Mennerick-- Ligand Binding Handout - 1 -_____________________________________________________________________________________PharmacologyThis institution (WUMS), like many medical schools, no longer has a Department of Pharmacology. Nevertheless all physicians prescribe drugs, and research scientists will all inevitably use pharmacology as a tool at some point in their research. Thus, despite the poor reputation that pharmacology has in today’s post-genomic era (“all drugs are dirty”), pharmacology continues to be ubiquitous, and I think it’s important that students are exposed to basic pharmacology principles. Whether we’re talking about ligand-gated ion channels or about GPCRs, some basic principles apply. First, the ligand’s interaction with the receptor can be modeled as a reversible, bi-molecular reaction. This means that we can write chemical equations to represent the drug-receptor interaction (subsequent pages).Second, many terms are applicable no matter what the receptor type. Here is a partial glossary.Ligand: any molecule that binds to a receptor. Examples: Nicotine, curare, and mecamylamine are ligands for the muscle nicotinic receptor.Agonist: a ligand that activates the receptor (opens a ligand-gated channel or stimulates a G protein). Example: Nicotine is an agonist at the nicotinic receptor.Antagonist: a ligand that has no biological effect on the receptor when it binds but reverses an agonist’s effect. Example: Curare and mecamylamine are antagonists at the endplate nicotinic receptor.Competitive antagonist: An antagonist that competes with an agonist for the same (or overlapping) binding site. The effect of a competitive antagonist at steady state can therefore be overcome with higher free [agonist]. Example: Curare is a competitive antagonist at the endplate nicotinic receptor. Non-competitive antagonist: An antagonist that binds to a site other than the agonist binding site.Mecamylamine is a non-competitive antagonist at the nicotinic endplate receptor. Picrotoxin is a non-competitive antagonist at the GABAA receptor. Uncompetitive antagonist: Like a non-competitive antagonist, binds to a separate site from the agonist, but requires channel opening for binding. Example: Jim Huettner showed in 1988 that MK-801 is an interesting example of an uncompetitive antagonist of the NMDA receptor (PNAS 85:1307). Ketamine (ananesthetic) and memantine (used in treatment of Alzheimer’s disease) are additional examples of uncompetitive NMDA receptor antagonists. [For simplicity, I sometimes dispense with the term “uncompetitive” and use “non-competitive”. This has gotten me into trouble with some peer reviewers]Partial agonist. An agonist that binds to the receptor but does not activate the “full” response. For ligand-gated ion channels, this would be an agonist that binds but produces a lower channel opening/closing rate ratio than a full agonist. Inverse agonist. A ligand that binds the receptor at the agonist site, but unlike a competitive antagonist, promotes a conformational change in the receptor that promotes channel closure. For example: Joe Henry Steinbach’s lab showed in 1997 that bicuculline, long thought to be a competitive antagonist at the GABAA receptor, is actually an inverse agonist (J Neurosci 17:625).Allosteric. A ligand that works from a site other than a reference site of action, usually the site of agonist binding. Example: benzodiazepines positively allosterically regulate GABAA receptor function. Potency: A dangerous term because it means different things to different people. I use potency as an empirical term equivalent to EC50 (agonist) or IC50 (antagonist) (see lecture). Others use it with a connotation closer to Kd. Efficacy: How “full” is the agonist action? A partial agonist is a low-efficacy agonist (but it can still have high potency if concentration needed to generate the response is low). An antagonist has zero efficacy.Mennerick-- Ligand Binding Handout - 2 -_____________________________________________________________________________________Start with the simple scheme of drug binding to a single site:k1 = rate constant for association (units: M-1 s-1)k2 = rate constant for dissociation (units: s-1)A = drug Y = proportion of receptors occupied by drug (=[AR]/([AR]+[R])R = receptorAR = receptors bound by agonistRtotal = total receptors (=[AR] + [R])Note that AR  A + R is a first order reaction, like radioactive decay. The rate of dissociation will be dependent on the concentration of remaining [AR]. It is an exponential decay process with a time constant the reciprocal of k2.The reaction A + R  AR in the other direction is called a pseudo first-order reaction. This is when agonist [A] is present in great excess compared to [R]. [A] will not change over the course of the experiment, and [A]kdtd[AR]1[R][A]kdtd[AR]1 (1)[AR]kdtd[AR]2 (2)At equilibrium dtARddtARd ][][ Therefore, ][][][21ARkRAk Rearranging to define the ratio of the two rate constants:12][]][[kkARRA (3)k2/k1 is the dissociation constant (KD), a measure of the receptor's affinity for the agonist. Units are concentration2/concentration = concentration.We will uncover some more of the significance by some algebraic rearrangements.Equations 1 and 2 can be rewritten totalRY[A]kdtd[AR]][11A + RARk1k2Mennerick-- Ligand Binding Handout - 3 -_____________________________________________________________________________________totalRYkdtd[AR]][2Again, at equilibrium totaltotalRYkRY[A]k ][][121 YkY[A]k211  YkYAk[A]k211][ Solve for Y: ][121AkkY[ A]k ][][121AkkAkY][][12AkkAY][][AkAYD (4)so ][][][][AKARARYDtotal (5)At this point you’ve just derived the Michaelis-Menten equation, the Langmuir isotherm, and the equation of A.J. Clark applying the law of mass action to receptors (all formally equivalent equations).Mennerick-- Ligand Binding Handout - 4 -_____________________________________________________________________________________Getting back to the significance of the dissociation constant KD, consider the condition where half