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Application of Equilibrium and Non-equilibrium Theory for the Analysis of GPC Spin Column Eluates

An excellent reference discussing the theory and applications of receptor binding is the text edited by E.C. Hulme entitled ''Receptor-ligand interactions: a practical approach'' [14].

2.1.4.1 Sample Prepared Under Equilibrium Conditions Prior to Spin Column Treatment

The binding of a small molecule ligand to a protein receptor follows a bimolecu-lar association reaction with second-order kinetics. For the reversible reaction of a ligand L and a protein P to form a non-covalently bound complex C at equilibrium, Eq. (1) applies where kon and kog represent the forward and reverse mass transfer rate constants. kon

koff

The equilibrium dissociation constant Kd is then given by:

If [P]o and [L]o are the initial total protein and ligand concentrations, respectively, where:

and:

the equilibrium in Eq. (2) can be transformed into a quadratic equation and solved, giving:

[C] = 1 (Kd + [P]0 + [L]J - f1/4(Kd + [P]0 + [L]0)2 - [L]0[P]0}1/2 (5)

where [C] is the equilibrium concentration of the protein-ligand complex, referred to also as [C] . Equation (5) can be used to calculate the concentration of complex present at equilibrium for initial protein and ligand concentrations and Kd during the incubation step in the GPC spin column screening experiment.

Typically, in most GPC spin column screening experiments, concentrations of the target protein and small molecule compounds are >5 mM. Figure 2.3 illustrates the relationship between the concentration of the protein-ligand complex [C] present at equilibrium as a function of the binding constant for a variety of initial protein and ligand concentrations, [P]o and [L]o, respectively, >5 mM. These initial concentrations are used so that sufficient complex is formed so that even weakly binding drugs with Kd values <20 mM form complexes of sufficient concentration so that they are easily detectable using ESI-Time-of-Flight (Tof) mass spectrometry.

2.1.4.2 Calculation for Predicting the Concentration of Sample Complex Eluted From the Spin Column

The GPC spin column fractionation step is a non-equilibrium process. During the gel permeation chromatography step, the unbound small molecules in solu

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