Changes in anisotropic conduction caused by remodeling cell size and the cellular distribution of gap junctions and Na(+) channels.

Because gene therapy presents a new frontier in the treatment of arrhythmias, it has become important to know how manipulation of the cellular distribution of proteins changes electrical events within individual cells, and whether these cellular changes affect conduction at the larger macroscopic size scale. However, experimental limitations in cardiac bundles prevent measurement of conduction delays across specific gap junctions, as well as the intracellular distribution of the maximum rate of rise of the action potential (V(max)). In view of these limitations, we used immunohistochemical morphological results as a basis to develop two-dimensional cellular models of neonatal and mature canine ventricular muscle in order to obtain insight into the electrophysiological effects of changes in the cellular distribution of proteins; eg, the major protein of cardiac gap junctions, connexin43. Morphological results showed that when the cells enlarged after birth, the gap junctions shifted from the sides to the ends of ventricular myocytes. At birth, V(max) was not different during longitudinal and transverse propagation. However, growth hypertrophy produced a selective increase in mean transverse V(max) with no significant change in longitudinal V(max). Two-dimensional cellular computational models of neonatal and mature ventricular muscle showed that the observed changes in the cellular distribution of the gap junctions and change in cell size accounted for the experimental results. The results unexpectedly showed that cellular scaling (cell size) is as important (or more so) as changes in gap junction distribution in determining the properties of transverse propagation. The results suggest that in pathological states that are arrhythmogenic, maintenance of cell size during remodeling the distribution of gap junctions is important in sustaining a maximum rate of rise of the action potential.

Electrophysiological effects of remodeling cardiac gap junctions and cell size: experimental and model studies of normal cardiac growth.

The increased incidence of arrhythmias in structural heart disease is accompanied by remodeling of the cellular distribution of gap junctions to a diffuse pattern like that of neonatal cardiomyocytes. Accordingly, it has become important to know how remodeling of gap junctions due to normal growth hypertrophy alters anisotropic propagation at a cellular level (V(max)) in relation to conduction velocities measured at a macroscopic level. To this end, morphological studies of gap junctions (connexin43) and in vitro electrical measurements were performed in neonatal and adult canine ventricular muscle. When cells enlarged, gap junctions shifted from the sides to the ends of ventricular myocytes. Electrically, normal growth produced different patterns of change at a macroscopic and microscopic level. Although the longitudinal and transverse conduction velocities were greater in adult than neonatal muscle, the anisotropic velocity ratios were the same. In the neonate, mean V(max) was not different during longitudinal (LP) and transverse (TP) propagation. However, growth hypertrophy produced a selective increase in mean TP V(max) (P<0.001), with no significant change in mean LP V(max). Two-dimensional neonatal and adult cellular computational models show that the observed increases in cell size and changes in the distribution of gap junctions are sufficient to account for the experimental results. Unexpectedly, the results show that cellular scaling (cell size) is as important (or more so) as changes in gap junction distribution in determining TP properties. As the cells enlarged, both mean TP V(max) and lateral cell-to-cell delay increased. V(max) increased because increases in cell-to-cell delay reduced the electric current flowing downstream up to the time of V(max), thus enhancing V(max). The results suggest that in pathological substrates that are arrhythmogenic, maintaining cell size during remodeling of gap junctions is important in sustaining a maximum rate of depolarization.

Extracellular discontinuities in cardiac muscle: evidence for capillary effects on the action potential foot.

It has become of fundamental importance to understand variations in the shape of the upstroke of the action potential in order to identify structural loading effects. One component of this goal is a detailed experimental analysis of the time course of the foot of the cardiac action potential (Vm foot) during propagation in different directions in anisotropic cardiac muscle. To this end, we performed phase-plane analysis of transmembrane action potentials during anisotropic propagation in adult working myocardium. The results showed that during longitudinal propagation there was initial slowing of Vm foot that resulted in deviations from a simple exponential; corollary changes occurred at numerous sites during transverse propagation. We hypothesized that the effect on Vm foot observed in the experimental data was created by the microscopic structure, especially the capillaries. This hypothesis predicts that the phase-plane trajectory of Vm foot will deviate from linearity in the presence of a high density of capillaries, and that a linear trajectory will occur in the absence of capillaries. Comparison of the results of Fast and Kléber (Circ Res. 1993;73:914-925) in a monolayer of neonatal cardiac myocytes, which is devoid of capillaries, and our results in newborn ventricular muscle, which is rich in capillaries, showed drastic differences in Vm foot as predicted. Because this comparison provided experimental support for the capillary hypothesis, we explored the underlying biophysical mechanisms due to interstitial electrical field effects, using a "2-domain" model of myocytes and capillaries separated by interstitial space. The model results show that a propagating interstitial electrical field induces an inward capacitive current in the inactive capillaries that causes a feedback effect on the active membrane (source) that slows the initial rise of its action potential. The results show unexpected mechanisms related to extracellular structural loading that may play a role in selected conduction disturbances, such as in a reperfused ischemic region surrounded by normal myocardium.

The stochastic nature of cardiac propagation at a microscopic level. Electrical description of myocardial architecture and its application to conduction.

The object of this study is to present evidence that the myocardial architecture creates inhomogeneities of electrical load at the cellular level that cause cardiac propagation to be stochastic in nature; ie, the excitatory events during propagation are constantly changing and disorderly in the sense of varying intracellular events and delays between cells. At a macroscopic level, however, these stochastic events become averaged and appear consistent with a continuous medium. We examined this concept in a two-dimensional (2D) model of myocardial architecture by exploring whether experimentally observed Vmax variability reflected different patterns of intracellular excitation events and junctional delays. The patterns of Vmax variability at randomly chosen intracellular sites were similar experimentally and in the 2D model. The 2D cellular model produced marked variability in gap junction delays; however, on the average, different gap junctions were used for cell-to-cell charge flow during conduction in different directions. During longitudinal propagation (LP), the velocity increased from the proximal to the distal end of each myocyte, and Vmax was lowest proximally, increased to a maximum at the distal fourth of the cell, and decreased distally. Transverse propagation (TP) produced rapid intracellular conduction with variable intracellular excitation sequences. TP Vmax was greater than LP Vmax in most subcellular regions, but near the ends of some myocytes, a reversed "TP > LP Vmax" relation occurred. Total charge carried by the sodium current varied inversely with Vmax, demonstrating feedback effects of cellular loading on the subcellular sodium current and the kinetics of the sodium channels. The results suggest that the stochastic nature of normal propagation at a microscopic level provides a considerable protective effect against arrhythmias by reestablishing the general trend of wave-front movement after small variations in excitation events occur.

Cellular Vmax reflects both membrane properties and the load presented by adjoining cells.

This study was designed to test the hypothesis that the electrical load seen at a microelectrode impalement site is sensitive to the direction of propagation of the approaching wavefront as a reflection of an altered spatial relationship between the impalement site and the surrounding microscopic electrical boundaries located up- and downstream. These boundaries correspond to the different sizes and shapes of the impaled and surrounding cells as well as to the distribution of the associated electrical connections between the cells. The effects of changes in these geometric relationships on maximum rate of rise of transmembrane potential (Vmax) were investigated in canine ventricular muscle by measuring Vmax in different cells while the direction of propagation was changed from along the longitudinal axis to the transverse axis of the fibers or the direction of conduction was reversed along either of these axes. Comparison of the Vmax values for longitudinal propagation (LP) and transverse propagation (TP), each in one direction, showed that TP Vmax was significantly greater than LP Vmax (P < 0.001). However, the values of Vmax were different from cell to cell during LP (93-139 V/s) and TP (110-181 V/s). The absolute values of LP Vmax and TP Vmax at the same site varied independently of each other, e.g., some of the lowest LP Vmax values occurred at the same site as the highest TP Vmax values. Furthermore, at the same site, Vmax changed considerably when propagation was maintained along the longitudinal axis but the direction of conduction was reversed. Similar prominent changes in Vmax occurred when the direction was reversed along the transverse axis.(ABSTRACT TRUNCATED AT 250 WORDS)

A multidimensional model of cellular effects on the spread of electrotonic currents and on propagating action potentials.

This study was designed to develop a two-dimensional cellular model of uniform anisotropic muscle and to determine how irregularities of shape and variations in size of cardiomyocytes influence the passive (electrotonic) spread of currents at a microscopic level. A secondary purpose was to determine how the passive transfer of impressed currents across the gap junctions is related to the charge flow across the gap junctions during active propagation of depolarization. The decrease in electrotonic Vm with distance at a large size scale was described by a single exponential in both the longitudinal and transverse directions, as occurs in a continuous anisotropic medium. At a microscopic level, however, the falloff of Vm with distance was directionally different. Longitudinally, Vm decreased primarily along the length of cells, with small step-like decreases at the intercalated disks. Transversely, Vm was more nearly isopotential throughout each cell, and most of the decay in Vm occurred as large step-like decreases across the borders of the cells. Different gap junctions were used for charge flow for longitudinal versus transverse electrotonus. Remarkably similar results were obtained for propagating action potentials, i.e., different gap junctions were used for longitudinal versus transverse conduction. A major implication of the results is that it may be possible to gain information about the different longitudinal and transverse effects of the nonhomogeneous distribution of the cellular connections by improved measurements of propagation at a microscopic level.

Interaction of inhomogeneities of repolarization with anisotropic propagation in dog atria. A mechanism for both preventing and initiating reentry.

Having found the regional differences in right atrial action potentials shown in an accompanying article, we tested two seemingly paradoxical hypotheses: 1) The spatial pattern of repolarization provides a protective mechanism against reentry, and 2) repolarization inhomogeneities interact with anisotropic discontinuous propagation to produce reentry. Measurement of multidimensional refractory periods demonstrated an anisotropic distribution within large bundles with the longest refractory periods in the medial upper crista terminalis (sinus node area), a distribution similar to that of action potential durations. Also, discontinuities of repolarization were found at muscle bundle junctions. Early premature impulses originating in the sinus node area propagated throughout the right atrial preparations without conduction disturbances or reentry. Conversely, early premature impulses that originated at sites distal to the sinus node area resulted in localized conduction block at multiple sites, which frequently produced complex conduction changes and reentry. The critical nature of the site of origin of a premature impulse in initiating reentry was related to locations where the steepest repolarization gradients occurred: within anisotropic bundles in the direction of highest axial resistance (across fibers) and at muscle bundle junctions that represented localized discontinuities of axial resistance. The multiple conduction abnormalities at localized sites interacted to produce different types of reentry at a larger size scale (25 mm2 to several cm2). In each case, neither repolarization inhomogeneities (leading circle concept) nor anisotropic discontinuous propagation was the only "mechanism" involved. That is, reentry at a macroscopic size scale occurred as a result of a combined repolarization-anisotropic discontinuous propagation mechanism.

Influence of the passive anisotropic properties on directional differences in propagation following modification of the sodium conductance in human atrial muscle. A model of reentry based on anisotropic discontinuous propagation.

Available models of circus movement reentry in cardiac muscle and of drug action on reentrant arrhythmias are based on continuous medium theory, which depends solely on the membrane ionic conductances to alter propagation. The purpose of this study is to show that the anisotropic passive properties at a microscopic level highly determine the propagation response to modification of the sodium conductance by premature action potentials and by sodium channel-blocking drugs. In young, uniform anisotropic atrial bundles, propagation of progressively earlier premature action potentials continued as a smooth process until propagation ceased simultaneously in all directions. In older, nonuniform anisotropic bundles, however, premature action potentials produced either unidirectional longitudinal conduction block or a dissociated zigzag type of longitudinal conduction (a safer type of propagation, similar to transverse propagation). Directional differences in the velocity of premature action potentials demonstrated that anisotropic propagation was necessary for a reentrant circuit to be contained within an area of 50 mm2, even with very short refractory periods. Quinidine produced Wenckebach periodicity, which disappeared after acetylcholine shortened the action potential. Quinidine also produced use-dependent dissociated zigzag longitudinal conduction in the older, nonuniform anisotropic bundles but not in the young, uniform anisotropic bundles. The electrophysiological consequence was that propagation events differed in an age-related manner in response to the same modification of the sodium conductance. The electrical events at microscopic level showed that conditions leading to obliteration of side-to-side electrical coupling between fibers (e.g., aging and chronic hypertrophy) provide a primary mechanism for reentry to occur within very small areas (1-2 mm) due to a variety of propagation phenomena that do not occur in tissues with tight electrical coupling in all directions.

Propagating depolarization in anisotropic human and canine cardiac muscle: apparent directional differences in membrane capacitance. A simplified model for selective directional effects of modifying the sodium conductance on Vmax, tau foot, and the propagation safety factor.

As yet there is no model or simulation that accounts for the anisotropic difference in the shape of the upstroke and safety factor of propagating cardiac action potentials: fast upstrokes occur with slow transverse propagation and slow upstrokes occur with fast longitudinal propagation. The purpose of this paper is to demonstrate, however, that a simplified cable model based on directional differences in the effective membrane capacitance predicts in detail the experimentally measured directionally dependent behavior of the upstroke in response to modification of the sodium conductance. Quinidine and lidocaine produced greater relative decreases in Vmax and conduction velocity with longitudinal propagation than with transverse propagation, as predicted on the basis that the shape differences should produce an anisotropic distribution in the membrane uptake of sodium channel binding drugs. The simulation predictions of the effects of positive shifts of the take-off potential due to premature action potentials were also confirmed experimentally: there was a greater relative decrease in conduction velocity, Vmax, and Vamp with a greater increase in tau foot during longitudinal propagation than with transverse propagation. The major anisotropic differences in shape occurred when the take-off potential approached the least negative value that produced a propagated response. The extensive experimental verification of the results of a simplified model based on directional differences of effective membrane capacitance, combined with directional differences in effective axial resistivity, provides an initial quantitative basis for the anisotropic behavior of propagating depolarization in response to modification of the sodium conductance in cardiac muscle.

Ultrastructure and morphometry of the stomach muscle of Amphiuma tridactylum.

An ultrastructural and stereological examination was performed on stomach smooth muscle of the salamander Amphiuma. This tissue has very large cells, ranging up to 12 X 1500 micron when relaxed. The extracellular space is 31% of the tissue volume, and the tissue contains 84.6% water. These values are similar to those of other amphibian and mammalian gastrointestinal smooth muscle. The cells possess the usual smooth muscle organelles. Thick, thin and intermediate filaments are present, along with membrane-associated and cytoplasmic dense regions. There is a well-developed sarcoplasmic reticulum and many microtubules. Caveolae are found in rows along the cellular surface; the caveolae increase the cellular surface area by about 70%. The ratio mean volume: surface area of the cells is 1.26 micron. This tissue appears to be typical of gastrointestinal smooth muscle, with the exception of the very large size of the cells.

The kinetics of ouabain-sensitive ionic transport in the rabbit carotid artery.

1. Ouabain (0.1 mM)-sensitive 42K influx and 24Na efflux have been measured in rabbit carotid arteries under conditions of high cellular potassium, [K]i, as well as sodium, [Na]i. About 50% of the total fluxes are ouabain-sensitive (active) under conditions of high [K]i. 2. The extracellular space, determined by 60Co-EDTA, was relatively large in comparison to cellular water. The ionic concentrations in normal solution, estimated from isotope flux components, are: [Na]i = 24; [K]i = 169; [Cl]i = 68 mmol/l cell water. 3. The ouabain=sensitive 42K influx and 24Na efflux in high-K tissues were measured at varying external concentrations of potassium, [K]o, and normal concentrations of external sodium, [Na]o. Sigmoidal kinetics were observed and fitted to a co-operative interaction model. The maximal efflux of 24Na, 0.245 muequiv/g wet weight per minute, was about 1.4 times that for 42K influx. Half-maximal stimulation was achieved at [K]0.5o of 2.4 mM for Na, and 3.4 mM for K transport. The flux ratio of Na to K approximated 1.5. 4. Increased 42K efflux was found in the presence of ouabain and the passive influx of 42K was corrected for this effect. In the absence of this correction the ouabain-sensitive 42K influx would be reduced, and the Na/K flux ratio raised to about 2. 5. The [K]o-dependence of ouabain-sensitive fluxes was measured on Na-loaded tissues. 24Na efflux exhibited saturation kinetics with a maximum of 1.18 muequiv/g wet weight per minute and [K]0.5o = 3.1 mM. The 42K influx was two thirds the active Na efflux for [K]o less than or equal to 5 mM. At high [K]o, however, the influx greatly exceeded the predicted levels. Evidence is presented for a ouabain-sensitive membrane hyperpolarization being responsible for an additional influx of 42K. 6. The ouabain-sensitive 24Na efflux showed a sigmoidal dependence on [Na]i in the presence of [K]o = 10 mM and normal [Na]o. The maximal efflux was 0.88 muequiv/g weight per minute and [Na]0.5i = 49 mmol/l cell water, which is about twice the physiological operating point. 7. It is concluded that active Na and K transport in rabbit carotid artery follow sigmoidal kinetics and the flux ratio is about 1.5. Changes in [K]o and [Na]i over the physiological range can markedly affect transport, and may regulate vascular contraction by their action on electrogenic transport.