Question

(7) The Histamine 3 (H₃) Receptor is a G-protein linked receptor that, in its active conformation, interacts with a G-protein leading to (among other effects) closing Ca⁺² channels that otherwise let Ca⁺² into a cell: i.e. H₃ receptor activation leads to a decrease in (lower) Ca⁺² influx. The H₃ receptor is important in regulation of how much neurotransmitter neurons release into synapses and dysregulation of H₃ receptor activity is implicated in a number of neurological disorders including narcolepsy, ADHD, Tourette’s syndrome and schizophrenia. For each condition described below, indicate whether a cell (in a cell culture) that expresses the H₃ receptor will have (i) higher, (ii) lower or (iii) equal Ca⁺² influx as a comparable cell not exposed to any compound binding the H₃ receptor. Assume that all the ligands bind in the same location on the protein surface, unless otherwise indicated (1 point each, binding constants from Parsons and Ganellin, 2006 or Wikipedia, accessed 11 April 2018)

(A) Addition (to a concentration of 10 ?M) of histamine which binds the active state of the H₃ receptor, with a K_d of 5 ?M, but not to the inactive state

(B) Addition (to a concentration of 0.5 nM) of Clobenpropit, which binds both the active and inactive states of the H₃ receptor with a K_d of 0.6 nM

(C) Addition of histamine (to a concentration of 10 nM) and Clobenpropit (to a concentration of 1 nM).

(D) Addition of histamine (to a concentration of 10 ?M) and Clobenpropit (to a concentration of 0.5 nM)

(E) Addition of Pitolisant (to a concentration of 1 nM) which binds the inactive form of the H₃ receptor with a K_d of 0.2 nM

Answer 1

Answer.

The Histamine H3 receptor-ligand binding can be represented as,

R + L => RL

The forward reaction, or binding is measured by a constant called binding constant, Kb

Kb = [R] [L] / [RL]

Since the interaction is reversible, the dissociation of ligand from receptor-ligand complex can be represented as,

RL => R + L

This is also measured by a constant called dissociation constant, Kd

Kd = [RL] / [R] [L]

At equilibrium, the rate of ligand binding to receptor and dissociation of receptor-ligand complex is equal,

Rate of ligand binding or rate of formation of receptor ligand complex = Rate of dissociation of receptor-ligand complex;

Kb [R] [L] = Kd [RL],

Also,

     Kb = 1 / Kd

From this expression the binding constants can be calculated for each of the four situations.

Q (A) Addition (to a concentration of 10 ?M) of histamine which binds the active state of the H₃ receptor, with a K_d of 5 ?M, but not to the inactive state.

By substituing values of various terms in binding equation,

We find that, the ratio [RL] / [L] is of the order of 40:1. Hence the proportion of receptor-ligand complex is large as compared to free ligand. Here, influx of calcium ions will not occur.

Q.(B) Addition (to a concentration of 0.5 nM) of Clobenpropit, which binds both the active and inactive states of the H₃ receptor with a K_d of 0.6 nM.

Like the previous case, here the ratio between [RL] / [R] is 3:1. That indicated a lower receptor-ligand complex and hence influx of calcium ions will take place.

Q.(C) Addition of histamine (to a concentration of 10 nM) and Clobenpropit (to a concentration of 1 nM).

The cumulative effect will result in no influx of calcium ions. While histamine will disallow calcium influx, Clobenpropit will have an equilibrium between receptor and ligand allowing partial influx ([RL] / [L] =1:1.16). Since the concentration of histamine is greater, no influx is going to occur.

Q.(D) Addition of histamine (to a concentration of 10 ?M) and Clobenpropit (to a concentration of 0.5 nM).

In this case the ratio of receptor-ligand complex will be 3:1, disallowing influx due to clobenpropit as well as by histamine.