The concept of equilibrium also applies to the binding of one molecule to another without covalent changes to either molecule. Many important cellular processes depend on such binding “reactions,” which involve the making and breaking of various noncovalent interactions rather than covalent bonds, as discussed above. A common example is the binding of a ligand (e.g., the hormone insulin or adrenaline) to its receptor on the surface of a cell, which triggers an intracellular signaling pathway (see Chapter 15). Another example is the binding of a protein to a specific sequence of bases in a molecule of DNA, which frequently causes the expression of a nearby gene to increase or decrease (see Chapter 9). If the equilibrium constant for a binding reaction is known, the stability of the resulting complex can be predicted.

To illustrate the general approach for determining the concentration of noncovalently associated complexes, let’s calculate the extent to which a protein (P) is bound to DNA (D), forming a protein-DNA complex (PD):

P + D ⇌ PD

Most commonly, binding reactions are described in terms of the dissociation constant (K_d), which is the reciprocal of the equilibrium constant. For this binding reaction, the dissociation constant is calculated from the concentrations of the three components when they are at equilibrium by

It is worth noting that in such a binding reaction, when half of the DNA is bound to the protein ([PD] = [D]), the concentration of P is equal to K_d. The lower the K_d, the lower the concentration of P needed to bind to half of D. In other words, the lower the K_d, the tighter the binding (the higher the affinity) of P for D.

Typically, a protein’s binding to a specific DNA sequence exhibits a K_d of 10^–10 M, where M symbolizes molarity, or moles per liter (mol/L). To relate the magnitude of this dissociation constant to the intracellular ratio of bound to unbound DNA, let’s consider the simple example of a bacterial cell having a volume of 1.5 × 10^–15 L and containing 1 molecule of DNA and 10 molecules of the DNA-binding protein P. In this case, given a K_d of 10^–10 M and the total concentration of the P in the cell (∼111 × 10^–10 M, about a hundredfold higher than the K_d), 99 percent of the time this specific DNA sequence will have a molecule of protein bound to it and 1 percent of the time it will not, even though the cell contains only 10 molecules of the protein! Clearly P and D have a high affinity for each other and bind tightly, as reflected by the low value of the dissociation constant for their binding reaction. For protein-protein and protein-DNA binding, K_d values of ∼10^–9 M (nanomolar) are considered to be tight, ∼10^–6 M (micromolar) modestly tight, and ∼10^–3 M (millimolar) relatively weak.

A large biological macromolecule, such as a protein, can have multiple binding surfaces for binding several molecules simultaneously (Figure 2-24). In some cases, these binding reactions are independent, with their own distinct K_d values that are independent of each other. In other cases, binding of a molecule at one site on a macromolecule can change the three-dimensional shape, or conformation, of a distant site, thus altering the binding interactions of that distant site with some other molecule. The modifications of amino acid side chains—mentioned above—often contribute to the molecular shapes required for such binding interactions. These covalent and noncovalent binding reactions are important mechanisms by which one molecule can alter, and thus regulate, the structure and binding activity of another. We examine this regulatory mechanism in more detail in Chapter 3.

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