The propagation of the nerve impulse.

A partial differential equation for the propagated action potential is derived using symmetry, charge conservation, and Ohm's law. Charge conservation analysis explicitly includes the gating charge when applied in the laboratory frame. When applied in the system of reference in which capacitive currents are zero, it yields a relation between orthogonal components of the ionic current allowing us to express the nonlinear ionic current in terms of the voltage-dependent membrane capacitance C(V) and the axial current that satisfies Ohm's law. The ionic current is shown to behave as C(V)V[C(V)V2]' at the foot of the action potential while the gating current behaves as C(V)V[Cg(V)V]' where Cg(V) is the capacitance associated with gating. Improved knowledge of the nonlinear current makes it possible to describe the propagated action potential in an approximated way with quasilinear partial differential equations. These equations have analytical solutions that travel with constant velocity, retain their shape, and account for other properties of the action potential. Furthermore, the quasilinear approximation is shown to be equivalent to the FitzHugh-Nagumo equation without recovery making apparent its physical content.     

Theoretical studies of impulse propagation in serotonergic axons

Impulse propagation in small-diameter (1–3 m) axons with inhomogeneous geometry was simulated. The fibres were represented by a series of 3 m-long compartments. The cable equation was solved for each compartment by a finite-difference approximation (Cooley and Dodge 1966). First-order differential equations governing temporal changes in membrane potential or Hodgkin-Huxley (1952) conductance parameters were solved by numerical integration. It was assumed that varicosity and intervaricosity segments had the same specific cable constants and excitability properties, and differed only in length and diameter. A single long varicosity or a clump of 3 m-long varicosities changed the point-to-point (axial) conduction velocity within as well as to either side of the geometrically inhomogeneous regions. When 2 m-diameter, 3 m-long varicosities were distributed over the 1 m-diameter fiber length as observed in serotonergic axons, mean axial conduction velocity was between that of uniform-diameter 1 and 2 m fibers, and changed predictably with different cable parameters. Fibers with inexcitable varicosity membranes also supported impulse propagation. These simulations provided a general theoretical basis for the slow (< 1 M/s) conduction velocity attributed to small-diameter unmyelinated varicose axons.     

Gangliosides of the bovine heart impulse conducting system

The ganglioside analysis of the heart impulse conducting system was carried out, comparing it with that of ordinary myocardium. The heart impulse conducting system contained about 3-times more gangliosides than ordinary myocardium and showed a distinctly different ganglioside composition. These observations seemed to indicate that the differentiation between myoblasts and each type of cardiac muscle cell, impulse conducting system and ordinary myocardium cells, resulted in their characteristic ganglioside compositions.     

Gap junctions and impulse propagation in embryonic epithelium of Amphibia

Summary Epithelium of amphibian embryos (Cynops orientalis, Xenopus laevis) was found in preceding experiments to generate and conduct impulses during a limited stage (26–37) of development. In order to elucidate the structural basis of impulse propagation, epithelial cells of four stages were examined by the freeze-etching method: (I) before and (II) during acquisition of conductivity; (III) when propagation was fully established, and (IV) when it was no longer present. Only few gap junctions (GJ) of small size were found in groups I and IV. GJ in epithelia of group III were increased in number and size, and appeared morphologically coupled, i.e., with more loosely arranged connexons. The size of gap-junctional particles did not differ significantly between coupled and uncoupled stages. Zonulae occludentes seemed leaky in stage I, and tight in stages II–IV. Thus, the morphological characteristics of specialized junctions between non excitable cells correlated with the opening and closing of low resistance intercellular current pathways during embryonic development.Gap junctions in particular seem to form an essential link in the non-neural stimulus-response system, which may facilitate the mobility of the embryo during early phases of aquatic life before the reflex pathways have been established. Coupling and uncoupling of gap junctions may also play an important role in the regulation of cell differentiation and morphogenetic movement. The experimental model used in this study provides a useful tool for further investigations of structural correlates of gap junctional permeability under physiological conditions.     

Rhythmogenesis in the heart sinoatrial node

The most significant experimental data on the formation of the common rhythm of the heart sinoatrial node are presented for both the intact heart sinoatrial node and cardiomyocytes in cell structures. The basic mathematical models for studying the synchronization processes in the sinoatrial node, including the Noble equation, Bonhoffer-van der Pol model, and modified axiomatic models, are described. The basic results obtained with the mathematical models are presented. The most important causes affecting the formation of the common rhythm—the pacemaker potential shape in the slow diastolic depolarization phase, its porosity, the coupling force between pacemakers, and the electrical power of pacemakers—are revealed. Rhythmogenesis is studied using the modified axiomatic model. The method allows the calculation of the common rhythm of the sinoatrial node, with allowance for the mutual effect of the pacemaker cells, including the coupling force, electric power of cells, and possibility of the cells clustering. It has been shown that the common rhythm of the sinoatrial node is generally formed at the intermediate level of the rhythms of all pacemaker cells.     

Model of the sino-atrial and atrio-ventricular nodes of the conduction system of the human heart.

The coupled sino-atrial and atrio-ventricular nodes of the heart are discussed using a dedicated non-linear oscillator model. Several modes by which the oscillations cease in the system are obtained (asystole models). The oscillations of the model are compared with heart rate variability in heart block patients.     

Electron microscopy of the impulse conducting system op the sheep heart

Summary Electron micrographs of the conducting system of the sheep heart show it to be strictly cellular in nature. All protoplasmic components are restricted to areas defined by the individual plasma membranes of the cells. The individual cells are surrounded by a common interspace and groups of cells are separated from neighboring connective tissue by a common, longitudinal basement membrane. The extracytoplasmic interspace shows occasional enlargements, probably corresponding to the intracytoplasmic vacuoles visualized in the light microscope. The apposing plasma membranes, along which ephaptic thickenings may occur, and their interspace form the intercalated discs of the system.Myofibrils are few and are situated preferentially immediately beneath the plasma membrane. Chains of myofibrils, interrupted at the intercalated discs, appear to course through the whole tissue. In some myofibrils the pattern of long periods may be interrupted by a small-period pattern for several sarcomeres.The cytoplasmic matrix consists mainly of fine filaments of unknown composition. The relatively scarce mitochondria are found near the nucleus, myofibrils and cell surface. The endoplasmic reticulum is poorly developed and its arrangement is a comparatively loose one.The above results and their physiologic consequences are discussed, particularly with regard to the core conduction theory in conducting tissue.This study was aided, in part, by grant number H-3493, from the National Heart Institute of the National Institutes of Health, Department of Health, Education and Welfare, Bethesda, Maryland.