Receptor association rate constants

A more detailed analysis of ligand binding is possible by determination of the association rate constant ( on-kinetics ) of the dissociation rate constant ( off-kinetics ). The methodology of these estimations is illustrated for the cardiac DHP receptor. 

For any given system, there is a tendency for ligand and receptor to remain associated (the association rate constant k,m) and for the ligand-receptor complex to... 

Shown are the measured number of receptors per cell RT, the association rate constant kf, the dissociation rale constant k and the equilibrium dissociation, constant Ka = kT/k,. The lime required to reach 95% of equilibrium receptor binding when no bound receptors are initially, present, is calculated from r,5 = - ln(0.05)/[Ar( 1 + La/KD)] for the case of /. = Ka. HepG2 - human hepatoma cell line ... 

Because the interaction of isolated receptors and ligands in solution is typically close to a reaction-limited situation (as seen in the previous section), kon is essentially the association rate constant that would be experimentally measured for an isolated receptor in free solution if there... 

Fig. 10. Variation of the per receptor association and dissociation rate constants, fcf and kr, with the number of free receptors. Although the assumption is typically made that kt and kT are constants, this is not strictly true when diffusion effects are significant [see Eqs. (41) and (43)]. (fcf)maxrec and ( r)maxrcc> the maximum values of kt and kt, are given by kon and k0fl. The per cell association rate constant (kt )tdl also varies with the number of free receptors [see Eq. (40)] the maximum value (fcf)masCeii is given by (k + )ccll. 0 is the fractional surface coverage of cell area by receptors. For calculation of , s - 10 nm, a = 10 /nm, kon = 107 M 1 s , and D — 10-6 cm2/s.

Fig. 11. Experimental data and model fit on the variation of the per receptor and per cell association rate constants with the total number of receptors. Reproduced from the Biophysical Journal, Erickson et al. (1987), vol. 52, pp. 657-662, by copyright permission of the Biophysical Society.

Confusingly, all of these terms are in current use to express the position of the equilibrium between a ligand and its receptors. The choice arises because the ratio of the rate constants k and k can be expressed either way up. In this chapter, we take KA to be k, kA and it is then strictly a dissociation equilibrium constant, often abbreviated to either dissociation constant or equilibrium constant. The inverse ratio, k+l k x, gives the association equilibrium constant, which is usually referred to as the affinity constant. 

To measure the dissociation rate constant, all that is necessary, in principle, is first to secure a satisfactory occupancy of the receptors by the radioligand and then to prevent further association, either by adding a competing agent in sufficient concentration or by lowering [L] substantially by... 

The interaction between the receptor and the G-protein is transient and rapidly reversible. This is indicated, for example, by the fact that a single light-activated rhodopsin molecule may activate 500 to 1000 transducin molecules during its 1 to 3 sec lifetime. Hence, the interaction should, in the endpoint, be governed by the normal laws of chemical interaction and expressible in terms of association and dissociation rate constants and binding affinity. The question then arises as to whether the affinity of different receptors for different G-proteins varies. That is, is there specificity in receptor-G-protein coupling, and, if so, what determines this ... 

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-covalendy bound complex C at equilibrium, Eq. (1) applies where kon and kgS represent the forward and reverse mass transfer rate constants. 

Another alternative to occupancy theory is rate theory. Rate theory was developed by Paton through examination of receptors that bind stimulants.30 Paton proposed that a response is caused by the act of binding, not the state of being bound or free (Scheme 5.8). This seemingly subtle difference shifts the theory away from KD and toward kon and fcoff, the rate constants of association and dissociation. Interestingly, at equilibrium, KD is equal to koa/kon (Equations 5.19-5.21). For this reason, occupancy and rate theory are closely related. 

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