Four-Site Systems: Hemoglobin
The extension of the theoretical framework required to deal with systems having four (or more) sites is straightforward. Formally, the extension involves the addition of one more summation to the GPF of the system; see Eq. (6.2.1) below. Conceptually, the only new quantity that appears in the PF is the quadruplet correlation. Like the triplet correlation it may, or may not, be pairwise additive, depending on the specific origin of the correlation. As in the three-site system, where we have compared the behavior of the linear and triangular arrangements, here we examine three different arrangements: the linear, the square, and the tetrahedral (Fig. 6.1a). We shall see that even when the subunits are identical (both chemically and structurally), the four sites may be either different, identical in a weak sense, or identical in a strict sense. The origin of these differences is discussed in Sections 6.3–6.5. We then examine the correlations in two experimental examples: the first are correlations between protons in benzene-tetracarboxylic acid; the second, the hemoglobin molecule—no doubt the most important and most studied cooperative biomolecule.
KeywordsUtility Function Pair Correlation Average Correlation Tetracarboxylic Acid Center Subunit
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