Modelling and measuring electromechanical coupling in the rat heart.

Tension-dependent binding of Ca(2+) to troponin C in the cardiac myocyte has been shown to play an important role in the regulation of Ca(2+) and the activation of tension development. The significance of this regulatory mechanism is quantified experimentally by the quantity of Ca(2+) released following a rapid change in the muscle length. Using a computational, coupled, electromechanics cell model, we have confirmed that the tension dependence of Ca(2+) binding to troponin C, rather than cross-bridge kinetics or the rate of Ca(2+) uptake by the sarcoplasmic reticulum, determines the quantity of Ca(2+) released following a length step. This cell model has been successfully applied in a continuum model of the papillary muscle to analyse experimental data, suggesting the tension-dependent binding of Ca(2+) to troponin C as the likely pathway through which the effects of localized impaired tension generation alter the Ca(2+) transient. These experimental results are qualitatively reproduced using a three-dimensional coupled electromechanics model. Furthermore, the model predicts that changes in the Ca(2+) transient in the viable myocardium surrounding the impaired region are amplified in the absence of tension-dependent binding of Ca(2+) to troponin C.

Elasticity, unexpected contractility and the identification of actin and myosin in lobster arteries.

Lobster arteries, which exhibit non-uniform elasticity when stretched, have a trilaminar organization. The inner layer is an elastic connective tissue and the outer layer is a collagenous connective tissue; the middle layer of an artery is an aggregation of cells containing microfilaments. Arterial cells possess actin, myosin and tropomyosin. Except for the dorsal abdominal artery, striated muscle cells are not evident in the walls of any of the vessels. The neurotransmitter glutamic acid and the neurohormone proctolin elicit slow circumferential contractions in all of the arteries leaving the lobster heart. Only the dorsal abdominal artery contracts when stimulated electrically. Longitudinal strips of the arteries do not respond to either drugs or electrical stimulation. Arterial contraction will have profound effects on resistance to blood flow and may be an important component of the control mechanisms regulating blood distribution.

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.

Sites and modes of action of proctolin and the FLP F2 on lobster cardiac muscle.

At the threshold concentration (1-10 pmol l(-1)), the neuropeptide hormones proctolin (PR) and the FLRFamide-like peptide (FLP) F(2) cause an increase in amplitude of electrically evoked contractions (each contraction is a brief tetanus) of lobster heart ostial muscle. At higher concentrations each peptide also induces an increase in tonus (contracture). The PR-induced contracture and augmentation of tetani are proportional to increases in [Ca2+]i. The rate of onset and recovery of peptide-induced effects on both tetani and contracture appeared to reduced by Ca2+ storage by the sarcoplasmic reticulum (SR). Enhanced tetani following a contracture may be due to enhanced voltage-gated Ca2+ current and sarcoplasmic reticular (SR) Ca2+ loading. The SR Ca2+ loading appears to be specific for PR and F2, since glutamic-acid-induced contractures are not followed by increased tetani. The prolonged elevation of [Ca2+]i during contracture causes a right-ward shift in the force-pCa curve indicating a decrease in myofibrillar sensitivity to Ca2+. Blocking voltage-gated Ca2+ channels with Cd2+, nifedipine or verapamil, while reducing tetani, does not prevent peptide-induced contracture and enhanced tetani. Opening SR Ca2+ channels and depleting SR Ca2+ with either caffeine or ryanodine blocked tetani but permitted accelerated peptide-induced contractures. We conclude that PR and F2 at low concentration enhance voltage-dependent Ca2+ induced Ca2+ release from the SR, while higher hormone levels directly gate Ca2+ entry across the sarcolemma.

Congestive heart failure after myocardial infarction in the rat: cardiac force and spontaneous sarcomere activity.

The causes of reduced cardiac force development in congestive heart failure (CHF) are still uncertain. We explored the subcellular mechanisms leading to decreased force development in trabeculae from rats with a myocardial infarction. We defined CHF according to clinical and pathological criteria and compared properties of trabeculae from animals with CHF (cMI) to those of animals with a myocardial scar but without evidence of CHF (uMI), and sham-operated animals. The new findings of this study on properties of cMI trabeculae are that (1) maximal twitch force following post-extrasystolic potentiation is unchanged; (2) the sensitivity of cMI trabeculae to [Ca(2+)](o) is increased; (3) spontaneous diastolic sarcomere length (SL) fluctuations (SA) are increased in cMI at all levels of SR Ca(2+) loading; and (4) SA is accompanied by a proportional reduction of F(max). The results suggest that the probability of spontaneous diastolic opening of SR Ca(2+) channels is increased in CHF. These data provide the basis for a novel mechanism underlying systolic and diastolic dysfunction as well as arrhythmias in hearts in CHF. If SA proves to be a component of myocardial dysfunction in human CHF, our thinking about therapy of the patient with CHF may be profoundly changed.

The steady-state force-Ca2+ relationship in intact lobster (Homarus americanus) cardiac muscle.

The heart of the decapod crustacean is activated by regular impulse bursts from the cardiac ganglion. The cardiac pump function depends on ganglionic burst frequency, burst duration, and burst impulse frequency. Here, we activated isolated lobster cardiac ostial muscle (Orbicularis ostii muscle, OOM) by stimulus trains in vitro in order to characterize the response of the contractile apparatus to [Ca2+]i. We employed stimulus trains that generate a steady state between the [Ca2+]i and force in order to estimate the Ca2+ sensitivity of myofilaments. Force and [Ca2+]i transients were simultaneously recorded using a silicon strain gauge and the fluorescence of iontophoretically microinjected fura-2 salt. We examined the effects of tetanus duration (TD), the interval between trains, and 6 microM cyclopiazonic acid, an inhibitor of the SR Ca2+ pump, on the steady-state force-[Ca2+]i relationship. The instantaneous force-[Ca2+]i relationships appeared sigmoidal (EC50 and Hill coefficient, 98.8+/-32.7 nM and 2.47+/-0.20, mean +/- SD, respectively), as did the curves superimposed after 500 ms following the start of stimulation, indicating that the force-[Ca2+]i relationship had reached a steady state at that time. Also, the maximum activated force (Fmax) was estimated using the steady-state force-[Ca2+]i relationship. Prolonged stimulus trains, decreasing the interval between recurrent trains from 5 to 2.5 s, and cyclopiazonic acid each increased the measured EC50 without changing Fmax. The EC50 correlated strongly with averaged [Ca2+]i over time. We conclude that the steady-state force-[Ca2+]i relationships in the OOM indicate cooperation between force generation and Ca2+ binding by the myofilaments. Our data also suggest the existence of a novel Ca2+-dependent mechanism which reduces Ca2+ sensitivity and accelerates relaxation of lobster cardiac muscle myofilaments.

Excitation-contraction coupling in cardiac muscle of lobster (Homarus americanus); the role of the sarcolemma and sarcoplasmic reticulum.

The T-tubules and sarcoplasmic reticulum (SR) serving excitation-contraction (EC) coupling in lobster (Homarus americanus) cardiac muscle are similar to those in mammalian myocardium. Tetanic contraction is elicited by a burst of action potentials from the cardiac ganglion. In this study we evaluated the roles of the sarcolemma and SR in EC coupling of the ostial valve muscle (orbicularis ostii m. or OOM) of lobster heart. The OOM was mounted in a bath with saline on a microscope stage; force was measured by strain gauge. [Ca2+]i was measured using iontophoretically micro-injected fura-2 salt. Peak [Ca+]i, peak tetanic force and time to peak [Ca2+]i increased with that of stimulus train duration (TD), to a maximum at a TD of 500 ms. Force increased with [Ca2+]. Cd2+ reduced force by 90%; ryanodine and caffeine reduced tetanic [Ca2+]i transients by 80% and 70%, and force by 90% and 80%, respectively. Ryanodine, caffeine and cyclopiazonic acid slowed the decline of [Ca2+]i and force during relaxation. Relaxation required [Na+]o. The rate of decline of [Ca2+]i appeared to be a sigmoidal function of the [Ca2+]i and increased for any [Ca2+]i with TD. Inactivity slowed relaxation of force; stimulation accelerated relaxation. These data suggest important contributions of Ca2+ transport both across the sarcolemma and across the SR membrane during EC-coupling of lobster cardiac muscle, while average cytosolic [Ca2+]i regulates the rate of [Ca2+]i elimination during relaxation.

Stretch and quick release of rat cardiac trabeculae accelerates Ca2+ waves and triggered propagated contractions.

Rapid shortening of active cardiac muscle [quick release (QR)] dissociates Ca2+ from myofilaments. We studied, using muscle stretches and QR, whether Ca2+ dissociation affects triggered propagated contractions (TPCs) and Ca2+ waves. The intracellular Ca2+ concentration was measured by a SIT camera in right ventricular trabeculae dissected from rat hearts loaded with fura 2 salt, force was measured by a silicon strain gauge, and sarcomere length was measured by laser diffraction while a servomotor controlled muscle length. TPCs (n = 27) were induced at 28 degrees C by stimulus trains (7.5 s at 2.65 +/- 0.13 Hz) at an extracellular Ca2+ concentration ([Ca2+]o) = 2.0 mM or with 10 microM Gd3+ at [Ca2+]o = 5.2 +/- 0.73 mM. QR during twitch relaxation after a 10% stretch for 100-200 ms reduced both the time between the last stimulus and the peak TPC (PeakTPC) and the time between the last stimulus and peak Ca2+ wave (PeakCW) and increased PeakTPC and PeakCW (n = 13) as well as the propagation velocity (Vprop; n = 8). Active force during stretch also increased Vprop (r = 0.84, n = 12, P < 0.01), but Gd3+ had no effect (n = 5). These results suggest that Ca2+ dissociation by QR during relaxation accelerates the initiation and propagation of Ca2+ waves.

A 2D finite element model of the interventricular septum under normal and abnormal loading.

The interventricular septum is the structure that separates the left and right ventricles of the heart. Under normal loading conditions, it is concave to the left ventricle, but under abnormal loading the septum flattens and occasionally inverts. In the past, the septum has frequently been modelled as integral to the left ventricle with the effects of pressure from the right ventricle being ignored. Under abnormal loading, the septum has been described as behaving equivalent to a "flapping sail". There has been no consideration of structural behaviour under these conditions. A 2-D plane stress FE model of the septum was used to investigate the difference in structural behaviour of the septum during diastole between normal and abnormal loading. The biaxial stress patterns that develop are distinctively disparate. Under normal loading, the septum behaves much like a thick-walled cylinder subject to internal and external pressure, with the resulting stresses being circumferential tension and radial compression, both varying with radius. These stresses are very low throughout most of diastole. However, under abnormal loading, the septum behaves in an arch-like fashion, with high compressive stresses almost circumferential in direction, combined with radial compression. We conclude that right ventricular pressures cause bending effects in the wall of the heart, and that under abnormal loading, the compressive stresses that develop in the septum may lead to an understanding of certain, previously unexplained, pathological conditions.

A novel technique for measurement of pericardial pressure.

To determine whether pericardial liquid pressure accurately measures pericardial constraint, we developed a technique in which a catheter was positioned perpendicular to the epicardial surface. This device, which occupies little or no pericardial space, couples the thin film of liquid to a transducer. In six open-chest dogs, we also measured left ventricular (LV) end-diastolic pressure (LVEDP) and anteroposterior and septum-to-free wall diameters. LVEDP was raised incrementally to approximately 25 mmHg by saline infusion. With the use of the product of the two diameters as an index of area (A(LV)), LVEDP-A(LV) relationships were obtained with the pericardium closed and again after the pericardium had been widely opened to obtain the isovolumic difference in LVEDP (DeltaLVEDP). In all dogs, the technique yielded values of pericardial pressure equal to DeltaLVEDP as well as equal to that measured using a previously placed balloon transducer in the same location and at the same A(LV). We conclude that, when the pressure of the pericardial liquid is appropriately measured, it (in addition to the balloon-measured contact stress) defines the diastolic constraining effect of the pericardium. Furthermore, we suggest that earlier measurements of pericardial "liquid pressure" were low, due to an artifact of measurement.

Effect of transient stretch on intracellular Ca2+ during triggered propagated contractions in intact trabeculae.

Transient stretch of cardiac muscle during a twitch contraction may dissociate Ca2+ from myofilaments into the cytosol at the moment of quick release of the muscle. We studied the effect of stretch and quick release of trabeculae on changes in intracellular Ca2+ ([Ca2+]i) during triggered propagated contractions (TPCs). Trabeculae were dissected from the right ventricle of 9 rat hearts. [Ca2+]i was measured using electrophoretically injected fura-2. Force was measured using a silicon strain gauge and sarcomere length was measured using laser diffraction techniques. Reproducible TPCs (n = 13) were induced by trains of electrical stimuli (378 +/- 19 ms interval) for 7.5 s at [Ca2+]o of 2.0 mM (27.9 +/- 0.2 degrees C). The latency of the TPC force and the underlying increase in [Ca2+]i was calculated from the time (TimeF) between the last stimulus and the peak of TPC force (PeakF), or the time (TimeCa) between the last stimulus and the peak of the increase in [Ca2+]i during the TPCs (PeakCa). As a result of a 10% increase in muscle length for 150-200 ms during the last stimulated twitches, TimeF and TimeCa decreased and PeakF and PeakCa increased significantly (n = 13). In addition, transient stretch sometimes induced a twitch contraction subsequent to the accelerated TPC and its underlying increase in [Ca2+]i. These results suggest that Ca2+ binding and dissociation from the myofilaments by the stretch and quick release of muscle may modulate the TPC force and the underlying increases in [Ca2+]i and play an important role in the induction of arrhythmias.

Damage induced arrhythmias: mechanisms and implications.

Little is known about the role played by non-uniform myocardial stress and strain distributions and by non-uniform excitation contraction coupling in mechanisms underlying the premature beats that initiate an arrhythmia. We will review the evidence in support of a mechanism in which both non-uniform contraction and increased Ca2+ load of cells adjacent to acutely damaged cells are essential in the "spontaneous" generation of Ca2+ transients during the relaxation phase of the electrically driven twitch. The putative mechanism of initiation of the propagating Ca2+ waves involves feedback of rapid length (or force) changes to dissociation of Ca2+ from the contractile filaments. A novel aspect of this concept is that these mechanically elicited Ca2+ transients induce propagating Ca2+ waves that travel into the adjacent normal myocardium and cause after-depolarizations, which, in turn, may cause premature action potentials. These premature action potentials will further load the cells with Ca2+, which promotes the subsequent generation of propagating Ca2+ transients and leads to triggered arrhythmias. The damage-induced premature beats may also initiate re-entry arrhythmias in non-uniform myocardium. These observations strongly support the concept that abnormal cellular Ca2+ transport plays a crucial role in the initiation of arrhythmias in damaged and non-uniform myocardium.

Ca(2+)-dependence of passive properties of cardiac sarcomeres.

Rat cardiac trabeculae constitute a well-known experimental model in studies of cardiac contraction at the sarcomere level. Continuous measurement of length of the sarcomeres (SL) by laser diffraction technique permits one to monitor the active shortening of the contractile units during generation of force. When the preparation is stimulated repetitively (0.5 Hz) by electrical pulses, active shortenings are separated by periods corresponding approximately to the diastolic interval in the heart and wherein normally no major contractile event would have been expected. In contrast to this expectation, studies conducted with high-resolution (2-4 nm) SL measurements technique revealed that sarcomeres continuously lengthened (by 10-60 nm) from the end of twitch relaxation to the next stimulation. Such lengthening resulted from an internal expansion of the sarcomere and not from stretch exerted by extra-sarcomeric sources. We further characterized diastolic changes by measuring sarcomere stiffness (Sarc-Stiff) estimated from the response to short bursts (30 ms) of sinusoidal perturbations (frequency: 500 Hz) at 5 moments of the resting interval separating twitches. Sarc-Stiff increased continuously by approximately 30% during the diastolic interval (29 degrees C, pH: 7.4, [Ca2+]o = 1 mM). We then investigated during the same period the intracellular dynamics of Ca2+, as a major determinant of sarcomere motions in muscle. Intracellular free-Ca2+ concentration ([Ca2+]i) was measured continuously in trabeculae microinjected with the fluorescent Ca(2+)-probe Fura-2 and stimulated at 0.5 Hz. It appeared that the Ca(2+)-transient, which drives the twitch, did not end with the apparent relaxation of the force. Instead, [Ca2+]i kept decreasing in an exponential manner throughout the diastolic interval. At [Ca2+]o = 1 mM, [Ca2+]i decreased from 230 to 90 nM with a time constant of approximately 250 ms. The similarity in time courses of Ca(2+)-decline and of Sarc-Stiff increase suggested that properties of resting sarcomeres were related to [Ca2+]i in the sub-micromolar range. In order to examine this possibility, Sarc-Stiff was measured in chemically skinned trabeculae, i.e. in a preparation allowing control of [Ca2+] surrounding the sarcomeres. Sarc-Stiff was measured at different [Ca2+] from 1 to 450 nM. We found that 1) below 70 nM, Sarc-Stiff was independent on [Ca2+], 2) between 70 and 200 nM, i.e., approximately the range wherein [Ca2+]i decreased during diastole in intact muscle, Sarc-Stiff decreased by approximately 50% with increase of [Ca2+] and 3) above 200 nM, Sarc-Stiff increased steeply with increase of [Ca2+] as was expected from Ca(2+)-dependent attachment of cross-bridges between actin and myosin. The data fitted accurately to the sum of 2 sigmoid functions: 1) at [Ca2+] < 200 nM, Sarc-Stiff decreased with increase of [Ca2+] with a Hill coefficient (nH) = -2.6 and [Ca2+] at half maximal activation (EC50) = 0.16 +/- 0.013 microM; 2) at [Ca2+] > 200 nM, Sarc-Stiff increased with [Ca2+] (nH: 2.1; EC50:3.4 +/- 0.3 microM) consistent with Ca(2+)-dependent attachment of cross-bridges. It was possible to reproduce the diastolic variation of Sarc-Stiff observed in intact muscle by using the time course of [Ca2+]i in the Sarc-Stiff--[Ca2+] relationship determined from skinned trabeculae. We conclude that physical properties of the sarcomeres are inversely related to Ca2+ below 200 nM, i.e., in a range of concentrations where the myocytes operate during diastole while the influence of cross-bridges is negligible.

The effect of sarcomere shortening velocity on force generation, analysis, and verification of models for crossbridge dynamics.

The study tests the hypothesis that the transition rate (G) of the cardiac cross-bridge (XB) from the strong force generating state to the weak state is a linear function of the sarcomere shortening velocity (V(SL)). Force (F) was measured with a strain gauge in six trabeculae from the rat right ventricle in K-H solution [(Ca]0 = 1.5 mM, 25 degrees C). Sarcomere length (SL) was measured with laser diffraction techniques. Twitch F at constant SL and the F response to shortening at constant V(SL) (0-8 microm/s; deltaSL 50-100 nm) were measured at varied times during the twitch. The F response to shortening consisted of an initial fast exponential decline (tau = 2 ms), followed by a slow decrease of F. The instantaneous difference (deltaF) between the isometric F (F(M)) and F during the slow phase depended on the duration of shortening (deltat), the instantaneous F(M) and V(SL). deltaF = G1 x F(M) x deltat x V(SL) x (1 -V(SL)/V(MAX)), where V(MAX) is the unloaded V(SL) and G1 was 6.15+/-2.12 microm(-1) (mean +/- s.d.; n=6). DeltaF/F(M) was independent of the time onset of shortening. The linear interrelation between deltaF and V(SL) is consistent with the suggested feedback, whereby XB kinetics depends on V(SL). This feedback provides a more universal description of the interrelation between shortening and force, as well as the observed linear relation between energy consumption and the mechanical energy output.

Ca2+ waves during triggered propagated contractions in intact trabeculae. Determinants of the velocity of propagation.

During triggered propagated contractions, Ca2+ waves travel along cardiac trabeculae with a constant velocity (Vprop) ranging from 0. 34 to 5.47 mm/s. To explore the determinants of Vprop, we studied (1) the relationship between [Ca2+]i and Vprop and (2) the effect of low concentrations of caffeine on Vprop. Trabeculae were dissected from the right ventricle of rat hearts. [Ca2+]i was measured using electrophoretically injected fura-2 and an image-intensified CCD camera. Force was measured using a silicon strain gauge, and sarcomere length was measured using laser diffraction techniques. After induction of reproducible Ca2+ waves by trains of electrical stimuli (2.5 Hz) at 21.9+/-0.2 degrees C, the number of stimuli or [Ca2+]o was varied in 9 trabeculae. In 5 trabeculae, the effects of caffeine (0.1 to 1.0 mmol/L) at [Ca2+]o of 2.2+/-0.3 mmol/L were determined. All images were recorded under stable conditions of wave propagation. The increment in [Ca2+]i during the last electrically stimulated transient (DeltaCaT) and [Ca2+]i just before onset of the Ca2+ waves (CaD) were used to estimate the Ca2+ loading of the sarcoplasmic reticulum (SR) and the myoplasm, respectively. The ratio (DeltaCaW/DeltaCaT) of the [Ca2+]i increment during the waves (DeltaCaW) to DeltaCaT was used to estimate the probability of opening of the SR-Ca2+ release channel during wave propagation. As a result of an increase of the number of stimuli or [Ca2+]o, Vprop increased in proportion to (1) DeltaCaT (r=0.82); (2) CaD (r=0.88); (3) DeltaCaW (r=0.85); and (4) DeltaCaW/DeltaCaT (r=0.74). The addition of caffeine (

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.

Ca(2+)-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.