A mathematical model of the effects of acetylcholine pulses on sinoatrial pacemaker activity.

Michaels, D C; Matyas, E P; Jalife, José

doi:10.1161/01.res.55.1.89

Cited by 56 publications

(24 citation statements)

References 39 publications

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“…13 We investigated how the phase-dependent response of the sinus node to ACh affects the shape of PRC. 7 Once during each cardiac cycle, we abruptly increased [ACh] from 0 nM to a nonzero level of [ACh]. We maintained [ACh] at that level for 40 msec, and then we instantaneously degraded all of the ACh.…”

Section: Phase Response Curvesmentioning

confidence: 99%

“…ACh that is applied to pacemaker cells at ASts that correspond to the negative slope region of PRC has little effect on SCL because the ACh is applied during fast depolarization, 7 when |I K ^1 < < \\ aim \ (Figure 3). By the time diastolic depolarization starts, much of the ACh has been hydrolyzed.…”

Section: Phase Response Carvesmentioning

confidence: 99%

“…By the time diastolic depolarization starts, much of the ACh has been hydrolyzed. ACh that is applied to pacemaker cells at ASts that correspond to the positive slope regions of PRC can prolong SCL because the ACh is applied during diastolic depolarization, 7 when |I KACh I^I^I ( Figure 3). The rates of activation and inactivation of AChactivated K + channels do not depend significantly on V, over the range of V included in diastolic depolarization.…”

Section: Phase Response Carvesmentioning

confidence: 99%

“…The simulated (Equations 1, 2, and 4) latency between vagal stimulation and hyperpolarization of pacemaker cells equals 30 msec. 7 The latency between stimulation and hyperpolarization equals 80 msec in the rabbit 14 ; we do not know the value in the dog. We incorporated a delay of 50 msec in our model ( Figure 1) to adjust for the difference between the measured and simulated latencies.…”

mentioning

confidence: 98%

“…The 50-msec discrepancy may represent, at least partially, the time required for ACh to diffuse in neuroeffector junctions from vagal nerve endings to pacemaker cells. 7 Measurements of the sinoatrial conduction time in normal dogs vary widely: 60-110 msec, 15 30-175 msec, 16 80 msec, 17 and 30 msec. 18 The estimates of the sinoatrial conduction time may differ so much because the accuracy of a measurement depends on the ability to locate the portion of the sinus node from which electrical activity originates.…”

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confidence: 99%

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Mathematical model of the changes in heart rate elicited by vagal stimulation.

Dexter

Levy

Rudy

1989

Circulation Research

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We developed a mathematical model of the underlying cellular mechanisms responsible for the changes in sinus cycle length (SCL) elicited by vagal stimulation in intact animals. The model incorporated a stimulation-mediated depletion of the releasable pool of acetylcholine (ACh) in the nerve endings, the in vitro reaction kinetics of acetylcholinesterase, and the electrical activity of a pacemaker cell with six membrane ionic currents. SCL increased linearly with the frequency of simulated vagal stimulation, as it does in animal experiments, because the concentration of ACh in the neuroeffector junction ([ACh]) saturated as the frequency of stimulation was increased and because SCL increased geometrically in response to increases in [ACh]. The dependence of SCL on the timing of vagal stimulation in the cardiac cycle resulted, in part, from the dependence of [ACh] on SCL. Simulated vagal stimulation entrained the sinus node because the rate of activation and inactivation of ACh-activated K + channels depended only weakly on membrane potential during diastolic depolarization. SCL increased geometrically with [ACh], because 1) during diastolic depolarization, the amplitude of the ACh-activated K + current was approximately equal to the amplitude of the sum of the other ionic currents, 2) [ACh] was low enough to saturate neither acetylcholinesterase nor the cellular system that activates the ACh-activated K + channels, 3) the pacemaker cell membrane behaved electrotonically like a capacitor, and 4) the sum of all the ionic currents increased linearly with the amplitude of the ACh-activated K + current. (Circulation Research 1989;65:133O-1339) O ur goal is to explain the cellular basis for the changes in sinus cycle length (SCL) elicited by vagal stimulation by using mathematical models of the underlying cellular physiology. In recent papers, we have presented mathematical models of the release of acetylcholine (ACh) from vagal nerve endings, the degradation of ACh in the neuroeffector junctions of the sinus node, and the changes in SCL elicited by ACh.1 . 2 By combining these mathematical models of the underlying cellular physiology, we create a more complete mathematical model that predicts the changes in SCL elicited by vagal stimulation in the intact animal. Our principal goal is to determine how the underlying cellular physiology, which we represented mathematically in our computer model, causes changes in SCL. Methods Mathematical ModelsACh release. Figure 1); the letter v was chosen because the releasable pool of ACh may be stored in intracellular vesicles.3 Let r equal the fastest rate of renewal of the releasable pool of ACh. Let p equal the fraction of the releasable pool of ACh, v, that is released by each vagal stimulus. Let u represent the vagal firing pattern. The change in the quantity of ACh that is available for release is represented by the equation: dv/dt=r(l-v)-pvu(t) (1) where u(t)=l if the vagus nerve is stimulated at time t, and u(t)=0 otherwise (t=0 msec at the start of the stimulation). AC...

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Section: Phase Response Curvesmentioning

confidence: 99%

Section: Phase Response Carvesmentioning

confidence: 99%

Section: Phase Response Carvesmentioning

confidence: 99%

mentioning

confidence: 98%