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Pain Medicine  |   July 2000
Effects of Halothane and Isoflurane on the Intracellular Ca2+Transient in Ferret Cardiac Muscle
Author Affiliations & Notes
  • Philippe R. Housmans, M.D., Ph.D.
    *
  • Laurel A. Wanek, B.A.
  • Edmund G. Carton, M.D.
  • Anna E. Bartunek, M.D.
    §
  • *Associate Professor of Anesthesiology, Mayo Foundation. †Research Technician, Mayo Foundation. ‡Consultant, Department of Anesthesia, Mater-Misericordiae Hospital, Dublin, Ireland. §Research Fellow, Mayo Foundation.
Article Information
Pain Medicine
Pain Medicine   |   July 2000
Effects of Halothane and Isoflurane on the Intracellular Ca2+Transient in Ferret Cardiac Muscle
Anesthesiology 7 2000, Vol.93, 189-201. doi:
Anesthesiology 7 2000, Vol.93, 189-201. doi:
THE volatile anesthetics halothane and isoflurane, in clinically useful concentrations, depress myocardial contractility in vitro  . 1,2 Their negative inotropic effects have been attributed to a decrease in transsarcolemmal Ca2+influx, 3 Ca2+uptake and release from the sarcoplasmic reticulum (SR), 4 and Ca2+sensitivity of the contractile proteins. 5,6 Although there is much experimental evidence that these anesthetics decrease intracellular Ca2+availability, a decrease of Ca2+sensitivity of the contractile proteins has been shown only in skinned fibers 5,6 and indirectly in intact, living fibers. 1,2,7 The purposes of the current study were to test the hypothesis that halothane and isoflurane decrease myofibrillar Ca2+sensitivity in intact, living cardiac fibers by detecting the [Ca2+]itransient with the Ca2+-regulated photoprotein aequorin, 8 and to quantify the relative importance of changes in myofibrillar Ca2+sensitivity versus  changes in myoplasmic Ca2+availability in the overall inotropic effect of these anesthetics.
Materials and Methods
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 (Lmax) 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 Lmax, 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. 1 Anesthetic vapor concentration was measured continuously using a calibrated acoustic gas analyzer. 1 The 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.
Detection of the [Ca2+]iTransient
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 8 to 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. 9 The 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 9,10 designed 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 (tL25), and the slope of the logarithm of aequorin luminescence from 50% peak to 10% peak (k50/10). 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.
Experimental Design
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. 1 When 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 Lmax. 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 Lmax, 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. 11 This 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.
Theoretical Analysis
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.  12 to 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. 9,15 We calculated the amplitude and time course of the Ca2+transient for many combinations of new values of SR Ca2+release and myofibrillar Ca2+sensitivity (koff(TnC.Ca)) by solving differential equations 2, 3, and 9(1) 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.
Statistical Analysis
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.
Results
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 Lmax(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 1,7 without 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 Lmax(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 tL25(tables 1 and 2), yet the slope k50/10of the logarithm of aequorin luminescence from 50% peak to 10% peak was not changed in isometric twitches (table 1).
Fig. 1. Concentration–response experiment for isoflurane. (Top  ) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom  ) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
Fig. 1. Concentration–response experiment for isoflurane. (Top 
	) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom 
	) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
Fig. 1. Concentration–response experiment for isoflurane. (Top  ) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom  ) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
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Table 1. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 8) and Isoflurane (n = 8) in Group 1 Muscles in Isometric Twitches at the Preload of Lmax
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Table 1. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 8) and Isoflurane (n = 8) in Group 1 Muscles in Isometric Twitches at the Preload of Lmax
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Table 2. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 6) and Isoflurane (n = 6) in Group 1 Muscles in Isotonic Twitches at the Preload of Lmax
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Table 2. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 6) and Isoflurane (n = 6) in Group 1 Muscles in Isotonic Twitches at the Preload of Lmax
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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).
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
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Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left  ) and peak developed force (right  ) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top  ) and isoflurane (bottom  ) as a function of extracellular Ca2+. *P  < 0.05. NS = not significantly different.
Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left 
	) and peak developed force (right 
	) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top 
	) and isoflurane (bottom 
	) as a function of extracellular Ca2+. *P 
	< 0.05. NS = not significantly different.
Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left  ) and peak developed force (right  ) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top  ) and isoflurane (bottom  ) as a function of extracellular Ca2+. *P  < 0.05. NS = not significantly different.
×
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 koff(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(Ls− Lo)2, as a function of SR release and the variable B (which determines koff(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, | Δs-o[Ca.T]max| , as a function of SR release and koff(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 koff(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 koff(TnC.Ca)value found previously for the aequorin luminescence signal in the back-titrated twitch.
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top  ) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center  ) Traces of aequorin luminescence obtained by computational simulation, except if marked measured  . (Bottom  ) Calculated traces of Ca2+occupancy of TnC.
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top 
	) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center 
	) Traces of aequorin luminescence obtained by computational simulation, except if marked measured 
	. (Bottom 
	) Calculated traces of Ca2+occupancy of TnC.
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top  ) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center  ) Traces of aequorin luminescence obtained by computational simulation, except if marked measured  . (Bottom  ) Calculated traces of Ca2+occupancy of TnC.
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Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in 1) on the sums of squared differences between observed and simulated aequorin luminescence (top  ) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom  ) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in appendix) on the sums of squared differences between observed and simulated aequorin luminescence (top 
	) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom 
	) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in 1) on the sums of squared differences between observed and simulated aequorin luminescence (top  ) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom  ) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
×
Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y  plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in 1) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control twitch.
Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y 
	plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in appendix) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control twitch.
Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y  plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in 1) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control 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/koff(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.
Fig. 7. Relative effects of halothane (left  ) and isoflurane (right  ) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P  < 0.05. NS = not significantly different.
Fig. 7. Relative effects of halothane (left 
	) and isoflurane (right 
	) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P 
	< 0.05. NS = not significantly different.
Fig. 7. Relative effects of halothane (left  ) and isoflurane (right  ) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P  < 0.05. NS = not significantly different.
×
Discussion
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. 9,10 Drawbacks 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. 16 Some [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, 17 rat, 18,19 and guinea pig papillary muscle. 2 Halothane 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. 20 Na+-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. 21 The 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, 22–25 resulting 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. 26 The 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). 25 Under physiologic conditions, halothane and to a lesser extent isoflurane caused a small distinct decrease in SR Ca2+uptake. 4 The 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, 2 cat, 17 and ferret papillary muscles seen in the current study and in canine Purkyňe fibers 25 may 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. 9 Changes 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 koff(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, 15 and a Michaelis–Menten kinetic scheme for SR Ca2+uptake. 30,31 The values of VMAX(1,000 μm · l−1· s−1) and KM(0.3 μm) 32,33 were 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. 4 Even 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 (VMAX) 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.  , 12 because the starting point of the analysis is the experimentally measured Ca2+transient. In other simulation studies, either a fixed Ca2+transient was assumed 33 or a fixed pattern of SR release was chosen to result in plausible Ca2+transients. 30,32 With 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, VMAX, KM, koff(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. 9,34 Accurate 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. 34,35 Yet 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. 5,6 Halothane, 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. 37 In 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. 34,35 There is a relative paucity of information of anesthetic effects on levels beyond skinned fibers. Halothane did not change 38 or slightly increased 39 the Ca2+affinity of isolated cardiac TnC in vitro  , and it decreased koff(TnC.Ca)in human recombinant cardiac TnC. 40 These 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. 41 In skinned rat cardiac fibers, halothane decreased the number of strongly attached force-generating cross-bridges and decreased cross-bridge mean force. 42,43 If 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. 43 Such 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 43 would 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 1,7 and skinned 5 cardiac 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 1,2,7 and in skinned cardiac fibers 5,6,42,43 are 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.
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Appendix
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. 9,15 The 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 9 that relates [Ca2+]i(in m) to fractional luminescence (f.l.):MATHin which KTR= 154.8 and KR= 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, kon(TnC.Ca)= 3.9 × 107m−1· s−1; koff(TnC.Ca)= a function of force (78.4 s−1at 0 fractional force; see Section 3); kon(C.Ca)= 108m−1· s−1; and koff(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. koff(TnC.Ca)was calculated from a variety of equations (linear, exponential, logarithmic) that related koff(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, 14 based 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):MATHin which KM= 0.3 μm and VMAX= 1,000 μm · l−1· s−1.
  • 7. cytoplasmic Ca2+delivery
From equation 6, it follows that cytoplasmic Ca2+delivery equals the following:MATHwhich 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 koff(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:MATH
Fig. 1. Concentration–response experiment for isoflurane. (Top  ) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom  ) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
Fig. 1. Concentration–response experiment for isoflurane. (Top 
	) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom 
	) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
Fig. 1. Concentration–response experiment for isoflurane. (Top  ) Aequorin luminescence and force traces as functions of time during a cumulative concentration–effect experiment on isoflurane in isometric twitches. Sixty-four twitches were averaged. (Bottom  ) Aequorin luminescence, shortening, force, and velocity of shortening traces as functions of time during a cumulative concentration–response experiment on isoflurane in isotonic twitches at Lmax. Sixteen twitches were averaged. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus. Top and bottom panels are records from different muscles.
×
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
Fig. 2. Aequorin luminescence and force traces as a function of time during an isometric Ca2+back-titration experiment for halothane 1.0%. The small vertical arrow near the origin of the aequorin signal indicates the time of the stimulus.
×
Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left  ) and peak developed force (right  ) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top  ) and isoflurane (bottom  ) as a function of extracellular Ca2+. *P  < 0.05. NS = not significantly different.
Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left 
	) and peak developed force (right 
	) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top 
	) and isoflurane (bottom 
	) as a function of extracellular Ca2+. *P 
	< 0.05. NS = not significantly different.
Fig. 3. Summary of isometric Ca2+back-titration experiments for peak aequorin luminescence (left  ) and peak developed force (right  ) during control, during anesthetic exposure, and during anesthetic in raised extracellular Ca2+at equal peak force, for halothane (top  ) and isoflurane (bottom  ) as a function of extracellular Ca2+. *P  < 0.05. NS = not significantly different.
×
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top  ) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center  ) Traces of aequorin luminescence obtained by computational simulation, except if marked measured  . (Bottom  ) Calculated traces of Ca2+occupancy of TnC.
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top 
	) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center 
	) Traces of aequorin luminescence obtained by computational simulation, except if marked measured 
	. (Bottom 
	) Calculated traces of Ca2+occupancy of TnC.
Fig. 4. Analysis of isometric Ca2+back-titration experiment (part 1 of 3). (Top  ) Aequorin luminescence and force traces as a function of time in a typical Ca2+back-titration experiment to isoflurane 1.5%. One hundred twenty-eight twitch contractions were averaged. (Center  ) Traces of aequorin luminescence obtained by computational simulation, except if marked measured  . (Bottom  ) Calculated traces of Ca2+occupancy of TnC.
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Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in 1) on the sums of squared differences between observed and simulated aequorin luminescence (top  ) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom  ) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in appendix) on the sums of squared differences between observed and simulated aequorin luminescence (top 
	) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom 
	) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
Fig. 5. Analysis of isometric Ca2+back-titration experiment (part 2 of 3). Effects of myoplasmic Ca2+availability (described here as SR release) and of myofibrillar Ca2+sensitivity (described here as the variable B of equation 4in 1) on the sums of squared differences between observed and simulated aequorin luminescence (top  ) and absolute difference between observed and simulated Ca2+occupancies of TnC (bottom  ) for the Ca2+back-titration experiment of figure 4. The solid line on each mesh plot runs through the minimal values of the surface.
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Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y  plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in 1) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control twitch.
Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y 
	plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in appendix) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control twitch.
Fig. 6. Analysis of isometric Ca2+back-titration experiment (part 3 of 3). Summary of the analysis of the Ca2+back-titration experiment of figure 4. The solid lines in this diagram correspond to the lines of minima of each of the two three-dimensional diagrams of figure 5projected in the x–y  plane. The intersection of the lines (myoplasmic Ca2+delivery = 109.5%, myofibrillar Ca2+sensitivity variable B = 63 s−1) (see eq. 4in 1) defines the conditions for a least-squares fit to the aequorin signal of the Ca2+back-titrated twitch and a same peak [Ca.T] as in the control twitch.
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Fig. 7. Relative effects of halothane (left  ) and isoflurane (right  ) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P  < 0.05. NS = not significantly different.
Fig. 7. Relative effects of halothane (left 
	) and isoflurane (right 
	) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P 
	< 0.05. NS = not significantly different.
Fig. 7. Relative effects of halothane (left  ) and isoflurane (right  ) on myoplasmic Ca2+availability and myofibrillar Ca2+sensitivity. The data points (mean ± SD) are derived from the same number of experiments as indicated in figure 3. *P  < 0.05. NS = not significantly different.
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Table 1. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 8) and Isoflurane (n = 8) in Group 1 Muscles in Isometric Twitches at the Preload of Lmax
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Table 1. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 8) and Isoflurane (n = 8) in Group 1 Muscles in Isometric Twitches at the Preload of Lmax
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Table 2. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 6) and Isoflurane (n = 6) in Group 1 Muscles in Isotonic Twitches at the Preload of Lmax
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Table 2. Aequorin Luminescence and Variables of Contractility during Cumulative Concentration–Response Experiments to Halothane (n = 6) and Isoflurane (n = 6) in Group 1 Muscles in Isotonic Twitches at the Preload of Lmax
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