Effects of Halothane and Isoflurane on the Intracellular Ca²⁺Transient in Ferret Cardiac Muscle

All experimental procedures were reviewed and approved by the Animal Care and Use Committee of Mayo Foundation, with protocols completed in accordance with the National Institutes of Health guidelines (Bethesda, Maryland) and in accordance with the Guide for the Care and Use of Laboratory Animals (Institute of Laboratory Animal Resources Commission on Life Sciences, National Research Council, Washington, DC). We used papillary muscles from the right ventricle of adult male ferrets (weight 1,100–1,500 g, aged 16–19 weeks). The animals were anesthetized with sodium pentobarbital (100 mg/kg intraperitoneally), and the heart was removed quickly through a left thoracotomy. Immediately after cardiectomy, the heart was placed in a warm, (30°C) oxygenated physiologic solution for a few minutes, during which the solution was changed several times. The hearts kept beating vigorously throughout this period and during dissection of papillary muscles, which was performed during generous superfusion of the opened right ventricle. Suitable papillary muscles were excised and mounted horizontally in a temperature-controlled (30°C) muscle chamber filled with a physiologic salt solution made up in glass-distilled water and having the following composition: Na⁺: 140 mm; K⁺: 5 mm; Ca²⁺: 2.25 mm; Mg²⁺: 1 mm; Cl⁻: 103.5 mm; HCO³⁻: 24 mm; HPO⁴²⁻: 1 mm; SO⁴²⁻: 1 mm; acetate: 20 mm; and glucose: 10 mm. This solution was equilibrated with 95% O²and 5% CO², and the pH was 7.4. Suitable preparations were selected on the basis of the following criteria: length at which twitch active force was maximal (L^max) 3.5 mm or more, mean cross-sectional area 1.2 mm²or less, and ratio of resting to total force 0.25 or less. The tendinous end of each muscle was tied with a thin, braided polyester thread (size 9.0, Surgical Tevdek; Deknatel, Fall River, ME) to the lever of a force-length servo transducer (University of Antwerp, Antwerp, Belgium), with an equivalent moving mass of 250 mg and a static compliance of 0.28 μm/millinewton (mN). The ventricular end of each muscle was held in a miniature Lucite (Dupont, Wilmington, DE) clip with a built-in platinum punctate electrode; two platinum wires were arranged longitudinally, one on each side of the muscle, and served as an anode during punctate stimulation. Rectangular pulses 5 ms in duration were delivered using a Grass S88D stimulator (Astro-Med, Inc., West Warwick, RI) at intervals of 4 s. Stimuli 10% above threshold (range 1–12 V) were used to minimize the release of endogenous norepinephrine by the driving stimuli. The muscles were made to contract in alternating series of four isometric and four isotonic twitches at preload only during a 1- to 2-h period of stabilization before the onset of further procedures. The solution was changed at least once during this stabilization period. At the end of this stabilization period, initial muscle length was set at L^max, stimulation was discontinued, and aequorin was microinjected. All ferret papillary muscles were pretreated with 10⁻⁷m (±)-bupranolol HCl before the onset of the experiment, to abolish any β-adrenergic effects.

Methods of delivery of anesthetic have been described previously. 1Anesthetic vapor concentration was measured continuously using a calibrated acoustic gas analyzer. 1The concentration of halothane and isoflurane in fluid was measured by a gas chromatograph (Hewlett Packard 5880A, Palo Alto, CA). The partial pressure of anesthetic in fluid followed closely the imposed changes of anesthetic vapor concentration in the gas phase.

After the initial 1- to 2-h stabilization period, electric stimulation was discontinued and multiple superficial cells were microinjected with the Ca²⁺-regulated photoprotein aequorin 8to allow for subsequent detection of the [Ca²⁺]ⁱtransient. Aequorin (> 95% pure) was donated by John R. Blinks, M.D. (Friday Harbor Laboratories, University of Washington, Friday Harbor, WA). In brief, 1 μl filtered aequorin solution (2 mg/ml in 5 mm piperazine-N,N′-bis(ethanesulfonic acid) (PIPES), 150 mm KCl; pH 7.0) was loaded in a glass micropipette pulled from capillary tubing with an internal filament (TW150F-4; World Precision, Sarasota, FL) to a resistance of 5–10 MΩ. The pipette was inserted in a holder that provided for an airtight seal at the butt of the pipette with a Teflon (Ineos Acrylics Inc., Cordova, TN) collar. A platinum wire inside the pipette made electrical contact with the solution in the electrode tip. A superficial cell was impaled by the pipette mounted on a micromanipulator, until a reasonable and stable membrane potential was obtained. Nitrogen pressure was applied to the inside of the pipette. Injection was discontinued at the first sign of appreciable changes (3–7 mV) in resting membrane potential. The electrode then was withdrawn and another cell impaled for microinjection of aequorin. It usually was necessary to microinject 30–100 cells. After microinjection, muscles were not stimulated for 2 h, to allow for resealing of the plasma membranes of the injected cells. The muscles then were transferred carefully for mounting in a vertical muscle chamber that allows for simultaneous detection of variables of contractility and of aequorin luminescence. 9The aequorin-injected muscle was positioned in a narrow glass extension at the base of the organ chamber at one focal point of a bifocal ellipsoidal reflector. The photocathode of a bialkali photomultiplier (9235QA; Electron Tubes, Inc., Rockaway, NJ) resided at the other focal point. Blinks 9,10designed this optical arrangement, known as the “vertical egg,” which optimized light collection and ensured that the recorded light signals were free of motion artifacts. It usually was necessary to average luminescence and force signals of 16–256 twitches to obtain a satisfactory signal-to-noise ratio in aequorin luminescence signals. We quantified peak systolic aequorin luminescence and time to peak aequorin luminescence. The decrease of the aequorin signal was quantified by measuring the time from the stimulus to the time at which aequorin luminescence decreased to 25% of its peak value (t^L25), and the slope of the logarithm of aequorin luminescence from 50% peak to 10% peak (k^50/10). The measurement of this slope is based on the facts that the decrease of aequorin signals in isometric (but not isotonic 10) twitches follows an exponential decrease and aequorin luminescence is approximately a 2.5-power function of [Ca²⁺]ⁱ.

Two experimental protocols were used to evaluate the mechanism of the inotropic effect of halothane and isoflurane. Each muscle served as its own control. In group 1, muscles (n = 16) were exposed to incremental concentrations of anesthetic (for halothane, between 0 and 1.5% (vol/vol) in steps of 0.5%; for isoflurane, from 0 and 2.25% (vol/vol) in steps of 0.75%). This design allowed us to compare inotropic effects at exact equipotent anesthetic concentrations because each step corresponded to an increment of 0.5 minimum alveolar concentration (MAC) of the respective anesthetic in the ferret at 37°C. 1When contractility reached a new steady state and maintained it for 5 min (usually after 15–30 min of equilibration with a particular anesthetic concentration), variables of contraction and relaxation were determined from isometric twitches and from isotonic twitches at the preload of L^max. From isometric twitches we measured peak developed force, time to peak force, and time from peak force to half-isometric relaxation. From isotonic twitches at the preload of L^max, we measured peak shortening, time to peak shortening, and peak velocity of lengthening. Signals of force, length, velocity, and aequorin luminescence were averaged using a digital storage oscilloscope (4094C; Nicolet, Madison, WI); averaged signals were stored on 5.25-in floppy disks and transferred to a personal computer, in which amplitude and time variables of each waveform of interest were measured.

For muscles in group 2 (n = 23), we determined whether halothane and isoflurane altered myofibrillar Ca²⁺sensitivity. After measurement of control variables of the isometric twitch, muscles were exposed to 0.5, 1.0, or 1.5 MAC of either halothane or isoflurane. When aequorin luminescence and peak isometric force reached steady state, extracellular Ca²⁺([Ca²⁺]^o) was increased rapidly by adding small aliquots of a concentrated CaCl²solution (112.5 mm) to the bathing solution, until peak developed force was equal to that in the control twitch. In four experiments we needed to add 10–50 μl EGTA (0.2 m, pH 7.00) to match peak force to the control twitch amplitude precisely. Free [Ca²⁺]^oin the Ca²⁺back-titrated twitch was calculated using a program by Fabiato. 11This protocol of “Ca²⁺back-titration” allowed us to compare aequorin luminescence signals in the absence (control) and presence of volatile anesthetics at equal peak developed force. If the magnitude of the [Ca²⁺]ⁱtransient in the presence of anesthetic (at peak force equal to that in control) is different from that in the control twitch, it is likely that myofibrillar Ca²⁺sensitivity changed in the presence of anesthetic. This experimental construct has been analyzed quantitatively using a simple mathematical derivative model to assess the relative effects of anesthetic on Ca²⁺availability versus  myofibrillar Ca²⁺sensitivity.

The approach of back-titrating twitches in the presence of drugs to the same twitch height provides for a crude qualitative assessment of changes in Ca²⁺sensitivity. Our aim was to assess quantitatively possible changes in Ca²⁺sensitivity in relation to effects of anesthetic on myoplasmic Ca²⁺delivery (mainly SR release), SR Ca²⁺uptake, and Ca²⁺binding to various Ca²⁺binding sites (troponin C [TnC], calmodulin) from measurements of free [Ca²⁺]ⁱand force alone. We used the deductive procedure of Baylor et al.  12to derive SR Ca²⁺release within the context of a multicompartment model with the following compartments: free [Ca²⁺]ⁱ, Ca²⁺bound to TnC and its force dependence 13,14, Ca²⁺bound to calmodulin, and SR Ca²⁺release and uptake. At this time all compartments are characterized, and one can predict the time course of the Ca²⁺transient if one were to change one or more of the compartment values. Rate constants for each of the compartments were taken from the literature. 9,15We calculated the amplitude and time course of the Ca²⁺transient for many combinations of new values of SR Ca²⁺release and myofibrillar Ca²⁺sensitivity (k^off(TnC.Ca)) by solving differential equations 2, 3, and 9( appendix) that govern the fate of intracellular Ca²⁺in myocardium using Runge–Kutta fourth-order numeric integration. This analysis was performed to simulate the Ca²⁺transient of the isometric twitch in anesthetic and high [Ca²⁺]^o. The waveform of SR Ca²⁺release (derived from the control isometric twitch) and values of myofibrillar Ca²⁺sensitivity were changed in very small steps, and aequorin luminescence signals were generated until a unique combination of SR Ca²⁺release and myofibrillar Ca²⁺sensitivity was found that produced a least-squares-differences simulation of the Ca²⁺transient in high [Ca²⁺]^oand anesthetic, and  a Ca²⁺occupancy of TnC with the same peak as in the control twitch. This procedure yielded a value of myofibrillar Ca²⁺sensitivity in anesthetic. Ca²⁺availability in anesthetic was found by deriving the SR release value that gave the best least-squares fit to the aequorin signal in anesthetic in control [Ca²⁺]^oand kept Ca²⁺sensitivity at the same level as found earlier.

Concentration–response relations between anesthetic concentration and measured variables of contractility and aequorin luminescence were tested for differences with repeated-measures analysis of variance; pairwise comparisons with control were performed with paired Student t  tests with Bonferroni corrections. For each variable, halothane and isoflurane were compared with the Student t  test. Aequorin luminescence and peak developed force in Ca²⁺back-titration experiments were analyzed using repeated-measures analysis of variance; pairwise comparisons with control were performed using paired Student t  tests with Bonferroni corrections. Relative values of Ca²⁺sensitivity and availability for a given anesthetic were compared using paired Student t  tests. Absolute values of aequorin luminescence varied from muscle to muscle, depending on the amount of aequorin injected, the number and location of cells injected, the optical conditions of the experiment, and the high voltage on the photomultiplier. Therefore, percentage values of aequorin luminescence and relative changes are reported, in which each muscle serves as its own control. Differences were considered significant at the P < 0.05 level. Data are presented as the mean ± SD.

Figure 1illustrates a typical concentration–response experiment to incremental concentrations of isoflurane on aequorin luminescence and contractility in isometric twitches (top) and in isotonic twitches at the preload of L^max(bottom). Tables 1 and 2summarize the values of variables of contractility and aequorin luminescence during control and cumulative concentration–response experiments involving halothane and isoflurane during isometric and isotonic twitches. Halothane decreased developed force and peak aequorin luminescence more than isoflurane (P < 0.01) in a concentration-dependent, reversible manner. Halothane (at 1.0 and 1.5 MAC) but not isoflurane slowed the increase of the aequorin luminescence to peak values, as demonstrated by the increase in time to peak light (table 1). Halothane and isoflurane decreased time to peak force and time from peak force to half-isometric relaxation, as previously was demonstrated 1,7without differences among anesthetics. Halothane and isoflurane caused a concentration-dependent, reversible decrease in peak shortening and peak aequorin luminescence in isotonic twitches at the preload of L^max(fig. 1, table 2). Although there was no difference of effect among anesthetics on peak shortening, halothane decreased peak aequorin luminescence more than isoflurane (P < 0.05). Time to peak light was not changed significantly. Time to peak shortening was prolonged by halothane only (table 2). Maximal velocity of lengthening was decreased in a concentration-dependent fashion by halothane and isoflurane with no difference of effect between halothane and isoflurane. Halothane but not isoflurane caused a slight prolongation of the decrease of aequorin luminescence measured by t^L25(tables 1 and 2), yet the slope k^50/10of the logarithm of aequorin luminescence from 50% peak to 10% peak was not changed in isometric twitches (table 1).

A typical isometric Ca²⁺back-titration experiment is shown in figure 2. Aequorin luminescence and isometric force were measured in control (fig. 2, left) and during exposure to halothane 1.0% (fig. 2, middle), both in [Ca²⁺]^o2.25 mm. [Ca²⁺]^owas increased rapidly until developed force in halothane was equal to that in the control twitch. At equal peak developed force, aequorin luminescence was higher in the presence of halothane and elevated [Ca²⁺]^o(fig. 2, right) than in its absence (fig. 2, left). Figure 3shows that peak aequorin luminescence was higher in back-titrated twitches than in controls at equal peak developed force at all concentrations of halothane and isoflurane evaluated. To reach force equal to that in the control, [Ca²⁺]^oneeded to be increased more at higher anesthetic concentrations (fig. 3).

We analyzed the isometric Ca²⁺back-titration experiments with the following assumptions: Peak Ca²⁺occupancy of TnC is the same at equal developed force with or without anesthetic, and the rate of Ca²⁺uptake by the SR is the same with or without anesthetic. These assumptions are addressed in Discussion. Figure 4shows a typical Ca²⁺back-titration experiment to isoflurane 1.5% (fig. 4, top) and part of the analysis procedure (fig. 4, center and bottom). We simulated aequorin luminescence signals that would match the amplitude and time course of aequorin luminescence in anesthetic in high [Ca²⁺]^o(fig. 4, top right). To this effect, we varied SR release and k^off(TnC.Ca)over wide ranges to generate aequorin luminescence signals of different amplitudes and time courses. We calculated and plotted the sum of squares of the differences between each simulated and experimentally observed aequorin luminescence signal, Σ(L^s− L^o)², as a function of SR release and the variable B (which determines k^off(TnC.Ca)); this is shown in figure 5(top). Any of the combinations of SR release and B on the line of the minima (curved line in trough of the surface) is a least-squares solution that generates an aequorin luminescence signal that best fits the experimentally measured aequorin luminescence signal (fig. 4, top and center right). Next we calculated and plotted the difference (in absolute values) between simulated and control peak Ca²⁺occupancy of TnC, | Δ^s-o[Ca.T]^max| , as a function of SR release and k^off(TnC.Ca)(fig. 5, bottom). At equal peak force with and without anesthetic, peak TnC Ca²⁺occupancies should be the same (fig. 4, bottom). This condition is fulfilled along the line of minima in figure 5(bottom). The intersection of the least-squares luminescence difference line (fig. 5, top) and the line of minimal differences in Ca²⁺occupancy of TnC (fig. 5, bottom), both plotted in figure 6, defines the unique combination of values of SR release and k^off(TnC.Ca)for which simulated aequorin luminescence is the best least-squares fit to the measured aequorin signal of the back-titrated twitch and  peak Ca²⁺occupancies of TnC in control and in anesthetic plus high [Ca²⁺]^oare the same at equal peak force. The final step was to find out what the myoplasmic Ca²⁺delivery was in anesthetic in control [Ca²⁺]^o(fig. 4, top, middle). The effect of anesthetic in controls [Ca²⁺]^oon myoplasmic Ca²⁺delivery (mostly SR Ca²⁺release) was found by searching the least-squares fit to the experimentally measured aequorin luminescence signal (fig. 4, middle) by varying SR release only and using the k^off(TnC.Ca)value found previously for the aequorin luminescence signal in the back-titrated twitch.

Figure 7summarizes the analyses for all Ca²⁺back-titration experiments and shows the relative effects of halothane and isoflurane on myoplasmic Ca²⁺availability and on myofibrillar Ca²⁺sensitivity. Myofibrillar Ca²⁺sensitivity was defined as 1/k^off(TnC.Ca)and was expressed as a percentage of the value in the nonanesthetic control. The results are that halothane and isoflurane decrease myoplasmic Ca²⁺availability in a concentration-dependent manner; halothane decreases myoplasmic Ca²⁺availability more than isoflurane (P < 0.05); halothane and isoflurane decrease myofibrillar Ca²⁺sensitivity to extents that are not statistically different from each other; the anesthetic-induced decrease of myofibrillar Ca²⁺sensitivity is not concentration-dependent and is fully present already at 0.5 MAC halothane and 1.0 MAC isoflurane; halothane decreases myoplasmic Ca²⁺availability more than myofibrillar Ca²⁺sensitivity (P < 0.05); and isoflurane decreases myoplasmic Ca²⁺availability and myofibrillar Ca²⁺sensitivity to the same relative extent except at 1.5 MAC, at which isoflurane decreases Ca²⁺availability more than Ca²⁺sensitivity.

We used the photoprotein aequorin as indicator for [Ca²⁺]ⁱbecause of the demonstrated absence of motion artifacts in cardiac muscle, its lack of toxicity, its exclusive cytoplasmic localization, its wide range of Ca²⁺sensitivity, and its lack of effect on contractility. 9,10Drawbacks are the nonlinear nature of the Ca²⁺-luminescence relation, and the relatively slow rate constant of Ca²⁺binding to aequorin (20 s⁻¹at 21°C), which would cause aequorin luminescence to lag behind and underestimate rapidly rising Ca²⁺transients. In cardiac muscle, however, twitches and [Ca²⁺]ⁱtransients are sufficiently slow that aequorin kinetic delays most likely do not represent a distorted view of the [Ca²⁺]ⁱtransient. The nonlinear Ca²⁺-luminescence relation is sensitive to Ca²⁺gradients, but this concern is obviated by a recent study in which no subsarcomeric Ca²⁺gradients were detected during the cardiac Ca²⁺transient in intact rat ventricular myocytes. 16Some [Ca²⁺]ⁱgradients have been observed in cat atrial but not cat and rabbit ventricular muscle most likely because of the absence of T tubules in atrial tissue, which makes intracellular Ca²⁺movements diffusion-dependent. Our observations regarding the effects of halothane and isoflurane on the amplitude and time course of the [Ca²⁺]ⁱtransient detected with aequorin are in general agreement with those made in cat, 17rat, 18,19and guinea pig papillary muscle. 2Halothane but not isoflurane lengthened the declining phase of the aequorin luminescence signal. A prolonged aequorin signal and the abbreviation of isometric relaxation suggest a decrease in Ca²⁺sensitivity. With a smaller Ca²⁺transient, however, the declining phase of the corresponding aequorin signal is slightly longer, because of the nonlinear nature of the relation between aequorin luminescence and [Ca²⁺]ⁱ.

The availability of myoplasmic Ca²⁺ions for the activation of contraction is determined by initial trigger Ca²⁺influx at the beginning of the action potential; Ca²⁺release from the SR; Ca²⁺uptake by the SR Ca²⁺adenosine triphospate–dependent pump; Ca²⁺entry through sarcolemmal L-type Ca²⁺channels; sarcolemmal Na⁺-Ca²⁺exchange; and the sarcolemmal Ca²⁺adenosine triphosphatase export pump. SR release and uptake of Ca²⁺ions are quantitatively the most important Ca²⁺handling processes in mammalian ventricular myocardium. 20Na⁺-Ca²⁺exchange contributes to contractile activation during early systole and competes with the SR to remove Ca²⁺from the cytoplasm during relaxation and diastole. The SR Ca²⁺pump and Na⁺–Ca²⁺exchange account for 70 and 27%, respectively, of the time course of the [Ca²⁺]ⁱdecrease. 21The sarcolemmal Ca²⁺adenosine triphosphatase pump and mitochondrial Ca²⁺transport play small roles in the beat-to-beat removal of myoplasmic Ca²⁺. 20,21 

Studies on isolated SR vesicles, single cells, skinned cardiac fibers, and intact papillary muscles suggest that halothane decreases the amount of Ca²⁺in the SR, 22–25resulting in a net loss of Ca²⁺from the SR. Halothane activates the Ca²⁺release channel by increasing the duration of channel-open time; isoflurane has no effect. 26The smaller amount of Ca²⁺released from the SR and the decreased transsarcolemmal Ca²⁺entry may account for the halothane-induced slowing of the increase and later peak of the [Ca²⁺]ⁱtransient (table 1). 25Under physiologic conditions, halothane and to a lesser extent isoflurane caused a small distinct decrease in SR Ca²⁺uptake. 4The effects of halothane on SR Ca²⁺loss, SR Ca²⁺release, and SR Ca²⁺uptake are more pronounced than those of isoflurane; these differences may explain the fact that isoflurane depresses myocardial contractility less than halothane. The slower decrease of [Ca²⁺]ⁱin halothane in guinea pig, 2cat, 17and ferret papillary muscles seen in the current study and in canine Purkyňe fibers 25may result from effects on SR Ca²⁺uptake, Na⁺–Ca²⁺exchange, or myofibrillar Ca²⁺sensitivity.

Myofibrillar Ca²⁺sensitivity in ventricular myocardium has been defined as the contractile response (usually force) to a given [Ca²⁺]ⁱ. 9Changes in myofibrillar Ca²⁺sensitivity can result from one or more of the following processes located “downstream” from the [Ca²⁺]ⁱtransient: affinity of TnC for Ca²⁺, or more specifically the off-rate of the Ca²⁺-specific binding site II of TnC, because the on-rate is very fast and only limited by diffusion 27; interactions of TnC with troponin I and troponin T; the state of phosphorylation of TnI that changes the Ca²⁺affinity of TnC 28; signal transduction through tropomyosin to actin; the interaction of actin with myosin heads through the formation of cross-bridges; regulation of contraction through the myosin light chains 29; and possibly other mechanisms. To assess whether halothane and isoflurane altered myofibrillar Ca²⁺sensitivity, we compared peak aequorin luminescence with and without anesthetic at equal peak force in Ca²⁺back-titration experiments and analyzed [Ca²⁺]ⁱtransients in the context of a simple model comprising SR Ca²⁺release, Ca²⁺uptake, and binding to the principal intracellular Ca²⁺buffers, TnC and calmodulin. For the sake of simplicity, we have lumped all sources of myoplasmic Ca²⁺delivery (transsarcolemmal Ca²⁺current, Na⁺–Ca²⁺exchange, and SR Ca²⁺release) into one myoplasmic Ca²⁺delivery term. Likewise, changes in myofibrillar Ca²⁺sensitivity were expressed conveniently as changes in k^off(TnC.Ca), with the understanding that any of the seven mechanisms listed previously could generate changes in Ca²⁺sensitivity. We used published values for rate constants of association and dissociation of Ca²⁺to the intracellular buffers TnC and calmodulin, 15and a Michaelis–Menten kinetic scheme for SR Ca²⁺uptake. 30,31The values of V^MAX(1,000 μm · l⁻¹· s⁻¹) and K^M(0.3 μm) 32,33were not allowed to vary, because we assumed that the effects of volatile anesthetics on SR Ca²⁺uptake were minimal, which is consistent with data that under physiologic conditions the effects of halothane and isoflurane are limited. 4Even if anesthetics would significantly inhibit SR Ca²⁺uptake, neither the amplitude nor the time course of the aequorin signal would be much affected.

Using the multicompartment computer model, we assessed the impact of isolated changes of SR Ca²⁺release, SR Ca²⁺uptake rate, and Ca²⁺sensitivity on amplitude and time course of the aequorin signal. SR Ca²⁺release is the major determinant of the amplitude of the aequorin signal. Changes in Ca²⁺sensitivity and SR Ca²⁺uptake have much smaller effects. The time course of decrease of aequorin luminescence is most influenced by SR Ca²⁺uptake and changes in Ca²⁺sensitivity. Inhibition of SR Ca²⁺uptake causes, not unexpectedly, a slower decrease of the Ca²⁺transient, but the effect is not very pronounced: a signal 5 ms longer (measured at the midpoint of the decrease) for a 20% decrease in SR Ca²⁺uptake rate (V^MAX) under the experimental conditions of this study. The amplitude of the aequorin signal has a minor effect on the time course of aequorin signals: Larger amplitudes are accompanied by faster and earlier decreases.

To obtain the time course and magnitude of SR release, we used the method of Baylor et al. , 12because the starting point of the analysis is the experimentally measured Ca²⁺transient. In other simulation studies, either a fixed Ca²⁺transient was assumed 33or a fixed pattern of SR release was chosen to result in plausible Ca²⁺transients. 30,32With SR release and various rate constants of uptake and binding known, one can predict the amplitude and time course of aequorin signals if one or more processes, buffer concentrations, or rate constants (e.g. , SR release, V^MAX, K^M, k^off(TnC.Ca)) are changed. Anesthetic-induced decreases in myofibrillar Ca²⁺sensitivity were already maximal at 0.5 MAC halothane and 1.0 MAC isoflurane. This suggests a saturable process, the nature of which remains undefined. In intact muscle, the relation between peak force or peak rate of force development and peak [Ca²⁺]ⁱ(assessed from aequorin luminescence) has been used to assess myofilament Ca²⁺sensitivity. 9,34Accurate determination of myofilament Ca²⁺sensitivity, however, requires that Ca²⁺and contraction have sufficient time to reach equilibrium, at which [Ca²⁺] and binding affinity determine myofilament Ca²⁺binding. Equilibrium conditions are not achieved during a typical twitch at the time of peak [Ca²⁺]ⁱ; peak force occurs later than peak [Ca²⁺]ⁱ, and the relation between peak [Ca²⁺]ⁱand force during a twitch underestimates true myofilament Ca²⁺sensitivity found in steady-state tetanus. 34,35Yet the twitch is the physiologic mode of contraction, and qualitative or quantitative analysis of Ca²⁺sensitivity needs to be interpreted with these considerations in mind. Nevertheless, halothane accelerated isometric relaxation of tetanized cardiac muscle, an effect that reflects decreased myofibrillar Ca²⁺sensitivity. 36 

Volatile anesthetics decrease myofibrillar Ca²⁺sensitivity in skinned cardiac fibers. 5,6Halothane, enflurane, and isoflurane had significantly different effects on the contractile apparatus and Ca²⁺regulatory system depending on the kind and degree of skinning procedure used to disrupt the sarcolemma. 37In those preparations that appeared to be least disrupted during the skinning procedure, volatile anesthetics showed a significant increase  in the Ca²⁺sensitivity. Results from skinned-fiber studies are difficult to relate to findings in intact myocardium, because surface membrane regulation of myofibrillar Ca²⁺sensitivity is lost in most skinned-fiber preparations. Moreover, the probable absence of certain natively present intracellular constituents may account for the observation that myofibrillar sensitivity to Ca²⁺is considerably higher and the pCa-force curve steeper in intact living muscle than in skinned fibers of the same species. 34,35There is a relative paucity of information of anesthetic effects on levels beyond skinned fibers. Halothane did not change 38or slightly increased 39the Ca²⁺affinity of isolated cardiac TnC in vitro , and it decreased k^off(TnC.Ca)in human recombinant cardiac TnC. 40These findings do not explain the decrease in myofibrillar Ca²⁺sensitivity seen in skinned and intact fibers and suggest that halothane acts at sites “downstream” from the binding of Ca²⁺to TnC. In rabbit papillary muscle in Ba²⁺contracture, halothane and isoflurane appeared to decrease the total number of cross-bridges. 41In skinned rat cardiac fibers, halothane decreased the number of strongly attached force-generating cross-bridges and decreased cross-bridge mean force. 42,43If interpreted in a two-state cross-bridge model, these findings reflect a decrease in the cross-bridge apparent attachment rate and an increase in the detachment rate. 43Such changes would keep cross-bridges in the force-generating state for a shorter period of time, and fewer cross-bridges would be attached at any given time even in the presence of an unchanged Ca²⁺transient. Consequently, halothane-induced changes in cross-bridge kinetics in skinned fibers 43would be detected as decreased myofibrillar Ca²⁺sensitivity. The relation between the time it takes for a cross-bridge to complete a cycle and the time Ca²⁺remains bound to TnC also determines myofibrillar Ca²⁺sensitivity. If the cycle rate is decreased, a smaller fraction of TnC Ca²⁺-binding sites must be occupied to keep a given fraction of cross-bridges active 44. The acceleration of isometric relaxation in intact 1,7and skinned 5cardiac fibers therefore can be accounted for by a decreased affinity of TnC for Ca²⁺or a shorter average cross-bridge lifecycle.

The results of this study must be interpreted in the context of the experimental conditions under which they were obtained. Results obtained here at 30°C and a stimulus interval of 4 s may differ from those that could be obtained at conditions closer to physiologic conditions for he animal, 37–38°C and 200 beats/min.

The results of this study and of previous studies in intact papillary muscle 1,2,7and in skinned cardiac fibers 5,6,42,43are consistent with the hypothesis that the negative inotropic effect of halothane is mostly a consequence of a decrease of intracellular Ca²⁺availability with a minor decrease in myofibrillar Ca²⁺sensitivity. The negative inotropic effect of isoflurane results from equal decreases in Ca²⁺availability and Ca²⁺sensitivity. Anesthetic-induced decreases in myofibrillar Ca²⁺sensitivity already are expressed maximally at low anesthetic concentrations. Further insight into the pharmacology of heart muscle will benefit from analytic computational modeling of intracellular Ca²⁺handling mechanisms that also incorporates variables of transsarcolemmal Ca²⁺entry, Na⁺–Ca²⁺exchange, and other contractile regulatory mechanisms in cardiac muscle. 14,45 

The authors thank Dr. John R. Blinks, Friday Harbor Laboratories, University of Washington, Friday Harbor, Washington, for the generous gift of aequorin.

This method quantifies buffering of intracellular Ca²⁺, sarcoplasmic reticulum (SR) Ca²⁺release and uptake, and free [Ca²⁺]ⁱ, based on experimentally recorded aequorin signals and published rate constants. 9,15The analysis consists of the following steps:

• 1. convert aequorin luminescence signal to [Ca²⁺]ⁱ

The recorded aequorin luminescence signal is converted to [Ca²⁺]ⁱby an equation 9that relates [Ca²⁺]ⁱ(in m) to fractional luminescence (f.l.):

in which K^TR= 154.8 and K^R= 6.35 × 10⁶. 9 

• 2. calculate Ca²⁺bound to TnC (Ca.T) and to calmodulin (Ca.C)

From the law of mass action one obtains:equations 2 and 3in which T = total troponin (70 μm); Ca.T = troponin occupied with Ca²⁺; C = total calmodulin (24 μm); and Ca.C = calmodulin occupied with Ca²⁺. The on- and off-rates for binding of Ca²⁺to TnC and to calmodulin are, respectively, k^on(TnC.Ca)= 3.9 × 10⁷m⁻¹· s⁻¹; k^off(TnC.Ca)= a function of force (78.4 s⁻¹at 0 fractional force; see Section 3); k^on(C.Ca)= 10⁸m⁻¹· s⁻¹; and k^off(C.Ca)= 238 s⁻¹. These calculations are performed initially for equilibrium conditions at rest to determine initial [Ca.T] and [Ca.C], values that then are used at time 0 in equations 2 and 3.

• 3. force dependence of affinity of TnC for Ca²⁺

The rate of release of Ca²⁺from TnC is slowed by the presence of cross-bridges. k^off(TnC.Ca)was calculated from a variety of equations (linear, exponential, logarithmic) that related k^off(TnC.Ca)to force. The best fit to experimental aequorin (and [Ca²⁺]ⁱ) waveforms was obtained with in which fractional force is on a scale from 0 to 1 (control conditions) and A and B are constants (A = 40 and B = 40 in control). This exponential function of force is similar to that of Landesberg and Sideman, 14based on experimental observations in cardiac and skeletal muscle.

• 4. the total amount of cytoplasmic (free and bound) Ca²⁺is given by:

• 5. net rate of change of total cytoplasmic Ca²⁺

The first derivative of the total [Ca²⁺] represents the algebraic sum of Ca²⁺delivery (Ca²⁺release, Ca²⁺entry) and of Ca²⁺export out of the cytoplasm (SR Ca²⁺uptake, other mechanisms):

• 6. SR Ca²⁺uptake

Sarcoplasmic reticulum Ca²⁺uptake is a saturable first-order reaction (Michaelis–Menten kinetics):

in which K^M= 0.3 μm and V^MAX= 1,000 μm · l⁻¹· s⁻¹.

• 7. cytoplasmic Ca²⁺delivery

From equation 6, it follows that cytoplasmic Ca²⁺delivery equals the following:

which almost entirely represents Ca²⁺released from the SR.

• 8. simulation of [Ca²⁺]ⁱtransient

At this stage, all components of the multicompartment model are characterized. One can vary one of more components and assess the resultant changes in the intracellular Ca²⁺transient. Intracellular calcium transients were simulated for a change in Ca²⁺delivery, a change in k^off(TnC.Ca)(by changing B in equation 4, or a combination of these, by solving equations 2, 3, and 9:

Equation 9states that the change in free [Ca²⁺]ⁱis the resultant of total Ca²⁺delivery minus the rate of Ca²⁺bound to TnC (Ca.T) and to calmodulin (Ca.C), minus the rate of Ca²⁺removal by SR uptake. The SR uptake term in equation 9introduces a small Ca²⁺“leak” to maintain diastolic [Ca²⁺]ⁱat a nearly constant level.

• 9. conversion to simulated aequorin luminescence signal

The simulated Ca²⁺transient was converted back to aequorin luminescence with the equation: