Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins: -Protein-Ligand Interactions Can Be Described Quantitatively

The function of myoglobin depends on the protein’s ability not only to bind oxygen but also to release it when and where it is needed. Function in biochemistry often revolves around a reversible protein-ligand interaction of this type. A quantitative description of this interaction is therefore a central part of many biochemical in vestigations. In general, the reversible binding of a protein (P) to a ligand (L) can be described by a simple equilibrium expression:

The reaction is characterized by an equilibrium con stant, Ka, such that

The term Ka is an association constant (not to be confused with the K_a that denotes an acid dissociation constant; p. 63). The association constant provides a measure of the affinity of the ligand L for the protein. K_a has units of M_-1; a higher value of K_a corresponds to a higher affinity of the ligand for the protein. A re arrangement of Equation 5–2 shows that the ratio of bound to free protein is directly proportional to the con centration of free ligand:

When the concentration of the ligand is much greater than the concentration of ligand-binding sites, the binding of the ligand by the protein does not appreciably change the concentration of free (unbound) ligand—that is, [L] remains constant. This condition is broadly applicable to most ligands that bind to proteins in cells and simplifies our description of the binding equilibrium. We can now consider the binding equilibrium from the standpoint of the fraction, (theta), of ligand binding sites on the protein that are occupied by ligand:

Substituting Ka[L][P] for [PL] (see Eqn 5–3) and re arranging terms gives

The value of Kacan be determined from a plot of versus the concentration of free ligand, [L] (Fig. 5–4a). Any equation of the form x=y/(y+z) describes a hyper bola, and is thus found to be a hyperbolic function of [L]. The fraction of ligand-binding sites occupied ap proaches saturation asymptotically as [L] increases. The [L] at which half of the available ligand-binding sites are occupied (at 0.5) corresponds to 1/Ka. It is more common (and intuitively simpler), however, to consider the dissociation constant, K_d, which is the reciprocal of K_a (K_d=1/Ka) and is given in units of molar concentration (M). Kd is the equilibrium con stant for the release of ligand. The relevant expressions change to

When [L] is equal to Kd, half of the ligand-binding sites are occupied. As [L] falls below Kd, progressively less of the protein has ligand bound to it. In order for 90% of the available ligand-binding sites to be occupied, [L] must be nine times greater than Kd. In practice, K_d is used much more often than Kato express the affinity of a protein for a ligand. Note that a lower value of Kd corresponds to a higher affinity of ligand for the protein. The mathematics can be reduced to simple statements: Kd is equivalent to the molar con centration of ligand at which half of the available ligand binding sites are occupied. At this point, the protein is said to have reached half-saturation with respect to lig and binding. The more tightly a protein binds a ligand, the lower the concentration of ligand required for half the binding sites to be occupied, and thus the lower the value of Kd. Some representative dissociation constants are given in Table 5–1. The binding of oxygen to myoglobin follows the pat terns discussed above. However, because oxygen is a gas, we must make some minor adjustments to the equations so that laboratory experiments can be carried out more conveniently. We first substitute the concentration of dissolved oxygen for [L] in Equation 5–8 to give

As for any ligand, Kd is equal to the [O₂] at which half of the available ligand-binding sites are occupied, or [O₂]0.5. Equation 5–9 thus becomes

In experiments using oxygen as a ligand, it is the partial pressure of oxygen in the gas phase above the solution, pO₂, that is varied, because this is easier to measure than the concentration of oxygen dissolved in the solution. The concentration of a volatile substance in solution is always proportional to the local partial pressure of the gas. So, if we define the partial pressure of oxygen at [O₂]0.5 as P₅₀, substitution in Equation 5–10 gives

A binding curve for myoglobin that relates to pO2 is shown in Figure 5–4b.

FIGURE 5–4 Graphical representations of ligand binding. The fraction of ligand-binding sites occupied,

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مواضيع ذات صلة

Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins:- Myoglobin Has a Single Binding Site for Oxygen

Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins:- Oxygen Can Be Bound to a Heme Prosthetic Group

Protein Denaturation and Folding:- Some Proteins Undergo Assisted Folding

Protein Denaturation and Folding:- Polypeptides Fold Rapidly by a Stepwise Process

Protein Denaturation and Folding: - Amino Acid Sequence Determines Tertiary Structure

Protein Tertiary and Quaternary Structures: -Protein Quaternary Structures Range from Simple Dimers to Large Complexes

Protein Tertiary and Quaternary Structures: -Protein Motifs Are the Basis for Protein Structural Classification

Protein Tertiary and Quaternary Structures: -Analysis of Many Globular Proteins Reveals Common Structural Patterns

Protein Tertiary and Quaternary Structures:- Globular Proteins Have a Variety of Tertiary Structures

Protein Tertiary and Quaternary Structures:- Myoglobin Provided Early Clues about the Complexity of Globular Protein Structure

Protein Tertiary and Quaternary Structures: -Structural Diversity Reflects Functional Diversity in Globular Proteins

Protein Tertiary and Quaternary Structures: -Fibrous Proteins Are Adapted for a Structural Function