Solvent/solute partitioning models

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

Proper condensed phase simulations require that the non-bond interactions between different portions of the system under study be properly balanced. In biomolecular simulations this balance must occur between the solvent-solvent (e.g., water-water), solvent-solute (e.g., water-protein), and solute-solute (e.g., protein intramolecular) interactions [18,21]. Having such a balance is essential for proper partitioning of molecules or parts of molecules in different environments. For example, if the solvent-solute interaction of a glutamine side chain were overestimated, there would be a tendency for the side chain to move into and interact with the solvent. The first step in obtaining this balance is the treatment of the solvent-solvent interactions. The majority of biomolecular simulations are performed using the TIP3P [81] and SPC/E [82] water models. 

Solute Flux Solute partitioning between the upstream polarization layer and the solvent-filled membrane pores can be modeled by considering a spherical solute and a cylindrical pore. The equilibrium partition coefficient 0 (pore/bulk concentration ratio) for steric exclusion (no long-range ionic or other interactions) can be written as... 

In MLC, the mobile phase consists of surfactants at concentrations above their critical micelle concentration (CMC) in an aqueous solvent with an alkyl-bonded phase (52). Retention behavior in MLC is controlled by solute partitioning from the bulk solvent into micelles and into stationary phase as well as on direct transfer from the micelles in the mobile phase into the stationary phase. Eluent strength in MLC is inversely related to micelle concentration. A linear relationship exists between the inverse of retention factor and micelle concentration. Similar to what is observed in RPLC, a linear relationship exists between retention in MLC and , the volume fraction of the organic modifier. Modeling retention in MLC is much more complicated than in RPLC. The number of parameters is important. Micelles are obviously a new domain in both liquid chromatography and electrophoresis. Readers interested in the topic will appreciate Ref. 53, a special volume on it. 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

Pi is the reference solvent and HBj is an H-bonding parameter. Leahy et al. suggested that a more sophisticated approach incorporating four model systems would be needed to adequately address issues of solute partitioning in membranes (121). Thus, four distinct solvent types were chosen— apolar, amphiprotic, proton... 

The interactions between the QM part and the MM part are treated by a combination of quantum-chemical and force-field contributions. If the system can be separated into a QM solute and an MM solvent, the partitioning of interactions arises naturally The electrons of the QM part feel the electric field of the partial charges of the solvent molecules which enter the one-electron Hamiltonian as additional point charges. The dispersion attraction and the short-range repulsion are modelled by a Lennard-Jones 6-12 potential. If, on the other... 

The micelle has too small an aggregation number to be considered as a phase in the usual sense, and yet normally contains too many surfactant molecules to be considered as a chemical species. It is this dichotomy that makes an exact theory of solubilization by micelles difficult. The primary theoretical approaches to the problem are based on either a pseudophase model, mass action model, multiple equilibrium model, or the thermodynamics of small systems [191-196]. Technically, bulk thermodynamics should not apply to solute partitioning into small aggregates, since these solvents are interfacial phases with large surface-to-volume ratios. In contrast to a bulk phase, whose properties are invariant with position, the properties of small aggregates are expected to vary with distance from the interface [195]. The lattice model of solute partitioning concludes that virtually all types of solutes should favor the interface over the interior of a spherical micelle. While for cylindrical micelles, the internal distribution of solutes... 

Eqn. 5 provides a very clear theoretical basis for the data of Fig. 1 (and similar data on other systems, as we shall see). The measured permeability coefficients for a set of solutes should parallel the measured partition coefficients, if the model solvent corresponds exactly in its solvent properties to the permeability barrier of the cell membrane. In addition, the molecular size of the solute is very likely to be an important factor as it will affect the diffusion coefficients within the membrane barrier phase. Data such as those of Fig. 1 will convince us that we have in our chosen solvent a good model for the solvent properties of the membrane s permeability barrier. We can now calculate values of PLx/K for the various solutes, and obtain estimated values of the intramembrane diffusion coefficient, and are in a position to study what variables influence this parameter. Fig. 3 is such a study in which data from Fig. 1 are plotted as the calculated values of f>n,c,n/A.t (calculated as P/K) against the molecular weight of the permeating solute. The log/log plot of the data has a slope of — 1.22, which means that one can express the dependence of diffusion coefficient on molecular weight (A/) in the form where... 

In the second stage, the solute partitions between the motde phase and the stationary phase. In this process, the solute disjriaces the solvents from the stationary phase depending on the molecular sizes r of the solute s and the solvents i. On the basis of this model, one can write the equation for the equilibrium constant K, i between the solute and the solvent ... 

Hartley 46) speculated that a solvent action of the oily constituents of the organic matter might be important for soil uptake. Swoboda and Thomas 98) expressed a similar view in their study of parathion on soil. The chromatographic sorption model of Lambert (59) is compatible with the idea of solute partitioning between soil organic matter and water. 

In order to quantify intermolecular solute-IL interactions, (Abraham et al., 2003 Acree Abraham, 2006) reported mathematical correlations based on the general Abraham solvation parameter model for the gas-to-solvent, Kl, and water-to-solvent, P, partition coefficients. Recently, (Sprunger et al, 2007 Sprunger et al., 2008 Sprunger et al., 2009a Sprunger et al., 2009b) modified the Abraham solvation parameter model ... 

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