A model of slow conduction in bullfrog atrial trabeculae.

The success or failure of the propagation of electrical activity in cardiac tissue is dependent on both cellular membrane characteristics and intercellular coupling properties. This paper considers a linear arrangement of individual bullfrog atrial cells that are resistively coupled end to end to form a cylindrical strand. The strand, in turn, is encased by an endothelial sheath that provides a restricted extracellular space and an ion diffusion barrier to the outer bathing medium. This encased strand serves as an idealized model of an atrial trabeculum. Excitable membrane characteristics of the atrial cell are specified in terms of a Hodgkin-Huxley type of model that is quantitatively based on single-microelectrode voltage clamp data from bullfrog atrial myocytes. This membrane model can simulate the behavior of normal cells as well as of ischemic cells that exhibit depressed electrophysiological behavior (e.g., decreased resting potential, upstroke velocity, peak height, and action potential duration). Depressed activity can be easily simulated with variation of a single model parameter, the gain of the Na+/K+ pump current (INaK). Intercellular coupling properties are specified in terms of a lumped resistive T-type network between adjacent cells. The atrial strand model provides a means for studying the theoretical aspects of slow conduction in a "hybrid" strand that consists of a central region of cells having abnormal membrane or coupling properties, flanked on either side by normal atrial cells. Both uniform and discontinuous conduction are simulated by means of appropriate changes in the coupling resistance between cells. In addition, by varying either the degree of depressed electrical activity or the intercalated disc resistance in the central zone of the strand, slow conduction or complete conduction block in that region is demonstrated. Since the cellular model used in this study is based on experimental data and closely mimics both the atrial action potential and the underlying membrane currents, it has the potential to (1) accurately represent the current and voltage wave-forms occurring in the region of intercalated discs and (2) provide detailed information regarding the mechanisms in intercellular current spread in the region of slow conduction.     

A model of the muscarinic receptor-induced changes in K(+)-current and action potentials in the bullfrog atrial cell.

A model is formulated for characterizing the behavior of the acetylcholine (ACh)-sensitive K+ membrane channel (muscarinic channel) in bullfrog atrial myocytes. Parameters of the muscarinic current model are chosen in fit available data from the literature on bullfrog atrial myocytes (3, 4, 45). This model is subsequently incorporated into a large mathematical model of the bullfrog myocyte that is based on quantitative whole-cell voltage clamp data (40). Simulations are conducted on the active atrial cell model in bathing media containing ACh at different concentrations to explore the effect of this muscarinic channel on the electrical behavior of the myocyte. The model predicts a progressive shortening of the action potential with increasing [ACh], as well as an indirect influence of the muscarinic K+ current on the other membrane currents of the atrial cell. Interpretation of the simulation results provides suggestions for the probable mechanisms underlying the shortening of the action potential due to activity of the muscarinic channel. Specifically, the model predicts that with an increase in ACh concentration: (a) the outward muscarinic current, IK,ACh(t), increases in magnitude but shortens in duration; (b) the calcium current, ICa(t), may increase in magnitude, but when it does so it decreases in duration compared with the control conditions; (c) the intracellular Ca2+ concentration [Ca2+]i waveform during the action potential decreases in both magnitude and duration. Because the contractile activity of the cell is controlled by the [Ca2+]i waveform, the model predicts a decrease in contractile strength with an increase in ACh concentration in the bathing medium; i.e., a negative inotropic effect.     

A single compartment model of pacemaking in dissasociated Substantia nigra neurons

Spontaneous oscillations in the mid-brain dopaminergic neurons are an important feature of motor control. The degeneration of these neurons is involved in movement disorders, particularly Parkinson’s Disease. Modelling of this activity is an important part of developing an understanding of the pathogenic process. We develop a mathematical paradigm to describe this activity with a single compartment approach and a CellML version is made publicly available. The model explicitly describes the dynamics of the transmembrane potential with changes in the levels of important cations and is consistent with two major observations in the literature regarding its behaviour in the presence of channel blockers. Stability of the model behaviour is determined from the properties of its Monodromy matrix. We also discuss from the perspective of energy, a pharmacological intervention suggested in the treatment of Parkinson’s Disease.     

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.     

Tuning in the bullfrog ear.

When electrical resonances were observed in acoustic sensory cells of lower vertebrates, the hearing research community was presented with the exciting possibility that tuning in the ears of those animals might be explained directly in terms of familiar molecular devices. It is reported here that in the frog sacculus, where electrical resonances have been observed in isolated hair cells, the effects of those resonances are completely obscured in the tuning properties of the sacculus in the intact ear. This observation has important implications not only for students of the ear, but for reductionist biologists in general. All of the dynamic properties of a system of connected, bidirectional processes are consequences of all of those processes at once; in such a system, the properties of an experimentally isolated subsystem may be totally obscured in the operation of the system as a whole.     

Negative chronotropic effects of thyroxine on the isolated bullfrog heart

An acute application of L-thyroxine (T4) to everted sinus-atrium preparations of bullfrog showed negative chronotropic effects consisting of two processes: an initial peak at 2-5 min and a delayed plateau at 40-60 min. The initial effect was blocked by Cd2+ and tetraethyl-ammonium (TEA). The delayed effect was suppressed by Cd2+ and NaCN.     

A model for energy flow in the inner ear of the bullfrog (Rana catesbeiana)

We present a quantitative mathematical model that represents the main features of the bullfrog inner ear. Calculated responses based on this model predict the observed frequency separation between the amphibian papilla and basilar papilla responses. The origin of this separation can be traced to the effect of the contact membranes on the impedance of the respective paths. Additionally, we calculated the input impedance of the periotic canal and showed that at low frequencies it acts as a bypass for most of the energy entering the ear, shunting it away from the amphibian-basilar papilla complex. As this shunting decreases with increasing frequency, we propose that the periotic canal functions as a protection mechanism to prevent overload of the amphibian papilla and basilar papilla during ventilation and for quasi-static pressure equalization. Our model explains the main features of the empirical data obtained from direct measurement of the amphibian papilla and basilar papilla contact membranes reported in an accompanying paper (this issue). Accepted: 9 March 2000     

Leukotriene C4 action and metabolism in the isolated perfused bullfrog heart

The effects of leukotrienes (LTs) have been widely studied in the isolated perfused mammalian heart; however, little is known about the effect or metabolism of LTs in the isolated bullfrog heart. Isolated perfused bullfrog hearts were administered randomized doses of LTC4, LTD4, or LTE4. The cardiac parameters of heart rate, developed tension, and its first derivative (dT/dt) were recorded. LTC4 was the most potent of the leukotrienes tested in eliciting positive inotropic effects. LTD4 and LTE4 were equally effective but about one order of magnitude less potent than LTC4. None of the LTs showed any chronotropic effects in this preparation. A series of [3H]LTC4 metabolism experiments were carried out using whole perfused hearts and minced bullfrog heart tissue. Isolated perfused bullfrog hearts administered [3H]LTC4 converted significant amounts to [3H]LTD4, and to a lesser degree, [3H]LTE4, during the 6-min course of collection. Both minced atrial and ventricular tissue converted [3H]LTC4 to radioactive metabolites that co-migrated with authentic LTD4 and LTE4 standards. In both tissues, the major product was [3H]LTD4, with smaller amounts of [3H]LTE4 produced. The atrium converted significantly more [3H]LTC4 to its metabolites than did the ventricle. The metabolism of [3H]LTC4 to [3H]LTD4 by both tissues was virtually abolished in the presence of serine borate. Cysteine had no effect on [3H]LTE4 production. The data in this study demonstrate that leukotrienes have the opposite inotropic effect on the heart when compared with mammals. Also in contrast to mammals, frogs metabolize LTC4 to a less potent compound and may use the LTC4 to LTD4 conversion as a mechanism of LTC4 inactivation.     

Developmental regulation of interstitial cell density in bullfrog skeletal muscle

Denervation of skeletal muscle results in striking connective tissue remodelling in junctional areas of muscle. Since extracellular matrix molecules mediate axonal growth and synaptic differentiation, it is likely that the interstitial cells and matrix molecules that accumulate near synaptic sites after denervation influence the regrowth and regeneration of synaptic connections. The experiments presented here addressed the question of whether the junctional connective tissue in developing bullfrog skeletal muscle was also specialized in its cellular and molecular composition. Denervation responses of muscle, such as extrajunctional sensitivity to acetylcholine, often reproduce the characteristics of developing muscle during synaptogenesis. In developing muscle, the distribution of interstitial cells was nonuniform during the period of muscle fibre birth and synaptogenesis. Interstitial cells were concentrated near synaptic sites as in denervated adult muscle. Unlike denervated adult muscle, there were no junctional accumulations of fibronectin or tenascin, matrix molecules produced by interstitial cells, in developing muscles. These results demonstrate that the junctional connective tissue in developing muscle is identified by a high density of interstitial cells that may play a role in the identification and formation of synaptic sites. Further, the junctional matrix environment of developing muscle is distinct from the matrix remodelling that occurs in response to denervation, suggesting that the matrix production by interstitial cells during development is regulated differently from that after denervation of the neuromuscular junction.     

Intracellular Ca2+ oscillations, a potential pacemaking mechanism in early embryonic heart cells

Early (E9.5-E11.5) embryonic heart cells beat spontaneously, even though the adult pacemaking mechanisms are not yet fully established. Here we show that in isolated murine early embryonic cardiomyocytes periodic oscillations of cytosolic Ca(2+) occur and that these induce contractions. The Ca(2+) oscillations originate from the sarcoplasmic reticulum and are dependent on the IP(3) and the ryanodine receptor. The Ca(2+) oscillations activate the Na(+)-Ca(2+) exchanger, giving rise to subthreshold depolarizations of the membrane potential and/or action potentials. Although early embryonic heart cells are voltage-independent Ca(2+) oscillators, the generation of action potentials provides synchronization of the electrical and mechanical signals. Thus, Ca(2+) oscillations pace early embryonic heart cells and the ensuing activation of the Na(+)-Ca(2+) exchanger evokes small membrane depolarizations or action potentials.     

Force-interval relationship in heart muscle of mammals. A calcium compartment model.

A mathematical model was derived that describes peak force of contraction as a function of stimulus interval and stimulus number in terms of Ca2+ transport between three hypothetical Ca2+ compartments. It includes the conventional uptake and release compartments and recirculation of a fraction r of the activator Ca2+. Peak force is assumed to be proportional to the amount of activator Ca2+ released from the release compartment into the sarcoplasm. A new extension is a slow exchange of Ca2+ with the extracellular space via an exchange compartment. Six independent parameters were necessary to reproduce the different effects of postextrasystolic potentiation, frequency potentiation, and post-rest potentiation in isolated heart muscle from the rat. The normalized steady state peak force (F/Fmax) under standard conditions varied by a factor of ten between preparations from rat heart. Analysis with the model indicated that most of this variation was caused by two variables: the Ca2+ influx per excitation and the recirculating fraction of activator Ca2+. The influence of the Ca2+ antagonist nifedipine of the force-interval relationship was reproduced by the model. It is concluded that the model may serve to analyze the variability of contractile force and the mode of actions of drugs in heart muscle.     

Muscle cell differentiation in the ascidian heart.

The simple tubular heart of tunicates consists of a single layer of striated muscle cells which display distinct electrical properties at the luminal and extraluminal surfaces. We have investigated heart morphogenesis and cytodifferentiation in the ascidian, Botryllus schlosseri. Myocardium is formed by invagination from the wall of the heart primordium. Cell polarity is clearly apparent in the undifferentiated cells of the heart primordium and is maintained throughout the whole course of cardiac muscle differentiation. Myocardium cells are initially cubic in appearance, then undergo a progressive flattening with the formation of characteristic protrusions at the luminal surface. The first sign of muscle cell differentiation is the formation of close associations between sarcoplasmic reticulum cisterns and the plasma membrane at the luminal and junctional surface. Myofibrillogenesis also occurs near the luminal surface, whereas the cell portion facing the pericardial cavity maintains an undifferentiated structure. The findings support the hypothesis that membrane changes precede and influence myofibril formation in developing muscle cells.     

The effect of variations in sodium conductances on pacemaking in a dopaminergic retinal neuron model

Dopaminergic neurons in the retina show spontaneous tetrodotoxin-sensitive pacemaking, which has been explained by a reduced Hodgkin-Huxley-type computer model. The present study used this model to investigate the effect of variations in transient and persistent sodium conductance values on pacemaking, under variable leakage conductance levels. This study indicated that transient sodium conductance plays an indispensable role in pacemaking, which occurs under conditions in which only a persistent sodium conductance is considerably reduced, thus contributing to a detailed understanding of the relationship between sodium conductance and pacemaking.