Effects of Myosin Heavy Chain Isoform Switching on Ca2+-Activated Tension Development in Single Adult Cardiac Myocytes
Abstract—Cardiac myosin heavy chain (MHC) isoforms are known to play a key role in defining the dynamic contractile behavior of the heart during development. It remains unclear, however, whether cardiac MHC isoforms influence other important features of cardiac contractility, including the Ca2+ sensitivity of isometric tension development. To address this question, adult rats were treated chemically to induce the hypothyroid state and cause a transition in the ventricular cardiac MHC isoform expression pattern from predominantly the α-MHC isoform to exclusively the β-MHC isoform. We found a significant desensitization in the Ca2+ sensitivity of tension development in β-MHC–expressing ventricular myocytes (pCa50=5.51±0.03, where pCa is –log[Ca2+], and pCa50 is pCa at which tension is one-half maximal) compared with that in predominantly α-MHC–expressing myocytes (pCa50=5.68±0.05). No differences between the 2 groups were observed in the steepness of the tension-pCa relationship or in the maximum isometric force generated. Instantaneous stiffness measurements were made that provide a relative measure of changes in the numbers of myosin crossbridges attached to actin during Ca2+ activation. Results showed that the relative stiffness-pCa relationship was shifted to the right in β-MHC–expressing myocytes compared with the α-MHC–expressing cardiac myocytes (pCa50=5.47±0.05 versus 5.76±0.05, respectively). We conclude that MHC isoform switching in adult cardiac myocytes alters the Ca2+ sensitivity of stiffness and tension development. These results suggest that the activation properties of the thin filament are in part MHC isoform dependent in cardiac muscle, indicating an additional role for MHC isoforms in defining cardiac contractile function.
Cardiac muscle contraction results from cyclical interactions between the contractile proteins myosin and actin via a complex chemomechanical coupling process supported by the hydrolysis of ATP.1 Cardiac myosin is a hexamer consisting of 2 myosin heavy chains (MHCs) and 2 pairs of myosin light chains (MLCs). There are 2 MHC isoforms expressed in the myocardium, the β-MHC and the α-MHC isoforms.2 3 During the development of small mammals, including rats, there is a transition in MHC isoform expression in the ventricles of these animals from predominantly the β-MHC in fetuses/neonates to predominantly the α-MHC in young adults. This transition in MHC isoform expression is correlated to marked differences in the dynamic function of the myocardium, which are most notably evident in the maximum velocity of muscle shortening.2 3 4 It is not clearly established, however, whether the switching of cardiac MHC isoforms may also affect other important aspects of cardiac muscle function, including the relationship between isometric force production and [Ca2+].
Ca2+ activation of cardiac muscle contraction is regulated by the thin-filament regulatory proteins, an allosteric system of which the troponin ternary complex and tropomyosin are 2 major components.5 There is good evidence that myosin interaction with actin also affects the activation of the contractile apparatus.6 7 8 9 In this regard, both Ca2+ and myosin are considered activating ligands of the thin-filament regulatory system.6 In addition, different chemomechanical states of the myosin-actin interaction may differentially influence thin-filament activation. It has been reported that cycling crossbridges have a greater effect than noncycling rigor crossbridges to cause alterations in Ca2+ binding affinity to the thin filament.8 This finding, together with the known marked differences in crossbridge cycling rates between α-MHC and β-MHC isoforms,4 raises the possibility that cardiac myocytes predominantly expressing the α- or β-MHC isoform may exhibit differing steady-state tension responses to activation by Ca2+. Earlier studies examining this question have produced conflicting results ranging from no change in Ca2+ sensitivity10 to an increase in Ca2+ sensitivity of tension in β-MHC–expressing cardiac muscle.11
The primary aim of this study was to determine the effects of cardiac MHC isoform composition on the sensitivity of the contractile apparatus to activation by Ca2+ using the single cardiac myocyte preparation. Furthermore, as a means to shed light on the mechanism of possible changes in Ca2+-activated tension generation, we examined the effects of MHC isoform switching on the instantaneous stiffness-Ca2+ relationship to estimate relative changes in numbers of attached crossbridges at varied [Ca2+]s in predominantly α-MHC and predominantly β-MHC isoform–expressing adult cardiac myocytes. Results from ventricular myocytes obtained from euthyroid adult animals, which predominantly express the α-MHC isoform, were compared with myocytes from adult rats treated chemically to induce hypothyroidism, which causes the exclusive expression of the β-MHC isoform.2 3
Materials and Methods
Single Cardiac Myocyte Preparation
Whole hearts were removed from female Sprague-Dawley rats, and the ventricles were dissected from the atria and minced in relaxing solution (see below). The minced tissue was placed in a Waring blender and homogenized for ≈6 to 10 seconds at low speed, as described previously.12 13 14 The cell suspension was centrifuged at 120g for 1 to 2 minutes, and the pellet was resuspended in 10 mL of relaxing solution that contained the protease inhibitor leupeptin (0.1%, final concentration). The mechanical isolation procedure appeared to permeabilize the sarcolemma, because exposure of the cells to 0.2% Triton X-100 for up to 30 minutes did not alter maximum tension or the tension-pCa relationship (data not shown). However, because brief exposure to Triton improves resolution of the sarcomere pattern, cells were exposed to Triton X-100 for 15 to 30 seconds before collection of mechanical data.
Experimental Apparatus and Procedures
An experimental chamber was constructed for attaching cardiac myocytes to the recording apparatus and for the activation and relaxation of the isolated cell. The chamber, similar to that described previously,13 15 measured 15×15×1.5 cm and was constructed out of stainless steel and aluminum. Four troughs were milled out of the stainless steel section (volume ≈200 μL) and provided wells for attaching and for relaxing and activating the cardiac myocyte. The chamber was positioned on an antivibration table to isolate the apparatus from vibrations within the building. Tension and length signals were recorded, digitized, and stored on magnetic disks for subsequent analysis using a Nicolet oscilloscope (model 310). The temperature of the experimental chamber was controlled to 15±0.1°C using thermoelectric modules (Melcor Inc) coupled to a recirculating water bath heat sink. The cardiac myocyte attachment procedure was adapted from an earlier study16 and is briefly summarized here. Borosilicate glass micropipettes were pulled to a tip diameter of ≈1 μm and inserted into an output tube of a force transducer (Cambridge Technology, model 403A; sensitivity, ≈1 μg; 1 to 99% response time, 1 ms) and a piezoelectric translator (Physik Instruments) or Cambridge Technology 6350 optical scanner (moving-coil galvanometer). The force transducer and piezoelectric translator/Cambridge motor were attached to 3-way positioners to allow exact positioning of the pipettes. The cardiac myocyte attachment procedure involved placing a drop of solution that contained the isolated cardiac myocytes onto a coverslip. The tips of the micropipettes were first broken (OD, ≈5 μm), coated with a silicone adhesive (Dow Chemical), and then positioned over an individual cardiac myocyte that was selected on the basis of a rod-shaped appearance and dimensions consistent with that of an isolated single cardiac myocyte. The micropipettes were then lowered onto the ends of the isolated myocyte. After ≈10 to 30 minutes, the silicone cured sufficiently (ie, tack free) to make a strong, low-compliance attachment. The preparation was then carefully raised up from the coverslip, and additional silicone was applied to the undersurface of each attachment site, using a third micropipette to ensure that silicone surrounded the entire cross section of the micropipette tip-cardiac myocyte interface. The sarcomere length of the attached cardiac myocyte was adjusted to 2.10 to 2.20 μm. The average dimensions of the attached cardiac myocyte were ≈100 μm in length (measured as the distance between the 2 silicone attachment points) and ≈20 μm in width. For comparison, the dimensions of enzymatically isolated single cardiac myocytes from rats average 120 μm in length and 20 μm in width (Reference 1717 and unpublished observations, J. Metzger, 1996). Thus, the attached cardiac myocyte preparation used in this study has the dimensions of a segment of a single isolated cardiac myocyte.
At each pCa, steady isometric tension developed, after which the fiber was rapidly (<0.5 ms) slackened to obtain the tension baseline. The myocyte was then relaxed. The difference between steady tension and the tension baseline after the slack step was measured as total tension. To obtain active tension, resting tension measured at pCa 9.0 (≈1% of total tension in skeletal fibers and ≈10% of total in myocytes; sarcomere length, 2.10 to 2.20 μm for cardiac myocytes) was subtracted from total tension. The preparations were transferred to relaxing solution after each activation at a given pCa. Tension-pCa relations were determined in each preparation by expressing tensions (P) at various submaximal Ca2+ concentrations as fractions of the maximum value (Po). The submaximal activations were bracketed by maximal Ca2+ activations.18
Relaxing and Ca2+ Activating Solutions
Relaxing and Ca2+ activating solutions contained the following (in mmol/L): EGTA 7, free Mg2+ 1, MgATP 4, creatine phosphate 14.5, imidazole 20, and sufficient KCl to yield a total ionic strength of 180 mmol/L. Solution pH was adjusted to 7.00 with KOH. Relaxing solution had a pCa (ie, –log [Ca2+]) of 9.0, whereas the pCa of the solution for maximal activation was 4.5 to 4.0. A computer program of A. Fabiato19 was used to calculate the final concentrations of each metal, ligand, and metal-ligand complex, using the stability constants listed by Godt and Lindley.20 The apparent stability constant for Ca2+-EGTA was corrected for ionic strength, pH, and experimental temperature. Experimental temperature was set at 15°C.
Induction of Hypothyroidism
Adult rats were rendered hypothyroid by adding propylthiouracil (0.6%) to the drinking water for a period of 6 to 8 weeks.21
Measurement of Instantaneous Stiffness
Instantaneous stiffness is defined as the change in tension in response to a sudden change in length. Stiffness was determined by applying small-amplitude (1 to 3 nm/half sarcomere) sinusoidal changes in sarcomere length, over a range of frequencies from 1.0 to 3.0 kHz in skeletal fibers and 0.65 to 1.0 kHz in cardiac myocytes (see Appendix for force transducer response and linearity tests) while measuring the magnitude of the resultant change in tension.22 Comparable results were obtained over these frequency ranges. In the Results, only the data obtained at 1.0 kHz are shown. The small-amplitude oscillations used here were required so as not to physically detach attached crossbridges during the perturbation in length. This was satisfied here, given that estimates of the working distance of an attached crossbridge are ≈5 to 15 nm per half sarcomere.1 The speed of the length change also must be more rapid than the average lifetime of an attached crossbridge. The oscillation frequency range used was sufficiently fast, as demonstrated previously by the plateau of the apparent stiffness value, as frequency was increased above ≈500 Hz in skeletal fibers.23 The resultant tension response (ΔP) was measured, and the average of 10 to 20 consecutive readings of ΔL and ΔP was used to determine instantaneous stiffness (ie, ΔP/ΔL).
Cardiac myocyte or soleus fiber segments were placed in a 0.5-mL microfuge tube containing SDS sample buffer (10 μL/mm of segment length) and stored at –80°C for analysis of contractile and regulatory protein content by SDS-PAGE and scanning densitometry, as described previously.13 14 Briefly, the gel electrophoresis procedure used a multiphasic buffer system that incorporated the following features: (1) acrylamide-piperazine diacrylamide ratio of 200:1, (2) pH 9.3 for running gel buffer, and (3) running gel buffer molarity of 0.75 mol/L. The gels for SDS-PAGE were prepared with 3.5% acrylamide in the stacking gel and 12% acrylamide in the separating gel. Samples were separated by SDS-PAGE at constant current (20 mA) for 5 hours. Stained gels were then fixed with glutaraldehyde overnight, washed, silver stained, and dried between Mylar and cellophane sheets. Gels were analyzed by measuring the areas under the peaks corresponding to MHC isoforms, troponin C (TnC), and MLCs using Molecular Analyst software (Bio-Rad) and an Arcus II scanner.
Immunoblotting was carried out as described by Westfall et al.14 After protein separation by SDS-PAGE (above) gels were transblotted onto polyvinylidene difluoride membrane (0.45 μm; Millipore) for 2000 volt-hours and fixed in PBS (Sigma) containing 0.25% glutaraldehyde. Immunodetection was carried out by initially blocking nonspecific binding sites with Tris-buffered saline containing 5% nonfat dry milk overnight. Blots were then incubated with an anti-troponin I (TnI) antibody (Ab) (monoclonal Ab 1691, Chemicon; 1:500) for 1.5 hours and washed in Tris-buffered saline with 0.5% milk. Ab binding was detected by enhanced chemiluminescence (ECL; Amersham) after a 1-hour incubation in horseradish peroxidase–conjugated goat anti-mouse Ab (Sigma; 1:1000). Blots were stripped and reprobed with JLT-12 anti-troponin T (TnT) Ab (1:200; Sigma) and then stripped and reprobed again using an anti-tropomyosin Ab (1:1 000 000; Sigma clone Tm311). The 3 primary antibodies used here recognize all muscle isoforms of their respective proteins.
To derive values for the midpoint (termed pCa50 or K) and Hill coefficient (n) from the stiffness-pCa and tension-pCa relationships, data were fit using the Marquardt-Levenberg nonlinear least-squares-fitting algorithm using the Hill equation in the following form: P=[Ca2+]n/(Kn+[Ca2+]n), where P is the fraction of maximum tension (or stiffness) obtained at pCa 4.0.
When more then 2 data sets were compared, ANOVA was used to determine whether significant differences exist between groups. When interactions among the various groups were indicated by ANOVA, a Student 2-tailed t test was used as a post hoc test to determine significant differences between 2 mean values using Bonferroni corrected values for multiple comparisons. The mean value was derived from a sample size of 6 to 10 preparations. A probability level of P<0.05 was selected as indicating significance. Values are given as mean±SEM.
MHC Isoforms and Ca2+-Activated Tension Development
To investigate the effects of altered cardiac MHC isoform expression on the steady-state Ca2+-tension relationship in single ventricular myocytes isolated from adult rats, the MHC isoform expression pattern was modified in adult rats by treating them chemically to induce the hypothyroid state. The hypothyroid state of these animals was confirmed by assaying serum concentrations of T3 and T4. The serum concentrations of T3, T4total, and T4free were, respectively, 8.2±1.8 (mean±SD) ng/dL, <1 μg/dL, and 0.15±0.04 ng/dL for hypothyroid rats (n=6) and 60±9.5 ng/dL, 2.1±0.4 μg/dL, and 1.62±0.13 ng/dL for euthyroid rats (n=3).
The steady-state dependence of tension on [Ca2+] differed significantly between cardiac myocytes isolated from hypothyroid and control animals. Specifically, the tension-pCa relationship was shifted to the right, representing a 48% increase in free [Ca2+] required to achieve half-maximal tension and indicating a desensitization of the contractile apparatus to Ca2+ activation in cardiac myocytes isolated from hypothyroid compared with control animals (Figure 1⇓, Table⇓). This result differs from earlier studies that reported no change10 or a 0.06-pCa unit leftward shift in the tension-pCa relationship in myocardium from hypothyroid animals.11 The basis for these conflicting findings is unknown. One challenge in reconciling this conflict is that details of the experiments differed significantly among the studies. For example, the earlier studies examined multicellular cardiac preparations, whereas we used the single myocyte preparation. The single myocyte preparation has advantages over multicellular preparations owing to the reduced diffusion distance of the single cardiac myocyte. In addition, some difficulties associated with larger multicellular preparations, including issues of uniform activation and relaxation of the contractile machinery, are minimized in a single myocyte preparation. Thus, from a mechanical standpoint, the single cell has distinct advantages over the multicellular preparation. However, other experimental differences are also apparent among the studies, including species used (rat, rabbit, and human), which could have contributed to these disparate results. A full accounting of the basis of these differing findings will require additional future studies.
In other findings, the Hill coefficient, which reports the steepness of the tension-pCa relation and is reflective of the cooperativity of the thin-filament regulatory system, was not different between the 2 groups (Table⇑). Maximum Ca2+-activated tension was also not significantly different in myocytes from hypothyroid (22.9±7.3 kN/m2; n=10) compared with control animals (22.1±3.1 kN/m2; n=10), a result in agreement with a previous study using permeabilized rat trabeculae.11
The mechanism of the altered Ca2+ sensitivity of contraction in myocytes from hypothyroid animals is not known, although it is possible that the hypothyroid state may have induced alterations in the expression of key regulatory proteins. Induction of hypothyroidism resulted in a transition in cardiac MHC isoforms from predominantly the α isoform to exclusively the β isoform (Figure 2⇓), as shown previously.2 3 21 We also analyzed the expression pattern of several key myofilament proteins to examine whether their expression pattern was altered (Figures 2⇓ and 3⇓). Western blot analyses showed no differences in adult isoform expression pattern for TnI, TnT, and tropomyosin in adult cardiac myocytes isolated from hypothyroid animals as compared with those isolated from euthyroid animals (Figure 3⇓). Using SDS-PAGE, there was no detectable change in the normal ventricular isoform expression pattern of MLCs 1 and 2 between the euthyroid and hypothyroid groups (Figure 2⇓). In addition, densitometric analyses of myocyte samples run on 5 separate gels showed no significant alteration (P>0.05) in the stoichiometry of MLCs 1 and 2, or for TnC [the hypothyroid (n= 28) and euthyroid (n=13)], calculated as fractions [(eg, LC/(LC1+LC2)] or ratios (eg, LC1/LC2). These calculated values for the hypothyroid and euthyroid groups were, respectively: 0.59±0.02 and 0.64±0.02 for LC1/(LC1+LC2), 0.40±0.02 and 0.36±0.02 for LC2/(LC2+LC1), 2.1±0.6 and 1.9±0.2 for LC1/LC2, and 0.16±0.02 and 0.11±0.02 for TnC/(TnC+LC1)]. Taken together, these results are evidence that only the MHC isoform had been altered in adult cardiac myocytes obtained from the hypothyroid animals (Figure 2⇓). These findings, however, do not fully preclude the possibility that small changes in the stoichiometry of the contractile apparatus or in isoform expression, which may have gone undetected in the SDS-PAGE and Western analysis, could have contributed to the alteration in Ca2+ sensitivity of tension shown in Figure 1⇑.
To provide insight into the basis of altered Ca2+-activated contraction found in myocytes from hypothyroid animals, we examined the instantaneous dependence of tension on length (ΔP/ΔL ie, instantaneous stiffness) to estimate the relative number of strong crossbridge attachments in single cardiac myocytes over a wide range of activating [Ca2+]s. A representative record of the tension response to a small-amplitude (3 nm/half sarcomere) sinusoidal oscillation (1.0 kHz) in end-to-end length for an isolated cardiac myocyte is shown in Figure 4⇓. Stiffness was calculated by subtracting the stiffness obtained at pCa 9.0 from the stiffness values recorded at pCa 7.0 to 4.0. Results showed a rightward shift in the relative stiffness-pCa relationship for cardiac myocytes isolated from hypothyroid compared with control animals (Figure 4⇓, Table⇑). Plots of the tension-stiffness relationship were well fit by single straight lines, with slopes near unity, and with no significant difference between the hypothyroid and control groups (Figure 4C⇓).
The main new findings of this study are the significant rightward shifts in both the tension-pCa and relative stiffness-pCa relationships in the β-MHC–expressing adult single cardiac myocytes compared with the predominantly α-MHC–expressing adult single cardiac myocytes. The mechanism of this shift in Ca2+ sensitivity is not known. The observed desensitization of the thin-filament regulatory system in β-MHC–expressing cardiac myocytes appears unrelated to possible differences in force-generating capacity of the β-MHC compared with the α-MHC isoform, because (1) maximum Ca2+-activated force generation was not significantly different between these groups and (2) the slope of the relative stiffness–relative tension relationship was not different between groups, suggesting that force production per strong crossbridge interaction, or the distribution of force-generating crossbridge states, is not cardiac MHC isoform dependent.
One potential mechanism of the rightward shift in Ca2+ sensitivity centers on the role of myosin binding to influence activation of the thin-filament regulatory system. There is now good evidence of reciprocal interactions between Ca2+ binding to the thin filament and myosin binding to actin.6 7 8 9 In addition, as there appear to be differences in this reciprocal coupling process dependent on whether the myosin interaction with actin is noncycling (rigor) or cycling,8 it seems possible that crossbridges with different inherent rates of cycling may also differentially affect the activation of the thin filament. An increase in duty cycle in relation to the time Ca2+ is bound to TnC has been proposed to cause a leftward shift in the tension-pCa.24 Our finding, however, of a rightward shift, rather than a leftward shift, of the tension-pCa and relative stiffness–pCa relationships in the β-MHC–expressing versus α-MHC–expressing cardiac myocytes provides experimental evidence in opposition to this model. The rightward shift in the tension-pCa relationship could be caused by alterations in the phosphorylation status of TnI; however, earlier reports indicate a decrease in basal TnI phosphorylation,25 which would tend to shift the tension-pCa to the left, not the right. Thus, although the actual mechanism of the rightward shift in the tension-pCa relationship is not resolved in the present study, our work does suggests that crossbridge factors, including possible roles of actin-myosin state transitions that are MHC isoform dependent, could underlie the observed alteration of Ca2+-activated mechanical function reported here.
Our findings may also help explain the basis of altered contraction in intact cardiac muscle preparations isolated from hypothyroid animals. Peak isometric twitch tension is significantly reduced in papillary muscles obtained from hypothyroid rodents.26 27 An earlier study that found a reduced amplitude and increased duration of the Ca2+ transient associated with the cardiac twitch concluded that these effects may be sufficient to account for the decreased myocardial force found in hypothyroid animals.26 Our finding, however, of a desensitization of the contractile apparatus to Ca2+ activation in permeabilized myocytes isolated from hypothyroid animals would also be expected to contribute to reductions in twitch force in the intact myocardium. This is evident when considering that under normal conditions, the myoplasmic [Ca2+] increases from a baseline level of ≈10–7 mol/L and approaches a peak value of ≈10–5 mol/L, depending on the inotropic state of the heart. That is to say, Ca2+ typically fluctuates within the submaximal range in terms of force production. Thus, at any given submaximal [Ca2+], the force produced by the β-MHC–expressing cardiac myocytes would be predicted to be reduced in comparison with the α-MHC cardiac myocytes, using the assumption that tension results obtained during steady-state calcium conditions are applicable to the forces in response to dynamic alterations in calcium. The magnitude of shift in pCa50s reported here, 0.17 pCa units for tension and 0.29 pCa units for stiffness, represent a 48% and a 95% increase, respectively, for the calcium concentration required for one-half maximum activation. On a physiology scale, this represents a large alteration in the calcium sensitivities of tension and stiffness, which would be expected to contribute to altered mechanical function in vivo. In support of this idea, recent data on muscle preparations obtained from patients with hypertrophic cardiomyopathy have reported comparatively small alterations in pCa50s for tension (≈0.05 pCa units28 ). This appears to underscore the importance of tightly regulated control of the tension-calcium relationship, in that seemingly small deviations from control could, over time, have significant consequences to the overall mechanical performance of the myocardium in vivo.
Analysis of the Linearity of the Force Transducers
In this study, instantaneous stiffness measurements were used to estimate relative changes in the numbers of strongly attached crossbridges in single cardiac myocyte preparations. Because some of the stiffness measurements made here were obtained at frequencies above the resonant frequencies of the transducers, it was important to verify the linearity of the transducers at these frequencies. Thus, control experiments were performed to characterize the linearity of the model 403A and 400A force transducers under nearly identical conditions used in the experiments. This was accomplished by recording the amplitude of force in response to small-amplitude sinusoid length changes introduced via the motor. The first criterion that needed to be satisfied was the selection of a natural or synthetic material that would have an elastic modulus approximating that of a muscle during contraction, that is, ≈107 N/m2.22 Second, it was critical that this material be purely elastic in nature, that is, it must obey Hookes’ Law: f=k(x), where f is force, k is a constant, and x is displacement, because the stiffness of a purely elastic element is frequency independent. Natural rubber fiber appears to satisfy these criteria.29 Natural rubber has an elastic modulus of 1.05×106/m2, and after a pretest stretch is considered purely elastic for small length excursions.29 Small fibers from natural rubber bands (dimensions ≈7 mm in length and 200 μm in width) were dissected and attached to the apparatus in the same way that either skeletal fibers or cardiac myocytes are attached, except that in the case of the myocyte-like attachment procedure, paraffin wax was used to attach the rubber fiber to the micropipettes rather than the silicone adhesive. Small-amplitude sine waves (amplitude ≈0.1% of overall rubber fiber length) were then introduced to the rubber fiber over the frequency range 10 Hz to 4 kHz while the force response was recorded. The results showed that for the model 403A force transducer, which was used to record tension in cardiac myocytes, stiffness measurements can be determined up to at least 2.0 kHz. This was demonstrated in an experiment in which a 2.0-kHz sinusoid of varying peak-to-peak amplitude was introduced to the rubber fiber and the amplitude of the force response was found to vary linearly with changes in the amplitude of the length perturbation (slope=1.10). Thus, under these experimental conditions using the natural rubber fiber, it was demonstrated that the 403A force transducer remains linear at 2.0 kHz. For the model 400A force transducer, the same type of experiment was done, and it was determined that this force transducer was linear up to at least 3.5 kHz under these experimental conditions, in which the slope of the change in force in response to change in length relationship was linear (slope=1.04). For both the model 403A and model 400A transducers, the frequency of the force sinusoid was identical to that of the length sinusoid. It is known that attenuation of the amplitude (roll-off) response of the transducer occurs at frequencies above the resonant frequency. However, because we report here relative alterations in instantaneous stiffness at a fixed oscillation frequency, the attenuation response did not influence the results. This is shown in experiments in which, in soleus fibers, the relative stiffness data collected at 1.0, 2.0, and 3.0 kHz were all highly comparable.
This work was supported by grants from the National Institutes of Health, The Whitaker Foundation, and The American Heart Association. M.V.W. was supported in part by the University of Michigan Cardiovascular Research Center and by the American Heart Association. J.M.M. is an Established Investigator of the American Heart Association. We thank the University of Michigan ligand laboratory for measuring serum concentrations of T3 and T4.
- Received June 8, 1998.
- Accepted April 5, 1999.
- © 1999 American Heart Association, Inc.
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