Browsing by Author "Shumaker, John Michael"

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    A mathematical model of the amphibian muscarinic channel
    (1989) Shumaker, John Michael; Clark, John W., Jr.
    A modification of the Osterrieder-Noma-Trautwein model of the ACh-sensitive K$\sp+$ I$\sb{K,ACh}$ current in the rabbit SA node is used to study the behavior of the ACh-sensitive K$\sp+$ channels in bullfrog atrial and sinus venosus myocytes. The parameters of the modified description of the muscarinic current are chosen to fit available data from the literature on bullfrog atrial myocytes. This model is incorporated into larger mathematical models of bullfrog myocytes that are based on quantitative whole-cell voltage clamp data and simulations are run to discern the effects of this muscarinic channel on the electrical behavior of the cell membrane. Simulations of the electrical behavior of the sinus venosus myocyte predict that the effects of ACh on the pacemaker action potential are dependent on both the phase of ACh delivery and rate of removal of the ACh. Model-generated phase response curves (PRC's), inhibition curves (IC's) and entrainment curves are produced. (Abstract shortened with permission of author.)
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    Conduction in a bullfrog atrial trabeculum: Active and passive properties, and modifications produced by acetylcholine
    (1992) Shumaker, John Michael; Clark, John W., Jr.
    A model of $\beta$-adrenergic and muscarinic cholinergic stimulation of the bullfrog atrial myocyte has been developed that mimics the dose-dependent effects of isoprenaline (ISO) on the action potential duration (APD); i.e., low doses of ISO lengthen the APD, while high doses shorten the ADP. This reduction in APD is modeled as the result of (1) calcium-dependent inactivation of $I\sb{Ca}$ resulting from the enhancement of $I\sb{Ca}$ by ISO and (2) an enhancement of $I\sb{K}$ due to both an ISO-induced increase in the rate of activation of $I\sb{K}$ and an increase in peak action potential height. The effect of acetylcholine (ACh) is to reduce the ISO-induced increase in $I\sb{Ca}$ and $I\sb{K}$ through a reduction in relative (cAMP) as well as to stimulate the ACh-sensitive $K\sp{+}$ current $I\sb{K,ACh}.$ At low (ISO) levels or high (ACh) levels, the muscarinic cholinergic effect dominates over the $\beta$-adrenergic effect. However, for a large (ISO) and a small (ACh), this pattern of changes in transmembrane currents is different; in this case the model predicts that ACh can actually increase APD. A distributed parameter model of an idealized bullfrog atrial trabeculum is developed. Individual cardiac cells are resistively coupled end to end via intercalated discs to form an idealized cylindrical cardiac strand encased in a resistive-capacitative trabecular sheath which, in turn, is located in a finite cylindrical volume conductor. A second-order implicit finite numerical integration method is used to calculate the time-varying potentials within the intracellular $(V\sp{i}),$ interstitial $(V\sp{e}),$ and the outer volume conductor $(V\sp{o})$ media of the concentric cylindrical structure. 'Reduced' cell membrane models which lack the complete complement of transmembrane currents are compared with regard to their accuracy in representing the foot, upstroke, and plateau regions of the propagated action potential in the complete model. A reduced cell membrane model should contain the sodium current $I\sb{Na},$ the calcium current $I\sb{Ca}$ and the background rectifying $K\sp{+}$ current $I\sb{K1}.$ A cell membrane model which contains a linear background $K\sp{+}$ current $I\sb{L}$ instead of $I\sb{K1}$ produces a poor approximation to the upstroke, plateau and conduction velocity of an action potential. The trabecular sheath reduces the extracellular resistance seen by the cell by shunting current away from highly resistive interstitial medium into the volume conductor medium which is of low resistance, and thereby increases conduction velocity. Finally, the effects of the cholinergic neurotransmitter, acetylcholine (ACh), on both the passive and active properties of the trabeculum are investigated. The addition of ACh to the extracellular medium reduces the space constant and input resistance of the trabeculum, as well as the conduction velocity of electrical activity propagating through it.