H. E. D. J. Ter Keurs

Modelling the mechanical properties of cardiac muscle.

A model of passive and active cardiac muscle mechanics is presented, suitable for use in continuum mechanics models of the whole heart. The model is based on an extensive review of experimental data from a variety of preparations (intact trabeculae, skinned fibres and myofibrils) and species (mainly rat and ferret) at temperatures from 20 to 27 degrees C. Experimental tests include isometric tension development, isotonic loading, quick-release/restretch, length step and sinusoidal perturbations. We show that all of these experiments can be interpreted with a four state variable model which includes (i) the passive elasticity of myocardial tissue, (ii) the rapid binding of Ca2+ to troponin C and its slower tension-dependent release, (iii) the kinetics of tropomyosin movement and availability of crossbridge binding sites and the length dependence of this process and (iv) the kinetics of crossbridge tension development under perturbations of myofilament length.

Comparison between the sarcomere length-force relations of intact and skinned trabeculae from rat right ventricle. Influence of calcium concentrations on these relations.

To investigate the extent to which the properties of the cardiac myofibrils contribute to the length-force relation of cardiac muscle, we determined the sarcomere length-force relations for rat ventricular trabeculae both before and after the muscles were skinned with the detergent Triton X-100 Sarcomere length was measured continuously by laser diffraction. In the unskinned trabeculae stimulated at 0.2 Hz, the relation between active force and sarcomere length at an extracellular calcium concentration of 1.5 HIM was curved away from the sarcomere length axis, with zero force at sarcomere length of 1.5–1.6 μm. At 0 3 mM calcium, the sarcomere length-force relation was curved toward the sarcomere length axis Chemical skinning of the muscle with 1% Triton X-100 in a “relaxing solution” caused an increase in intensity and decrease in dispersion of the first order diffraction beam, indicating an increased uniformity of sarcomere length in the relaxed muscle During calcium-regulated contractures in the skinned muscles, the central sarcomeres shortened by up to 20%. As the calcium concentration was increased over the range 1–50 μM, the relation between steady calcium-regulated force and sarcomere length shifted to higher force values and changed in shape in a manner similar to that observed for changes in extracellular calcium concentration before skinning. The sarcomere length-force relations for the intact muscles at an extracellular calcium concentration of 1 5 mM were similar to the curves at calcium concentration of 8 9 μM in the skinned preparations, whereas the curves at an extracellular calcium concentration of 0 3 mM in intact muscles fell between the relations at calcium concentrations of 2.7 and 4.3μM in the skinned preparations A factor contributing to the shape of the curves in the skinned muscle at submaximal calcium concentrations was that the calcium sensitivity of force production increased with increasing sarcomere length. The calcium concentration required for 50% activation decreased from 7 71 ± 0.52 μM to 3.77 ± 0.33 μM for an increase of sarcomere length from 1 75 to 2 15 μm. The slope of the force-calcium concentration relation increased from 2.82 to 4.54 with sarcomere length between 1.75 and 2.15μm. This change in calcium sensitivity was seen over the entire range of sarcomere lengths corresponding to the ascending limb of the cardiac length-force relation. It is concluded that the properties of the cardiac contractile machinery (including the length-dependence of calcium sensitivity) can account for much of the shape of the ascending limb in intact cardiac muscle.

Tension Development and Sarcomere Length in Rat Cardiac Trabeculae: Evidence of Length-Dependent Activation

We studied the influence of inotropic factors on the shape of the relation between tension and sarcomere length.Tension measurements were performed on thin trabeculae dissected from the right ventricle of the rat heart. Sarcomere length was measured by laser diffraction techniques and controlled by a servomotor system. The relations between tension and sarcomere length were derived from contractions at various extracellular calcium concentrations [Ca2+]o. The time course of tension development was dependent on both sarcomere length and [Ca2+]o. At all [Ca2+]o, the tension attained during contraction was zero at sarcomere lengths of 1.55-1.60 pm and maximal at a sarcomere length of 2.35 /im. Neither a summit nor a descending limb was found in the sarcomere length-tension relation. At [Ca2+]o = 0.5 mM, tension increased linearly with sarcomere length, whereas at [Ca2+]o = 2.5 mM, it approached maximal tension exponentially with sarcomere length. The relations between tension and sarcomere length derived from isometric contractions of the muscle and of sarcomeres were identical, and this suggests that shortening of sarcomeres does not contribute significantly to the effect of [Ca2+]o. The relations between tension and sarcomere length obtained at [Ca2+]o = 0.5 mM from contractions 30 seconds after a potentiating burst of stimuli (4 seconds at 4 Hz) were identical to the relation between tension and sarcomere length at [Ca2+]o = 2.5 mm. Our results are consistent with the hypothesis that cardiac muscle length affects contractile performance by its influence on excitation contraction coupling. CircRes 46: 703-714, 1980

Force and velocity of sarcomere shortening in trabeculae from rat heart. Effects of temperature.

The effect of temperature on the force-sarcomere velocity relation (20 degrees, 25 degrees, and 30 degrees C) and maximum velocity of sarcomere shortening (Vo; range 15 degrees-35 degrees C) was studied in trabeculae from rat heart. Sarcomere length and Vo were measured by laser diffraction techniques. Sarcomere length and sarcomere velocity, determined from each of the first-order diffraction lines, differed by less than 4%. Slack sarcomere length in the trabeculae appeared to be 1.9 microns. Isovelocity release techniques were used to obtain sarcomere velocity and Vo directly. Sarcomere velocity was measured at SL = 1.9-2.0 microns for elimination of contributions of parallel elastic force and restoring force to the external load of the sarcomeres. Peak twitch force development (Fo) was maximal (Fo-max) at 25 degrees C at [Ca2+]o = 1.5 mM. Lowering of the temperature below 25 degrees C led to development of spontaneous sarcomere activity and depression of Fo; both responses could be prevented by the addition of 0.5 mM procaine. Increase of temperature above 25 degrees C reduced twitch duration and Fo. Hills rectangular hyperbola fitted the force-velocity data if the load during shortening was less than 70% of Fo. Vo appeared to be independent of the level of activation at all temperatures when Fo was maintained above 90% of Fo-max, either by an increase of [Ca2+]o (to 3.0 mM) or by paired pulse stimulation. Vo increased with increasing temperature; the parameter a, calculated from force-velocity relations measured at 20 degrees, 25 degrees, and 30 degrees C, decreased with increasing temperature. The Arrhenius plot of Vo was studied in detail over a wider temperature range (15 degrees-35 degrees C) and in smaller temperature increments. The relation was linear between 18 degrees and 33 degrees C; the observed Q10, defined as the ratio of Vo measured at temperature (T) over Vo at T-10 degrees C, was 4.6 A Q10 of 4.6 for Vo is consistent with the reported temperature dependence of rat cardiac actin-activated myosin ATPase, which suggests that the same reaction step may limit the activity of the enzyme in vitro and during shortening of the cardiac sarcomeres at zero external load.

Experimental determination of force—length relations of intact human gastrocnemius muscles

The purpose of this study was to determine force-length relations of intact human gastrocnemius muscles experimentally. Changes in maximal active isometric forces of the gastrocnemius muscle were calculated from resultant ankle joint moments of carefully executed maximal effort contractions at systematically changing knee and ankle joint configurations. Changes in muscle lengths were obtained using second-order polynomial regression equations that relate the length of the gastrocnemius muscle-tendon unit to knee and ankle joint angles. From these changes in muscle lengths, changes in muscle fibre lengths were estimated based on assumptions about fibre structure and series elastic properties. The results indicate that intact human gastrocnemius muscles operate on the ascending limb of the force-length relation, and that passive forces are minimal within a normal range of ankle and knee joint configurations.

Lack of effect of isoproterenol on unloaded velocity of sarcomere shortening in rat cardiac trabeculae.

Several recent reports have indicated that catecholamines may act directly on the crossbridge cycle, independent of intracellular calcium concentration changes. The present study investigated the effect of isoproterenol on peak force during twitches at constant sarcomere length and unloaded velocity of sarcomere shortening in isolated right ventricular trabeculae of hearts with V1 or V3 isomyosin obtained from euthyroid and hypothyroid rats, respectively. Hypothyroidism was induced by treatment of the rats with propylthiouracil for 6 weeks. Electrophoretic analysis showed that the hearts of hypothyroid animals were composed only of V3 isomyosin, whereas the hearts of euthyroid animals were composed predominantly of V1 isomyosin. Force development was measured with a silicon strain gauge and sarcomere length with laser diffraction techniques; the shortening velocity was determined from contractions in which sarcomere length was initially held constant followed by a quick release to zero load and a controlled release at zero load. Both isometric twitch force and unloaded sarcomere shortening velocity were sigmoidal functions of [Ca2+]o and of the concentration of isoproterenol. At optimal [Ca2+]o, unloaded shortening velocity was 40% lower in myocardium of hypothyroid animals than in myocardium of euthyroid animals. Isoproterenol increased the sensitivity of isometric twitch force and unloaded shortening velocity to [Ca2+]o in trabeculae from both euthyroid and hypothyroid animals. Isoproterenol did not increase unloaded shortening velocity at optimal [Ca2+]o, regardless of the thyroid state. From these results we conclude that beta-adrenergic stimulation per se does not accelerate the rate limiting step in the crossbridge cycle that determines unloaded sarcomere shortening velocity in the intact cardiac cell.

Role of the sarcolemma in triggered propagated contractions in rat cardiac trabeculae.

We have recently described that after contractions propagate through multicellular cardiac muscle preparations. These propagating contractions are triggered in damaged regions of rat right ventricular trabeculae during relaxation of electrically stimulated twitches. Propagation of triggered contractions has been attributed to calcium ions that diffuse along the preparation, causing calcium-induced calcium release from the sarcoplasmic reticulum in adjacent cells. In the present study we have investigated a possible role of the sarcolemma and delayed afterdepolarizations (DADs) in the initiation and propagation of triggered propagated contractions (TPCs) in multicellular preparations. We studied whether 1) TPCs are accompanied by delayed sarcolemmal depolarizations, 2) such depolarizations mediate local contraction, and 3) an intact sarcolemma is required for propagation of contractions. TPCs that remained stable for prolonged periods of time could be induced by trains of 15 stimuli (2 Hz, 15-second intervals) at lowered temperature (19-21 degrees C) of the superfusing Krebs-Henseleit medium and a [Ca(2+)]o of 1.0-1.5 mM. Although TPCs could be induced at 38 degrees C and a [Ca2+]o of 3.0-4.0 mM, they disappeared within 10 minutes. Force was measured with a silicon strain gauge; length and shortening of sarcomeres were measured at two sites of the muscle using laser diffraction techniques. Membrane potential was measured with flexible microelectrodes. Saponin was used to selectively render the sarcolemma permeable to small ions and molecules. Propagation velocity of TPCs in intact trabeculae varied from 1.7 to 13.4 mm/sec at 19-21 degrees C. TPCs were accompanied by DADs that could reach threshold and induce triggered arrhythmias. Changes in latency, duration, and force of TPCs, induced by changing [Ca(2+)]o or the number of conditioning stimuli, were closely matched by changes in latency, duration, and amplitude of DADs; DADs consistently preceded TPCs, on average by 60 msec. Local heating of the muscle, by applying a current through an insulated platinum wire (diameter 100 microns) that touched the muscle, interrupted propagation of TPCs reversibly. DADs were, in the absence of a local contraction, still recorded distal to the heated site. In muscles that were treated with saponin and exposed to solutions approximating the intracellular milieu, spontaneously occurring local contractions that propagated in both directions (at velocities of 70-200 microns/sec) were elicited at a bathing calcium concentration of approximately 0.6 microM. Below this threshold, propagated contractions could be triggered by pressure ejection of a calcium-containing solution from a microelectrode positioned close to the trabecula.(ABSTRACT TRUNCATED AT 400 WORDS)

Ca2+-dependence of diastolic properties of cardiac sarcomeres: involvement of titin

The stiffness of the sarcomeres was studied during the diastolic interval of 18 stimulated (0.5 Hz) cardiac trabeculae of rat (pH 7.4; temperature = 25 degrees C). Sarcomere length (SL) and force (F) were measured using, respectively, laser diffraction techniques (resolution: 4 nm) and a silicon strain gauge (resolution: 0.63 microN). Sinusoidal perturbations (frequency = 500 Hz) were imposed to the length of the preparation. The stiffness was evaluated from the corresponding F and SL sinusoids by analysis of both signals together either in the time domain or in the frequency domain. A short burst (duration = 30 ms) of sinusoidal perturbations was repeated at 5 predetermined times during diastole providing 5 measurements of stiffness during the time interval separating two twitches. These measurements revealed that stiffness increases by approximately 30% during diastole, while a simultaneous expansion of the sarcomeres (amplitude = 10-60 nm) was detected. Measurements of the fluorescence of fura-2 under the same conditions revealed a continuous exponential decline of [Ca2+]i from 210 to 90 nM (constant of time approximately 300 ms) during diastole. In order to test the possibility that the increase of sarcomere stiffness and the decline of [Ca2+]i were coupled during diastole of intact trabeculae, we studied the effect of different free Ca(2+)-concentrations ([Ca2+]) between 1 and 430 nM on sarcomere stiffness in rat cardiac trabeculae skinned by saponin (n = 17). Stiffness was studied using 500 Hz sinusoidal perturbations of muscle length (ML). We found that, below 70 nM, the stiffness was independent of [Ca2+]; between 70 and 200 nM, the stiffness declined with increase of [Ca2+]; above 200 nM, the stiffness increased steeply with [Ca2+]. The data fitted accurately to the sum of two sigmoids (Hill functions): (1) at [Ca2+] < 200 nM the stiffness decreased with [Ca2+] (EC50 = 160 +/- 13 nM; n = -2.6 +/- 0.7) and (2) at [Ca2+] > 200 nM, stiffness increased with [Ca2+] (EC50 = 3.4 +/- 0.3 microM; n = 2.1 +/- 0.2) due to attachment of cross-bridges. From these results, it was possible to reproduce accurately the time course of diastolic stiffness observed in intact trabeculae and to predict the effect on stiffness of a spontaneous elevation of the diastolic [Ca2+]. Identical stiffness measurements were performed in 4 skinned preparations exposed to a cloned fragment of titin (Ti I-II) which has been shown to exhibit a strong interaction with F-actin in vitro. It was anticipated that Ti I-II would compete with endogenous titin for the same binding site on actin in the I-band. Below 200 nM, Ti I-II (2 microM) eliminated the Ca(2+)-dependence of stiffness. These results are consistent with the hypothesis that the Ca(2+)-sensitivity of the sarcomeres at [Ca2+] < 200 nM, i.e. where the myocytes in intact muscle operate during diastole, involves an association between titin molecules and the thin filament.

Triggered Propagated Contractions in Rat Cardiac Trabeculae: Inhibition by Octanol and Heptanol

We studied the role of Ca2+ diffusion through gap junctions (GJs) in triggering and propagation of damage-induced contractions in cardiac muscle (TPCs) by evaluating effects of the GJ blockers octanol and heptanol (O&H) on TPCs. TPCs were elicited in trabeculae from rat right ventricle superfused with Krebs-Henseleit solution at 20 degrees C and 0.7 to 1.75 mmol/L [Ca2+]o. Force was measured with a silicon strain gauge; sarcomere length, by laser diffraction techniques. O&H (3 to 300 mumol/L) decreased force, propagation velocity, and triggering rate of TPCs in a dose-dependent manner. At 300 mumol/L, O&H decreased TPC force to 21.3% and 25.7%, propagation velocity to 15.4% and 13.0%, and triggering rate to 26.5% and 25.7%. At 300 mumol/L. O&H decreased twitch force to 79.0% and 77.8% and reduced time to 90% relaxation by 10% to 15%. Above 1 mmol/L, O&H abolished twitch force and TPCs. Image analysis of spread of the fluorescence profile of microinjected fura 2 salt revealed an effective diffusion coefficient for fura 2 of 21.0 +/- 3.3 microns2/s, which decreased to 12.6+/-1.5 and 7.07 +/- 0.7 microns2/s after 1 and 3 hours of exposure, respectively, to 100 mumol/L octanol, with a time constant of decline of 1.5+/-0.5 hours. These results are consistent with the hypothesis that propagation of TPCs is due to Ca(2+)-induced Ca2+ release mediated by Ca2+ diffusion from cell to cell through GJs. Reduction of propagation velocity reduces the number of activated sarcomeres in the TPC, which reduces TPC force. O&H slow triggering of TPCs, presumably by blocking Ca2+ diffusion from myocytes within damaged areas to adjacent normal cells.

T-tubule profiles in Purkinje fibres of mammalian myocardium

Purkinje (P)-fibres are cardiac myocytes that are specialized for fast conduction of the electrical signal. P-fibres are usually defined as having the following identifying features: lack of T tubules; frequent lateral cell junctions; deep indentations at the intercalated discs level; the CX40 isoforms of gap junction proteins and, in large mammals, paucity of myofibrils and abundance of glycogen. We have examined the ultrastructure of P-fibres in free running P-strands from right and left ventricles of small (mouse and rat) intermediate (rabbit) and large (dog) size mammals focusing on presence and distribution of the T tubules. In contrast with previous studies, we find that P-fibres do have T tubules which form normal dyadic associations with the sarcoplasmic reticulum and that the frequency of tubules varies with the size of the animal. Profiles of T tubules and dyads are present over short segments of individual P-cells flanked by totally T tubule-free segments. It is thought that lack of T tubules in P-cells is necessary to reduce capacitance and thus accelerate action potential spread. This may not be as important in a small heart.