Mathematical model of acetylcholine kinetics in neuroeffector junctions

Abstract

Acetylcholine (ACh) kinetics in neuroeffector junctions (NEJ) of the sinus node plays a key role in vagal control of heart rate. Prior studies have shown that the concentration of ACh ([ACh]) in NEJ appears to follow first-order linear kinetics. To find out the reason why, we examine mathematically diffusion, degradation, and receptor binding of ACh in NEJ. We identify seven conditions that potentially influence ACh kinetics. Because these conditions are satisfied for NEJ in the sinus node, 1) the nonlinearity of ACh binding to muscarinic receptors has little effect on [ACh]; 2) [ACh] does not depend on the distribution of acetylcholinesterase between the interstitial space and the pacemaker cells; 3) the interval from trough to subsequent peak [ACh] at the pacemaker cells is negligible; 4) the mean [ACh] at the pacemaker cells is proportional to the frequency of vagal activity multiplied by the amount of ACh released per vagal stimulus and divided by the rate coefficient of ACh degradation; and 5) [ACh] at pacemaker cells nearly follows first-order linear kinetics but does not at other sites in the NEJ. We conclude that earlier studies showed that [ACh] follows first-order linear kinetics, because they predicted [ACh] only at pacemaker cells. ACh kinetics at other sites in the NEJ, such as at nerve endings, is different.