Apolar-polar repulsive free energy

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... 

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 ... 

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. 

Specific effects described below are known for shifting the equilibrium in the direction of either the T or the R state. These effects are explicable in terms of the AT -mechanism for moving the T,-divide and the approximately equivalent Gibbs free energy of hydrophobic association, AGha, and its component the apolar-polar repulsive free energy of hydration, AGap. In all cases ion-pair formation associated with hydrophobic domains drives hydrophobic association. 

If the above mechanism, based as it is on an inverse temperature transition, is indeed responsible for the formation of infectious prion protein aggregates, then the variables that lower the value of T, would be expected to favor fiber formation and infectivity. Increase in hydrophobicity and decrease in charge either by neutralization or by mutation would be expected to favor fiber formation and growth. Also as described above, because the free energy that favors the association of P-chains is described as an apolar-polar repulsive free energy of hydration, the presence of limiting hydration would lead to an increase in P-sheet propensity. 

Thus the P-sheet structure may be identified as the infective, self-propagating, structural element, and we believe the argument to be compelling that the driving force for selfpropagation derives from the special coupling of this structural feature with apolar-polar repulsive free energy of hydration, AG.p, that increases with increased hydrophobicity. 

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