Nonlinear propagation of spherical calcium waves in rat cardiac myocytes.

Spontaneous calcium waves in enzymatically isolated rat cardiac myocytes were investigated by confocal laser scanning microscopy (CLSM) using the fluorescent Ca2+-indicator fluo-3 AM. As recently shown, a spreading wave of enhanced cytosolic calcium appears, most probably during Ca2+ overload, and is initiated by an elementary event called a "calcium spark." When measured by conventional fluorescence microscopy the propagation velocity of spontaneous calcium waves determined at several points along the cardiac myocyte was previously found to be constant. More precise measurements with a CLSM showed a nonlinear propagation. The wave velocity was low, close to the focus, and increased with increasing time and propagation length, approaching a maximum of 113 microns/s. This result was surprising, inasmuch as for geometrical reasons a decrease of the propagation velocity might be expected if the confocal plane is not identical with that plane where the focus of the wave was localized. It is suggested that the propagation velocity is essentially dependent on the curvature of the spreading wave. From the linear relationship of velocity versus curvature, a critical radius of 2.7 +/- 1.4 microns (mean +/- SD) was worked out, below which an outward propagation of the wave will not take place. Once released from a sufficiently extended cluster of sarcoplasmic reticulum release channels, calcium diffuses and will activate its neighbors. While traveling away, the volume into which calcium diffuses becomes effectively smaller than at low radii. This effect is the consequence of the summation of elementary events (Ca2+ sparks) and leads to a steeper increase of the cytosolic calcium concentration after a certain diffusion path length. Thus the time taken to reach a critical threshold of [Ca2+]i at the neighboring calcium release sites decreases with decreasing curvature and the wave will propagate faster

Velocity-curvature relationship of colliding spherical calcium waves in rat cardiac myocytes.

Colliding spherical calcium waves in enzymatically isolated rat cardiac myocytes develop new wavefronts propagating perpendicular to the original direction. When investigated by confocal laser scanning microscopy (CLSM), using the fluorescent Ca2+ indicator fluo-3 AM, "cusp"-like structures become visible that are favorably approximated by double parabolae. The time-dependent position of the vertices is used to determine propagation velocity and negative curvature of the wavefront in the region of collision. It is evident that negatively curved waves propagate faster than positively curved, single waves. Considering two perfectly equal expanding circular waves, we demonstrated that the collision of calcium waves is due to an autocatalytic process (calcium-induced calcium release), and not to a simple phenomenon of interference. Following the spatiotemporal organization in simpler chemical systems maintained under conditions far from the thermodynamic equilibrium (Belousov-Zhabotinskii reaction), the dependence of the normal velocity on the curvature of the spreading wavefront is given by a linear relation. The so-called velocity-curvature relationship makes clear that the velocity is enhanced by curvature toward the direction of forward propagation and decreased by curvature away from the direction of forward propagation (with an influence of the diffusion coefficient). Experimentally obtained velocity data of both negatively and positively curved calcium waves were approximated by orthogonal weighted regression. The negative slope of the straight line resulted in an effective diffusion coefficient of 1.2 x 10(-4) mm2/s. From the so-called critical radius, which must be exceeded to initiate a traveling calcium wave, a critical volume (with enhanced [Ca2+]i) of approximately 12 microm3 was calculated. This is almost identical to the volume that is occupied by a single calcium spark

Calcium waves in agarose gel with cell organelles: implications of the velocity curvature relationship.

Calcium oscillations and waves have been observed not only in several types of living cells but also in less complex systems of isolated cell organelles. Here we report the determination of apparent Ca2+ diffusion coefficients in a novel excitable medium of agarose gel with homogeneously distributed vesicles of skeletal sarcoplasmic reticulum. Spatiotemporal calcium patterns were visualized by confocal laser scanning fluorescence microscopy. To obtain characteristic parameters of the velocity curvature relationship, namely, apparent diffusion coefficient, velocity of plane calcium waves, and critical radius, positively and negatively curved wave fronts were analyzed. It is demonstrated that gel-immobilized cell organelles reveal features of an excitable medium. Apparent Ca2+ diffusion coefficients of the in vitro system, both in the absence or in the presence of mitochondria, were found to be higher than in cardiac myocytes and lower than in unbuffered agarose gel. Plane calcium waves propagated markedly slower in the in vitro system than in rat cardiac myocytes. Whereas mitochondria significantly reduced the apparent Ca2+ diffusion coefficient of the in vitro system, propagation velocity and critical size of calcium waves were found to be nearly unchanged. These results suggest that calcium wave propagation depends on the kinetics of calcium release rather than on diffusion

Analysis of ryanodine receptor clusters in rat and human cardiac myocytes

Single rat ventricular myocytes and human ventricle tissue sections were labeled with antibodies against the ryanodine receptor (RyR) and α-actinin to examine the 3D distribution of RyRs with confocal microscopy. Image contrast was maximized by refractive index matching and deconvolution. The RyR label formed discrete puncta representing clusters of RyRs or “couplons” around the edges of the myofilaments with a nearest-neighbor spacing of 0.66 ± 0.06 μm in rat and 0.78 ± 0.07 μm in human. Each bundle of myofibrils was served by approximately six couplons, which supplied a cross-sectional area of ≈0.6 μm2 in rat and ≈0.8 μm2 in human. Although the couplons were in reasonable registration with z-lines, there were discontinuities in the longitudinal position of sarcomeres so that dislocations in the order of RyR clusters occurred. There was ≈53% longitudinal registration of RyR clusters, suggesting a nonrandom placement of couplons around the sarcomere. These data can explain the spherical propagation of Ca2+ waves and provide quantitative 3D data sets needed for accurate modeling of cardiac Ca2+-induced Ca2+ release. By quantifying labeling intensity in rat ventricular myocytes, a lower limit of 78 RyRs per cluster (on average) was obtained. By modeling the couplon as a disk wrapping around a t-tubule and fitting cluster images, 95% of couplons contained between 120 and 260 RyRs (assuming that RyRs are tight packed with a spacing of 29 nm). Assuming similar labeling efficiency in human, from the fluorescence intensity alone we estimate that human ventricular myocytes contain ≈30% fewer RyRs per couplon than rat

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

The synergetic modulation of the excitability of central gray matter by a neuropeptide: two protocols using excitation waves in chick retina

The isolated chick retina provides an in vitro tissue model, in which two protocols were developed to verify the efficacy of a peptide in the excitability control of the central gray matter. In the first, extra-cellular potassium homeostasis is challenged at long intervals and in the second, a wave is trapped in a ring of tissue causing the system to be under self-sustained challenge. Within the neuropil, the extra-cellular potassium transient observed in the first protocol was affected from the initial rising phase to the final concentration at the end of the five-minute pulse. There was no change in the concomitants of excitation waves elicited by the extra-cellular rise of potassium. However, there was an increase on the elicited waves latency and/or a rise in the threshold potassium concentration for these waves to appear. In the second protocol, the wave concomitants and the propagation velocity were affected by the peptide. The results suggest a synergetic action of the peptide on glial and synaptic membranes: by accelerating the glial Na/KATPase and changing the kinetics of the glial potassium channels, with glia tending to accumulate KCl. At the same time, there is an increase in potassium currents through nerve terminals.<br>Retinas de pinto isoladas proporcionam um modelo de tecidos in vitro, para o qual dois protocolos foram desenvolvidos para verificar a eficácia de um peptídeo no controle da excitabilidade da matéria cinzenta central. No primeiro, a homeostase do potássio extra-celular é desafiada por intervalos longos (1 hora) e no segundo, uma onda é capturada em um anel de tecido, de tal maneira que o sistema permaneça em estado de desafio auto-sustentado. Dentro da neuropil, o transiente de potássio extra-celular observado no primeiro protocolo foi afetado da fase de início de aumento à concentração final, ao final do pulso de cinco minutos. Não há mudanças nos parâmetros concomitantes das ondas de excitação geradas pelo aumento do potássio extra-celular. Entretanto, houve um aumento da latência das ondas geradas e/ou um aumento no nível de concentração de potássio necessário para gerar a onda. No segundo protocolo, os parâmetros concomitantes da onda e sua velocidade de propagação foram afetados pelo peptídeo. Os resultados sugerem uma ação sinergética do peptídeo nas membranas gliais e sinápticas: acelerando o Na/KATPase glial e mudando a cinética dos canais de potássio gliais, com a glia tendendo a acumular KCl. Nesse período, não há aumento nas correntes de potássio nas terminações nervosas