Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers

ARTICLE IN PRESS Journal of Biomechanics 42 (2009) 2011–2016

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Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers Sampath K. Gollapudi a, David C. Lin a,b,c, a

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, USA Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman, WA, USA c Department of Veterinary and Comparative Anatomy, Pharmacology, and Physiology, Washington State University, Pullman, WA, USA b

a r t i c l e in fo

abstract

Article history: Accepted 10 June 2009

The objectives of this study were to measure the active and passive force–length (F–L) relationships in type-I human single muscle fibers and to compare the results to predictions from the sliding filament model (the ‘‘standard model’’). We measured isometric forces in chemically skinned fibers at different sarcomere lengths (SLs) in separate maximal activations. The experimental tolerance interval for optimal SL was calculated to be (2.37, 2.95 mm), which included the prediction by the standard model (2.64, 2.81 mm). Average passive slack length was 2.2270.08 mm, and the passive F–L relationship was well described by an exponential function. Best fit lines were used to estimate the ascending and descending limbs from the active F–L data using the average SL obtained from a digital image of the fiber. The experimental descending limb was also estimated using the shortest SL to address the possible effects of sarcomere inhomogeneity (SI). The experimental slopes of the ascending and descending limbs, 0.42 Fo/mm and 0.52 Fo/mm (vs. 0.55 Fo/mm with the shortest SL) respectively, Fo being the maximal isometric force, were significantly less in magnitude than those from the standard model. These results suggested that the difference between experimental and standard models was not fully explained by SI and other factors could be important. The broader experimental F–L curve compared to the standard model implies that human muscle has functionally a wider operating length range where its force-generating capacity is not compromised. & 2009 Elsevier Ltd. All rights reserved.

Keywords: Force–length Human slow Type-1 Sarcomere Muscle fiber

1. Introduction The isometric relationship between muscle length and force is a fundamental property of skeletal muscle. It is used as a basis for almost all models of muscle contractile properties and can be used to predict the kinematic range of optimal function, such as the joint angles for maximal strength. Therefore, precise measurement of the force–length (F–L) property is crucial for understanding in vivo muscle function. Measurement of the F–L curve at the most elemental level of muscle, i.e., the sarcomeric F–L curve, is important because it is assumed to be generally applicable to all skeletal muscles. In intact frog single fibers, measurements of the sarcomeric F–L curve by Gordon et al. (1966) matched the prediction from the sliding filament model with thick (myosin) and thin (actin) filament length estimates from electron micrographs. Specifically, the model predicted the length range over which force was maximal

(i.e., the ‘‘plateau region’’) and the slopes of the ascending and descending limbs. In this paper, we will refer to the F–L curve based on the sliding filament model as the ‘‘standard model’’. To our knowledge, there has been no direct experimental verification of the sliding filament model in human muscle based upon the work in frog fibers with filament length estimates from electron microscopy. Therefore, the objectives of this study were to measure the active and passive F–L curves within a limited sarcomere length (SL) range encompassing the plateau region in type-I chemically skinned human single muscle fibers and to compare our results with the standard F–L model. Specifically, our aims were to: (1) calculate tolerance limits for optimal sarcomere length (SLo); (2) estimate the lines of the ascending and descending limbs; (3) estimate slack length (SLp); and (4) estimate the passive exponential F–L curve.

2. Methods  Corresponding author at: Voiland School of Chemical Engineering and Bioengineering, Washington State University, P.O. Box 646520, Pullman, WA 99164-6520, USA. Tel.: +509 335 7534; fax: +509 335 4650. E-mail address: [email protected] (D.C. Lin).

0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.06.013

2.1. Single fiber preparation and experimental apparatus Two thin strips of the lateral gastrocnemius muscle were harvested from a human subject with no previous musculoskeletal abnormalities during an ankle

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fracture repair surgery. The strips were maintained at a length with slight tension and were immediately washed with a series of relaxing and skinning solutions (see below for respective compositions) containing 1% (w/v) Triton X-100 at 3 1C for complete removal of the connective tissue. These strips were further dissected into smaller bundles and stored in skinning solution with 1% Triton X-100 at 20 1C. Protease inhibitors (phenylmethylsulfonyl fluoride, 0.2 M; leupeptin, 0.04 mM; E64, 0.01 mM) were included in all solutions to prevent protein degradation. These procedures were approved by the Washington State University Institutional Review Board. Single fibers measuring 2.0–3.0 mm long were separated out and the ends of each fiber were attached to small aluminum clips by superglue (cyanoacrylate). The fiber was then suspended between a force transducer (AE801, Sensor One Technologies, Sausalito, CA) and a servo motor (model 308, Aurora Scientific, Aurora, Canada) in a chamber containing relaxing solution. During each activation, SL was measured using two techniques: (1) a He–Ne laser beam was directed in the middle section of the fiber, perpendicular to its long axis. The resulting diffraction pattern was recorded at 50 Hz with a digital line scan camera (LD3500, PerkinElmer, Waltham, MA) and SL was computed from the images (Lieber et al., 1984); (2) a digital image of the central segment of the fiber (1.07 mm in length) was captured by a high-resolution camera (12 megapixels) (Fujifilm S7000) after the fiber attained the steady-state activation (defined as a change in the force less than 1% over a period of 1 s). The distribution of SLs along the section of the fiber was determined from the image (see Data Analysis). Fiber diameters at every 0.5 mm were also measured in relaxing solution to estimate the average cross-sectional area of each fiber, assuming the fiber was cylindrical (Debold et al., 2004; Metzger and Moss, 1987). 2.2. Experimental protocol All experiments on each fiber were conducted at 20 1C with a maximum variation of 70.5 1C (maintained by a water bath and monitored using a thermocouple). Fibers were bathed in three different solutions (relaxing, preactivating, activating) with the following concentrations (in mM): 5.88 Di-sodium Adenosine tri-phosphate; 10 ethylene-glycol tetra-acetic acid; 40 N,N-bis (2Hydroxyethyl)-2-aminoethanesulfonic acid 6.56 Mg2+, 1 dithiothreitol; and 15 Disodium Creatine Phosphate (Fukuda et al., 2003). Ionic strength was adjusted by Kpropionate to 180 mM, pH adjusted to 7.0, and 100 U/ml Creatine Phosphokinase added before the start of the experiments. pCa of each solution was adjusted by CaCO3-EGTA for the relaxing (pCa ¼ 9.0), pre-activating (pCa ¼ 9.0; HDTA instead of EGTA), and activating solutions (pCa ¼ 4.5). All the reagent concentrations were based upon the program by Fabiato (1988). A fiber was first bathed in relaxing solution and then incubated in preactivating solution for 3 min (to facilitate activation). The SL based upon laser diffraction was set to a desired value, e.g., 2.6 mm, by adjusting the fiber length. Time-based force and length recordings were initiated prior to replacing relaxing with activating solution and the recordings were continued for 40 s. The activating solution was then replaced with relaxing solution and the passive force was measured at the same SL recorded during activation. The fiber was relaxed for 5 min and the cycle was repeated at five other SLs. For each fiber, forces were measured at six different SLs spanning from 2.0 to 4.0 mm in six separate activation/relaxation sequences (more than six activations could result in fiber degradation). This measurement range was determined by the lack of clear sarcomere patterns at shorter lengths and the disruption of orderly sarcomere patterns at the longer lengths. We randomized the order of the different SLs to avoid biasing from the sequence of lengths. Randomized SLs were chosen from a probability distribution where twice as many measurements were made from 2.5 to 3.0 mm over other lengths for the entire fiber population. This was done to improve the statistical analysis in the region where SLo has been estimated previously (see Discussion). Upon experiment completion, the fiber was typed for myosin heavy chain (MHC) isoform by electrophoresis following the protocol of Bamman et al. (1999). 2.3. Data analysis Large amounts of inhomogeneity in SLs can greatly influence the F–L relationship, causing a broadening of the curve (see Discussion). Our strategy to avoid this artifact was to: (1) only analyze fibers which had less than a certain amount of sarcomere inhomogeneity (SI) and (2) use methods from a previous study to determine the appropriate SL to plot with the recorded force. The criteria for minimal SI were (justification of criteria is found in Discussion): (1) Creep, or a slow continuous increase in force, is a indication of inter-sarcomere dynamics (Julian et al., 1978; Julian and Morgan, 1979). We considered that a fiber did not exhibit creep if the force rise became less than 1% over a period of 1 s. (2) Due to compliance at the attached ends of the fiber, shortening of the central segment usually occurred (see Results). The acceptable amount of shortening upon activation of the diffraction-based SL was 10%. (3) SI was assessed directly by subdividing the digital image of the activated fiber into eight segments of equal length and determining the average SL of each segment by imposing a fast Fourier transform (FFT) (Slawnych et al., 1994). The acceptable

amount of SI was a coefficient of variation (CV) of the SLs less than 5%. In addition, to ensure that a fiber activated maximally, we only analyzed fibers whose maximum isometric stress at optimal SL was greater than 100 kPa (Bottinelli et al., 1996; Galler and Hilber, 1994; Hilber and Galler, 1997; Julian and Morgan, 1979). When there is a distribution of SLs along the length of the fiber, deciding which SL value to use for plotting the F–L curve is problematic. In our initial analysis, we used the average of the calculated SLs of the eight subdivided segments. In order to correct for SI at SLs greater than the estimated plateau region, the shortest SL of the eight segments was used to plot the F–L curve (see Discussion for method rationale). We assumed that the force measured in activating solution was the combination of both active and passive forces (i.e., the total force). The active force was calculated as the difference between the total and passive forces. The active and passive F–L curves for each fiber were normalized by the maximum active force from all the activations of that fiber. SLo was estimated as the length where the peak force occurred in each active F–L curve and the 95% (a ¼ 0.05) tolerance interval computed from the pooled SLos. Tolerance intervals statistically represent the range of possible SLo, as opposed to an estimate of the mean value (i.e., a confidence interval). The standard F–L model was calculated using the sliding filament model of Gordon et al. (1966) and the electron microscopy estimates of Walker and Schrodt (1974) (I segment length ¼ 2.64 mm, thick filament length ¼ 1.6 mm, bare ˚ Four points on the standard F–L curve zone ¼ 0.17 mm, Z-line thickness ¼ 1000 A). were determined following the calculations of Gordon et al. The force at SL ¼ 1.7 mm (when Z-line meets the thick filament) was calculated as length of thick–thin filament overlap without thin–thin filament overlap (interference) divided by length of the thick filament where myosin is present (1.47 mm). All tests in this study were performed above this SL (1.7 mm) because of experimental limitations, and hence we did not have to consider frictional forces which occur when the thin filaments overlap extensively (Trombitas and Tigyi-Sebes, 1985). The shortest SL of the plateau region was where thin filaments meet. The longest SL of the plateau was where the thin filaments are no longer in the bare zone. Lastly, the force at SL ¼ 4.24 mm (no filament overlap) was assumed to be zero. Forces at SLs between the four points were determined by linear interpolation. To compare the experimental ascending and descending limbs to the standard model, the 95% confidence intervals (CI) of the best fit lines were calculated from the pooled data for SLs shorter and longer than the plateau region of the standard model (2.64 and 2.81 mm) To estimate the beginning of the passive F–L curve, we fitted the passive F–L data of each fiber to an exponential function (Zajac, 1989): FðSLÞ ¼ AebðSLSLp Þ

ð1Þ

where F is the passive force, SL is the sarcomere length, SLp is the slack length at which the passive force begins to be nonzero, and A and b are the fitted constants.

3. Results We obtained data which satisfied the criteria for quality control from 10 type-I fibers out of 31 fibers tested. The mean diameter of the fibers was 0.10370.006 mm, and mean maximal isometric stress was 133726 kPa (at an average SL ¼ 2.7 mm). More measurements were made within the range of 2.4–3.0 mm (Fig. 1). Upon fiber activation, force rise was marked by an initial rapid phase followed by a plateau in all trials (Fig. 2) and sarcomeres in the central region shortened from their passive lengths (Fig. 3). In general, shortening upon activation was greater for shorter than longer lengths (average amount of shortening was 6.4% for SLso2.8 mm and 1.5% for SLs42.8 mm). The scatter plot of the pooled F–L data showed qualitatively ascending limb, plateau, and descending limb regions (Fig. 4). Estimates of SLo ranged from 2.54 to 2.78 mm (Fig. 5), with a mean and standard deviation of 2.66 and 0.085 mm, respectively. The 95% tolerance interval for SLo was (2.37, 2.95) mm. A scatter plot of the passive data resembled qualitatively an exponential function (Fig. 6). Passive F–L relationships from individual fibers were fitted well by exponential functions (average r2 of 0.89470.085), with a mean and standard deviation of 2.22 and 0.08 mm, respectively, for SLp. The 95% CIs for the lines of the ascending and descending limbs based upon the experimental data were compared to the standard model (Fig. 7). When the average SL was used for the F–L plot, the slope for the ascending limb was 0.42 Fo/mm (CI ¼ (0.31, 0.52) Fo/mm), and the slope for the descending limb was 0.52 Fo/

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Fig. 1. Distribution of the SLs measured during maximal activation for all fibers tested. Passive SLs were set within the range of 2.0–4.0 mm. The SLs used were the average values obtained from the corresponding power spectra of the eight segmented fiber images of the central section of the fiber (see Methods). Twice as many measurements were made within (2.5 3.0) mm to improve the statistical analysis for the plateau region estimation.

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Fig. 3. SL changes based on the laser diffraction technique during maximal activation for the same fiber shown in Fig. 2. Time axis corresponds to that in Fig. 2 and traces a–f correspond to the shortest and longest SLs in Fig. 2. Sarcomere recordings could only be made after the solution exchange was complete and before the digital image was captured. At shorter SLs, some amount of shortening (as high as 10%) occurred due to the attachment compliance and initial slack in the fiber. At longer SLs, the initial shortening was considerably less.

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Fig. 2. Recordings of forces at six different SLs from an individual fiber. The initial transient results from the exchange of pre-activating to activating solution. Crosssectional area of the fiber was 0.008 mm2 and isometric stress was 152 kPa at a SL of 2.67 mm.

mm (CI ¼ (0.60, 0.44) Fo/mm). When the shortest SL was used for the F–L plot (Fig. 4), the descending limb slope was 0.55 Fo/ mm (CI ¼ (0.60, 0.44) Fo/mm). The fitted passive curve was calculated with SLp equal to 2.22 mm, and A and b from Eq. (1) for the population data were equal to 0.009 Fo and 2.25 mm1, respectively (Fig. 6).

4. Discussion The most extensive measurements of sarcomeric F–L properties have been made using frog single fibers. There has been

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Fig. 4. Scatter plot of the active F–L data from 10 fibers which passed the analysis criteria. Force data from each fiber were normalized to the maximum active force recorded at all the SLs tested within that fiber. F–L measurements were made using the average SL (J) and with the SLs adjusted using the method of Julian and Moss (1980) on the descending limb (+).

general visual agreement between the standard model and experimental data obtained either with intact fibers or segments of skinned fibers (Gordon et al., 1966; Moss, 1979). In mammalian single fibers, F–L measurements have only been made from rodent muscle (Edman, 2005; Stephenson and Williams, 1982; ter Keurs et al., 1978). This study represents the first attempt to compare F–L measurements in human muscle fibers to the sliding filament model predictions. In single fibers, SI during isometric conditions has a profound effect on the F–L curve, especially on the descending limb, where pronounced SI results in a broadening of the F–L curve

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Fig. 5. Histogram of the optimal SL estimates directly estimated based on the F–L relationship measured for each fiber. SLo was estimated as the length where the peak force occurred in each active F–L curve.

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Fig. 6. Scatter plot of the passive F–L data from all 10 fibers. Force data from each fiber was normalized to the maximum active force recorded at all the SLs tested within that fiber. The solid curve is the best exponential fit using all the pooled passive F–L data.

(Altringham and Bottinelli, 1985; Julian and Moss, 1980; ter Keurs et al., 1978). It is important to note that maintaining the SL within a short segment of the fiber reduces the amount of SI considerably (Bagni et al., 1988; Edman and Reggiani, 1984, 1987; Edman, 2005; Granzier and Pollack, 1990). While creep was shown to be totally eliminated by length-clamping of very short segments (70–80 mm) in the study by Bagni et al. (1988), force measurements under segment control with longer segments still exhibited visible creep (and presumably SI) (cf., Fig. 4 of Edman, 2005; Fig. 4 of Granzier and Pollack, 1990). Because the important quantity that explains the differences in F–L relationship between many studies is the amount of SI, we chose to use those fibers not showing appreciable SI, instead of relying on the segment control to reduce SI. Our criteria for acceptable SI were based upon comparisons of F–L measurements with varying amounts of SI with the standard

model in frog single fibers (Edman and Reggiani, 1984; Edman et al., 1993). The first criterion, a less than 1% change in force over 1 s, was based upon minimizing creep, a result of SI. The specific value for this criterion could not be obtained from the literature as species-specific contractile dynamics, temperature, and activation procedures made comparison to our measurements impossible. The value which was chosen correlated well with minimal SI as measured by analysis of the digital image (see below). We excluded 7 out of 31 fibers due to this criterion, especially at lengths greater than 3.5 mm. The second criterion, a less than 10% shortening of the diffraction-based SL upon activation, was based upon that unloaded shortening of 20% during the rising phase of activation and did not cause significant SI in single fibers (Edman et al., 1993). In addition, shortening at longer lengths, where SI due to shortening is more problematic, was on average only 1.5%. Seven out of 31 fibers failed in this criterion. The third criterion, a CV of the SLs less than 5% based upon the study by Edman et al. (1993), implies a maximum of 10% change in force from the standard model prediction. Although this criterion could create more SI at longer lengths, we used this measure of SI to be consistent with the previous study in order to estimate the influence of SI on the measured F–L relationship. Note that we were only able to image slightly over 1 mm of fiber length, roughly one-half to one-third of the total length. However, we visually observed that the ends of the fiber (0.1–0.2 mm in length) lengthened (not shown), presumably due to compliance at the fiber attachment to the experimental apparatus (Chase and Kushmerick, 1988). We assumed that this lengthening caused shortening of the central portion, which was usually fairly uniform as judged by the image analysis. The average of the SLs recorded in the image of the central portion was used to plot the F–L relationship (Fig. 4). For the ascending limb and plateau region, plots using the average SL in skinned single frog fibers can replicate the standard model predictions, even with at least 5% CV for SI (Moss, 1979). However, on the descending limb, using average SL tends to produce a broader, more extended F–L curve (Julian and Moss, 1980). To rectify this artifact in frog single fibers with as much as 25% CV for SI, Julian and Moss (1980) used the shortest SL recorded to plot the descending limb of the F–L curve and obtained better visual correspondence. The justification for this method is that the isometric force is most reflective of the shortest sarcomeres due to the directional asymmetry in the force-velocity relationship (Granzier and Pollack, 1990). Our plateau region of (2.37, 2.95 mm) included the SLo estimate of (2.64, 2.81 mm) by Walker and Schrodt (1974). Experimental tolerance limits are always wider than the range of measurements (2.54, 2.78 mm). Furthermore, the transition between the ascending limb and plateau region has been described as ‘‘rounded’’ (Gordon et al., 1966), which may cause experimental estimates to be wider. The ascending limb of the standard model was on the outer bounds of the CI of the experimental data (Fig. 7). This is reflected by the slope of 0.57 Fo/mm for the standard model is slightly greater than the upper bound of the CI for estimated slope (0.52 Fo/mm). A reason for the reduced experimental slope could be that the linear fit may have included the ‘‘rounded’’ transition from the plateau to ascending limb (as described in Gordon et al., 1966). It is important to note that two additional factors could influence the slope of the ascending limb. First, SI can cause a depression of force (Edman and Reggiani, 1984; Julian and Morgan, 1979; Julian and Moss, 1980). However, this effect would make the slope steeper than that of the standard model. Second, swelling in the skinned fiber preparation could alter the lattice spacing and crossbridge interactions (Godt and Maughan, 1977). However, compression of skinned fibers by dextran causes the ascending

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Fig. 7. (A) The standard model (solid line) compared to the experimental F–L relationship for both limbs (dashed lines) using average SLs. 95% confidence intervals (dotted lines) are shown for the ascending and descending limbs. (B) The standard model compared to the experimental F–L relationship for descending limb for which the SL measurements were adjusted using the method of Julian and Moss (1980). No adjustments were made on the ascending limb. Standard F–L model is a series of line segments between four points derived from sliding filament model of Gordon et al. (1966) and filament length estimates of Walker and Schrodt (1974) (see Methods).

limb slope to decrease (Allen and Moss, 1987), implying that the magnitude of the slope obtained in skinned fibers is high. Thus, compression of the fiber should accentuate the difference between the experimental value obtained here and that from the standard F–L model. The descending limb of the standard model was not within the CI calculated from the data using average SL (Fig. 7A) with a slope 17% larger than that from the experimental best fit. When the F–L curve was plotted with SL of the shortest segment to correct for the possible effects of SI, the agreement was slightly better (Fig. 7B). However, the slope only changed slightly (0.55 vs. 0.52 Fo/ mm), and the standard model slope was greater than the upper bound of slope’s CI (0.70 vs. 0.63 Fo/mm). This result supports the idea that the difference between the experimental data and standard model is only partly explained by SI. Other potential factors, such as cooperativity between actin and myosin filaments or intrinsic variability in A and I filament lengths, could cause the relationship between filament overlap and force to be nonlinear or change its slope (Allen and Moss, 1987; Edman and Reggiani, 1987; Gordon et al., 2000), which would impact the linear slope estimation. We found that mean SLp was 2.22 mm. Our estimate of the passive F–L curve compares well to previous measurements in skinned human soleus single fibers where SLp equaled 2.0 mm and the passive force was 2.6% of maximal isometric force at SL ¼ 2.75 mm and 28.9% at 3.75 mm (Trombitas et al., 1998). It is worth noting that passive forces due to stretch are reduced by as much as 60–80% in chemically skinned fibers when compared to the intact fibers (Bagni et al., 1995; Mutungi and Ranatunga, 1998). Hence in this study, we assumed that the chemical skinning process removed all the parallel connective tissue and that titin, connecting the thick filament to the z-discs (Trombitas et al., 2003), is primarily responsible for the passive force recorded here. Experimental measurement of the human skeletal muscle F–L curve has important consequences for the application of muscle

models in interpreting motor function. For example, simulations of muscle forces during human running are very sensitive to the estimate of SLo and the width of the F–L curve (Scovil and Ronsky, 2006). In comparison to the standard F–L model, the experimental data suggest that the F–L curve for human type-I skeletal muscle has a slightly wider plateau region and less steep ascending and descending limbs within the measured SL range of 2.0 to 4.0 mm. Although these observations may be in part due to the presence of at most 5% SI, an F–L curve with moderate amount of SI could be more representative of physiological function. For example, the difference in SLs measured in passive in vivo mouse muscle can be as much as 20% (Llewellyn et al., 2008).

Conflict of interest I confirm that there have been no conflicts of interest interfering with the manuscript, ‘‘Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers’’ by S.K. Gollapudi and D.C. Lin.

Acknowledgements We wish to thank Richard Lasher, Drs. H. Graeme French, Anita Vasavada, and Kenneth B. Campbell for their helpful support and comments on the manuscript. Funding was provided by the Whitaker Foundation.

Appendix 1. Supporting Information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech.2009.06.013.

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