Kinetic Modelling of Ligand Trapping Inside Acidic Vesicles Containing Alpha-4 Beta-2 Nicotinic Receptors As an Explanation for Long-Term Cessation Effect of Varenicline (Chantix)

Govind's et. al. 2017 paper proposes that the smoking cessation effect of varenicline (or epibatidine) is caused by these molecules being trapped inside acidic vesicles containing α4β2 nicotinic receptors. These ligands are weak bases with high affinity to these receptors. The trapping would lead to their slower release and longer desensitization of the receptors, thereby reducing nicotine upregulation. Meanwhile, nicotine, with lower pKa and lower binding affinity is not trapped within the vesicles. It is unclear whether the acidity of the vesicles and the presence of receptors is sufficient to explain the biphasic trapping behavior observed empirically. To better understand this phenomenon, we model flux of ligands between cellular compartments using Flick's first law of diffusion and the Nernst-Plank Equation. The ratio of neutral to charged ligands within each compartment is calculated via Henderson-Hasselbach equation. Main parameters in the model include the number of vesicles, receptors per vesicle, ratio of vesicles to non-vesicle receptors, pH, membrane permeability, pKa and dissociation constants of the ligand. The system is solved numerically using MATLAB and optimized against empirical data. The results show the experimentally observed biphasic release of epibatidine, affirming the hypothesis of trapping inside the vesicles. Our model also shows that the main trapping effect is due to the presence of receptors inside vesicles, not those located on the cell surface and the high affinity of these ligands to the receptors. The exact acidity level inside the vesicles is not as important. Our model is also able to predict the much faster nicotine outward flow compared with epibatidine. This model can be used to predict the kinetics of other weak basic ligands like those used in positron emission tomography.