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RESEARCH COMMUNICATION |
a Service de Physiologie UFR Paris XI, CHU Bicêtre, Assistance Publique-Hôpitaux de Paris, INSERM U451, LOA-ENSTA-Ecole Polytechnique, F91120 Palaiseau, Département d'Anesthésie-Réanimation, CHU Pitié-Salpétrière, Paris, France
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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), CB number per mm3 (m'), peak mechanical efficiency (Effmax), and turnover rate of myosin ATPase (kcat); m', , and Effmax were lower in CHF than in C in both twitch and tetanus. The marked decline in m' and accounted for the fall in diaphragm strength. In the overall population of C and CHF, Effmax was linearly related to . Conversely, there was no relationship between Vmax and kcat. Dissociation between Vmax and kcat might be explained by the crucial role attributed to two apparently nonconserved surface `loops' on the motor domain of myosin head.—Lecarpentier, Y., Chemla, D., Blanc, F. X., Pourny, J. C., Joseph, T., Riou, B., Coirault, C. Mechanics, energetics, and crossbridge kinetics of rabbit diaphragm during congestive heart failure. FASEB J. 12, 981–989 (1998)
Key Words: myosin • molecular motors • cardiac hypertrophy • muscle efficiency
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The goal of our study was to determine, on the basis of Huxley's theory (19), the CB kinetics (20–22) in rabbit diaphragm subjected to chronic cardiac overload. Three main steps of the CB cycle were investigated: attachment, power stroke, and detachment (
Fig. 1;
steps 3, 4, and 5, respectively) (11–13). We tested the hypothesis that during CHF changes in diaphragm force generation may be associated with modifications in the total number and single force of myosin molecular motors.
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MATERIALS AND METHODS |
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Mounting procedure and mechanical analysis (11)
After brief anesthesia with sodium pentobarbital, animals were thoracotomized and laparotomized. The heart was quickly removed and a left ventricular (LV) papillary muscle was carefully excised and mounted on a force transducer in a chamber containing a Krebs-Henseleit solution at 29°C and bubbled with 95% O2-5% CO2. The LV papillary muscle was electrically stimulated by two platinum electrodes delivering 5 ms rectangular pulses at 0.17 Hz. A muscle strip was carefully dissected out from the ventral part of the costal diaphragm. Tendinous insertions on the ribs and central tendon were left intact. The two tendinous extremities were held in spring clips and the muscle strip was attached to another force transducer in a chamber containing the same Krebs-Henseleit solution bubbled with 95% O2-5% CO2, maintained at 22°C and pH 7.40. The diaphragm strip was electrically stimulated in twitch mode by two platinum electrodes delivering 5 ms rectangular pulses at 0.17 Hz. The diaphragm strip was also stimulated under tetanic conditions: 5 ms stimulus at 33 Hz; train duration: 400 ms; train frequency: 0.17 Hz. For both muscles, experiments were carried out at Lo, the initial resting length that corresponds to the apex of the length-active tension curve. The cross-sectional area (CSA in mm2) of muscles was calculated from the ratio of fresh muscle weight to muscle length at Lo.
Protocol of the study
For the LV papillary muscle, maximum unloaded shortening velocity of contraction Vmax (in Lo·s-1) was measured from the contraction abruptly clamped to zero-load just after stimulus. Peak isometric tension, i.e., peak force normalized per CSA (in mN·mm-2), was measured from the fully isometric contraction.
For the diaphragm strip, Vmax was calculated from the contraction abruptly clamped to zero-load just after stimulus and peak isometric tension from the fully isometric contraction. The hyperbolic tension–velocity relationship was derived from the peak velocity (V) of 7 to 10 afterloaded contractions plotted against the isotonic load level normalized per CSA (P) by successive load increments, from zero-load up to the isometric tension. The experimental P–V relationship was fitted according to Hill's equation (24):
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Characteristics of crossbridges and energetics
Theoretical considerations
Huxley's equations were used to calculate the rate of total energy release (E, in mW·mm-2), isotonic tension (PHux, in mN·mm-2), and rate of mechanical energy (WM, in mW·mm-2) as a function of velocity (V) (19). E is given as:
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is the angle formed by the longitudinal axis of the myosin head with the actin filament, f1 and g1 correspond to 45° < < 90° and g2 (which appears in ) corresponds to < 45° (22); e is the free energy required to split one ATP molecule; l is the distance between two actin sites; 
= (f1+g1) h/s (19), where h is the stroke size (defined by the translocation distance of an actin filament per ATP hydrolysis and produced by the swing of the myosin head) (20); s is the resting sarcomere length at Lo.
The minimum value of rate of total energy release (Eo) occurs under isometric conditions; Eo is equal to the product of a x b (19, 24) and is also given by the equation:
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Calculations of crossbridge characteristics
Calculations of f1, g1, g2, m, and the elementary force per single CB () are detailed in the Appendix; f1, g1, and g2 (s-1) are given by equations:
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From , the CB number per mm2 at peak isometric tension is then given by equation:
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The CB number per mm3 at peak isometric tension is m' = m/Lo.
The elementary force per single CB [, in piconewtons (pN)] is:
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Values of Huxley's equation parameters
The step size ranges from 6 nm to circa 20 nm and is based on the physical dimensions of the myosin head (12, 13). These estimates are consistent with previous observations (21). A stroke size of 11 nm has been determined by using optical tweezers (16). In our study, the stroke size value (h) was chosen to be equal to 11 nm; this supports a one-to-one coupling for ATP energy transduction, which is inherent to Huxley's theory (19–22). The standard free-energy change 
G° for ATP is equal to 7.3 kcal·mol-1. The free energy required to split one ATP molecule per contraction site is e = 5.1 x 10-20 J. The mechanical work (w) of a single CB is equal to 0.75 e (19), so that w = 3.8 x 10-20 J; resting sarcomere length at Lo (s) was assumed to be 2.2 µm. The distance (l) is equal to 36 nm.
Statistical analysis
Data are expressed as means ± SEM. Group values were compared using the Scheffé test after analysis of variance; P values < 0.05 were required to rule out the null hypothesis. Linear regression was based on the least squares method. The asymptotes -a and -b of the Hill hyperbola were calculated by multilinear regression and the least squares method.
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RESULTS |
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Table 1).
Clinical signs of CHF in overloaded animals were as follows: ascites in 8/9 animals; pericarditis in 7/9; pleuritis in 6/9; subcutaneous edema in 5/9; pulmonary congestion in 5/9; hepatic congestion in 5/9. In CHF, the mechanical performance of LV papillary muscles fell dramatically. Both total isometric tension and Vmax were reduced by half ( Table 1).
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Diaphragm crossbridge mechanics
In both twitch and tetanus modes, total tension, CB single force (), Vmax, and the total number of CB per mm3 (m') were significantly lower in CHF than in C ( Fig. 2).
The rate constant for CB attachment (f1) did not differ between groups ( Fig. 3).
The rate constant for CB detachment (g2) was significantly lower in CHF than in controls in twitch and tetanus ( Fig. 3). The results for g1 and kcat were similar: in twitch, g1 and kcat were higher in CHF than in C, but in tetanus neither g1 nor kcat varied when we compared C to CHF ( Fig. 3). In twitch and tetanus, Effmax and percent of total tension at Effmax were significantly lower in CHF than in C ( Fig. 4).
Conversely, the normalized peak rate of mechanical work (nWM) was lower in C than in CHF ( Fig. 4). Eo was significantly higher in CHF than in C in twitch, but not in tetanus ( Fig. 4).
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In the overall population, total tension was linked to both m' and . Indeed, there was a positive linear relationship between total tension and the total CB number ( Fig. 5).
However, there was a curvilinear relationship between total tension and ( Fig. 5). Effmax was strongly and linearly related to ( Fig. 6),
and the percentage of tension at Effmax increased curvilinearly with Effmax ( Fig. 6). Effmax was negatively and linearly related to nWM according to the equation Effmax = -92 nWM + 46 (r=0.93; P<0.001). There was no significant relationship between Vmax and kcat ( Fig. 7).
Conversely, Effmax increased when kcat declined ( Fig. 7). From and , and because of the linear relationship between Effmax and , Huxley's equations lead to the equation: Effmax = 
x (kcat/g1), being a constant. Thus, Effmax is not a simple and negative linear function of kcat, but also depends on g1. Particularly at high kcat values, Effmax did not vary ( Fig. 7). There was no relationship between g2 and f1 nor between g2 and kcat.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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In human patients and animal models, impaired diaphragmatic function during CHF is generally assessed by indirect techniques (1–6, 8, 10) such as maximum inspiratory and expiratory pressures and/or transdiaphragmatic pressure. Intrinsic mechanics of isolated strip allow a direct approach to diaphragm performance (11). The intrinsic mechanics of an isolated diaphragm strip have been studied in CHF dogs, but only under isometric conditions (9). In our CHF model, we present intrinsic diaphragm mechanics under both isotonic and isometric conditions; the fall in contractility can be attributed at least in part to an impaired cellular mechanism, i.e., the decline in both the total number and single force of CB. Our technique also provides an analytical means of calculating rate constants for CB attachment and detachment and the turnover rate of myosin ATPase (see Appendix). Despite the interest in new techniques like optical tweezers (16, 17), glass needles (15), and in vitro motility assay (14, 15), these techniques have not yet been used to study molecular mechanics of diaphragm under various load levels and during CHF.
Force and number of crossbridges
The CB characteristics, i.e., single force, number, and kinetics, were calculated from Huxley's classic equations (19). In skeletal muscle, the single force of one myosin head (ranging from 3 to 7 pN) has been measured by optical tweezers (16). In the absence of ATP, the average unbinding force between an actin filament and a single myosin head is 9.2 ± 4.4 pN (17). Glass needle techniques also permit measurement of CB single force in the piconewton range (15). In our study, CB single forces (
Fig. 2) were of the same order of magnitude as those previously reported (15–17).
Peak isometric tension was related to the number of CB per mm3 (m') and CB single force () ( Fig. 5). In our model of volume and pressure overload, both m' and fell in CHF diaphragm ( Fig. 2). This may partly account for the reduced respiratory muscle strength reported in experimental CHF (7–11). In cardiomyopathic Syrian hamsters, a model of generalized myopathy that differs strikingly from the pure CHF model described in our study, diaphragmatic tension fall is related to the decline in CB number without changes in (11). Moreover, during developmental changes, an increase in diaphragmatic tension is related to an increase in the CB number without changes in (26). However, impaired sarcoplasmic reticulum (27) and histological abnormalities (28) may also contribute to the decline in diaphragm strength. Another hypothesis is that a degree of edema would reduce the number of crossbridges per volume unit. However, there is no pathophysiological basis on which to predict liquid movement from the extracellular compartment into the intracellular diaphragm compartment. Furthermore, it has been shown that the diameter of diaphragm cells does not increase during CHF (28).
Turnover rate of myosin ATPase (kcat) and Vmax
There was no relationship between kcat and Vmax ( Fig. 7), as observed in diaphragm of cardiomyopathic Syrian hamsters (11) and during developmental changes (26). This finding contrasts with the classic linear relationship between Vmax and maximum actin-activated myosin ATPase activity in skeletal muscles (29). kcat is the inverse of the overall duration (tc) of the CB cycle; tc depends partly on the limiting step of the CB cycle, i.e., the attachment step characterized by f1 ( Fig. 1, step 3) (18, 22). ADP release ( Fig. 1, step 5) occurs after the power stroke ( Fig. 1, step 4) and may constitute the limiting step of the detachment process. Detachment is characterized by g2 and has been predicted to limit Vmax (19, 22). Huxley's equations show that Vmax and g2 vary in a similar manner (; Figs. 2 and 3). The absence of any relationship between Vmax and kcat may be explained by the crucial role recently attributed to two apparently nonconserved surface `loops' on the motor domain of the myosin head (18). Loop 1, located near the ATP binding pocket, may modulate the rate of ADP release and the maximum velocity of movement; loop 2, at the actin binding site, may `tune' the rate-limiting step in the myosin ATPase cycle and, consequently, kcat. Loops 1 and 2 might exert their regulatory function to some extent independent of each other. This might partly account for the absence of any relationship between kcat and Vmax ( Fig. 7). Thus, alterations in loop 2 markedly modify myosin ATPase activity without inducing corresponding changes in movement velocity in in vitro motility assays (14).
Reduced muscle efficiency (Effmax) in CHF
CHF is characterized by an increase in left ventricular filling pressure resulting in fluid accumulation within the lung tissue, which induces increased stiffness (30). In CHF, increased breathing effort is a consequence of pulmonary congestion associated with decreased lung compliance and increased airway resistance (30). In our study, Effmax was lower in CHF than in controls, and the percentage of total tension at peak efficiency was shifted toward lower levels of load in CHF ( Figs. 4 and 6). Given the increased breathing work, these two abnormalities placed the CHF diaphragm in particularly disadvantageous energetic conditions. Reduced efficiency of peripheral skeletal muscle can be explained in part by the reduced percentage of slow twitch type I fibers and the increased percentage of fast twitch type IIb fibers (31). Changes in crossbridge kinetics and energetics might be due to changes in the relative proportions of the different myosin heavy chains. However, in diaphragm, different myosin isoform patterns have been observed in human and experimental CHF (10, 28, 32). Further studies are needed to clarify this point.
Three findings must be emphasized regarding Effmax. First, as previously reported (11, 26), there was a direct linear relationship between Effmax and ( Fig. 6). This relationship cannot be analytically deduced from Huxley's equations (19). Second, there was an inverse linear relationship between Effmax and the normalized peak rate of mechanical work (nWM). Again, this relationship cannot be analytically deduced from Huxley's equations. Third, there was an inverse nonlinear relationship between Effmax and kcat ( Fig. 7). Thus, under tetanic conditions, Effmax significantly declined in CHF as compared to C, but kcat did not change. Such a dissociation between variations of Effmax and kcat has previously been observed in the diaphragm during development (26).
In conclusion, during experimental CHF, the kinetics of myosin molecular motors of the diaphragm were modified. Peak mechanical efficiency was lowered. These abnormalities were associated with a significant decline in the force and number of crossbridges. Further studies are needed to investigate whether this may partly explain the impairment of diaphragm strength observed in humans suffering from CHF.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Calculation of g2:
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Under unloaded conditions (i.e., V=Vmax and PHux=0), can be written as follows:
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In our range of experimental values, Y-1 = 0.995X + 0.011; r = 0.97, P < 0.0001. The slope and ordinate of this linear relationship did not differ from 1 and 0, respectively, so that (f1 + g1)/g2 ~ /Vmax and consequently:
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Calculation of f1:
Huxley's model (19) assumes that = (f1 + g1)h/s ~ b. In our range of experimental values, b = 0.97 + 0.04; r = 0.98; P < 0.0001. The slope and ordinate of this linear relationship did not differ from 1 and 0, respectively.
It is then deduced that:
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By replacing A and B in and , we obtained the equation of E as a function of PHux:
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Under near isometric conditions, where V can be neglected (V~0), E can be linearized as follows:
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In our range of experimental values, the asymptote -b = -0.977 ehf1/sw + 0.004; r = 0.99, P < 0.0001. The slope and ordinate of this linear relationship did not differ from 1 and 0, respectively, so that ehf1/sw ~ b, then:
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From and , we obtain:
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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tre, 78 rue du Général Leclerc F94275, Le Kremlin-Bictre cedex, France. E-mail: lecarpen{at}enstay.ensta.fr 
2 Abbreviations: CB, crossbridge or crossbridges; CHF, congestive heart failure; LV, left ventricular; CSA, cross-sectional area; V, velocity; P, isotonic load level normalized per CSA; C, controls.
Received for publication July 22, 1997. Accepted for publication February 25, 1998.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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-phosphate of ATP binds to the myosin head in the nucleotide binding pocket. This opens the narrow cleft and induces rapid disruption of the actin binding surface on myosin from actin. Step 2: closure of the nucleotide binding pocket around the base undergoes a major conformational bent; ATP is then rapidly hydrolyzed to ADP and Pi. Step 3: attachment of myosin to actin. This step begins with the putative `weak binding' of the loop Tyr626-GLn647. A stereospecific interaction with actin involving the lower and then the upper domains of the 50 kDa segment leads to strong binding of actin to myosin. This leads to closure of the narrow cleft, which is thought to lower the affinity of the myosin head for 
