Very Simple Solvation Models

Some particularly simple solvation models include all contributions to the solvation free energy (including the electrostatic contribution) in an equation of the following form 

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In addition to solvation effects, steric interactions of the head groups on opposing bilayers, as they approach one another, result in a short-range repulsion. These interactions are referred to as protrusion effects. A very simple analytical model, which captures the essence of these effects, was constructed by Is-raelachvili and Wennerstrom [140]. They superimposed non-overlapping, local, thermally-excited protrusions of lateral dimension a and extending a distance Zi from the surface, onto opposing flat surfaces. By allowing N such protrusions... 

Gu W, Rahi SJ, Heim V (2004) Solvation free energies and transfer free energies for amino acids from hydrophobic solution to water solution from a very simple residue model. J Phys... 

Simple cavity models have been used to study solvated electrons in liquid ammonia. In that case the dominant interactions arise from long range polarization effects, so that the energy of the localized state is not very sensitive to the fluid deformation in the vicinity of the localized charge. In the case of an excess electron in liquid helium, however, the electron-fluid interaction arises mainly from short range electron-atom interactions, and we shall show that the localized excess electron in a cavity in liquid helium lies lower in energy than the quasi-free electron. 

The aim of this contribution was to review the efforts that have been made so far in the formulation of a Lagrangian for the implicit solvation model. The goal is to provide a simple and computationally efficient way to describe the very complex phenomenon of solvation, which involve a large number of molecules, by using a strongly reduced set of degrees of freedom. 

Although few applications of these very recently implemented models have yet appeared, some calculations for free energies of transfer into aqueous solution are available.Polarization of the solute has been analyzed by reference to the molecular dipole moment,including comparison to a hybrid quantum mechanics/molecular mechanics approach,and the effect of aqueous solvation on conformational equilibria and simple nucleophilic reactions has been examined.] jo consideration of CDS solvation terms in conjunction with these models has appeared. 

The manifest linearity of the majority of free energy plots is paradoxical because the constant slope would indicate that the transition structure is substituent independent. Variation in structure might be expected to occur due to the change in substituent and thus yield curved relationships as indicated in Section 6.1. The relationship between reactivity and selectivity is based on a very simple model, to which most reactions do not conform because they involve not only at least two major bonding changes but solvation changes as well. 

The previous sections have focused on a generie model of a very simple solvent, in which solvation dynamics is determined by molecular translations and reorientations only. These in turn are controlled by the solvent molecular mass, moment of inertia, dipole moment and short-range repulsive interactions. When the solvent is more eomplex we may expect specific structures and interaetions to play signifieant roles. Still, numerical simulations of solvation dynamics in more eomplex systems lead to some general observations ... 

This simple definition then has been largely extended to treat more complex phenomena, including not only electrostatic effects and nowadays continuum solvation models represent very articulate methodologies able to describe different systems of increasing complexity. 

The Born equation is a very simple but surprisingly useful dielectric continuum model for solvation energetics. From the Bom equation... 

Experimental data show that the ratio of the solvation energy in the liquid phase to the sum of the stepwise enthalpies of solvation up to a given cluster size converges with as few as five or six solvent molecules for many different cations clustered both to water and to ammonia. These observations end support to the very simple Bom concept that to first order, solvation can be modeled by the immersion of a sph e of fixed radius and charge in a stmc-tureless dielectric continuum. Higher-order corrections to this simple picture come from consideration of surface tension effects. Convergence of these ratios to approximately the same value is indicative of the fact that, beyond the first solvation shell, the majority of the contribution to solvation is from electrostatic interactions between the central ion cavity and the surrounding medium. 

The above analysis demonstrates how complicated it is to build up an inventory of all possible solvent effects even for a very simple protein. Nevertheless, for a specific protein of known sequence and structure, the relative contributions of each specific residue can be estimated based on experimental data on small model compounds (see Appendix G). With an imaginative choice of such models it is in principle possible to estimate the contribution of all the conditional solvation Gibbs energies of single FGs, pair-correlated FGs, and triplet-correlated FGs. As we have seen above, the overall value of 5G would be the balance between many positive and negative contributions of the various FGs as well as the backbone. 

We consider two profile models. The first, which is very simple, was used in the past as an effective solvation potential [1,2,42], We call it THOMl (THread-ing Onion Model 1), and it suggests a clear path to an extension (which is our prime model), namely, THOM2. The onion level denotes the number of contact shells used to describe the environment of the amino acid. The THOMl model uses one contact shell of amino acids. The more detailed THOM2 energy model (to be discussed below) is based on two layers of contacts. 

In order to be able to evaluate the model itself, we shall examine a very simple case in which there is only one reactant and one product, having roughly the same molecular volume and the same polarizability in order to neglect the cavitation and dispersion contributions to the variation of the solvation free energy. Tautomeric equilibria offer us a good example of such systems. 

In the Polarizable Continuum Model for solvation, the molecular solute is hosted in a cavity of a polarizable dielectric medium representing the solvent The cavity is accurately modeled on the shape of the molecular solute (Miertus et al. 1981), and the dielectric medium is characterized by the dielectric permittivity e of the bulk solvent The physics of the model is very simple. The solute charge distribution polarizes the dielectric medium, which in turn acts back on the solute, in a process of mutual polarization that continues until self-consistence is reached. The polarization of the solvent is represented by an apparent charge distribution (ASC) spread on the cavity surface. In computational practice the ASC is discretized to a set of NTS point charges and the solute-solvent interaction is expressed as in terms of the interaction between these and the charge distribution of the molecular solute. 

The simplest and easiest-to-use tools for the interpretation of solvent effects are the phenomenological models, which rely on a very simple description of the solvent in terms of one (or more) empirical parameter, so that the solvation effects are interpreted in terms of the strength of the solvents on the basis on the values of such parameters. As a consequence, the different solvents are classilied in scales, on the basis of the value of the chosen parameters, and the experiments are interpreted consequently. One very popular approach tries to rationalise the solvent effects in terms of the solvent polarity, empirically defined as the overall solvation power, which can be estimated with the dielectric function or using other more refined and more case-specific approaches. 

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