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Table of contents
Intro to regression
Nonlinear regression
Curve fitting with Prism
Interpreting the results
Comparing two curves
Distributions of best-fit values
Radioligand binding
Saturation binding
Competitive binding

Kinetics of binding



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Dissociation
Association
Analysis checklist
Law of mass action
Competitive binding
Dose-response curves
Enzyme kinetics
Standard curves
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Using kinetic data to test the law of mass action

Standard binding experiments are usually fit to equations derived from the law of mass action. Kinetic experiments provide a more sensitive test than equilibrium experiments to determine whether the law of mass action actually applies for your system. To test the law of mass action, ask these questions:

Does the Kd calculated from kinetic data match the Kd calculated from saturation binding?

According to the law of mass action, the ratio of koff to kon is the Kd of receptor binding:

MathType Equation

The units are consistent: koff is in units of min^-1; kon is in units of M^1min^1, so Kd is in units of M.

If binding follows the law of mass action, the Kd calculated this way should be the same as the Kd calculated from a saturation binding curve.

Does kob increase linearly with the concentration of radioligand?

The observed association rate constant, kob, is defined by this equation:

MathType Equation

Therefore, if you perform association rate experiments at various concentrations of radioligand, the results should look like the figure below. As you increase the concentration of radioligand, the observed rate constant increases linearly. If the binding is more complex than a simple mass action model (such as a binding step followed by a conformational change) the plot of kob vs. [radioligand] may plateau at higher radioligand concentrations. Also, you should extrapolate the plot back to zero radioligand to determine the intercept which equals koff. If the law of mass action applies to your system, the koff determined this way should correspond to the koff determined from a dissociation experiment. Finally, this kind of experiment provides a more rigorous determination of kon than that obtained with a single concentration of radioligand.

Is specific binding 100% reversible, and is the dissociated ligand chemically intact?

Nonspecific binding at "time zero" should equal total binding at the end (plateau) of the dissociation. In other words, all of the specific binding should dissociate if you wait long enough. Use chromatography to analyze the radioligand that dissociates to prove that it has not been altered.

Is the dissociation rate consistent with different experimental conditions?

Determine the dissociation constant after binding various concentrations of radioligand for various lengths of time. If your ligand binds to a single site and obeys the law of mass action, you'll obtain the same dissociation rate constant in all experiments.

Is there cooperativity?

If the law of mass action applies, binding of a ligand to one binding site does not alter the affinity of another binding site. This also means that dissociation of a ligand from one site should not change the dissociation of ligand from other sites. To test this assumption, compare the dissociation rate after initiating dissociation by infinite dilution with the dissociation rate when initiated by addition of a large concentration of unlabeled drug. If the radioligand is bound to multiple noninteracting binding sites, the dissociation will be identical in both experimental protocols as shown in the left figure. Note that the Y axis is shown using a log scale. If there were a single binding site, you'd expect the dissociation data to appear linear on this graph. With two binding sites, the graph is curved even on a log axis.

The right figure shows ideal dissociation data when radioligand is bound to interacting binding sites with negative cooperativity. The data are different depending on how dissociation was initiated. If dissociation is initiated by infinite dilution, the dissociation rate will change over time. The dissociation of some radioligand will leave the remaining ligand bound more tightly. When dissociation is initiated by addition of cold drug, all the receptors are always occupied by ligand (some hot, some cold) and dissociation occurs at its maximal unchanging rate.

Kinetics of competitive binding


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