Free energy cooperativity

Huang Y, Ackers GK. Transformation of cooperative free energies between ligation systems of hemoglobin resolution of the carbon monoxide binding intermediates. Biochemistry 1996 35 704-718. 

Before we leave this subject we wish to mention a suggestion made by Guggenheim [1948, 1949, 1952]. In. order to force agreement between the simplified lattice model and experimental data, he proposes to regard the quasi-chemical equation (3.3.14) as defining w. Then w may be considered as a temperature dependent parameter which Guggenheim calls the cooperative free energy. This parameter is then adjusted to the experimental data. 

Table 9 shows that the value of AGn of the cooperative interaction between bonding centers is within the error in the determination of integral AG values. This fact can either indicate the slight mutual influence of the centers or be caused by the compensation between the enthalpy and entropy components of Gibbs free energy. 

Now — L is the Landau-Ginzburg free energy, where m2 = a(T — Tc) near the critical temperature, is a macroscopic many-particle wave function, introduced by Bardeen-Cooper-Schrieffer, according to which an attractive force between electrons is mediated by bosonic electron pairs. At low temperature these fall into the same quantum state (Bose-Einstein condensation), and because of this, a many-particle wave function (f> may be used to describe the macroscopic system. At T > Tc, m2 > 0 and the minimum free energy is at = 0. However, when T [Pg.173]

In practice, the deformation parameters e/ (l > 2) are determined from the minimization of the free-energy of the system in full analogy to the total momentum Q of a Cooper pair. And they can be determined in a volume conserv-... 

In summary, the intrinsic binding constant to be used throughout this book always refers to a specific set of sites. They are defined in terms of the molecular properties of the system through the corresponding canonical PFs. They are also interpreted as probability ratios or as free energies of binding processes. In subsequent chapters we shall see how to extract from these quantities various correlation functions or, equivalently, cooperativities. 

The concept of cooperativity can also be translated into free-energy change by the relation... 

Once again, we note that the triplet cooperativity is not simply related to the pair interactions—as expected from the triplet interaction energy, Eq. (5.10.7). It is neither a product of the pair correlation (as normally expected from nearest-neighbor interactions), nor the sum of pair correlations g a, b) and g b, c) as assumed by Ackers et al. (1982, 1986). Again, the difference between the free energy of... 

Individual operator sites are denoted O if vacant, or R2 if occupied by a repressor dimer. Pairwise interactions between adjacent occupied sites are denoted ( ) AG 2 and AG23 the free energies of cooperative interaction between adjacent occupied sites, defined as the difference between AG, for any species and the sum of the intrinsic free enei es of binding to occupied sites. 

Free Energies and Nonadditivities (in kcal/mol) of the Cooperativities for Bindii of Oxygen to Human Adult lib at Different Temperatures ... 

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