Apolar-polar repulsion

D.W. Urry, Function of the Fi-motor (Fi-ATPase) of ATP synthase by Apolar-polar Repulsion through Internal Interfacial Water. Cell Biol. Int., 33(1), 44-55,2006. 

Figure 2.18. Energies are shown that can be inter-converted by means of elastic-contractile model proteins capable of exhibiting inverse temperature transitions functioning by means of the competition for hydration between oil-like and charged groups called an apolar-polar repulsive free energy of hydration. See Chapter 5 for a more complete development of the phenomenology and physical basis and Chapter 8 for details of the molecular process.

Due to the struggle to survive under circumstances of limited food supply, organisms evolve to use the most efficient mechanism available to their composition. The most efficient mechanism available to the proteins that sustain Life would seem to be the apolar-polar repulsive free energy of hydration as observed for the inverse temperature transitions for hydrophobic association. The efficiency of designed elastic-contractile protein-based machines and a number of additional properties make designed protein-based materials of substantial promise for the marketplace of the future. 

Figure 2.21. The designed elastic-contractile model proteins function by means of the apolar-polar repulsive free energy of hydration to achieve zero order release with simultaneous dispersal of delivery...

Competition for hydration between polar (e.g., charged) and hydrophobic (apolar) groups, called the apolar-polar repulsive free energy of... 

CH2-CH2-CH2-NH-C[NH]-NH2 ), and glutamic acid (-CH2-CH2-COO"). We believe this to be another reflection of the component of AGha referred to as an apolar-polar repulsive free energy of hydration, AG p (see Equation [5.13] of section S.7.9.2 below). Thus, when the side chain is fully erect, as seen for certain residues in the crystal structures of the molecular chaperone, GroEL/GroES, and especially of the y-rotor of ATP synthase, the full value of AGha should be used for that residue. 

With the protein-based polymer poly [0.8GVGVP),0.2GEGVP)], at low pH when aU 4 of the Glu (E) residues/lOO residues are as COOH, the transition temperature is near 25° C and the heat of the transition, AH, = 0.97kcal/mole-pentamer (see Rgure 5.28). On raising the pH to the point of less than two C00"/100 residues, the heat of the transition has been reduced, and AH, = 0.27kcal/mole pentamers. The preferred interpretation over a decade ago was (1) that the formation of 2 C00 /100 residues structured almost three-fourths of the thermodynamically measured waters of hydrophobic hydration, and (2) that there exists a competition for hydration between apolar and polar residues, referred to as an apolar-polar repulsive free energy of hydration. 

Derivation of LGap, the Change in Gibbs Free Energy Due to the Apolar-Polar Repulsive Free Energy of Hydration... 

The Hill plots in Figure 5.31 provide remarkable insight into the hydrophobic-induced pKa shifts. Starting in the hydrophobically associated state for Model Protein v, on decreasing acid concentration, that is, raising the pH, the pKa of the first carboxyl to form carboxylate is 7.0. In Figure 5.31 A, this is the pKa for the most tightly bound proton. As more carboxylates form, further ionization becomes easier, and finally the last carboxyl to ionize does so with a pKa of 5.7. Remarkably, the last carboxyl to ionize does so with a pKa shifted 1.7 pH units from that of the unperturbed Glu pKa of about 4. Even in the completely unfolded state there remains an apolar-polar repulsion of 2.4 (= 1.7 X 2.3RT) kcal/mole-Glu. ... 

Positive Cooperativity of Model Proteins and Apolar-Polar Repulsion... 

Additionally, as shown in Figure 5.31A, pK shifts separate into an apolar-polar repulsive component that can be relaxed by a change in hydrophobic association and an apolar-polar repulsive component that is dictated by sequence and thereby retained even in the most unfolded and disassembled state. Expectedly, the pKa shift, relaxed by a disruption of all... 

The experimental titration data for the series of Model Proteins I, i, ii, iii, iv, and v are listed in Table 5.5 and shown in Figure 5.34, where the differential effects of charge-charge and apolar-polar repulsion become apparent. For Model Proteins i, ii, iii, iv, and v, for each systematic shift in pKa there occurs a corresponding increase in Hill coefficient. Model Protein I, however, does not fall within the series, because it exhibits a pKa shift without an increase in magnitude of the Hill coefficient. Model Protein I and iv exhibit essentially the same Hill coefficient of 2.7, whereas the pKa values differ by 0.3 pH units. 

From the analysis of the acid-base titration data in Figures 5.30 through 5.34, positive cooperativity results from the apolar-polar repulsive free energy of hydration, that is, from the competition for hydration between apolar (hydrophobic) and polar (e.g., charged) species. The general statement can be that the appearance on the scene of the first polar, for example, charged, species must do the work of destructuring hydrophobic hydration in order to achieve adequate hydration for itself. 

To the best of my knowledge, the hemoglobin oxygenation curve is historically the first example of a biologically essential positive cooperativity. Because of this, it becomes an important objective to explore the phenomenology of hemoglobin s positive cooperativity and compare it with that of the consilient mechanism due to an apolar-polar repulsive free energy of hydration (as is done in Chapter 7) and, in fact, to do so for a number of protein-based machines that exhibit positive cooperativity. 

The quantity that we wish to calculate is given by Equation (5.31) where the subscript ap stands for the apolar-polar repulsive free energy of hydration mechanism and cc stands for the charge-charge repulsion mechanism ... 

Figure 5.35. Visualization of the relative efficiencies of the electrostatic charge-charge repulsion and the apolar-polar repulsion mechanisms by comparison of acid-base titration curves for poly(methacrylic acid), which exhibits charge-charge repulsion (negative cooperativity), and for the Model Proteins i and V, which exhibit apolar-posar repulsion (positive cooperativity). The polymers are each compared with the Henderson-Hasselbalch curve as reference. Chemical energy is Ap>An, where Ap = 2.3RTApH for the change in pH to go from one state to the other, and An is the number of moles to go from a degree...

Other examples have emerged more recently. Prion proteins induce insolubility and cause the ravages of Alzheimer s and mad cow diseases. Then there are chaperones that reverse inappropriate insolubilities. In these latter cases considered mechanisms are not so deeply ingrained. In none of these, however, has the sense of an apolar-polar repulsive free energy of hydration, AG.p, emerged. In none of these has there been a suggestion of the competition for hydration between hydro-phobic and polar species that is the basis for repeated experimental demonstrations of large hydrophobic-induced pKa shifts. 

Stretch activation of muscle is a well-described phenomenon it was the subject of The Croonian Lecture (1977) given by Pringle,and it has been extensively researched and reported in the literature over the ensuing decades. For example, the basic description becomes When active insect flight muscle is stretched, its ATPase rate increases.. . This we take as yet another demonstration of a fundamental process whereby a phosphate present in a protein can be activated, energized, as the result of an increase in hydrophobicity. It is an example of the competition for hydration between apolar and polar species, that is, an example of the apolar-polar repulsive free energy of hydration active in muscle contraction. 

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