Independent identical binding sites

To obtain accurate estimates of the number of binding sites (n), binding experiments (usually titrations) need to be performed under conditions where the total concentration of A is relatively high, specifically that cAit0, 1 / KAs these conditions define a stoichiometric titration where effectively all of the B added is bound until the sites on A are saturated. Titrations under these conditions are insensitive to the value of the association constant, so to obtain reliable estimates of KAss, data are needed from titrations at much lower concentrations, where cA, toi- V-Kaw It should be clear from this discussion that it is not easy to evaluate both n and accurately, and it is usually necessary to do a global analysis of several data sets, obtained under different concentration conditions. 

---

The reaction is facilitated by a linear template T. We will assume that this template has two independent, identical, binding sites both bind substrates with the same microscopic binding constant K, to give a binary complex S-T and a ternary complex S T S. 

We see that, as a function of [S], Equation (4.33) has sigmoidal shape. This is the hallmark of the cooperativity the fraction of site occupied has a more sharp response to changes in [S] compared to the case of independent identical binding. 

In the special case of identical binding sites (KAssA = KAss2), the dependence of 012 on the total concentration of A (cAM) is weakly sigmoidal at low concentrations of B, and not hyperbolic this is a direct indication that A can bind more than one B. The total concentration of bound ligand (= 0 +02) follows a hyberbolic dependence, as expected since the sites are independent. 

An alternative approach to binding is based on the Scatchard equation [96]. If a protein has n independent and identical binding sites with intrinsic binding constants K and a fraction 0 of these are occupied at a given surfactant concentration [S], then a simple kinetic argument, in which the rate of binding is proportional to [S] times the fraction of vacant sites (1-0) and is equated to the rate of dissociation from the occupied sites proportional to 0, gives... 

In Eq. (1.1.17) we derived the GPF of a system having m independent sites. Statistical mechanics provide the recipe for constructing the GPF for more general systems. This is discussed in Section 1.4. Here, we present the general form of the GPF of a single adsorbent molecule with m (identical or different) binding sites, namely,... 

In this section we find it more convenient to start with an ensemble of M independent and indistinguishable systems (i.e., the systems are identical but not localized, as assumed in Section 2.4), each of which has a single binding site. We stress from the outset that the concept of cooperativity, as defined in Section 4.2, does not apply to such systems. What we shall show is that under certain conditions a single-site system can exhibit behavior that is similar to the behavior of a cooperative system. 

Another simplification can be made if all binding sites are independent (noncooperative binding) and they can be attributed to classes of identical sites. In protein-drug affinity studies the fraction of drug molecules bound (D4) per protein molecule (P) is given by... 

The two monoprotonated forms of pyridoxine are the tautomeric pair shown in Eq. 6-75 and whose concentrations are related by the tautomeric ratio, R = [neutral form]/[dipolar ion], a pH-independent equilibrium constant with a value of 0.204/0.796 = 0.26 at 25°C.75 Evaluation of microscopic constants for dissociation of protons from compounds containing non-identical groups depends upon measurement of the tautomeric ratio, or ratios if more than two binding sites are present. In the case of pyridoxine, a spectrophotometric method was used to estimate R. 

If a plot of v/[L] versus v yields a straight line, shown by the solid line in Figure E3.2, then all the binding sites on M are identical and independent, and and n are estimated as shown in the figure. 

Fig. 3 Simulated Scatchard plots for the binding of a ligand to various concentrations of identical and independent binding sites (N). (a) N = 10 8 mol g (b) N = 3 x 10-8 mol g-1 ...

The following drug-protein binding data were obtained. Calculate the number of binding sites and the binding constant. Prove that the binding occurs independently and is identical. 

An enzyme has four identical and independent binding sites for its substrate. The osmotic pressure of a solution of the enzyme was measured and found to be 2.4 x 10 3 atm at 20°C. The binding equilibrium between the enzyme and its substrate was carried out in a dialysis bag at 20°C. The concentration of unbound substrate outside the dialysis bag and the total substrate concentration inside the bag were found to be 1.0 xIO 4 and 3.0 x Qr M, respectively. Calculate the equilibrium constant for the binding of the substrate to the enzyme at 20°C. 

Two special cases of Equation (4.31) are particularly worth mentioning (i) If the two sites are identical and independent, then Kx = 2K and K2 = K/2, where K is the association constant for a single binding site. (Kx is equal to 2K because there are two sites for binding the first substrate K2 = K/2 because both sites can release a substrate.) In this case we have... 

The two iron-binding sites at the dinuclear ferroxidase center are not identical. Mutagenesis of residues E27 (in site A) and El 07 (site B) shows that site A can bind iron independently but requires site B for iron oxidation. In contrast, iron binding in site B is greatly decreased in the absence of site A, whereas oxidation is unaffected. ... 

Tab. 7.1. Relative values of the stability constants in the case of n identical and independent binding sites [7]...

---