Apolar surfaces

Based on these contributions (a-d), we may arrive at the predictive scheme presented in Table 1. Because of the relatively large contribution from dehydration, essentially all proteins adsorb from an aqueous environment on apolar surfaces, even under electrostatically adverse conditions. With respect to polar surfaces, distinction may be made between proteins having a strong internal coherence ( hard proteins) and those having a weak internal coherence ( soft proteins). The hard proteins adsorb at polar surfaces only if they are electrically attracted, whereas the structural rearrangements (i.e., reductions in ordered structure) in the soft proteins lead to a sufficiently large increase in conformational entropy to make them adsorb at a polar, electrostatically repelling surface. 

Two limiting mechanisms for solute retention can be imagined to occur in RPC binding to the stationary phase surface or partitioning into a liquid layer at the surface. In the previous treatment we assumed that retention is caused by eluite interaction with the hydrocarbonaceous surface, i.e., the first type of mechanism prevails. When the eluent is a mixed solvent, however, the less polar solvent component could accumulate near the apolar surface of the stationary phase. In the extreme case, an essentially stagnant layer of the mobile phase rich in the less polar solvent could exist at the surface. As a result eluites could partition between this layer and the bulk mobile phase without interacting directly with the stationary phase proper. 

This means that for an apolar surface, all apolar or monopolar compounds should fit the same straight line. We have already demonstrated this for a teflon surface in Fig. 3.7 (note that the vdW parameter used in this graph is proportional to Pi, Eqs. 11-5 and 11-6). 

Why does the sorption of organic vapors to polar inorganic surfaces generally decrease with increasing humidity Why does the relative humidity have a negligible influence on sorption of organic vapors to apolar surfaces ... 

One must identify and enumerate the interactions that characterize each of the states relevant to the folding/unfolding partition function. This can be accomplished from the structure, if known, utilizing accessible polar and apolar surface area calculations and specific interactions as described below. 

The strategy used in this review to dissect specific fundamental interactions is to isolate first the hydrophobic effects and subsequently other interactions. Within this context the hydrophobic effect is defined as that contribution to the overall thermodynamics of a process that is proportional to the amount of apolar surface that becomes exposed to the solvent (Hermann, 1972 Gill and Wadso, 1976 Livingstone etal, 1991). The apolar surface area exposed to solvent can be computed using various algorithms (Lee and Richards, 1971 Hermann, 1972 Shrake and Rupley, 1973 Connolly, 1983) that yield the accessible surface area (ASA) in units of square angstroms (A2). 

With the hydrophobic effect defined as the contribution to the thermodynamics that is proportional to the exposure of apolar surface area, it is then possible for a set of homologous compounds to separate the hydrophobic contribution from all other effects by plotting any thermodynamic function (for instance, AH0) versus the number of apolar hydrogens (or the apolar surface area) that become exposed to the solvent on transfer. To the extent that the other interactions make a constant contribution to the thermodynamics,... 

The measured heat capacity increment associated with the transfer of an apolar hydrogen from a crystalline amino acid solid into water is 6.7 0.3 cal K-1 mol-1 or 0.45 0.02 cal (mol A2)-1 of apolar surface (Murphy and Gill, 1990, 1991). This same value is observed for the transfer of 1-alkanols into water (Hall n et al., 1986). The same value is also observed for the transfer of liquid hydrocarbons into water (Gill and Wadso, 1976), and for the dissolution of alkane... 

These model compound studies provide us with estimates of the first two fundamental parameters of ACp ap = 0.45 cal K-1 (mol A2)-1 of buried apolar surface area and ACPjpoi = — 14.3 cal K-1 moT1 of hydrogen bonds. The average polar surface area buried per hydrogen bond in globular proteins is 54 7 A2 (see below) so that ACp>poj = - 0.26 cal K-1 (mol A2)-1 of buried polar surface. 

A//ap/ACp>ap. The value of Th is 71°C for the dipeptide solids, 36°C for the hydrocarbon liquids, and 117°C for the alkane gases. At these temperatures, the enthalpies of interactions of the apolar surfaces with water, including the enthalpy of water restructuring and the solute/solvent van der Waals interactions, are equal and opposite to the enthalpic interactions that the apolar surface experiences in the respective initial phases. As the apolar interaction with water is independent of the initial phase, greater apolar interactions in this phase result in a lower value for T. ... 

The apolar contribution to AS0, ASap, is better characterized than AHap. The value of Tt has been shown to be a universal temperature for all processes involving the transfer of an apolar surface into water and has a value of 112°C (Murphy et al., 1990). At this temperature the AS0 of transfer, ASf, represents the mixing entropy of the process. The universal value of Tt was determined using mole fraction concentration units, so that the liquid transfer ASf takes on a value of zero. The value of Tt remains the same using the local standard state of Ben-Naim (i.e., molar concentration units) (Ben-Naim, 1978), but the value of Ais increased by R ln(55.5), where R is the gas constant and 55.5 is the molarity of water. 

As discussed above, the thermodynamics of the hydrophobic effect are seen to be proportional to the apolar surface area exposed to the solvent. Based on the absence of a size dependence of AS0 on transfer... 

Analysis of the dependence of the structural thermodynamics of globular proteins on apolar surface area provides an estimation of the role of various contributions to protein stability. However, as mentioned above, proteins also show convergence temperatures that can yield similar information, given certain assumptions. 

Recently it has been shown that convergence of thermodynamic quantities at some temperature will occur when there are two predominant interactions that independently contribute to the thermodynamics (i.e., group additivity), provided that one of these interactions is constant for the set of compounds being investigated (Murphy and Gill, 1990, 1991). For example, the 1-alkanols have varying amounts of apolar surface, but each compound has only one —OH group. Under these conditions it was demonstrated that the apolar contribution to AH° is zero at (i.e., Th = Th) and that the... 

In contrast to the relatively constant number of hydrogen bonds per residue, a set of proteins must bury variable amounts of apolar surface area in order to show convergence (Murphy and Gill, 1991). At the temperature at which the apolar contribution to AH° is zero, no variation would be observed in AH° per residue and the constant polar contribution is all that should be observed. The breakdown into polar and apolar interactions can also be viewed in terms of buried surface area. Proteins bury an increasing amount of surface area per residue with increasing size, but the increase is due to increased burial of apolar surface, whereas the polar surface buried remains constant. This is illustrated in Fig. 2 for 12 globular proteins that show convergence of AH°. These proteins bury a constant 39 2 A2 of polar... 

Fig. 2. Dependence of buried area per residue on protein size. The lines are the linear least-squares fits. The total area buried per residue increases with increasing number of residues as does the apolar surface area buried per residue. In contrast, the polar area buried per residue is independent of the size of the protein. The proteins plotted are listed in Table IV.

The value of AH can also be compared to the helix unfolding AH0 of Scholtz et al. (1991). The buried surface area, relative to the extended chain, was calculated for a 50-residue alanine a helix. An average of 19.5 A2 of polar surface is buried per residue and an average of 3.2 A2 of apolar surface is overexposed (i.e., is less accessible in the extended chain than in the helix). Using the fundamental parameters for the polar and apolar ACP described above, a value of — 6.5 cal K-1 (mol res)-1 is estimated for ACp for the helix denatur-ation. At 100°C the extrapolated value of AH0 is about 1.0 kcal (mol res)-1, again in reasonable agreement with the value of AH of 1.35 kcal (mol res)-1. These results strongly support the assertion that the apolar contribution to AH0 is close to zero at 7h. 

Equations (6)—(13) allow calculation of the free energy change at any temperature using the parameters in Table II, the number of residues, Nres, and the buried polar and apolar surface areas evaluated from the crystallographic structure using standard algorithms. The equations can be applied to the entire protein, a single domain, or to interfaces between structural elements. 

Protein A res Buried apolar surface area (A2) Buried polar surface area (A2)... 

The formalism described above allows evaluation of the Gibbs free energy difference between specific structural states of the protein and the reference state, which is taken to be the native structure. The formalism requires access to the crystallographic structure of the protein under study so that, for each structurally defined state, the difference in hydrogen bonds, exposure of polar and apolar surfaces,... 

Analysis of the crystallographic structure also reveals that the two domains interact primarily through hydrophobic and hydrogen bond interactions at the interface. The number of apolar hydrogens that become exposed on the C domain on unfolding of the N domain is 49.4, and the number of apolar hydrogens exposed on the N domain on unfolding of the C domain is 44.8. These values correspond to 726 and 659 A2 of apolar surface area, respectively. In addition, nine... 

Fig. 9. Calculated overall free energy of stabilization (AGtota ) for yeast phos-phoglycerate kinase at pH 6.5 and 0.7 M GuHCl. This curve displays two zeros, corresponding to the temperatures of cold and heat denaturation. Also shown in the curve are the cooperative Gibbs free energies (AG ) associated with the uncompensated exposure of apolar surfaces on unfolding of each of the domains. For both domains, AG is positive for the heat denaturation and close to zero for the cold denaturation. This behavior results in a cooperative heat denaturation and a non-cooperative cold denaturation. [Reprinted from Freire el al. (1991).]...

The physical adsorption is characterized by weak intermolecular forces of the van der Waals type. The adsorbed particle must get close to the solid surface, since the van der Waals energy is proportional to the sixth power of reciprocal distance. The main feature of this interaction is its non-specificity, a considerable velocity and reversibility. An example of the physical adsorption is the adsorption of apolar molecules on an apolar surface resulting form disperse forces. Beside these forces the dipol-dipol interactions occur when molecules of the adsorbent or adsorbate can form permanent or induced dipoles (adsorption of gases or dipol liquids on apolar surfaces). 

The above discussion applies only to the design of peptides that form secondary structures in water or at the interface between an apolar surface and water. In nonpolar solvents, a helix and /3 sheet formation occurs much more readily in large part because solvent molecules cannot compete as readily for hydrogen bonding of the peptide amide groups. 

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