The energetics of rat papillary muscles undergoing realistic strain patterns
Department of Physiology, PO Box 13F, Monash University, Victoria 3800, Australia
*e-mail: Linda.Mellors{at}med.monash.edu.au
Accepted August 9, 2001
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Summary |
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Key words: mechanical efficiency, heat production, enthalpy output, work loop, cardiac muscle, rat, muscle.
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Introduction |
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In vitro studies of cardiac energetics have traditionally used the papillary muscle as a model of ventricular muscle. The protocols used in these types of studies have usually involved either isometric or afterloaded isotonic contractions (Gibbs and Chapman, 1979; Gibbs et al., 1967; Kiriazis and Gibbs, 1995; Kiriazis and Gibbs, 2000). Neither of these protocols results in a net output of mechanical work, and typically the contraction frequency is very low compared with physiological frequencies. These and other interpretative difficulties have been discussed extensively by Mellors et al. (Mellors et al., 2001).
Semafuko and Bowie (Semafuko and Bowie, 1975) highlighted the lack of correspondence between the strain patterns used in traditional in vitro studies and those measured from papillary muscles in situ. However, there have still been no studies of papillary muscle mechanics or energetics using realistic strain protocols and contraction frequencies. With current technology, it is possible to simulate in vivo papillary muscle strain patterns in vitro.
Two recent studies from this laboratory (Baxi et al., 2000; Mellors et al., 2001) employed a sinusoidal length change protocol as an approximation of in vivo papillary muscle contraction. This protocol did produce more realistic patterns of force and length changes, was performed at realistic contraction frequencies and resulted in net work output. However, the sinusoidal strain pattern, although more realistic than isometric or isotonic contractions, is still a relatively poor match to in situ strains.
The aims of the current study were (i) to determine, from published reports, a typical strain pattern of in situ papillary muscles, (ii) to incorporate this pattern into a contraction protocol for isolated papillary muscle preparations and (iii) to characterise the energetics of rat papillary muscles performing the realistic length change protocol. Because there is some variation in the fine details of the in situ strain pattern, the pattern of length changes used in this study was varied to encompass the most likely patterns.
A comprehensive search of the literature describing in situ papillary muscle strain dynamics revealed that the muscles undergo cyclic length changes during contraction [e.g. Cronin et al. (Cronin et al., 1969), Marzilli et al. (Marzilli et al., 1985), Rayhill et al. (Rayhill et al., 1994) and Semafuko and Bowie (Semafuko and Bowie, 1975)] and shorten by approximately 10 % of their resting length at a fairly constant velocity (Gorman et al., 1996; Hirakawa et al., 1977; Semafuko and Bowie, 1975). Some reports identified a brief period of isometric contraction at the start of ventricular systole (Armour and Randall, 1970; Hirakawa et al., 1977; Karas and Elkins, 1970; Rayhill et al., 1994), but the duration of this phase was variable. Other studies have reported that muscle length increased by a small amount at the beginning of ventricular systole rather than remaining isometric (Cronin et al., 1969; Marzilli et al., 1985; Semafuko and Bowie, 1975). Both these possibilities were encompassed by the protocols used in the present study. Following shortening, re-extension of the muscles to the length recorded at the start of each cycle also occurred at an approximately constant velocity.
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Materials and methods |
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The total enthalpy output from a contracting muscle is the sum of the heat and work outputs. Net work output during a contraction was calculated by integrating force with respect to the change in muscle length (i.e. net work output is equal to the area enclosed by a plot of force as a function of change in muscle length). This calculation determines the difference between the total work performed by the muscle during shortening and that performed on the muscle to re-lengthen it prior to starting the next length change cycle.
Experimental protocols
Once mounted, each preparation was set to the length at which active force production was maximal (Lmax). Muscles then performed isometric contractions at Lmax for 1.5 h at a rate of 0.2 Hz to allow mechanical performance to stabilise. The muscle preparation was kept at 27°C throughout the experiment. It has been shown previously, by modelling the diffusion of O2 into cylindrical muscles, that at this temperature diffusive O2 supply would be adequate to meet the metabolic needs of papillary muscles contracting at the frequencies used in this study (Baxi et al., 2000). At higher temperatures, it is possible that the O2 supply may not be adequate, leading to the formation of an anoxic region in the centre of the preparations.
Recordings of muscle enthalpy output were made with the muscle out of solution. Stimulation of the muscle ceased prior to drainage to allow any heat generated by the muscle during stimulation to dissipate into the solution. The muscle remained unstimulated for approximately 8 min prior to experimental recordings to allow the thermopile output to stabilise. The standard experimental protocol used in this study consisted of 40 twitches at a contraction rate of 2 Hz. The muscle was re-immersed in solution and stimulated at 0.2 Hz for 20 min between sets of measurements. At all times during experiments, the chamber containing the muscle was supplied with 95 % O2/5 % CO2.
Three experiments were performed. Experiment 1 investigated the effects of varying the strain dynamics, experiment 2 investigated the effects of varying the shortening duration at constant frequency and experiment 3 investigated the effects of varying the frequency of contraction while maintaining a constant duration of shortening.
Experiment 1: varying strain dynamics
In the first experiment, two aspects of the strain dynamics were investigated. First, the effects of varying the duration of the isometric phase at the start of contraction were studied. The duration was set to 10, 15 or 20 % of the cycle duration (one cycle is the interval between successive stimuli) (Fig. 1A). The consequences of incorporating an increase in muscle length (2 or 4 % Lmax) before the onset of shortening (15 % cycle duration) were also studied (Fig. 1B). Second, the amplitude of shortening was varied such that it equalled 5, 10 or 15 % Lmax (Fig. 1C). Each shortening amplitude was preceded by an isometric contraction accounting for 10, 15 or 20 % of the cycle duration.
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Experiment 3: varying contraction frequency
A contraction frequency of 2 Hz was selected as the basic frequency for this study. In a recent report on the energetics of rat papillary muscle, this frequency was found to be within the range for maximum work output and maximum net mechanical efficiency (Baxi et al., 2000). In addition, a number of experiments were performed at a contraction rate of 3 Hz. This 50 % increase in heart rate is comparable with the range of heart rate increases that occurs between rest and vigorous exercise in rats; e.g. Drexler et al. (Drexler et al., 1985) and Mullin et al. (Mullin et al., 1984). The total durations of the isometric and shortening phases were kept constant, while the duration of the lengthening phase was reduced for the contractions at 3 Hz (Miyazaki et al., 1990). Thus, the absolute duration of the combined isometric and shortening phase was the same in the 2 and 3 Hz contraction protocols.
Measurement of the stiffness of the series elastic component
In experiment 1, the velocity of shortening of the muscle was varied. To assess the probable effects of these alterations in whole-muscle shortening velocity on the velocity of the contractile component alone, the contractile component velocity was calculated using the following equation (Curtin and Woledge, 1993):
| (1) |
where VCC is the shortening velocity of the contractile component, VL is the shortening velocity of the whole muscle, S is the stiffness of the series elastic component (SEC) (which varied with force) and dP/dt is the rate of change in force.
The stiffness of the SEC of papillary muscle preparations was measured using the method described by Sonnenblick (Sonnenblick, 1964). Each muscle performed isotonic twitches (10 twitches at 0.2 Hz) against a series of afterloads between 0.2P0 and 0.8P0, where P0 is the maximum isometric twitch force (excluding passive force). Afterloaded isotonic twitches involve the muscle contracting isometrically until the force reaches the desired afterload, then shortening and re-lengthening while force output remains constant, and then relaxing isometrically (Fig. 2). Two runs were performed on each muscle with loads presented alternately in ascending and descending order. The required afterload was achieved using an adaptive force control algorithm (Mellors et al., 2001; Peterson et al., 1989). For each muscle at each load, the stiffness of the SEC (S) was calculated using the expression (Sonnenblick, 1964):
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![]() | (2) |
where dP/dt is the rate of force development immediately prior to the start of shortening and dL/dt the initial velocity of shortening (Fig. 2).
Calculations
Data normalisation
The blotted wet mass of each preparation was determined at the conclusion of each experiment (Mellors et al., 2001). Muscle force was normalised by cross-sectional area (CSA), which was calculated as mass/(lengthxdensity), assuming a density of 1.06 g cm3 (Hill, 1931).
Net mechanical efficiency
Net mechanical efficiency (Net) was defined as the percentage of the total, suprabasal enthalpy output (HTotal) that appeared as external, mechanical work:
![]() | (3) |
where WTotal was the sum of the net work output produced in each contraction in the series and HTotal was the total suprabasal enthalpy output (i.e. heat + work) and included metabolism due to both initial (i.e. ATP-utilizing) and recovery (i.e. ATP-synthesising) biochemical reactions.
Statistical analyses
All data are presented as the mean ±1 S.E.M. Data were analysed using analysis of variance (ANOVA) with repeated measures. Post-hoc testing was performed using the least significant difference test. All decisions concerning statistical significance were made at the 95 % confidence level.
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Results |
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Applying an initial stretch instead of holding the muscle isometric at the beginning of the contraction did not affect enthalpy output (Fig. 6). The work output per twitch, however, did increase with a greater magnitude of length increase (isometric, 1.04±0.12 mJ g1; 2 % Lmax increase, 1.15±0.12 mJ g1; 4 % Lmax increase, 1.29±0.14 mJ g1). There was no significant difference in Net between the contractions with an initial isometric phase (12.5±0.6 %) and those with a 2 % Lmax increase in length (13.0±1.1 %). However,
Net was significantly greater (14.6±1.2 %) when a 4 % Lmax increase in length was incorporated into the protocol in place of either a 0 or 2 % Lmax length increase.
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Using the protocol as a model of ventricular muscle
The shapes of the force/length loops in Fig. 4 differ from ventricular pressure/volume loops in that the latter generally exhibit a clear isovolumic relaxation phase [for a comprehensive review, see Sagawa et al. (Sagawa et al., 1988)]. It is unclear, from in situ strain and length change recordings, whether the papillary muscles remain isometric during the isovolumic relaxation phase, with reports indicating varying degrees of shortening (Hirakawa et al., 1977; Marzilli et al., 1985; Semafuko and Bowie, 1975), lengthening (Rayhill et al., 1994) or no significant length change (Hirakawa et al., 1977; Rayhill et al., 1994). Regardless of the disagreement in the literature, if papillary muscles are to be used as a linear model of ventricular muscle, the addition of an isometric relaxation phase would enhance the realism of the model. To determine whether this feature could easily be incorporated into the protocols used in this study, an experiment was carried out in which the muscle length was held constant during part of the relaxation phase. The isometric relaxation phase was incorporated into the length change pattern by selecting a time for shortening to end and by holding the length constant until relaxation was complete (Fig. 10). The results from these experiments are shown in Table 2. As the absolute shortening amplitude was increased, work output per twitch also increased. This result is in agreement with the findings of experiment 1. Once again, the enthalpy output per twitch varied over only a small range and, thus, Net reflected the variation in work output.
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An example of the results of this analysis is shown in Fig. 12A. The time course of changes in length of the whole muscle (controlled by the experimenter) is compared with the time courses of length changes in the contractile component and the SEC. The first notable feature is that the contractile component began to shorten and stretch the SEC as soon as the contraction started, as reported previously (Brady, 1971; Donald et al., 1980). In fact, in this example, in which the initial isometric phase lasted 100 ms, the contractile component had shortened by approximately 5 % Lmax before the applied shortening even started. During the applied constant-velocity shortening, the velocity of the contractile component was not constant but decreased steadily and reached almost zero by the time the applied shortening ended. During the subsequent re-lengthening, changes in the length of the contractile component and the whole preparation were quite similar because the rate of change in force was very low during this phase.
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It should be noted that the SEC is an integral component of papillary muscles (and all other muscles), and that the purpose of calculating contractile component length change was simply to try to understand the mechanisms underlying the constancy of energy cost.
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Discussion |
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Effects of varying contraction frequency in realistic and sinusoidal protocols
The present study tested the effects of increasing the contraction frequency from 2 Hz to 3 Hz (experiment 3). In this experiment, the power output (work output x cycle frequency) of the muscle increased by approximately 20 % and was accompanied by only a small decline in Net. This protocol allowed us to manipulate the length changes so that the durations of the shortening and lengthening periods could be set to allow adequate time for the muscle to complete contracting before being stretched back to its resting length. In sinusoidal protocols, both power output (Baxi et al., 2000; Layland et al., 1995) and
Net (Baxi et al., 2000) decreased substantially when contraction rate was increased because of the symmetrical strain pattern of that protocol. As contraction frequency was increased, the time for both shortening and lengthening was reduced (Baxi et al., 2000; Layland et al., 1995), and relaxation was not complete prior to the muscle being stretched back to its resting length (Baxi et al., 2000). Thus, more work was required to stretch the muscle, reducing the net work performed (Baxi et al., 2000; Josephson, 1993).
In the present study, work output per twitch did decrease when contraction frequency was increased, but only slightly. The reduction in work output occurred despite there being adequate time for force output to decline to resting levels before the lengthening phase occurred. How can the decrease in work output and maintenance of enthalpy output per twitch observed to accompany an increase in contraction frequency be explained? The constancy of enthalpy output implies that the total amount of ATP used in each twitch, by both ion pumps and cross-bridges, remained constant. Although the metabolic changes that might be expected with increased contraction frequency (e.g. increased intracellular concentrations of inorganic phosphate and hydrogen ions) could have slightly reduced the molar enthalpy output of phosphocreatine hydrolysis (Woledge and Reilly, 1988), any such effect would strengthen the argument that the total amount of ATP used did not decrease significantly with the increase in contraction frequency.
In rat cardiac muscle, increasing contraction frequency is sometimes associated with a decrease in the amount of Ca2+ released in each twitch; e.g. Frampton et al. (Frampton et al., 1991). This could account for a lower force, and hence work, output but would also be expected to result in a proportional reduction in total energy output. The expected changes in the concentrations of metabolites do have the potential to alter force output without necessarily reducing the total number of ATP-splitting cross-bridge cycles. An increased contraction rate is associated with an increase in inorganic phosphate concentration and acidosis (Elliott et al., 1994), both of which cause a decrease in force output in cardiac muscle (Palmer and Kentish, 1996). It has been suggested that increased concentrations of inorganic phosphate and hydrogen ions alter the equilibrium between the populations of attached but non-force-generating and force-generating cross-bridges, favouring the low-force state (Hibberd et al., 1985; Kentish, 1991; Palmer and Kentish, 1996). To be consistent with the present observations, the total number of cross-bridges completing ATP splitting cycles would have had to remain unaltered, despite any differences in the equilibrium between the attached states.
Efficiency of rat papillary muscle
The maximum net mechanical efficiency of rat papillary muscle using this protocol was approximately 12 % when the muscle shortened by 10 % Lmax and approximately 16 % when shortening was 15 % Lmax. These values are comparable with those reported for cardiac muscle of frog and rat performing sinusoidal length change protocols (Baxi et al., 2000; Mellors et al., 2001; Syme, 1994). The values are lower than those reported for rat papillary muscles during isotonic contractions, in which efficiency was stated to be 2025 %; e.g. Gibbs and Chapman (Gibbs and Chapman, 1979) and Kiriazis and Gibbs (Kiriazis and Gibbs, 1995). However, it has recently been demonstrated that the apparently high values can be reconciled with the lower values by correctly taking account of the pre-load when calculating work output in isotonic protocols (Mellors et al., 2001). When this is done, the values of all the studies are consistent, with a maximum efficiency of approximately 15 %.
It was suggested previously that the difference between reported values for the maximum net mechanical efficiency of intact hearts [approximately 2025 %, e.g. Elzinga and Westerhof (Elzinga and Westerhof, 1980) and Gibbs et al. (Gibbs et al., 1980)] and isolated papillary muscles [approximately 15 % (Baxi et al., 2000; Mellors et al., 2001)] might be reconciled if measurements with isolated muscles were made using a more realistic strain protocol (Mellors et al., 2001). However, the results of the present study are consistent with the notion that the maximum efficiency of papillary muscles is indeed approximately 15 %, regardless of protocol used. The reasons for the difference between the efficiencies of intact hearts and isolated muscles remain unclear.
Why was the energy cost per twitch unaffected by changes in strain pattern?
A striking observation from these experiments was that, at a given frequency, the enthalpy output per twitch varied little, despite the various alterations made to the protocol. As a result, changes in Net primarily reflected changes in work output.
In experiment 1, the applied shortening velocities ranged between 0.5 and 1.0 Lmax s1. This is a small range of shortening velocities compared with the complete range of velocities that can be attained in vitro using isotonic contractions. However, since the amplitude of shortening and the proportion of the cycle duration occupied by shortening were obtained from in situ measurements, the range of velocities used in this study corresponds to those experienced in vivo. As mentioned previously, the maximum shortening velocity (Vmax) of rat papillary muscle is approximately 3.25 Lmax s1 at 27°C. Velocities of 0.5 and 1.0 Lmax s1 thus correspond to approximately 0.15Vmax and 0.3Vmax, respectively. It appears likely, therefore, that papillary muscles operate over only a small fraction of the complete range of shortening velocities, and any inherent velocity-dependence of enthalpy output would be unlikely to be apparent using this protocol. The calculated time courses of change in contractile component length indicated that the insensitivity of the enthalpy output per twitch to the pattern of applied length changes was not due to the contractile component undergoing the same pattern of length changes in all cases.
It has been proposed that the energy cost of a cardiac twitch is insensitive to the pattern of mechanical activity during the twitch because cross-bridge kinetics are sufficiently slow that there is only enough time for each cross-bridge to perform a single cycle (Gibbs and Barclay, 1998; Rossmanith et al., 1986). Countering this idea is the observation that energy cost per twitch varies considerably with afterload in isotonic contractions (Kiriazis and Gibbs, 2000). However, isotonic contractions are difficult to interpret because of the variable time spent in an isometric state at the beginning of the contraction and the variation of shortening amplitude with afterload.
When the contractile filaments slide past one another during shortening, cross-bridges would be expected to detach when they are drawn sufficiently past the position at which their free energy is minimal. If they were then to reattach to another binding site further along the actin filament and split ATP in each cycle, more ATP would be hydrolysed in each twitch and the enthalpy output would be greater. The current results, and those of earlier investigations (Gibbs and Gibson, 1970; Holroyd and Gibbs, 1992), show that this is not the case; at best, there is only a very modest increase in enthalpy output per twitch between isometric and shortening contractions (compare values in Table 1 with those in Fig. 5). Thus, if cross-bridges do perform more cycles when a papillary muscle shortens than when it contracts isometrically, the cycles must not be accompanied by ATP splitting. Ideas of this kind have been proposed to account for the decline in rate of enthalpy output with increasing velocity often observed at high shortening velocities in skeletal muscle (Barclay, 1999; Huxley, 1973). An alternative explanation is that cross-bridges in cardiac muscle are unlikely to reattach to another binding site once they have detached. This idea is the basis of most models devised to account for the cardiac muscle phenomenon of shortening deactivation. Briefly, it is envisaged that, when a cross-bridge detaches at any time in a twitch other than the first 20 % of twitch duration, the probability of reattachment is low. This is likely to be a consequence of the combination of low intracellular Ca2+ levels at these times and the tension dependence of Ca2+troponin binding [for a review, see Hunter et al. (Hunter et al., 1998)].
Isometric relaxation
To simulate in vivo ventricular muscle length changes, the linear length change protocol was modified to include an isometric relaxation phase. This modification resulted in force/length (work) loops that resemble the pressure/volume loops of the intact ventricle (Sagawa et al., 1988). Initially, it was hypothesised that the force might increase when controlled shortening was abruptly stopped since the muscle was still actively generating force. However, force continued to decline steadily with time despite the abrupt cessation of shortening (Fig. 10C). This observation is consistent with the shortening-induced deactivation described above for cardiac muscle. Incorporating the isometric relaxation phase did not greatly affect the energetics of contraction. The ability to include an isometric relaxation phase allows the protocol developed in this study to simulate changes in end-systolic volume, which is not easily achieved using conventional protocols.
Comparison with studies of energy use in whole hearts
Using an excised, whole-heart model, Suga and colleagues have consistently reported a linear relationship between the pressure/volume area (PVA) and the rate of oxygen consumption (i.e. energy cost) in the left ventricle of dogs [reviewed by Suga (Suga, 1990)]. It should be noted that the PVA includes not only the work loop, as calculated in the present study, but also a potential energy term that is enclosed by the extrapolation of both the active and passive pressure/volume relationships to zero pressure. For papillary muscles, the two-dimensional analogue of PVA is the force/length area (FLA). There is also a linear relationship between FLA and the rate of oxygen consumption (Hisano and Cooper, 1987; Mast and Elzinga, 1990). Thus, both PVA and FLA provide indices of the energy cost of a cardiac twitch (Taylor et al., 1993).
The alteration in strain pattern that was likely to have had the greatest effect on FLA in the present study was altering the amplitude of shortening (see Fig. 4A). An estimate was made of the difference in FLA for contractions with the greatest and smallest amplitude length changes shown in Fig. 4A. Data about the form of the FLA for rat papillary muscles were taken from Kiriazis and Gibbs (Kiriazis and Gibbs, 2000). It was estimated that FLA for a shortening amplitude of 15 % Lmax would have been approximately 90 % of that for the 5 % Lmax shortening. If it is assumed that the dimensionless slope of the relationship between enthalpy per beat and FLA is 2.5 and that the enthalpy output when extrapolated to an FLA of zero is 4 mJ g1 (Kiriazis and Gibbs, 2000), then the difference in energy cost per beat between shortening amplitudes of 5 and 15 % Lmax would have been only approximately 1 %. Such a small difference would be undetectable using our, or any other, method. Thus, the observed constancy of energy cost per beat in the face of substantial changes in shortening amplitude does not conflict with the idea that FLA, or PVA, provides a good index of energy cost for cardiac muscle.
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Acknowledgments |
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