Am J Physiol Heart Circ Physiol 287: H196-H202, 2004.
First published March 4, 2004; doi:10.1152/ajpheart.00948.2003
0363-6135/04 $5.00
Single cell mechanics of rat cardiomyocytes under isometric, unloaded, and physiologically loaded conditions
Satoshi Nishimura,1
So-ichiro Yasuda,1
Masayoshi Katoh,1
Kelly P. Yamada,2
Hiroshi Yamashita,1
Yasutake Saeki,3
Kenji Sunagawa,4
Ryozo Nagai,1
Toshiaki Hisada,2 and
Seiryo Sugiura2
1Department of Cardiovascular Medicine, Graduate School of Medicine, and 2Biomechanics Division, Institute of Environmental Studies, Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033; 3Department of Physiology, School of Dental Medicine, Tsurumi University, Kanagawa 230-5801; and 4Department of Cardiovascular Dynamics, National Cardiovascular Center Research Institute, Osaka 565-8565, Japan
Submitted 10 October 2003
; accepted in final form 2 March 2004
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ABSTRACT
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One of the most salient characteristics of the heart is its ability to adjust work output to external load. To examine whether a single cardiomyocyte preparation retains this property, we measured the contractile function of a single rat cardiomyocyte under a wide range of loading conditions using a force-length measurement system implemented with adaptive control. A pair of carbon fibers was used to clamp the cardiomyocyte, attached to each end under a microscope. One fiber was stiff, serving as a mechanical anchor, while the bending motion of the compliant fiber was monitored for force-length measurement. Furthermore, by controlling the position of the compliant fiber using a piezoelectric translator based on adaptive control, we could change load dynamically during contractions. Under unloaded conditions, maximal shortening velocity was 106 ± 8.9 µm/s (n = 13 cells), and, under isometric conditions, peak developed force reached 5,720 nN (41.6 ± 5.6 mN/mm2; n = 17 cells). When we simulated physiological working conditions consisting of an isometric contraction, followed by shortening and relaxation, the average work output was 828 ± 123 J/m3 (n = 20 cells). The top left corners of tension-length loops obtained under all of these conditions approximate a line, analogous to the end-systolic pressure-volume relation of the ventricle. All of the functional characteristics described were analogous to those established by studies using papillary muscle or trabeculae preparations. In conclusion, the present results confirmed the fact that each myocyte forms the functional basis for ventricular function and that single cell mechanics can be a link between subcellular events and ventricular mechanics.
cardiomyocyte; mechanics; carbon fiber
SINGLE CARDIOMYOCYTE PREPARATIONS have been widely used to establish a link between subcellular molecular events and functional characteristics of the heart in the field of basic physiology (2, 3, 11, 23) and also for the evaluation of genetic modification of myocytes (8, 17). The simple geometry of a single cell offers great advantages over multicellular preparations due to uniformity in myofibril alignment and stress-strain distribution as well as homogeneous distribution of exogenous indicators or gene products. On the other hand, irritability of the sarcolemma devoid of collagen matrix makes cell attachment to the experimental apparatus difficult, thereby disturbing measurements of force, stiffness, and shortening velocity under a variety of loading and perturbational conditions. Thus existing methods were unable to provide a complete description of the mechanical component of the contractile process that can be related to underlying biochemical processes (3).
To overcome this problem, we have already reported a novel force measurement system for a single cardiomyocyte (26) in which carbon fibers enabled the stable recording of force with minimal requirements for technical skill. In addition, feedback control of fiber movement permitted the study of mechanics of a single cardiomyocyte under isometric as well as unloaded shortening conditions (25). Application of this method at the two extremes of loading conditions provided us with a unique opportunity to study the load dependence of contraction characteristics. The behavior of cardiomyocytes as they are in the wall of working heart is different. During the cardiac cycle, each cardiomyocyte in the ventricular wall faces varying loading conditions to trace a force-length loop analogous to the pressure-volume loops of the ventricles. Both experimental (13) and simulation studies (21, 22) of cardiomyocytes suggest considerable variations exist in the shape of force-length loops within the ventricular wall and under different loading conditions. To our knowledge, no study has reported such force-length loops and their characteristics of a single cardiomyocyte in vitro.
In this study, we succeeded in recording single cardiomyocyte contraction mechanics under physiological loading conditions and compared findings with those under isometric and unloaded conditions as well as under inotropic intervention in the same myocyte. Because noise in length signals hampered real-time feedback control, we adopted an adaptive control strategy in combination with digital filtering of the signal. The results are shown together with the simultaneous recording of sarcomere length to indicate the potential of this method in linking the cardiac function at molecular, cellular, and ventricular levels.
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METHODS
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Cell isolation.
All studies were conducted in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and were approved by the Institutional Animal Care and Use Committee. Single ventricular myocytes were enzymatically isolated using a modified dispersion technique that has been described previously (9). Briefly, the heart was quickly removed from male Wistar rats (7–10 wk old) under pentobarbital anesthesia. Retrograde perfusion was performed with Ca2+-free HEPES-Tyrode solution [containing (in mM) 137 NaCl, 5.4 KCl, 1.8 CaCl2, 0.5 MgCl2, 0.33 NaH2PO4, 5 HEPES, and 5 glucose; pH 7.4 adjusted by NaOH at 37°C] for 5 min, followed by an enzyme solution containing collagenase (0.4 mg/ml collagenase S-1, Nitta gelatin), protease (0.08 mg/ml, type XIV, Sigma), and 0.1 mM Ca2+ for 3.5 min. The ventricular tissue was then cut into small pieces and filtered with 200-µm nylon mesh. The calcium concentration of Tyrode solution was gradually increased to 1.1 mM, and the myocytes were transferred to the experimental chamber. The glass bottom of the chamber was coated with 2-hydroxyethyl methacrylate (Sigma) to prevent adhesion of cells.
Force-length measurements.
The basic principle of the single cardiomyocyte force-length measurement system has been described previously (25, 26). In each experiment, a single cardiomyocyte was selected under a microscope according to the following criteria: 1) rod-shaped cell with average sarcomere length > 1.65 µm (measured by on-line Fourier analysis of optical density traces of the sarcomere pattern of a myocyte image, SarcLen, IonOptix; Milton, MA); and 2) responded to electrical stimulation to contract over 5% of the total cell length. To each end of the selected myocyte, we attached a carbon fiber using micromanipulators. One of the fibers was compliant (diameter 7 µm, length 1–1.2 mm, stiffness 80–200 nN/µm), whereas the other thick one was rigid (diameter 30 µm, length 
1 mm, stiffness > 1,000 nN/µm), serving as a mechanical anchor. They were made from a mixture of fine graphite granules and resin oligomer and made by shaping into rods by thrusting through a thin hole in a block of sapphire (26). The image of the compliant fiber was projected onto a linear 1,024-element photodiode array (S3903, Hamamatsu Photonics) for monitoring its bending motion induced by active contraction or passive stretch. Furthermore, we controlled the position of the compliant fiber by moving the piezoelectric translator (PZT; P-841.40, Physik Instrumente) connected to it (Fig. 1). The cell was electrically stimulated at 0.5 Hz with pulses of 10-ms duration. Before force measurement, we stretched the diastolic cell length to 105% of the slack length while measuring sarcomere length (IonOptix). Streptomycin sulphate (10 µg/ml, Sigma) was added to the Tyrode solution to prevent stretch-induced arrythmia. All experiments were performed at 37°C (Thermoplate, TOKAIHIT).
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Fig. 1. Diagram of the experimental setup. Position of the fiber was detected by the photodiode array. The position signal was processed by a personal computer (PC), and the calculated command signal was applied to a piezoelectric translator (PZT) connected to the carbon fiber. The sarcomere pattern was captured by a charge-coupled device (CCD) camera, and sarcomere length was determined by fast Fourier transform (FFT).
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Estimation of force.
The stiffness of the carbon fiber was determined by pushing it against a glass fiber of known stiffness (27). The stiffness thus determined agreed well with the theoretical value (K) for a beam with a circular cross section derived from the following equation:
 | (1) |
where D is the diameter of the fiber (7 µm), l is the length of the fiber (1–1.2 mm), and E is Young's modulus of carbon (0.39 N/µm2). All previous studies including ours (16, 23, 25, 26) have used this stiffness value assuming that the cardiomyocyte applies concentrated lateral load to the free end of the cantilever beam (APPENDIX, Case A). However, the following experimental observations led us to consider an alternative model for the fiber displacement in which a bending moment is applied to the tip of the beam (APPENDIX, Case B): 1) the load was not concentrated at the tip because the myocyte attaches the fiber along its width; and 2) the myocyte shortened while always retaining its straight shape. We have examined the validity of models by closely monitoring the shape of the fiber while it was bent by motion of the myocyte. We measured the displacement of the fiber at multiple points from the tip of the fiber by shifting the photodiode array sensor along the image of the fiber during contraction. As shown in Fig. 2, we plotted the measured displacement (normalized by the displacement at the tip) and compared it with the predictions by cases A and B in the APPENDIX. In proximity to the tip, the carbon fiber moved in a parallel manner (without rotation) because of its firm attachment to the myocyte and its displacement was close to the prediction by case B. This result indicated that a bending moment was applied to the tip of the beam and thus must be taken into account for analysis (APPENDIX, Case B). Accordingly, we used the effective stiffness (K') defined as follows (see the APPENDIX) for the estimation of force:
 | (2) |
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Fig. 2. Displacement of the carbon fiber induced by myocyte contraction. The experimental data ( ) are compared with the predictions by case A (solid line) and case B (dashed line) in the APPENDIX. Displacement was normalized by the displacement at the tip.
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In this analysis, force (F) was calculated as
 | (3) |
where x is the shortening length of the myocyte and y is the displacement of the PZT.
Digital control of the system.
To enhance the ability of the system to achieve working conditions of a single myocyte, we replaced the analog circuit (26) with a personal computer (PC)-based digital control system. Cell length signals obtained by the photodiode array sensor were sampled and processed at 1 kHz, and the generated command signal was applied to the PZT driver with a 16-bit analog-to-digital, digital-to-analog converter (6035E, National Instruments) connected to the PC. We adopted a two-stage adaptive control strategy (19). During the preparation stage, which consisted of five paced contractions, the PZT was held at the neutral position to obtain the baseline force-length history. Next, in the adaptation stage, the command signal (y) was calculated from x and F of the preceding contraction. To obtain the isometric condition (x = 0), the error signal in the ith contraction was xi – 0 (= xi). Thus the command signal for the next contraction would be
 | (4) |
where A is a negative constant. Similarly, for an unloaded shortening contraction (F = 0), command for the (i + 1)th contraction would be
 | (5) |
where Fi is calculated by Eq. 3 and A is a constant. With an empirically determined A value, yi converged within three or four contractions, and measurement was performed in the next contraction. We simulated the physiological loading sequence by switching the control mode from isometric-isotonic contraction to isometric-auxotonic relaxation. When the myocyte was stimulated, myocyte length was held constant and isometric force developed. When the force reached a predetermined threshold, control mode was switched to isotonic and the myocyte was allowed to shorten. The myocyte length was then kept constant until the force became zero, and the myocyte was stretched to the original length under auxotonic length control.
We performed a single measurement for each protocol in each myocyte.
Data analysis.
All data were sampled at 1 kHz and recorded by an analog-to-digital converter connected to a PC (MacLab 8s, ADInstruments). It is known that isolated cells, when placed in physiological medium, assume a cross-sectional area that resembles a flattened ellipse (1, 24). We measured the long and short axes of myocytes by rolling them using carbon fibers under a microscope and determined the average ratio between long and short axes as 3:1 in a different set of experiments (data not shown). The cross-sectional area of the myocyte was estimated from videotaped images assuming an elliptical cross section with this value. Results are expressed as means ± SE.
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RESULTS
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We succeeded in measuring force and length relations in 20 cells (Table 1). The mean cell length between two attached carbon fibers was 67.0 ± 2.5 µm, the cell width was 25.9 ± 1.36 µm, and the diastolic sarcomere length was 1.74 ± 0.01 µm before stretch was applied.
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Table 1. The contractile functions under unloaded, isometric, and physiologically loaded conditions for each myocyte studied
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Load dependence of cardiomyocyte contraction.
Figure 3 shows typical records of the length and force changes under isometric and unloaded conditions obtained from the same cardiomyocyte. Under isometric conditions, the shortening length was <0.5 µm and the peak force was 5,720 nN (41.6 ± 5.6 mN/mm2; n = 17 cells), comparable to those obtained in papillary muscle preparations. Under unloaded conditions, cells shortened to 5.81 ± 0.27 µm (n = 18 cells), which was equal to 8.9% of the cell length under control (the segment between the fibers under resting conditions). The maximal shortening velocity was 106 ± 8.9 µm/s (n = 13 cells). Variability in the isometric force per unit cross-sectional area and percent shortening under unloaded conditions was fairly small, indicating the reproducibility of this experiment. The time course of contraction also showed a physiological response to load. That is, under isometric conditions, the duration of contraction shortened and the time to peak force was also decreased, as shown in Fig. 3.
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Fig. 3. Cell length and force during isometric and unloaded shortening contractions in the same myocyte. A: cell length during isometric (solid line) and unloaded shortening (dashed line) contractions. Length change during the isometric contraction was <0.5 µm. B: developed force during the isometric (solid line) and unloaded shortening (dashed line) contractions shown in A. During unloaded shortening, the force was zero. In this cell, cross-sectional area was 749 µm2.
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We succeeded in achieving the ejecting mode of contraction in 20 cells. The achieved physiological work loops in 20 cells were similar to those reported in both experimental (13) and simulation studies (Fig. 4) (22). We calculated the external work using force per myocyte (raw data: N) and length (in m) data. The achieved physiological work calculated thus determined in 20 cells was 828 ± 123 J/m3.
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Fig. 4. Force-length loop of a single cardiomyocyte under various loading conditions. Data were obtained during adaptive control for isometric and unloaded shortening as well as simulated ejection. The y-axis shows force (raw data) and force per cross-sectional area (in this cell, cross-sectional area was 749 µm2). Linear regression was applied to the top left corner points of the loops. The slope of the regression line was 1,730 nN/µm. External work produced by the ejecting contraction was 1,139 J/m3.
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We changed load and obtained a series of force-length loops. The curve connecting the top left corners of these loops was convex upward, analogous to the end-systolic pressure-volume relation of the rodent ventricle (Fig. 4) (12). Applying linear regression to these points yielded a slope of 1,260 ± 108 nN/µm (n = 17 cells).
By stretching the cells before the contraction, we could observe the effect of increasing preload. As shown in Fig. 5, not only the isometric force (Fig. 5A) and unloaded shortening length (data not shown) but also the external work (Fig. 5B) increased depending on the preload. Because muscle length and force at baseline varied considerably, we could not achieve statistical analysis of this findings, but similar preload dependence was found in 10 cells.
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Fig. 5. Preload dependence of contractile function A: isometric contractions under two different (solid line 1.78 µm; dashed line 1.71 µm) preloads. B: ejecting contractions under two different preloads showing the preload dependence of external work. The y-axis shows force (raw data) and force per cross-sectional area (in this cell, cross-sectional area was 323 µm2).
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Sarcomere length.
We measured sarcomere length and compared it with simultaneously recorded cell length. We confirmed that cell length always changed in parallel with sarcomere length under resting conditions as well as during contraction against low load (Fig. 6A). In 12 cells in which sarcomere length signals of good quality were obtained, similar observations were made. Although it was difficult to determine sarcomere length during isometric conditions due to blurring of the sarcomere pattern, we could record it in eight cells. Although small compared with sarcomere shortening during uncontrolled contraction under unloaded conditions (Fig. 6B, solid line), we observed internal shortening of sarcomeres (Fig. 6B, dashed line) of the same magnitude (0.1 µm) in 8 cells.
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Fig. 6. Relationship between cell length and sarcomere length. A: simultaneous recording of cell length (solid line) and sarcomere length (dashed line) during contraction under unloaded conditions. B: sarcomere length during isometric contraction (dashed line) and under unloaded conditions (solid line) recorded in the same cell.
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DISCUSSION
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Single cell mechanics by the carbon fiber technique.
In this study, we studied the mechanics of single rat cardiomyocytes over a wide range of loading conditions including isometric, unloaded, and physiological loading conditions. To our knowledge, this is the first time that physiological force-length loops have been reported in isolated myocytes. Because of its important role in relating subcellular molecular events to ventricular dynamics, many researchers have studied single cell mechanics of cardiomyocytes using various methods (11). Compared with other methodologies, the carbon fiber technique is superior in two aspects. First, it is relatively simple and does not require technical expertise. Second, attachment of carbon fibers results in minimal damage to the sarcolemma (11). With the use of carbon fibers (26), the overall success rate for establishing firm attachment to myocytes was over 80% in this series of experiments, and myocytes remained stable for 10 min of contractions by electric stimulation. This excellent stability enabled us to study myocyte mechanics under various loading conditions as well as under inotropic interventions in the same myocyte, which, in certain cases, was helpful in avoiding cell-to-cell variations. In addition, we obtained a peak isometric force of 5.72 µN in this study. This is in the highest range of twitch force reported so far [Ref. 3 and review by Bluhm et al. (2)] and is 75% of the maximally activated force (7.5 µN) (10) obtained in a single skinned rat cardiomyocyte, supporting its usefulness.
Physiological significance.
In rat trabeculae preparations, Janssen and de Tombe (14) reported an isometric twitch force of 45 mN/mm2 for muscle isometric twitches and 88.5 mN/mm2 for sarcomere isometric twitches. In a left ventricular papillary muscle preparation, isometric force was 
6 g/mm2 (60 mN/mm2) (5). The isometric force obtained in this study (41.6 ± 5.6 mN/mm2) was somewhat lower but close to these values. For shortening velocity, we obtained 106 ± 8.9 µm/s, which is equivalent to 1.58 lengths/s (37°C). In rat trabeculae, predominantly containing the V1 myosin isoform, an unloaded shortening velocity of 2.3 lengths/s (30°C) has been reported (20). On the other hand, Josephson et al. (15) measured the maximal shortening velocity of euthyroid rat ventricular myocytes at 29°C and reported a value of 1.17 lengths/s. Again, our results are close to these values, suggesting that carbon fiber attachment does not create extra load if its movement is properly controlled as in this study. However, the key feature required for single cell mechanics is how accurately it can reproduce and describe the behavior of the cell in the body. In response to change in afterload, we obtained a series of force-length loops. The top left corners of these loops distributed along a straight line, analogous to the end-systolic pressure-volume relation of the ventricle (Fig. 4). Furthermore, when inotropic intervention was applied to a single myocyte by adding isoproterenol (2 µM) to the medium, the slope of this line increased in a similar manner with the ventricular end-systolic pressure-volume relation (Fig. 7, A and B). Preload dependence was also confirmed (Fig. 5). Finally, using digital control, we could obtain physiological force-length loops of a single cardiomyocyte (Fig. 4) resembling those reported in experimental (13) and simulation studies (21, 22). The average work output per unit volume calculated from the stress-relative shortening area was 828 ± 123 J/m3. If we assume the density of cardiac muscle to be 1g/cm3, 1 g of the rat ventricle (cm3) would generate 0.83 mJ. This value is 13% of the external work done by a rat ventricle ejecting 500 µl of blood while generating 100 mmHg. The cause of this discrepancy is not clear, but the lack of sympathetic stimulation to the isolated myocyte could be one of the possibilities.
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Fig. 7. Force-length relation of a single cardiomyocyte before (A) and after (B) the addition of isoproterenol (2 µM) to the medium. Isometric force increased from 44 to 85 mN/mm2, and the slope of the regression line increased from 11 to 19 mN·mm–2·µm–1. The y-axis shows force (raw data) and force per cross-sectional area (in this cell, cross-sectional area was 197 µm2).
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Adaptive control of cell length and force.
With the real-time analog control system we used in previous studies (25, 26), it was very difficult to achieve physiological loading largely because of noise in the length signal. Adaptive control, together with zero-delay low-pass filtering, avoided transmission and amplification of noise and successfully circumvented this problem. Furthermore, once the proper command signal could be obtained, the high-intensity illumination for photodiode sensors was not required, allowing the recording of calcium indicator fluorescence for a longer period of time without causing photobleaching.
Study limitations.
The major concern with this attachment technique is to avoid damaging the ends of myocytes and to obtain uniform sarcomere spacing (18). Using real-time image analysis, we confirmed that static stretch applied to a resting myocyte could cause uniform stretch of the sarcomere in proportion to cell length. Because of the difficulty in keeping focus on the sarcomere, we could not accurately measure sarcomere length during isometric contractions. However, in the few cases where we could obtain the simultaneous recording of sarcomere length during isometric contraction, internal shortening did take place (Fig. 6B). To achieve precise control of sarcomere length, further improvement of the experimental setup may be necessary.
Finally, some myocytes were too irritable to obtain stable recordings, even with streptomycin in the medium as an inhibitor of stretch-activated channels. This might have lead to selection bias of myocytes and disturbed the experiment.
In summary, by adopting digital adaptive control, we studied the mechanics of a rat single cardiac myocyte over a wide range of loading conditions. All of the functional characteristics described were analogous to those established by a number of studies using papillary muscle (4, 6) or trabeculae preparations (7). The present results confirmed the fact that each myocyte forms the functional basis for ventricular function and that single cell mechanics can be a link between subcellular events and ventricular mechanics.
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APPENDIX: RELATION BETWEEN LOAD AND LATERAL DISPLACEMENT OF A BEAM
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Case A
When lateral force (P) applied to the free end of a cantilever beam [length (l)] causes displacement (y) (Fig. 8), they are related as
 | (A1) |
or
 | (A2) |
where I is the second moment of inertia of the cross section and E is Young's modulus.
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Fig. 8. Case A. Lateral force (P) applied to the free end of a cantilever beam [length (l)] causes displacement (y).
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For a beam having a circular cross section with diameter D
 | (A3) |
Case B
For the end of fiber to move in parallel manner (without rotation), an appropriate amount of bending moment (M) should also be applied (Fig. 9). Such a load can be calculated as
 | (A4) |
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Fig. 9. Case B. For the end of fiber to move in parallel manner (without rotation), an appropriate amount of bending moment (M) should also be applied.
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The displacement (y') induced by M is
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Total displacement (y) caused by lateral load P and moment load M is then
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or
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Similarly, for a beam having a circular cross section with diameter D
 | (A8) |
In case A, the displacement y at x from the free end is calculated as
 | (A9) |
or at the distance (z) from the fixed end as
 | (A10) |
In case B, the displacement y at x from the free end is calculated as
 | (A11) |
or at z from the fixed end as
 | (A12) |
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GRANTS
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This study was supported by grants from the Program for Promotion of Fundamental Studies in Health Sciences of the Organization for Pharmaceutical Safety Research, the Vehicle Racing Commemorative Foundation, the Fugaku Trust for Medical Research, and a Research Grant for Cardiovascular Disease from the Ministry of Health, Labor and Welfare. K. P. Yamada was supported by a Japan Society for the Promotion of Science postdoctoral fellowship for foreign researchers.
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ACKNOWLEDGMENTS
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We thank C. Miyazawa for excellent technical assistance.
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FOOTNOTES
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Address for reprint requests and other correspondence: S. Sugiura, Biomechanics Div., Institute of Environmental Studies, Graduate School of Frontier Sciences, Univ. of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan (E-mail: sugiura{at}k.u-tokyo.ac.jp).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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