Kr mM Kq mM nR nQ From Fig of

Human hemoglobin is the most intensively-studied of macromolecules (in this case a protein) in this regard. Blood contains ~ 150 g/lit of hemoglobin, or with a molecular weight of ~ 68000, a concentration of ~2200 |M. This protein has 4 cooperative sites for binding oxygen. When all sites on the protein molecule are empty, all exhibit a dissociation constant Ki = 25 |M; the second, third and fourth ligands exhibit K values of 37, 17, and 0.5 |M, respectively. Note that binding of the second site is anticooperative. The fourth site has a very low dissociation constant, meaning the O2 is very strongly bound to hemoglobin. This general behavior provides very efficient transfer of oxygen around the body because all four sites on each protein molecule are readily saturated. The binding sites on the hemoglobin molecule are iron atoms. An artist's rendition of a hemoglobin molecule is shown in Fig. 11.14. There are four chains of amino acids in the molecule, two designated as a and two as p. The iron atoms are contained in four heme groups, which are shown in the sketch as small curlicues in the top-center and bottom-center.

The molecule is designated as a tetramer a2p2. The situation is not that simple, though. The tetramer can dissociate into a|3 dimers by the equilibrium reaction a2|32 = 2(a|3).

Fig. 11.14 Depiction of the hemoglobin molecule. It has a molecular weight of about 64,000

Myoglobin is a degenerate case of hemoglobin, consisting of only one of the four chains found in hemoglobin and possessing only a single site for binding oxygen. The dissociation constant for this site is the same as the first of hemoglobin's, namely 25 mM. The site-saturation analysis of oxygen binding to myoglobin is the same as that presented in Sect. 11.6.1. However, both myoglobin and hemoglobin are special cases of ligand attachment to macromolecules with n cooperative and/or anticooperative sites. The following analysis takes n = 4 in order to keep the equations as transparent as possible. The notation used in the preceding sections is retained, but the identification is Hb = hemoglobin and L = O2 dissolved in the blood.

The liganded species are denoted by H-L, H-L2, H-L3 and H-L4. The dissociation reactions and their mass-action laws are:

Sites: h "" " "om a and ; amino acid chains

Fig. 11.14 Depiction of the hemoglobin molecule. It has a molecular weight of about 64,000

The conservation equations for protein and ligands are:

[Hbtot] = [Hb] + [Hb-L] + [Hb-L2] + [Hb-L3] + [Hb-L4]

[Lo] = [L] + [Hb-L] + 2[Hb-L2] + 3[Hb-L3] + 4[Hb-L4]

There are six equations to be solved for six unknowns. In addition to the binding equilibrium constants, [Hbtot] and [Lo] are specified parameters1. Sequentially solving the equilibrium equations yields: [Hb-L] = K- 1 [Hb][L]

[Hb-L2] = K -1 [Hb-L][L] = K- 1 K -1 [Hb][L]2 [Hb-Ls] = K - 1 [Hb-L2][L] = K- 1 K -1 K - 1 [Hb][L]3 [Hb-L4] = K -1 [Hb-L3][L] = K- 1 K - 1 K - 1 K -1 [Hb][L]4 Substituting these into Eqs (11.33) and (11.34) gives:

[Hbtot]/ [Hb] = 1 + K- 1 [L] + K- 1 K -1 [L]2 + K- 1 K - 1 K - 1 [L]3 + K- 1 K -1 K - 1 K - 1 [L]4 [Lo ] - [L] = K- 1 [L] + 2 K- 1 K -1 [L]2 + 3 K- 1 K -1 K - 1 [L]3 + 4 K- 1 K -1 K- 1 K - 1

The fraction of the heme sites on the hemoglobin molecule that are occupied by ligands is f = [Lo ] - [L] = 1 K- 1[L] + 2K-1K -^L]2 + 3K- 1K -^L]3 + 4K- 1K -¡[L]4

°2 4[Hbtot ] 4 1 + k-1[L] + K-1K-1[L]2 + K-1K -1K -^L]3 + K-1K -1K ^K -J[L]4

This is called the Adair equation, after its discoverer in 1925. Using the dissociation constants in Eq (11.32), Fig 11.15 is a plot of Eq (11.35) as a function of ligand concentration, L = O2. This system is a classic example of cooperative binding, wherein the site-ligand bond becomes stronger for every successive site occupied (i.e., Ki+1 < Ki). The importance of cooperativity in oxygen binding to hemoglobin compared to myoglobin is shown in this figure. Hemoglobin displays an S-shaped curve which rises from weak binding initially to maximal binding over a small oxygen concentration range. This provides for efficient loading and unloading of oxygen from the molecule. Myoglobin, on the other hand, requires very large oxygen concentrations to saturate the sites on the molecule.

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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