Origin of quasiperiodic dynamics in excitable media.

Analysis of the dynamic instabilities of periodic waves in a one-dimensional excitable ring medium demonstrates that driven oscillations of a pulse width display different oscillatory behavior at different values of stimulation frequency. Initial periodicity evolves to quasiperiodic dynamics when the propagation speed of a pulse approaches its minimal value determined by the dispersion relation of a medium.

Characteristic and critical excitation length scales in 1-D and 2-D simulations of reentrant cardiac arrhythmias using simple two-variable models.

We discuss major characteristic lengths as the lumped parameters characterizing kinematics and dynamics of excitation waves in idealized one- and two-dimensional myocardium. First we consider the directional dependence of the length scale in the anisotropic bi- and monodomain myocardium. Next, we show that there is a well-defined smallness parameter that allows one to consider the monodomain equations as the first approximation to the bidomain theory. Then we use this approximation and turn our attention to the dynamics and to finding the major physiologic parameters governing such transient processes as the formation of a reentrant wave and its subsequent degradation into the malignant cardiac arrhythmia--ventricular fibrillation. It appears that in both the one- and two-dimensional cases the stability of a reentrant periodic process (representing a VT rhythm) is determined by the same two physiologic parameters: the wave width lambda, which is approximately the size of depolarized zone, and ratio of lambda to the critical length L(h)cr, which is defined as the wave width of an action potential propagating with the minimum possible speed. The parameter L(h)cr determines the length scale (size) of an ectopic region that may initiate a wave. It also determines the duration of the vulnerable window for initiating the unidirectional block as well as a minimum permissible length of the reentrant circuit. We also present some evidence that depending on the value of lambda the waveforms of the simulated ECGs for reentrant activity vary from monomorphic to polymorphic.

Wavelet formation in excitable cardiac tissue: the role of wavefront-obstacle interactions in initiating high-frequency fibrillatory-like arrhythmias.

High-frequency arrhythmias leading to fibrillation are often associated with the presence of inhomogeneities (obstacles) in cardiac tissue and reduced excitability of cardiac cells. Studies of antiarrhythmic drugs in patients surviving myocardial infarction revealed an increased rate of sudden cardiac death compared with untreated patients. These drugs block the cardiac sodium channel, thereby reducing excitability, which may alter wavefront-obstacle interactions. In diseased atrial tissue, excitability is reduced by diminished sodium channel availability secondary to depolarized rest potentials and cellular decoupling secondary to intercellular fibrosis. Excitability can also be reduced by incomplete recovery between successive excitations. In all of these cases, wavefront-obstacle interactions in a poorly excitable medium may reflect an arrhythmogenic process that permits formation of reentrant wavelets leading to flutter, fibrillation, and sudden cardiac death. To probe the relationship between excitability and arrhythmogenesis, we explored conditions for new wavelet formation after collision of a plane wave with an obstacle in an otherwise homogeneous excitable medium. Formulating our approach in terms of the balance between charge available in the wavefront and the excitation charge requirements of adjacent medium, we found analytically the critical medium parameters that defined conditions for wavefront-obstacle separation. Under these conditions, when a parent wavefront collided with a primitive obstacle, the resultant fragments separated from the obstacle boundaries, subsequently curled, and spawned new "daughter" wavelets. We identified spatial arrangements of obstacles such that wavefront-obstacle collisions leading to spawning of new wavelets could produce high-frequency wavelet trains similar to fibrillation-like arrhythmias.

Proarrhythmic response to potassium channel blockade. Numerical studies of polymorphic tachyarrhythmias.

BACKGROUND: Prompted by the results of CAST results, attention has shifted from class I agents that primarily block sodium channels to class III agents that primarily block potassium channels for pharmacological management of certain cardiac arrhythmias. Recent studies demonstrated that sodium channel blockade, while antiarrhythmic at the cellular level, was inherently proarrhythmic in the setting of a propagating wave front as a result of prolongation of the vulnerable period during which premature stimulation can initiate reentrant activation. From a theoretical perspective, sodium (depolarizing) and potassium (repolarizing) currents are complementary so that if antiarrhythmic and proarrhythmic properties are coupled to modulation of sodium currents, then antiarrhythmic and proarrhythmic properties might similarly be coupled to modulation of potassium currents. The purpose of the present study was to explore the role of repolarization currents during reentrant excitation. METHODS AND RESULTS: To assess the generic role of repolarizing currents during reentry, we studied the responses of a two-dimensional array of identical excitable cells based on the FitzHugh-Nagumo model, consisting of a single excitation (sodium-like) current and a single recovery (potassium-like) current. Spiral wave reentry was initiated by use of S1S2 stimulation, with the delay timed to occur within the vulnerable period (VP). While holding the sodium conductance constant, the potassium conductance (gK) was reduced from 1.13 to 0.70 (arbitrary units), producing a prolongation of the action potential duration (APD). When gK was 1.13, the tip of the spiral wave rotated around a small, stationary, unexcited region and the computed ECG was monomorphic. As gK was reduced, the APD was prolonged and the unexcited region became mobile (nonstationary), such that the tip of the spiral wave inscribed an outline similar to a multipetaled flower; concomitantly, the computed ECG became progressively more polymorphic. The degree of polymorphism was related to the APD and the configuration of the nonstationary spiral core. CONCLUSIONS: Torsadelike (polymorphic) ECGs can be derived from spiral wave reentry in a medium of identical cells. Under normal conditions, the spiral core around which a reentrant wave front rotates is stationary. As the balance of repolarizing currents becomes less outward (eg, secondary to potassium channel blockade), the APD is prolonged. When the wavelength (APD.velocity) exceeds the perimeter of the stationary unexcited core, the core will become unstable, causing spiral core drift. Large repolarizing currents shorten the APD and result in a monomorphic reentrant process (stationary core), whereas smaller currents prolong the APD and amplify spiral core instability, resulting in a polymorphic process. We conclude that, similar to sodium channel blockade, the proarrhythmic potential of potassium channel blockade in the setting of propagation may be directly linked to its cellular antiarrhythmic potential, ie, arrhythmia suppression resulting from a prolonged APD may, on initiation of a reentrant wave front, destabilize the core of a rotating spiral, resulting in complex motion (precession) of the spiral tip around a nonstationary region of unexcited cells. In tissue with inhomogeneities, core instability alters the activation sequence from one reentry cycle to the next and can lead to spiral wave fractination as the wave front collides with inhomogeneous regions. Depending on the nature of the inhomogeneities, wave front fragments may annihilate one another, producing a nonsustained arrhythmia, or may spawn new spirals (multiple wavelets), producing fibrillation and sudden cardiac death.

Late Na channels in cardiac cells: the physiological role of background Na channels.

Two types of the late Na channels, burst and background, were studied in Purkinje and ventricular cells. In the whole-cell configuration, steady-state Na currents were recorded at potentials (-70 to -80 mV) close to the normal cell resting potential. The question of the contribution of late Na channels to this background Na conductance was investigated. During depolarization, burst Na channels were active for periods (up to approximately 5 s), which exceeded the action potential duration. However, they eventually closed without reopening, indicating the presence of slow and complete inactivation. When, at the moment of burst channel opening, the potential was switched to -80 mV, the channel closed quickly without reopening. We conclude that the burst Na channels cannot contribute significantly to the background Na conductance. Background Na channels undergo incomplete inactivation. After a step depolarization, their activity decreased in time, approaching a steady-state level. Background Na channel openings could be recorded at constant potentials in the range from -120 to 0 mV. After step depolarizations to potentials near -70 mV and more negative, a significant fraction of Na current was carried by the background Na channels. Analysis of the background channel behavior revealed that their gating properties are qualitatively different from those of the early Na channels. We suggest that background Na channels represent a special type of Na channel that can play an important role in the initiation of cardiac action potential and in the TTX-sensitive background Na conductance.

Genetic control of acid phosphatase Rm and its relation to control of peroxidase Rm in flax (Linum) genotrophs.

Evidence from various workers has indicated that isozyme relative mobility (Rm) may not be defined solely by the corresponding structural gene but may also be modified by alleles at other loci. The instances of numerous, small ongoing temporal or tissue changes in Rm for certain enzyme systems in plants may be another aspect of this modification due to interactions between genes. A further possible example of Rm modification occurs in connection with environmentally (fertilizer treatment) induced heritable changes within particular completely inbred and genetically homogeneous plant genotypes. Fertilizer-induced, persistent relative mobility (Rm) shifts for peroxidases are controlled by two alleles at one locus, a dominant for faster Rm and a recessive for slower Rm; codominance is completely absent. There are similar Rm shifts in acid phosphatases, likewise stemming from molecular weight changes. This study examined genetic control of the acid phosphatase Rm shift and its relation to peroxidase Rm control. It showed that the environmentally induced heritable acid phosphatase Rm shift is controlled by an identical system of a dominant (faster) and recessive (slower) allele, closely linked to the locus controlling peroxidases. The Rm shifts for both these enzyme glycoproteins are unidirectional, with no codominance; at least 10 other nonidentified glycoproteins display the same unidirectional Rm shifts. The results suggest modification, possibly posttranslational or transcriptional, controlled by modifier loci. This supports indications in other organisms that small numbers of modifier loci may control widespread Rm changes in the protein products of a genome.

Isozyme relative mobility (Rm) changes related to leaf position; apparently smooth Rm trends and some implications.

Relative mobilities (Rm's) of peroxidase and acid phosphatase isozymes were examined in leaves of flax (Linum usitatissimum L.). The leaves were sampled from four equidistantly spaced positions from main stem base to apex in various genotypes. Rm's for the two slowest-migrating isozymes of each enzyme system changed in a simple, coherent fashion in leaves from stem bases toward apices. The Rm trends up the stem seen in two highly branched flax types were somewhat different from those in two sparsely branched types. The coherent Rm trends in the four types, suggesting a smooth continuum and a potentially large number of slightly different forms of these isozymes, are discussed in relation to other data for such Rm trends. In the study reported here, both enzyme systems behaved similarly. This fact and the simple Mendelian genetical system with no codominance controlling Rm's in flax peroxidases and acid phosphatases suggest posttranscriptional or posttranslational modifications as plausible mechanisms underlying the numerous, presumably small molecular changes generating the small, consistent changes in Rm's.

Visualization of both peroxidase and acid phosphatase isozymes from flax (Linum) on the same gels.

The staining of both peroxidases (PERs) and acid phosphatases (APs) following electrophoresis on acrylamide gels is described. Scanning doubly stained gels at appropriate wavelengths reveals individual isozyme bands for both enzyme systems, giving essentially identical results to those obtained from separately run and stained gels. Collection of relative mobility (Rm) data is unaffected by such tandem staining. Few complications arise from overlapping PER and AP bands, or interactions between the two staining methods and PER or AP isozymes. Even if repeat scans of a gel at different wavelengths are needed to retrieve all isozyme information, dual staining provides distinct savings in time and sample material.