Hydrophobic effect model

Studies described in earlier chapters used cellular automata dynamics to model the hydrophobic effect and other solution phenomena such as dissolution, diffusion, micelle formation, and immiscible solvent demixing. In this section we describe several cellular automata models of the influence of the hydropathic state of a surface on water and on solute concentration in an aqueous solution. We first examine the effect of the surface hydropathic state on the accumulation of water near the surface. A second example models the effect of surface hydropathic state on the rate and accumulation of water flowing through a tube. A final example shows the effect of the surface on the concentration of solute molecules within an aqueous solution. 

A recent breakthrough in molecular theory of hydrophobic effects was achieved by modeling the distribution of occupancy probabilities, the pn depicted in Figure 4, rather than applying a more difficult, direct theory of po for cavity statistics for liquid water (Pohorille and Pratt, 1990). This information theory (IT) approach (Hummer et al., 1996) focuses on the set of probabilities pn of finding n water centers inside the observation volume, with po being just one of the probabilities. Accurate estimates of the pn, and po in particular, are obtained using experimentally available information as constraints on the pn. The moments of the fluctuations in the number of water centers within the observation volume provide such constraints. 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

Gomez, M. A. Pratt, L. R. Hummer, G. Garde, S., Molecular realism in default models for information theories of hydrophobic effects, J. Phys. Chem. B 1999,103, 3520-3523... 

Pratt, L. R. Pohorille, A., Hydrophobic effects and modeling of biophysical aqueous solution interfaces, Chem. Rev. 2002,102, 2671-2691... 

Ashbaugh, H. S. Asthagiri, D. Pratt, L. R. Rempe, S. B., Hydration of krypton and consideration of clathrate models of hydrophobic effects from the perspective of quasichemical theory, Biophys. Chem. 2003,105, 323-338... 

We present and analyze the most important simplified free energy methods, emphasizing their connection to more-rigorous methods and the underlying theoretical framework. The simplified methods can all be superficially defined by their use of just one or two simulations to compare two systems, as opposed to many simulations along a complete connecting pathway. More importantly, the use of just one or two simulations implies a common approximation of a near-linear response of the system to a perturbation. Another important theme for simplified methods is the use, in many cases, of an implicit description of solvent usually a continuum dielectric model, often supplemented by a simple description of hydrophobic effects [11]. 

A classical Hansch approach and an artificial neural networks approach were applied to a training set of 32 substituted phenylpiperazines characterized by their affinity for the 5-HTiA-R and the generic arAR [91]. The study was aimed at evaluating the structural requirements for the 5-HTiA/ai selectivity. Each chemical structure was described by six physicochemical parameters and three indicator variables. As electronic descriptors, the field and resonance constants of Swain and Lupton were used. Furthermore, the vdW volumes were employed as steric parameters. The hydrophobic effects exerted by the ortho- and meta-substituents were measured by using the Hansch 7t-ortho and n-meta constants [91]. The resulting models provided a significant correlation of electronic, steric and hydro-phobic parameters with the biological affinities. Moreover, it was inferred that the... 

It is important to propose molecular and theoretical models to describe the forces, energy, structure and dynamics of water near mineral surfaces. Our understanding of experimental results concerning hydration forces, the hydrophobic effect, swelling, reaction kinetics and adsorption mechanisms in aqueous colloidal systems is rapidly advancing as a result of recent Monte Carlo (MC) and molecular dynamics (MO) models for water properties near model surfaces. This paper reviews the basic MC and MD simulation techniques, compares and contrasts the merits and limitations of various models for water-water interactions and surface-water interactions, and proposes an interaction potential model which would be useful in simulating water near hydrophilic surfaces. In addition, results from selected MC and MD simulations of water near hydrophobic surfaces are discussed in relation to experimental results, to theories of the double layer, and to structural forces in interfacial systems. 

What is the likely future use of MC and MD techniques for studying interfacial systems Several promising approaches are possible. Continued investigation of double layer properties, "hydration forces", "hydrophobic effects", and "structured water" are clearly awaiting the development of improved models for water-water, solute-water, surface-water, and surface-solute potentials. 

The van der Waals model of monomeric insulin (1) once again shows the wedge-shaped tertiary structure formed by the two chains together. In the second model (3, bottom), the side chains of polar amino acids are shown in blue, while apolar residues are yellow or pink. This model emphasizes the importance of the hydrophobic effect for protein folding (see p. 74). In insulin as well, most hydrophobic side chains are located on the inside of the molecule, while the hydrophilic residues are located on the surface. Apparently in contradiction to this rule, several apolar side chains (pink) are found on the surface. However, all of these residues are involved in hydrophobic interactions that stabilize the dimeric and hexameric forms of insulin. 

In general, the standard enthalpy of micellization is large and negative, and an increase in temperature results in an increase in the c.m.c. the positive entropy of micellization relates to the increased mobility of hydrocarbon side chains deep within the micelle as well as the hydrophobic effect. Hoffmann and Ulbricht have provided a detailed account of the thermodynamics of micellization, and the interested reader will find that their tabulated thermodynamic values and treatment of models for micellar aggregation processes are especially worthwhile. 

Subsequent to CO2 association in the hydrophobic pocket, the chemistry of turnover requires the intimate participation of zinc. The role of zinc is to promote a water molecule as a potent nucleophile, and this is a role which the zinc of carbonic anhydrase II shares with the metal ion of the zinc proteases (discussed in the next section). In fact, the zinc of carbonic anhydrase II promotes the ionization of its bound water so that the active enzyme is in the zinc-hydroxide form (Coleman, 1967 Lindskog and Coleman, 1973 Silverman and Lindskog, 1988). Studies of small-molecule complexes yield effective models of the carbonic anhydrase active site which are catalytically active in zinc-hydroxide forms (Woolley, 1975). In addition to its role in promoting a nucleophilic water molecule, the zinc of carbonic anhydrase II is a classical electrophilic catalyst that is, it stabilizes the developing negative charge of the transition state and product bicarbonate anion. This role does not require the inner-sphere interaction of zinc with the substrate C=0 in a precatalytic complex. 

Fe-xS] ferredoxins, 33 54-55 rubredoxin, 33 44-51 hydrophobic effect, 33 60-62 significance, 33 40-44 metal complexes of, 7 218-220 model complexes, catalysis by, 33 61-62 Peptococcus aerogenes ferredoxin, structure, 38 242, 244-245... 

By introducing fluorine atoms to the polyenic system of retinal, the geometry, electronic properties, hydrophobicity, and absorption properties of the molecule will be modified. Thus, fluoro derivatives of retinal are useful tools to understand the interactions between retinal and opsin, especially on the level of charge and hydrophobic effects at the protein site. Moreover, fluorine atoms are probes in NMR and allow studies on model molecules of visual pigments Consequently, syntheses of mono-, di-, and trifluoro derivatives of retinal have been the subject of many investigations. 

All of these models predict that the hydrophobic effect provides a significant driving force for the exclusion of even highly polar, charged peptides from an aqueous environment to the nonpolar environment of the RPC sorbent. According to the solvophobic model, in order to place a peptide into a mobile phase, a cavity of the same molecular dimensions must first be created. The energy required to create this cavity is related to the cohesive energy density or the surface tension of the mobile phase. Conceptually, each solvent-accessible unit... 

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