Estimating Protein-Ligand Binding Affinity by NMR - New Developments in Medicinal Chemistry - page 172

Consequently, the most widely preferred quantitative measure of receptor-ligand
binding affinity is dissociation constant K D , since it is a measurement of stability
for bimolecular complexes and its meaning is clear. Moreover, K D has the units of
concentration. Therefore, a value of K D in mM range indicates a nearly 1:1000
ratio of free to bound states in an equimolar mixture of P and L and a K D in µM
range implies an approximately 1:1000,000 ratio of these states, i.e. , the higher
the binding affinity, the lower the value of K D [2].
To determine K D through NMR experiments it is necessary to perform a
quantitative analysis of solutions that are potentially µM in the observed nucleus.
When in the free state, the receptor and ligand maintain their individual NMR
parameters ( e.g. chemical shifts, relaxation rates, translational diffusion
coefficients). However, when in the bound state, the related binding affinity of
ligand and receptor leads to an exchange process that alternates two sets of
molecules between the free and bound states.
At equilibrium, the system presents free and bound state populations ([R], [L],
[RL]) consistent with Equation 1. In bound state, the ligand transiently adopts
NMR parameters characteristic of the typically much larger receptor. On the other
hand, analyzing receptor NMR parameters, the ligand briefly perturbs the binding
site environment, which may alter distribution of conformations of some receptor
molecules group [18]. In both cases, the NMR parameters are influenced by
intermolecular interaction. Thus, through NMR experiments may be possible to
observe the ligand, the receptor or both, but commonly only one species is chosen
as the target of observation. Analyzing the ligand signal it is possible to
distinguish between free [L] and bound [RL] ligand, so [L] and [RL] can be
quantified. Similarly, observing the receptor it becomes possible to separate
quantitatively free [R] and bound [RL] receptor signal [2].
In either case, the interaction modulates the NMR parameters of both molecules.
For a system in slow exchange (usually this means a system with high binding
affinity and low dissociation constant, K D = µM or lower), on the chemical shift
time scale, distinct signs for the free and bound states, i.e., [L] and [RL] might be
observed. However, in practice this is unviable due to the difficulty of detecting
signal in µM concentration. Furthermore, in fast exchange systems (system with