration and use either semi-empirical 19—21) or non-empirical methods 22—24). A non-empirical treatment of cation NH3 systems has also been performed recently (25). However the present state of the computations is still far from providing a complete description of the system including the medium. The latter may be taken into account by a Bom-type "solvaton (27,26). Heats of hydration may then be calculated (27). A discussion of this aspect of the problem is deferred to a later date, awaiting especially a more complete analysis of non-empirical calculations. In the course of the discussion of... 

A second important application of CMD has been to study the dynamics of the hydrated proton. This study involved extensive CMD simulations to determine the proton transport rate in on our Multi-State Empirical Valence Bond (MS-EVB) model for the hydrated proton. = Shown in Fig. 4 are results for the population correlation function, (n(t)n(O)), for the Eigen cation, HsO, in liquid water. Also shown is the correlation function for D3O+ in heavy water. It should be noted that the population correlation function is expected to decay exponentially at long times, the rate of which reflects the excess proton transport rate. The straight line fits (dotted lines) to the semi-log plots of the correlation functions give this rate. For the normal water case, the CMD simulation using the MS-EVB model yields excellent agreement with the experimental proton hopping... 

Marcus, Y. (1994). A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophys. Chem. 51, 111—127. 

The formaldehyde disproportionation has been examined by semi-empirical MO methods (Rzepa and Miller, 1985). With the MNDO procedure, transfer of hydride from hydrate mono-anion to formaldehyde is exothermic by 109 kJ mol-1, and the transition structure [29], corresponding to near symmetrical transfer of hydride, lies 72 kJ mol -1 above the separated reactants. Inclusion of two water molecules, to model solvation effects, stabilizes reactants and transition structures equally. Hydride transfer from the hydrate dianion was found to have a less symmetrical transition structure [30] not unexpected for a more exothermic reaction, but the calculated activation energy, 213 kJ mol-1, is unexpectedly high. Semi-classical primary kinetic isotope effects, kH/kD = 2.864 and 3.941 respectively, have been calculated. Pathways involving electron or atom transfers have also been examined, and these are predicted to be competitive with concerted hydride transfers in reactions of aromatic aldehydes. Experimental evidence for these alternatives is discussed later. 

Despite the fact that nonpolar hydration forces dominate whenever hydrophobic interactions [46] are important, the general availability of accurate models for the nonpolar component of the hydration-free energy is lacking. The structure and properties of proteins in water is highly influenced by hydrophobic interactions [47-50]. Hydrophobic interactions also play a key role in the mechanism of ligand binding to proteins [30,51-53], Empirical surface area models [54] for the nonpolar component of the solvation free energy are widely used [28,37,55-62]. Surface area models are useful as a first... 

The most expensive part of a simulation of a system with explicit solvent is the computation of the long-range interactions because this scales as Consequently, a model that represents the solvent properties implicitly will considerably reduce the number of degrees of freedom of the system and thus also the computational cost. A variety of implicit water models has been developed for molecular simulations [56-60]. Explicit solvent can be replaced by a dipole-lattice model representation [60] or a continuum Poisson-Boltzmann approach [61], or less accurately, by a generalised Bom (GB) method [62] or semi-empirical model based on solvent accessible surface area [59]. Thermodynamic properties can often be well represented by such models, but dynamic properties suffer from the implicit representation. The molecular nature of the first hydration shell is important for some systems, and consequently, mixed models have been proposed, in which the solute is immersed in an explicit solvent sphere or shell surrounded by an implicit solvent continuum. A boundary potential is added that takes into account the influence of the van der Waals and the electrostatic interactions [63-67]. 

The existing models can be grouped in two principal categories, black box models and structural models. Within the empirical black box models the membrane is considered a continuous, nonporous phase in which water of hydration is dissolved. An effective diffusion coefficient which is a characteristic function of the water content controls the water flux. 

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