Length vs. active force relationship in single isolated smooth muscle cells DAVID E. HARRIS AND DAVID M. WARSHAW Department of Physiology and Biophysics, College of Medicine, University of Vermont, Burlington, Vermont 05405
HARRIS, DAVID E., AND DAVID M. WARSHAW. Length VS. active force relationship in single isolated smooth muscle cells. Am. J. Physiol. 260 (Cell Physiol. 29): CllO4-C1112, 1991.The length vs. active force relationship (L-F) may provide information about changes in smooth muscle contractile protein interactions as muscle length changes. To characterize the L-F in single toad stomach smooth muscle cells, cells were attached to a force measurement system, electrically stimulated, and isometric force and elastic modulus (an estimate of the number of attached cross bridges) determined at different cell lengths. Cells generated maximum stress (Pm,, = 152.5 mN/mm”) and elastic modulus (Eact = 0.68 x lo4 mN/mm2) at their rest length (Lcell = 78.0 pm; distance between cell attachments). At shorter lengths, active force and elastic modulus declined proportionally with active force eliminated at 0.4 LCell. Stretching the relaxed cells up to 1.4 Lcell shifted the subsequent L-F along the length axis by the amount of the stretch but did not change P,,, or the shape of the L-F. In activated cells, force was a function of cell length rather than of shortening history. We interpret these findings as evidence that 1) Lcell is close to the optimum length for force generation, 2) the decline in force at lengths less than L cell results from a reduced number of attached cross bridges, and 3) stretching relaxed smooth muscle cells may not move the contractile units to new positions on their L-F.
contraction;
mechanics;
toad; cross bridge
RELATIONSHIP between muscle length and the active isometric force a muscle can produce is thought to provide fundamental information about the arrangement and interaction of contractile filament proteins in a variety of muscle types. Specifically, the reduction in isometric force when skeletal muscle is stretched beyond its optimum length [descending limb of the length vs. force relationship (L-F)] provides strong evidence that contraction occurs via a sliding filament mechanism powered by independent force generators, i.e., cross bridges (9). The qualitatively similar relationship observed in smooth muscle tissue stretched beyond its optimum length (15) may indicate that a similar mechanism is operative in smooth muscle. Several factors may be responsible for the decline in isometric force at lengths less than optimum (ascending limb of the L-F) in both skeletal and smooth muscle. 1) Excessive contractile filament overlap at short muscle lengths may reduce the number of force producing cross bridges either with (1) or without (23) an overall reduction in the number of attached cross bridges. 2) Increased THE
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lateral spacing of contractile filaments in shortened cells could reduce the amount of force produced by each attached cross bridge (13). 3) The process of shortening to lengths below the optimum for force generation may reduce the activation level of the muscle (18), causing a reduction in the number of attached cross bridges. 4) At very short lengths, an internal load, caused by abutment of contractile filaments (9) or compression of the cytoskeleton, could oppose isometric force development. Muscle stiffness contains information about the relative number of attached cross bridges (8,30). Thus, while each of the factors cited above could explain the reduced isometric force seen at short muscle lengths, they contain somewhat different predictions about how muscle stiffness will vary as force falls. This study characterizes changes in active isometric force and muscle stiffness when cell length is reduced in single isolated smooth muscle cells. It also reports how stretching relaxed cells beyond their rest length affects their subsequent L-F. METHODS
Cell Isolation Procedure The procedure for isolation of single smooth muscle cells from the gastric muscularis of the giant toad (Bufo marinus) has been described in detail elsewhere (7). Single smooth muscle cells were enzymatically isolated from the tissue and suspended in amphibian physiological saline (APS; Ref. 28). For experiments in which cell surface markers were required, Z-pm diameter charged anion exchange resin beads (Bio-Rad, Aminex) were added to the APS and allowed to adhere to the cells (29). A ZO-pl aliquot of cells was then transferred to a O.&ml bubble of APS containing 10 ,uM isoproterenol and viewed through an inverted microscope at X250 power. This concentration of isoproterenol helps keep the cells relaxed during attachment to the recording system. For attachment to the measurement system, cells were picked up with a micromanipulator and tied between a specially designed ultrasensitive force transducer (natural frequency, 345 Hz; sensitivity, 53 mV/pN; compliance, 0.13 ,um/pN) (28) and a piezoelectric length displacement device (Physik Instrumente model PZ-40; natural frequency, 1 kHz; maximum displacement, 40 pm). Once the cell was set to the desired length, it was stimulated with a l-Hz train of electrical field stimuli (60 mA, 0%ms duration) delivered by platinum electrodes. This supermaximal stimulation assured full activation of the American
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LENGTH
VS.
FORCE
1. Single smooth muscle cell dimensional and mechanical parameters TABLE
Cell LII,
Parameter
pm
CSA, pm* F nlsx, Ir N P max= F,,,/CSA, mN/mm* E,,,, X10* mN/mm*
Value
II
78.O-c5.1 12.6f1.4 1.50+0.14 152.5zk18.2 0.68t0.07 cells. L,,,,, length;
Values are means + SE; n, no. of sectional area; F,,,, active force; P,,, = F,,,/CSA, active Young’s modulus (at 100 Hz).
active
20 20 20 20 8 CSA, crossstress; E,,,,
the contractile machinery. However, once activated in this manner, cells no longer relax when the stimulus is withdrawn (30). Despite this limitation, maximally activated single smooth muscle cells do show stable mechanical characteristics for 15 s after peak force is reached (27). Therefore, all protocols were performed in a single contraction and completed within this time period. Cell force, length (as measured by the output of an eddy current sensor; KD2810-lu, Kaman Measuring Systems), and, when necessary, video images were all recorded simultaneously on a modified FM videorecorder Wetter model 875). Length, force, and video images were later digitized for computer analysis. All experiments were performed at room temperature (20°C). Reference Length (L,,,J Determination
Cell length was set in the following manner. Just prior to stimulation, cells attached to the measurement system
IN
SMOOTH
MUSCLE
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were stretched with the micromanipulator until a transient passive force of 0.2 PN was obtained. This tightened the attachment knots to prevent slippage during cell activation and set the cell segment length between knots to its relaxed length prior to tying (see RESULTS). This length of the cell between knots is referred to as Lcelland is unique for each cell because it is determined by the dimensions of the relaxed cell. As much as one-half of the cell’s length is taken up in the knots, and thus Lcell is about half the length previously reported for these cells relaxed and free in solution (20). Cell dimensions were measured with a calibrated eyepiece micrometer (Table 1). The value of Lcellwas inputted into a computer (IBM PC-XT), which calculated the length displacement device control signals needed to produce the desired cell length changes. Although Lcell is a unique length for each cell, we do not assume that changes in cell length are tightly coupled to changes in contractile unit length under all conditions of activation. For example, cells set to Lcellin the manner described above and activated at that length all produce similar L-F (see Fig. 6). This would be expected only if 1) these cells have similar contractile unit lengths, and 2) contractile unit length is tightly coupled to cell length in activated cells. However, the results of this study also suggest that length changes applied to relaxed cells may not produce changes in contractile unit lengths. Experimental Protocols Cell surface marker controls. The protocols
yses employed
and analin this study rest on two assumptions. 1)
A
FIG. 1. Attachment and stretch of relaxed cell. Digitized video images are shown. A: cell prior to attachment to force recording system. Cell surface markers are present (small arrowheads). B: cell after attachment to recording system. Large arrowheads show L,,,,. Distance between cell surface markers is unchanged from that in A. C: relaxed cell after stretch. Cell length and distance between cell surface markers have been increased by similar percentages of their original values (cell length, 12%; distance between markers, 10%).
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I,ENGTH
VS. FORCE IN SMOOTH
The tying procedure does not induce contraction or stretch of the part of the cell remaining between the knots. 2) In both relaxed and activated cells, length changes are distributed homogeneously along the cell length. To test these assumptions, the following controls were performed on cells decorated with surface marker beads. 1) The distance between two cell surface markers was measured before and after the cell was tied to the measurement system (Fig. 1) as described above. 2) After tying, relaxed cells were slowly stretched to 1.14 + 0.01 Lcell (n = 4). Cell length and the distance between two cell surface markers were measured before and after the A i
il
B
C
‘\
MUSCLE
stretch (Fig. 1). 3) Cell length and the distance between two surface markers were measured in activated cells at the peak of isometric force and at new lengths in the length vs. force protocol described below (Fig. 2). Length vs. force protocol. The purpose of this protocol was to 1) characterize the relationship between cell length and isometric force generating capacity and 2) determine the effect of stretching the relaxed cell on the subsequent L-F. Cells were tied and stimulated as described above. When maximum isometric force (F,,,) was reached, the computer was signaled with a keystroke and the length change protocol began. Cell length was reduced in four steps of -0.1 Lcell each. Then cell length was returned to its initial value in two ramps of equal size. Step length reductions were complete in 5 ms and each return ramp was performed over 500 ms. After each length change, the cell was held isometric for 2.0 s, sufficient time for it to develop nearly the maximum isometric force it was capable of at that length (Fig. 3). This protocol was performed starting at the following lengths: 1.0, 1.1, 1.2, and 1.4 &ii. Elastic modulus measurements. Cell elastic modulus provides an estimate of the relative number of attached cross bridges (30). To characterize cell elastic modulus changes during isometric force generation at reduced cell lengths, the length vs. force protocol was employed with sinusoidal length oscillations (frequency, 100 Hz; amplitude, 0.005 or 0.01 Lo,,) added to the length control signal (Fig. 3). Control protocol for shortening deactivation. Because shortening can reduce isometric force generating capacity (shortening deactivation) in smooth muscle tissue (lo), we performed a control protocol (Fig. 4) to determine whether isometric force at reduced cell lengths was a unique function of cell length or of the cell’s previous shortening history. At peak isometric force, cell length was reduced from 1.0 to 0.8 Lcell in two equal steps, then restretched to 0.9 L cell, and finally released again to 0.8 Lee,,.All step reductions in length were complete in 5 ms. The ramp stretch was completed over 500 ms. After each length change, the cells were given 2.0 s to redevelop isometric force. Isometric force was thus measured twice at 0.9 Lcell and twice at 0.8 Lcell so that two paired comparisons could be made to determine the effect of the cell’s previous shortening history on isometric force. Data Analysis Cell stiffness and elastic modulus. Cell stiffness and elastic modulus were computed as follows. Analog force and length signals were digitized at 2.5 kHz. The imposed
2srn
FIG. 2. Cell during length vs. force protocol. Digitized video images are shown. Large arrowheads show cell length, small arrowheads show cell surface marker positions. A: relaxed cell. B: cell at maximum isometric force (F,,,). Cell rotation has occurred and distance between cell surface markers has decreased by 0.07 I,,,,,. C: cell after first step reduction in length. Cell length, 0.91 &I; distance between surface markers, 0.86 value at I&l,. D: cell after second step reduction in length. Cell length, 0.81 L,,,,; distance between surface markers, 0.81 value at L,,,,. E: cell after third step reduction in length. Cell length, 0.70 &I; distance between surface markers, 0.71 value at Lc.s. F: cell after fourth step reduction in length. Cell length, 0.62 I&,,; distance between surface markers, 0.64 value at &I.
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LENGTH
VS. FORCE
IN
SMOOTH
lmoLcell
0.97
. 0.92 t
-
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MUSCLE
.. .. 0.74 .:’ .- .--
*- 0.83 0.71
. =;
4.”2’ : - ,,.“... J.- ,,-.-” . - . . . - .. .. .*.
Fmax-
a. .-..-* . -- .. .*. . ..
...._.‘Se
. .s . .* , . .*” ..* . **.. --w. *.a.*._. . .” l -*s*-*-,’ ;” 2..*
FIG. 3. Length vs. force protocol. Length (top trace) and force (bottom trace) are shown. Length sinusoid (0.005 L cell amplitude) for elastic modulus measurement begins at arrow. Inset shows enlargement of length and force traces on faster time scale. Numbers beside each length step indicate cell length normalized to Lcell at that step. Resting
1s
sinusoidal length change and the resultant sinusoidal force change were separated from the underlying length and force signals with a digital band-pass filter (cutoff frequencies, 95-105 Hz). Then cell stiffness amplitude (S) and phase angle (0) were computed from these sinusoids on a cycle-by-cycle basis (30). We define the cell stiffness amplitude as the ratio of the amplitude of the force sinusoid divided by the amplitude of the length sinusoid, and the phase angle as the difference in phase between the length and force sinusoids. Next, active Young’s modulus was computed (I& = S x L&CSA, where CSA is the cell cross-sectional area). Finally cell elastic modulus was computed (E, = Eact x COST)and averaged for the last 20 cycles (200 ms) of each isometric period in the length vs. force protocol. Elastic modulus is the contribution of elastic structures to overall cell stiffness. Video length analysis. Cell video data from surface marker control experiments were digitized by a computer equipped with a video grabber board (Coreco, Oculus 200). Digitized images were then analyzed to determine overall cell length and the distance between surface markers using a specially designed software routine (31). Statistics. Statistical comparisons of force between cells were made with a Student’s t test and within cells
with a paired Student’s t test. A difference was considered significant at P < 0.05. All data are presented as means t SE. RESULTS
Cell Surface Marker Controls The distance between two cell surface markers after tying the cell to the measurement system and setting its length to Lcellwas 1.02 t 0.03 (n = 3) times the distance between the same two markers measured before tying (Fig. 1). Therefore, the cell segment length between attachments (I,,& is the same as the length of that segment when the cell is free in solution. When relaxed cells were slowly stretched to 1.14 t 0.01 &I, the distance between two surface markers increased to 1.13 t 0.02 times its value prior to the stretch (n = 4; Fig. 1). Thus stretches of relaxed cells are homogeneously distributed and not simply taken up in compliant end regions. Finally, when cells with surface markers were activated and subjected to the length vs. force protocol, changes in overall cell length resulted in similar percentage changes in the distance between cell surface markers (Figs. 2 and 5).
0.91
-1
FIG. 4. Control protocol for shortening deactivat,ion. Length (top trace) and force (bottom trace) are shown. Length steps are numbered for reference purposes. Numbers beside each length step indicate cell length normalized to Lcell at that step. Resting force is zero. Lcell, 90.4 pm; F,,,,, 1.05 yN.
0.89 0.80
d-3
0.80 -4
Fmax
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LENGTH
VS.
FORCE
IN
SMOOTH
MUSCLE
0.3> I OG66 .
I 1.0
I 0.8
CELL 0.4 ’
LENGTH
I 1.2
J 1.4
(L/Lcell)
7. L-F following stretch. Results of length vs. force protocol when starting length is 1.0 L cell and above. Isometric force (normalized to F,,,) is plotted against cell length (normalized to Loll). Closed symbols, values after step reductions in length; open symbols, values after ramp increases in length. Circles, data from Fig. 6 for cells activated at 1.0 Lcell. Squares,mean values for cells activated at 1.1 Lcell (n = 3). Triangles, mean values for cells activated at 1.2 Lcell (n = 3). Inverted triangles, mean values for cells activated at 1.4 Lcell (closed, n = 5: open at 1.2 Lcell, n = 3; open at 1.4 Lcell, n = 2). FIG.
4t
I O”o.6
I 0.7
I 0.8
I 0.9
1.0
(1 -ALcelWcell FIG. 5. Cell surface marker control. Distance between two cell surface markers (normalized to value at LcelJ is plotted against cell length (normalized to Loll) for cells subjected to length vs. force protocol. Data from four cells are represented by different symbols. Closed symbols, measurements taken after step reductions in length; open symbols, measurements after ramp increases in length (Fig. 3). Identity line is included for visual reference.
0.8 0.8
I
3
0.6 -
$ 0.6 iz ”2; 0.4
0.4 -
f5 IL
0.2
0.2/t of -0.4 '
I OL I cY’o.4
I 0.6
CELL
I 0.8
LENGTH
I 1.0
(L/Lcell)
FIG. 6. L-F: results of length vs. force protocol when starting length is 1.0 Lcell. Isometric force (normalized to F,,,) is plotted against cell length (normalized to Loll). Closed symbols, values after step reductions in length; open symbols, values after ramp increases in length. Closed symbols are means of 6 cells, whereas open symbols are means of 3 cells. Linear regression line is shown. F/F,,, = 1.7 L/L,,n-0.68. R2,
0.95.
Length vs. Force Protocol The length vs. force protocol (Fig. 3) was used to characterize the relationship between cell length and isometric force producing capacity (Fig. 6). When relaxed cells were subjected to this protocol, no force response was obtained (data not shown). Because these cells do not sustain passive force, all measured force after stimulation is defined as active force. When cells were activated at 1.0 LCell,active isometric force production declined in an approximately linear fashion with reductions in cell length. The ramp increase in cell length back to Lcell (second stretch) returns force to a value appropriate for that length. This indicates that the damage sometimes associated with shortening and stretch in activated smooth muscle tissue (17) is not present in single cells, at least over the length range studied. There appears to be a tendency toward higher
I -0.3
I -0.2
SHORTENING FIG. 8. Effect of stretching relaxed replotted against extent of shortening are identical to those in Fig. 7. Linear
I -0.1
I 0
(aL/Lcell)
cell on L-F. Data from Fig. 7 are (normalized to L&. Symbols regression line is shown. F/F,,,
= 1.7 L/Lcen-1.0. R2, 0.98.
force values following the first stretch in this protocol than would be predicted from force measurements following releases. This higher force value may be the result of incomplete force equilibration following a length change. To estimate the extent of this effect, a sample set of force recoveries following length steps was fit to a double exponential. The equations of the fits suggest that recording force after only 2 s of recovery will overestimate (for stretches) and underestimate (for releases) force by an average of 3.5% F,,,. This could explain a small part of the tendency toward higher force levels following the initial stretches. However, the shape of the L-F is not substantially affected by this small error in estimating force recovery. Extrapolating the linear regression of the relationship between cell length and isometric force to zero force predicts that force production will be eliminated at 0.40 LCell. Figure 7 shows the relationship between isometric force and cell length when the relaxed cells are stretched beyond LCell,activated, and then subjected to the length vs. force protocol. In each case, the shape of the plot is unchanged from that observed when starting at 1.0 LCen.
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LENGTH
VS.
FORCE
IN
However, the relationship is shifted along the length axis by the amount of the stretch. This is clearly demonstrated when isometric force is plotted against the reduction in cell length for all cells regardless of starting length (Fig. 8). Activating cells at lengths above &I does not alter maximum isometric force. Cells activated at 1.0 Lcell produced an active stress of 158.9 t 18.4 mN/mm2 (n = 5), which was not significantly different from the 206.6 t 34.7 mN/mm” (n = 6) produced by cells activated at 1.4
SMOOTH
MUSCLE
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ening history on isometric force-generating capacity. Although conclusions are difficult to draw because of the limited sample size, our results (Table 2) fail to demonstrate a difference between the force at the end of isometric period 3 and that at the end of isometric period 1. Both of these forces are produced at an average length of 0.91 L&. Likewise, the force at the end of isometric period 4 is not different than that seen at the end of period 2. These two isometric forces are measured at 0.83 L cell-
Lell*
DISCUSSION
Elastic Modulus
at Reduced Cell Length
To distinguish among the possible explanations for the fall in force observed at reduced cell length (see introduction), we measured cell elastic modulus at the end of each isometric period in the length vs. force protocol (Fig. 3). These measurements were obtained from cells set at 1.0, 1.1, 1.2, and 1.4 Lcell prior to stimulation. Figure 9 demonstrates that cell elastic modulus falls in proportion to the reduction in isometric force regardless of the starting cell length. Effect of Previous Shortening History on Isometric Force Shortening deactivation may play a role in determining the observed relationship between isometric force and cell length. Therefore, we performed a control protocol (Fig. 4) to determine the effect of previous short-
The experiments reported here were performed on single isolated smooth muscle cells. This was done to obtain direct information about the smooth muscle contractile process without the ambiguities caused by the complex interaction between a heterogeneous population of cells and a connective tissue matrix that exists in smooth muscle tissue. However, in vivo, smooth muscle cells are thought to be connected to each other in both a “side-to-side” and “end-to-end” manner and to transmit force via these connections (22). The removal of these connections during cell isolation may affect the subsequent mechanical properties of single cells. Also, as discussed below, the requirement that the entire L-F be measured in the course of a single activation, due to the inability to obtain multiple maximal electrical activations in these cells, may affect the results obtained. With these concerns in mind, we will 1) present evidence that the fall in force observed at short cell lengths is a true representation of the smooth muscle cell’s L-F, 2) attempt to distinguish among possible explanations for the decline in isometric force at short muscle lengths, and 3) interpret the finding that stretching relaxed smooth muscle cells shifts the subsequent isometric L-F along the length axis by the amount of the stretch. L-F Relationship
0.2 I 0.4
OZ+'o.2
__
L---p-ipp__J 0.6 FORCE
0.8
1.0
(F/F,,,&
FIG. 9. Elastic modulus vs. force. Cell elastic modulus (normalized to maximum value) is plotted against isometric force (normalized to F,,,,) for cells subjected to length vs. force protocol with elastic modulus measurements. Circles, mean values for 2 cells activated at 1.0 Lcell. Squares, 1 cell activated at 1.1 Lcell. Triangles, 1 cell activated at 1.2 Lcell. Inverted triangles, mean values for 4 cells activated at 1.4 Lcell.
TABLE
2. Effect of shortening history on isometric force Step Number 1 3 2 4
L/L11 0.92t0.01 0.90t0.01 0.83kO.02 0.83kO.02
F/Rmx 0.94t0.02 0.99t0.06 0.72t0.05 0.75kO.05
Values are means t SE. Force and length are determined at end of each isometric period in control protocol for shortening deactivation. Length is normalized to relaxed value (L,,lJ and force is normalized to maximum value (F,,iJ. Two force values obtained at 0.9 L,--ll are compared and two force values obtained at 0.8 Lcell are compared. Experiment performed in 3 cells.
The results of the length vs. force protocol (Fig. 6) accurately represent the L-F of single smooth muscle cells only if 1) after activation, changes in activated cell length reflect changes in contractile unit length, and 2) cell length alone is the major determinant of active isometric force in this protocol. The evidence that these conditions are met is as follows. Homogeneous shortening. In skeletal muscle, isometric force can be related directly to the length of the contractile unit, the sarcomere (1,9,30). Because the morphology of the smooth muscle contractile unit is still uncertain, length vs. force studies in smooth muscle tissue (see Ref. 16 for review) and in single cells (6, 11) have only been able to relate isometric force to overall muscle length. However, investigators have proposed that series arrays of contractile units attach at two places on the cell membrane and shorten to cause smooth muscle cell shortening (6). If so, changes in smooth muscle length following activation may indeed reflect changes in contractile unit length. Although the qualitative similarities between the L-F of smooth and skeletal muscle (15, 19) mav support this nronosal. no concrete proof exists.
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LENGTH
VSFORCE
The minimum requirement for interpreting changes in muscle length as indicators of changes in contractile unit length is that length changes applied to the activated cell must be homogeneously distributed along the cell length and not merely taken up in compliant end regions. The results of cell surface marker controls (Figs. 2 and 5) show that this is the case, in agreement with the results of previous studies in these single cells (28, 29). Shortening deactiuation. The L-F in skeletal muscle (1, 23) and in smooth muscle tissue (14,19) is commonly obtained by a series of activations at different muscle lengths. Because this was not possible in these single smooth muscle cells (see METHODS), a protocol that determines the L-F in the course of a single contraction (Fig. 3) was employed. Studies in smooth muscle tissue indicate that determining the L-F in this manner may not affect the result obtained (26). It is still important, however, to ascertain that the dynamic nature of the protocol used in this study does not govern the relationship between isometric force and cell length. Shortening itself may reduce subsequent isometric force generation both in skeletal muscle (5) and in smooth muscle tissue (10). In skeletal muscle this deactivation is long lasting (5) and not abolished by restretch (4). If shortening deactivation also exists in single smooth muscle cells, it could cause the reductions in isometric force seen at short lengths. However, the similarity between the L-F obtained here for single cells and that previously measured in smooth muscle tissue by a series of activations at various lengths (14, 19) suggests that the dynamic nature of the length vs. force protocol (Fig. 3) may not affect the force values obtained. Furthermore, once the cell is activated at Lcell, isometric force appears to be a unique function of cell length (Table 2). Therefore, a shortening deactivation with properties described above is not a major determinant of force in these smooth muscle cells. A short-lived shortening deactivation that is reversed by restretch could still play a role. Ascending Limb of the L-F The finding that all cells activated at Lcellhave similar L-F (Fig. 6) suggests that, when activated, these cells have similar contractile unit lengths as well. Furthermore, linear regression analysis of this relationship predicts that active force will be eliminated at 0.40 Lcell. This is similar to the value of 0.39 optimum length estimated for smooth muscle tissue (14). Therefore, setting cell length to L cell and then activating the cells apparently results in the contractile units of all cells being close to the optimum length for force generation. The decline in isometric force seen at short lengths may occur through a reduction in the number of attached cross bridges caused by excessive contractile filament overlap and steric hindrance of cross-bridge attachment (1, 9). Alternatively, isometric force could fall without a decrease in the number of attached cross bridges as the result of an internal load (9) or a decrease in the force per cross bridge (13, 18, 23). Therefore, cell elastic modulus was used to estimate the relative number of attached cross bridges (830). A proportional relationship between
IN SMOOTH
MUSCLE
cell elastic modulus and isometric force was observed (Fig. 9). Because this relationship is similar to the one previously reported for these cells during activation (28, 30) where cross-bridge recruitment predominates, we believe that a reduction in the number of attached cross bridges may be responsible for the fall in force along the ascending limb of the L-F. In tissue, this matter can be addressed by stiffness measurements as well as via energetic determinations, the assumption being that an attached cycling cross bridge will both possessstiffness and use ATP. At short muscle lengths where isometric force is reduced, both stiffness and high energy phosphate usage remain constant in taenia coli, suggesting no change in the number of attached cross bridges (19). In contrast, oxygen consumption (i.e., ATP consumption) falls with force along the ascending limb of the L-F in mesenteric vein (16). Similarly, stiffness has been found to fall (although more slowly than force) in rabbit mesotubarium (12, 13) and rat mesenteric resistance vessels (14). Interpretation of these tissue data is complicated by the presence of a significant connective tissue matrix, introducing a noncellular elasticity (14) that could mask cellular stiffness. Contractile filament misalignment with shortening could also cause force and elastic modulus to decrease at short lengths without a reduction in the number of attached cross bridges. This would occur because both force (3) and elastic modulus, which are measured along the long axis of the cell, are related to the actual force and elastic modulus by the cosine of the angle that the contractile units make with the axis of force measurement. As the cell shortens, contractile filament angles relative to the cell’s long axis could increase, causing force and elastic modulus to fall in parallel. However, when contractile filament orientation was measured by electron microscopy in relaxed smooth muscle tissue (2, 25) and estimated from cell surface marker movement in single smooth muscle cells (29), values of tl0” to the long axis of the cell were obtained. Assuming a 10” starting contractile filament angle, isovolumic shortening to 0.6 Lcell would increase the filament angle to 20” and cause only about a 5% reduction in isometric force, far less than the 68% reduction observed (Fig. 6). Thus contractile unit reorientation cannot be the sole factor responsible for the decline in isometric force along the ascending limb of the L-F. Effect of Stretching Relaxed Cells When skeletal muscle is stretched beyond its optimum length for force generation, the extent of thick and thin filament overlap is reduced and isometric force-generating capacity falls proportionally (9). Smooth muscle tissue also exhibits a descending limb for its L-F, similar to that seen in skeletal muscle (15). Even giant single smooth muscle cells isolated from a molluscan preparation show a decline in peak twitch force at long lengths (11) However, smooth muscle also demonstrates a plasticity in its L-F not seen in skeletal muscle. Mulvany and Warshaw (14) reported that when relaxed smooth muscle tissue is stretched beyond the leng$h for optimum force
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LENGTH
VS.
FORCE
generation, the peak of the L-F is shifted to a longer length. Furthermore, preliminary results obtained from single isolated toad stomach smooth muscle cells indicate a capacity to generate substantial force even when activated at two times rest length (7). These findings suggest that muscle length and contractile filament length may not always be tightly linked in relaxed smooth muscle, as is the case in skeletal muscle. In this study, when relaxed smooth muscle cells were stretched beyond their resting length (L&, subsequent maximum active isometric force did not decrease and, to our surprise, no descending limb of the L-F was observed. Rather, stretched cells produced a L-F similar to that observed at Lcell but shifted along the length axis by the amount of the stretch (Figs. 7 and 8). This result is consistent with the possibility that the L-F in these cells is characterized by a broad plateau and that the decline in force seen after reductions in cell length is the result of shortening deactivation. As discussed above, however, the presence of a shortening deactivation similar to that seen in skeletal muscle is not apparent in these cells. However, a novel short-acting shortening deactivation is not ruled out. It is intriguing to speculate that stretching relaxed single smooth muscle cells does not change the position of the contractile units on their L-F. As previously concluded by VanDijk et al. (24), a viscous element may exist in relaxed smooth muscle cells. If this viscous element is connected in series with the contractile element, it could allow changes in cell length to occur without corresponding changes in contractile unit length in relaxed cells. Then, upon activation, significant cytostructural changes may occur that tightly couple contractile unit length to cell length. This proposal predicts that stretching relaxed smooth muscle will not decrease the extent of thin and thick filament overlap as in skeletal muscle (9). Interestingly, this has been shown to be the case. Somlyo et al. (21) demonstrated that thick filaments were still surrounded by thin filaments (i.e., evidence for overlap) in transverse sections of mesenteric vein stretched to a length at which active force was zero. Regardless of the mechanism, the shift of the L-F with stretch reported here appears to be a basic property of single smooth muscle cells. However, definition of the manner in which this property presents itself in the tissue awaits further study. We thank Janet Desrosiers and Heather Spring for their technical assistance, Steven Work for his computer program development, and Trish Warshaw for the illustrations. This work was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant AR-34872. D. M. Warshaw is an Established Investigator of the American Heart Association. Address reprint requests to D. M. Warshaw. Received
29 May
1990; accepted
in final
form
2 January
1991.
REFERENCES
1. ALLEN, J. D.,
AND R. L. MOSS. Factors influencing the ascending limb of the sarcomere length-tension relationship in rabbit skinned muscle fibers. J. Physiol. Lond. 390: 119-136, 1987. 2. ASHTON, F. T., A. V. SOMLYO, AND A. P. SOMLYO. The contractile apparatus of vascular smooth muscle: intermediate high voltage
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MUSCLE
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electron microscopy. J. Mol. Biol. 98: 17-29, 1975. 3. BAGBY, R. M. Organization of contractile/cytoskeletal elements. In: Biochemistry of Smooth Muscle, edited by N. L. Stephens. Boca Raton, FL: CRC, 1983, vol. 1, p. l-84. 4. EDMAN, K. A. P. Depression of mechanical performance by active shortening during twitch and tetanus of vertebrate muscle fibers. Acta Physiol. Stand. 109: 15-26, 1980. 5. EKELUND, M. C., AND K. A. P. EDMAN. Shortening induced deactivation of skinned fibers of frog and mouse striated muscle. Acta Physiol. Stand. 116: 189-199, 1982. 6. FAY, F. S. Structural and Function Features of Isolated Smooth Muscle Cells. Cold Spring Harbor, NY: Cold Spring Harbor Laboratory, 1976, p. 185-201. 7. FAY, F. S., R. HOFFMAN, S. LECLAIR, AND P. MERRIAM. Preparation of individual smooth muscle cells from the stomach of Bufo marinus. Methods Enzymol. 85: 284-292, 1982. 8. FORD, L. E., A. F. HUXLEY, AND R. M. SIMMONS. The relation between stiffness and filament overlap in stimulated frog muscle fibers. J. Physiol. Lond. 311: 219-249, 1981. 9. GORDON, A. M., A. F. HUXLEY, AND F. J. JULIAN. The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. Lond. 184: 170-192, 1966. 10. GUNST, S. J. Effect of length history on contractile behavior on canine tracheal smooth muscle. Am. J. Physiol. 250 (Cell Physiol. 19): C146-C154,1986. 11. ISHI, N., AND K. TAKAHASHI. Length-tension relation of single smooth muscle cells isolated from the pedal retractor muscle of Mytilus edulis. J. Muscle Res. Cell Motil. 3: 25-38, 1982. 12. MEISS, R. A. Dynamic stiffness of rabbit mesotubarium smooth muscle: effect of isometric length. Am. J. Physiol. 234 (Cell Physiol. 3): C14-C26, 1978. R. A. The effect of tissue properties on smooth muscle 13. MEISS, mechanics. In: Frontiers in Smooth Muscle Research, edited by N. Sperelakis and J. D. Wood. New York: Liss, 1990, p. 435-449. 14. MULVANY, M. J., AND D. W. WARSHAW. The active tension-length curve of vascular smooth muscle related to its cellular components. J. Gen. Physiol. 74: 85-104, 1979. 15. MURPHY, R. A. The mechanics of vascular smooth muscle. In: Handbook of Physiology. The Cardiovascular System. Muscle Mechanics. Bethesda, MD: Am. Physiol. Sot., 1980, sect. 2, vol. II, chapt. 13, p. 325-351. 16. PAUL, R. J., AND J. W. PETERSON. Relation between length, isometric force, and 0, consumption rate in vascular smooth muscle. Am. J. Physiol. 228: 915-922, 1975. 17. PETERSON, J. W., AND R. J. PAUL. Effects of initial length and active shortening on vascular smooth muscle contractility. Am. J. Physiol. 227: 1019-1024, 1974. M., AND R. J. PODOLSKY. Length-force relation of 18. SCHOENBERG, calcium activated muscle fibers. Science Wash. DC 176: 52-54, 1972. 19. SIEGMAN, M. J.: T. M. BUTLER, AND S. U. MOOERS. Energetic, mechanical, and ultrastructural correlates of the length-tension relationship in smooth muscle. In: Smooth Muscle Contraction, edited by N. L. Stephens. New York: Dekker, 1984, p. 189-198. 20. SINGER, J. J., AND F. S. FAY. Detection of contraction of isolated smooth muscle cells in suspension. Am. J. Physiol. 232 (Cell Physiol. 1): C138-C143, 1977. 21. SOMLYO, A. P., A. V. SQMLYO, C. E. DEVINE, AND R. V. RICE. Aggregation of thick and thin filaments into ribbons in mammalian smooth muscle. Nature New Biol. 231: 243-246, 1971. A. V. Ultrastructure of vascular smooth muscle. In: 22. SOMLYO, Handbook of Physiology. The Cardiovascular System. Structure. Bethesda, MD: Am. Physiol. Sot., 1980, sect. 2, vol. II, chapt. 2, p. 33-67. 23. STEPHENSON, D. G., A. W. STEWART, AND G. J. WILSON. Dissociation of force from myofibrillar MgATPase and stiffness at short sarcomere lengths in rat and toad skeletal muscle. J. Physiol. Lond. 410: 351-366, 1989. A. M., P. A. WIERINGA, M. VAN DER MEER, AND J. D. 24. VANDIJK, LAIRD. Mechanics of resting isolated single vascular smooth muscle cells from bovine coronary artery. Am. J. Physiol. 246 (Cell Physiol. 15): C277-C287,1984. 25. WALMSLEY, J. G., AND R. A. MURPHY. Force-length dependence of arterial lamellar, smooth muscle, and myofilament orientations. Circ. Ph.ysiol. 22): H1141-H1147, Am. J. Phvsiol. 253 (Heart 1987.
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FORCE
26. WARSHAW, D.M. Direct Correlation Between Structure and Function in Arterial Resistance Vessels in Young And Old Spontaneously Hypertensive Rats (PhD thesis). Burlington: Univ. of Vermont, 1978. 27. WARSHAW, D. M. Force:velocity relationship in single isolated toad stomach smooth muscle cells. J. Gen. Physiol. 89: 771-789, 1987. 28. WARSHAW, D. W., AND F. S. FAY. Cross-bridge elasticity in single smooth muscle cells. J. Gen. Physiol. 82: 157-199, 1983. 29. WARSHAW, D. W., W. J. MCBRIDE, AND S. S. WORK. Corkscrew-
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MUSCLE
like shortening in single smooth muscle cells. Science Wash. DC 236: 1457-1459, 1987. 30. WARSHAW, D. W., D. D. REES, AND F. S. FAY. Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells. J. Gen. Physiol. 91: 761-779, 1988. 31. WORK, S. S., AND D. M. WARSHAW. Detection of surface movements on single smooth muscle cells: digital video microscopy. Comput. Biol. Med. 18: 385-393, 1988.
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HARRIS, DAVID E., AND DAVID M. WARSHAW. Length VS. active force relationship in single isolated smooth muscle cells. Am. J. Physiol. 260 (Cell Physiol. 29): CllO4-C1112, 1991.The length vs. active force relationship (L-F) may provide information about changes in smooth muscle contractile protein interactions as muscle length changes. To characterize the L-F in single toad stomach smooth muscle cells, cells were attached to a force measurement system, electrically stimulated, and isometric force and elastic modulus (an estimate of the number of attached cross bridges) determined at different cell lengths. Cells generated maximum stress (Pm,, = 152.5 mN/mm”) and elastic modulus (Eact = 0.68 x lo4 mN/mm2) at their rest length (Lcell = 78.0 pm; distance between cell attachments). At shorter lengths, active force and elastic modulus declined proportionally with active force eliminated at 0.4 LCell. Stretching the relaxed cells up to 1.4 Lcell shifted the subsequent L-F along the length axis by the amount of the stretch but did not change P,,, or the shape of the L-F. In activated cells, force was a function of cell length rather than of shortening history. We interpret these findings as evidence that 1) Lcell is close to the optimum length for force generation, 2) the decline in force at lengths less than L cell results from a reduced number of attached cross bridges, and 3) stretching relaxed smooth muscle cells may not move the contractile units to new positions on their L-F.
contraction;
mechanics;
toad; cross bridge
RELATIONSHIP between muscle length and the active isometric force a muscle can produce is thought to provide fundamental information about the arrangement and interaction of contractile filament proteins in a variety of muscle types. Specifically, the reduction in isometric force when skeletal muscle is stretched beyond its optimum length [descending limb of the length vs. force relationship (L-F)] provides strong evidence that contraction occurs via a sliding filament mechanism powered by independent force generators, i.e., cross bridges (9). The qualitatively similar relationship observed in smooth muscle tissue stretched beyond its optimum length (15) may indicate that a similar mechanism is operative in smooth muscle. Several factors may be responsible for the decline in isometric force at lengths less than optimum (ascending limb of the L-F) in both skeletal and smooth muscle. 1) Excessive contractile filament overlap at short muscle lengths may reduce the number of force producing cross bridges either with (1) or without (23) an overall reduction in the number of attached cross bridges. 2) Increased THE
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$1.50
Copyright
0 1991
lateral spacing of contractile filaments in shortened cells could reduce the amount of force produced by each attached cross bridge (13). 3) The process of shortening to lengths below the optimum for force generation may reduce the activation level of the muscle (18), causing a reduction in the number of attached cross bridges. 4) At very short lengths, an internal load, caused by abutment of contractile filaments (9) or compression of the cytoskeleton, could oppose isometric force development. Muscle stiffness contains information about the relative number of attached cross bridges (8,30). Thus, while each of the factors cited above could explain the reduced isometric force seen at short muscle lengths, they contain somewhat different predictions about how muscle stiffness will vary as force falls. This study characterizes changes in active isometric force and muscle stiffness when cell length is reduced in single isolated smooth muscle cells. It also reports how stretching relaxed cells beyond their rest length affects their subsequent L-F. METHODS
Cell Isolation Procedure The procedure for isolation of single smooth muscle cells from the gastric muscularis of the giant toad (Bufo marinus) has been described in detail elsewhere (7). Single smooth muscle cells were enzymatically isolated from the tissue and suspended in amphibian physiological saline (APS; Ref. 28). For experiments in which cell surface markers were required, Z-pm diameter charged anion exchange resin beads (Bio-Rad, Aminex) were added to the APS and allowed to adhere to the cells (29). A ZO-pl aliquot of cells was then transferred to a O.&ml bubble of APS containing 10 ,uM isoproterenol and viewed through an inverted microscope at X250 power. This concentration of isoproterenol helps keep the cells relaxed during attachment to the recording system. For attachment to the measurement system, cells were picked up with a micromanipulator and tied between a specially designed ultrasensitive force transducer (natural frequency, 345 Hz; sensitivity, 53 mV/pN; compliance, 0.13 ,um/pN) (28) and a piezoelectric length displacement device (Physik Instrumente model PZ-40; natural frequency, 1 kHz; maximum displacement, 40 pm). Once the cell was set to the desired length, it was stimulated with a l-Hz train of electrical field stimuli (60 mA, 0%ms duration) delivered by platinum electrodes. This supermaximal stimulation assured full activation of the American
Physiological
Society
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LENGTH
VS.
FORCE
1. Single smooth muscle cell dimensional and mechanical parameters TABLE
Cell LII,
Parameter
pm
CSA, pm* F nlsx, Ir N P max= F,,,/CSA, mN/mm* E,,,, X10* mN/mm*
Value
II
78.O-c5.1 12.6f1.4 1.50+0.14 152.5zk18.2 0.68t0.07 cells. L,,,,, length;
Values are means + SE; n, no. of sectional area; F,,,, active force; P,,, = F,,,/CSA, active Young’s modulus (at 100 Hz).
active
20 20 20 20 8 CSA, crossstress; E,,,,
the contractile machinery. However, once activated in this manner, cells no longer relax when the stimulus is withdrawn (30). Despite this limitation, maximally activated single smooth muscle cells do show stable mechanical characteristics for 15 s after peak force is reached (27). Therefore, all protocols were performed in a single contraction and completed within this time period. Cell force, length (as measured by the output of an eddy current sensor; KD2810-lu, Kaman Measuring Systems), and, when necessary, video images were all recorded simultaneously on a modified FM videorecorder Wetter model 875). Length, force, and video images were later digitized for computer analysis. All experiments were performed at room temperature (20°C). Reference Length (L,,,J Determination
Cell length was set in the following manner. Just prior to stimulation, cells attached to the measurement system
IN
SMOOTH
MUSCLE
Cl105
were stretched with the micromanipulator until a transient passive force of 0.2 PN was obtained. This tightened the attachment knots to prevent slippage during cell activation and set the cell segment length between knots to its relaxed length prior to tying (see RESULTS). This length of the cell between knots is referred to as Lcelland is unique for each cell because it is determined by the dimensions of the relaxed cell. As much as one-half of the cell’s length is taken up in the knots, and thus Lcell is about half the length previously reported for these cells relaxed and free in solution (20). Cell dimensions were measured with a calibrated eyepiece micrometer (Table 1). The value of Lcellwas inputted into a computer (IBM PC-XT), which calculated the length displacement device control signals needed to produce the desired cell length changes. Although Lcell is a unique length for each cell, we do not assume that changes in cell length are tightly coupled to changes in contractile unit length under all conditions of activation. For example, cells set to Lcellin the manner described above and activated at that length all produce similar L-F (see Fig. 6). This would be expected only if 1) these cells have similar contractile unit lengths, and 2) contractile unit length is tightly coupled to cell length in activated cells. However, the results of this study also suggest that length changes applied to relaxed cells may not produce changes in contractile unit lengths. Experimental Protocols Cell surface marker controls. The protocols
yses employed
and analin this study rest on two assumptions. 1)
A
FIG. 1. Attachment and stretch of relaxed cell. Digitized video images are shown. A: cell prior to attachment to force recording system. Cell surface markers are present (small arrowheads). B: cell after attachment to recording system. Large arrowheads show L,,,,. Distance between cell surface markers is unchanged from that in A. C: relaxed cell after stretch. Cell length and distance between cell surface markers have been increased by similar percentages of their original values (cell length, 12%; distance between markers, 10%).
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I,ENGTH
VS. FORCE IN SMOOTH
The tying procedure does not induce contraction or stretch of the part of the cell remaining between the knots. 2) In both relaxed and activated cells, length changes are distributed homogeneously along the cell length. To test these assumptions, the following controls were performed on cells decorated with surface marker beads. 1) The distance between two cell surface markers was measured before and after the cell was tied to the measurement system (Fig. 1) as described above. 2) After tying, relaxed cells were slowly stretched to 1.14 + 0.01 Lcell (n = 4). Cell length and the distance between two cell surface markers were measured before and after the A i
il
B
C
‘\
MUSCLE
stretch (Fig. 1). 3) Cell length and the distance between two surface markers were measured in activated cells at the peak of isometric force and at new lengths in the length vs. force protocol described below (Fig. 2). Length vs. force protocol. The purpose of this protocol was to 1) characterize the relationship between cell length and isometric force generating capacity and 2) determine the effect of stretching the relaxed cell on the subsequent L-F. Cells were tied and stimulated as described above. When maximum isometric force (F,,,) was reached, the computer was signaled with a keystroke and the length change protocol began. Cell length was reduced in four steps of -0.1 Lcell each. Then cell length was returned to its initial value in two ramps of equal size. Step length reductions were complete in 5 ms and each return ramp was performed over 500 ms. After each length change, the cell was held isometric for 2.0 s, sufficient time for it to develop nearly the maximum isometric force it was capable of at that length (Fig. 3). This protocol was performed starting at the following lengths: 1.0, 1.1, 1.2, and 1.4 &ii. Elastic modulus measurements. Cell elastic modulus provides an estimate of the relative number of attached cross bridges (30). To characterize cell elastic modulus changes during isometric force generation at reduced cell lengths, the length vs. force protocol was employed with sinusoidal length oscillations (frequency, 100 Hz; amplitude, 0.005 or 0.01 Lo,,) added to the length control signal (Fig. 3). Control protocol for shortening deactivation. Because shortening can reduce isometric force generating capacity (shortening deactivation) in smooth muscle tissue (lo), we performed a control protocol (Fig. 4) to determine whether isometric force at reduced cell lengths was a unique function of cell length or of the cell’s previous shortening history. At peak isometric force, cell length was reduced from 1.0 to 0.8 Lcell in two equal steps, then restretched to 0.9 L cell, and finally released again to 0.8 Lee,,.All step reductions in length were complete in 5 ms. The ramp stretch was completed over 500 ms. After each length change, the cells were given 2.0 s to redevelop isometric force. Isometric force was thus measured twice at 0.9 Lcell and twice at 0.8 Lcell so that two paired comparisons could be made to determine the effect of the cell’s previous shortening history on isometric force. Data Analysis Cell stiffness and elastic modulus. Cell stiffness and elastic modulus were computed as follows. Analog force and length signals were digitized at 2.5 kHz. The imposed
2srn
FIG. 2. Cell during length vs. force protocol. Digitized video images are shown. Large arrowheads show cell length, small arrowheads show cell surface marker positions. A: relaxed cell. B: cell at maximum isometric force (F,,,). Cell rotation has occurred and distance between cell surface markers has decreased by 0.07 I,,,,,. C: cell after first step reduction in length. Cell length, 0.91 &I; distance between surface markers, 0.86 value at I&l,. D: cell after second step reduction in length. Cell length, 0.81 L,,,,; distance between surface markers, 0.81 value at L,,,,. E: cell after third step reduction in length. Cell length, 0.70 &I; distance between surface markers, 0.71 value at Lc.s. F: cell after fourth step reduction in length. Cell length, 0.62 I&,,; distance between surface markers, 0.64 value at &I.
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LENGTH
VS. FORCE
IN
SMOOTH
lmoLcell
0.97
. 0.92 t
-
Cl107
MUSCLE
.. .. 0.74 .:’ .- .--
*- 0.83 0.71
. =;
4.”2’ : - ,,.“... J.- ,,-.-” . - . . . - .. .. .*.
Fmax-
a. .-..-* . -- .. .*. . ..
...._.‘Se
. .s . .* , . .*” ..* . **.. --w. *.a.*._. . .” l -*s*-*-,’ ;” 2..*
FIG. 3. Length vs. force protocol. Length (top trace) and force (bottom trace) are shown. Length sinusoid (0.005 L cell amplitude) for elastic modulus measurement begins at arrow. Inset shows enlargement of length and force traces on faster time scale. Numbers beside each length step indicate cell length normalized to Lcell at that step. Resting
1s
sinusoidal length change and the resultant sinusoidal force change were separated from the underlying length and force signals with a digital band-pass filter (cutoff frequencies, 95-105 Hz). Then cell stiffness amplitude (S) and phase angle (0) were computed from these sinusoids on a cycle-by-cycle basis (30). We define the cell stiffness amplitude as the ratio of the amplitude of the force sinusoid divided by the amplitude of the length sinusoid, and the phase angle as the difference in phase between the length and force sinusoids. Next, active Young’s modulus was computed (I& = S x L&CSA, where CSA is the cell cross-sectional area). Finally cell elastic modulus was computed (E, = Eact x COST)and averaged for the last 20 cycles (200 ms) of each isometric period in the length vs. force protocol. Elastic modulus is the contribution of elastic structures to overall cell stiffness. Video length analysis. Cell video data from surface marker control experiments were digitized by a computer equipped with a video grabber board (Coreco, Oculus 200). Digitized images were then analyzed to determine overall cell length and the distance between surface markers using a specially designed software routine (31). Statistics. Statistical comparisons of force between cells were made with a Student’s t test and within cells
with a paired Student’s t test. A difference was considered significant at P < 0.05. All data are presented as means t SE. RESULTS
Cell Surface Marker Controls The distance between two cell surface markers after tying the cell to the measurement system and setting its length to Lcellwas 1.02 t 0.03 (n = 3) times the distance between the same two markers measured before tying (Fig. 1). Therefore, the cell segment length between attachments (I,,& is the same as the length of that segment when the cell is free in solution. When relaxed cells were slowly stretched to 1.14 t 0.01 &I, the distance between two surface markers increased to 1.13 t 0.02 times its value prior to the stretch (n = 4; Fig. 1). Thus stretches of relaxed cells are homogeneously distributed and not simply taken up in compliant end regions. Finally, when cells with surface markers were activated and subjected to the length vs. force protocol, changes in overall cell length resulted in similar percentage changes in the distance between cell surface markers (Figs. 2 and 5).
0.91
-1
FIG. 4. Control protocol for shortening deactivat,ion. Length (top trace) and force (bottom trace) are shown. Length steps are numbered for reference purposes. Numbers beside each length step indicate cell length normalized to Lcell at that step. Resting force is zero. Lcell, 90.4 pm; F,,,,, 1.05 yN.
0.89 0.80
d-3
0.80 -4
Fmax
l . y.x
. -. I*:M P-9&+ ’
.*.. “-8
.;*.p:**
;A-..
-:
l “&Jo*
s-
. .sY
.+4.:-.-r
,-
l
Fc-+ ,pk’
*A
: s
%.’
g’
“3
l 2
\ c-.
.
#*
.
.p
.
p.--’ o-+&e++
s- Y+-.. .*.” .-; ” l y.p. -.-r’ &. .
)
,
ti
#
p*
. 4
l‘=
.
. .
#
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Cl108
LENGTH
VS.
FORCE
IN
SMOOTH
MUSCLE
0.3> I OG66 .
I 1.0
I 0.8
CELL 0.4 ’
LENGTH
I 1.2
J 1.4
(L/Lcell)
7. L-F following stretch. Results of length vs. force protocol when starting length is 1.0 L cell and above. Isometric force (normalized to F,,,) is plotted against cell length (normalized to Loll). Closed symbols, values after step reductions in length; open symbols, values after ramp increases in length. Circles, data from Fig. 6 for cells activated at 1.0 Lcell. Squares,mean values for cells activated at 1.1 Lcell (n = 3). Triangles, mean values for cells activated at 1.2 Lcell (n = 3). Inverted triangles, mean values for cells activated at 1.4 Lcell (closed, n = 5: open at 1.2 Lcell, n = 3; open at 1.4 Lcell, n = 2). FIG.
4t
I O”o.6
I 0.7
I 0.8
I 0.9
1.0
(1 -ALcelWcell FIG. 5. Cell surface marker control. Distance between two cell surface markers (normalized to value at LcelJ is plotted against cell length (normalized to Loll) for cells subjected to length vs. force protocol. Data from four cells are represented by different symbols. Closed symbols, measurements taken after step reductions in length; open symbols, measurements after ramp increases in length (Fig. 3). Identity line is included for visual reference.
0.8 0.8
I
3
0.6 -
$ 0.6 iz ”2; 0.4
0.4 -
f5 IL
0.2
0.2/t of -0.4 '
I OL I cY’o.4
I 0.6
CELL
I 0.8
LENGTH
I 1.0
(L/Lcell)
FIG. 6. L-F: results of length vs. force protocol when starting length is 1.0 Lcell. Isometric force (normalized to F,,,) is plotted against cell length (normalized to Loll). Closed symbols, values after step reductions in length; open symbols, values after ramp increases in length. Closed symbols are means of 6 cells, whereas open symbols are means of 3 cells. Linear regression line is shown. F/F,,, = 1.7 L/L,,n-0.68. R2,
0.95.
Length vs. Force Protocol The length vs. force protocol (Fig. 3) was used to characterize the relationship between cell length and isometric force producing capacity (Fig. 6). When relaxed cells were subjected to this protocol, no force response was obtained (data not shown). Because these cells do not sustain passive force, all measured force after stimulation is defined as active force. When cells were activated at 1.0 LCell,active isometric force production declined in an approximately linear fashion with reductions in cell length. The ramp increase in cell length back to Lcell (second stretch) returns force to a value appropriate for that length. This indicates that the damage sometimes associated with shortening and stretch in activated smooth muscle tissue (17) is not present in single cells, at least over the length range studied. There appears to be a tendency toward higher
I -0.3
I -0.2
SHORTENING FIG. 8. Effect of stretching relaxed replotted against extent of shortening are identical to those in Fig. 7. Linear
I -0.1
I 0
(aL/Lcell)
cell on L-F. Data from Fig. 7 are (normalized to L&. Symbols regression line is shown. F/F,,,
= 1.7 L/Lcen-1.0. R2, 0.98.
force values following the first stretch in this protocol than would be predicted from force measurements following releases. This higher force value may be the result of incomplete force equilibration following a length change. To estimate the extent of this effect, a sample set of force recoveries following length steps was fit to a double exponential. The equations of the fits suggest that recording force after only 2 s of recovery will overestimate (for stretches) and underestimate (for releases) force by an average of 3.5% F,,,. This could explain a small part of the tendency toward higher force levels following the initial stretches. However, the shape of the L-F is not substantially affected by this small error in estimating force recovery. Extrapolating the linear regression of the relationship between cell length and isometric force to zero force predicts that force production will be eliminated at 0.40 LCell. Figure 7 shows the relationship between isometric force and cell length when the relaxed cells are stretched beyond LCell,activated, and then subjected to the length vs. force protocol. In each case, the shape of the plot is unchanged from that observed when starting at 1.0 LCen.
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LENGTH
VS.
FORCE
IN
However, the relationship is shifted along the length axis by the amount of the stretch. This is clearly demonstrated when isometric force is plotted against the reduction in cell length for all cells regardless of starting length (Fig. 8). Activating cells at lengths above &I does not alter maximum isometric force. Cells activated at 1.0 Lcell produced an active stress of 158.9 t 18.4 mN/mm2 (n = 5), which was not significantly different from the 206.6 t 34.7 mN/mm” (n = 6) produced by cells activated at 1.4
SMOOTH
MUSCLE
Cl109
ening history on isometric force-generating capacity. Although conclusions are difficult to draw because of the limited sample size, our results (Table 2) fail to demonstrate a difference between the force at the end of isometric period 3 and that at the end of isometric period 1. Both of these forces are produced at an average length of 0.91 L&. Likewise, the force at the end of isometric period 4 is not different than that seen at the end of period 2. These two isometric forces are measured at 0.83 L cell-
Lell*
DISCUSSION
Elastic Modulus
at Reduced Cell Length
To distinguish among the possible explanations for the fall in force observed at reduced cell length (see introduction), we measured cell elastic modulus at the end of each isometric period in the length vs. force protocol (Fig. 3). These measurements were obtained from cells set at 1.0, 1.1, 1.2, and 1.4 Lcell prior to stimulation. Figure 9 demonstrates that cell elastic modulus falls in proportion to the reduction in isometric force regardless of the starting cell length. Effect of Previous Shortening History on Isometric Force Shortening deactivation may play a role in determining the observed relationship between isometric force and cell length. Therefore, we performed a control protocol (Fig. 4) to determine the effect of previous short-
The experiments reported here were performed on single isolated smooth muscle cells. This was done to obtain direct information about the smooth muscle contractile process without the ambiguities caused by the complex interaction between a heterogeneous population of cells and a connective tissue matrix that exists in smooth muscle tissue. However, in vivo, smooth muscle cells are thought to be connected to each other in both a “side-to-side” and “end-to-end” manner and to transmit force via these connections (22). The removal of these connections during cell isolation may affect the subsequent mechanical properties of single cells. Also, as discussed below, the requirement that the entire L-F be measured in the course of a single activation, due to the inability to obtain multiple maximal electrical activations in these cells, may affect the results obtained. With these concerns in mind, we will 1) present evidence that the fall in force observed at short cell lengths is a true representation of the smooth muscle cell’s L-F, 2) attempt to distinguish among possible explanations for the decline in isometric force at short muscle lengths, and 3) interpret the finding that stretching relaxed smooth muscle cells shifts the subsequent isometric L-F along the length axis by the amount of the stretch. L-F Relationship
0.2 I 0.4
OZ+'o.2
__
L---p-ipp__J 0.6 FORCE
0.8
1.0
(F/F,,,&
FIG. 9. Elastic modulus vs. force. Cell elastic modulus (normalized to maximum value) is plotted against isometric force (normalized to F,,,,) for cells subjected to length vs. force protocol with elastic modulus measurements. Circles, mean values for 2 cells activated at 1.0 Lcell. Squares, 1 cell activated at 1.1 Lcell. Triangles, 1 cell activated at 1.2 Lcell. Inverted triangles, mean values for 4 cells activated at 1.4 Lcell.
TABLE
2. Effect of shortening history on isometric force Step Number 1 3 2 4
L/L11 0.92t0.01 0.90t0.01 0.83kO.02 0.83kO.02
F/Rmx 0.94t0.02 0.99t0.06 0.72t0.05 0.75kO.05
Values are means t SE. Force and length are determined at end of each isometric period in control protocol for shortening deactivation. Length is normalized to relaxed value (L,,lJ and force is normalized to maximum value (F,,iJ. Two force values obtained at 0.9 L,--ll are compared and two force values obtained at 0.8 Lcell are compared. Experiment performed in 3 cells.
The results of the length vs. force protocol (Fig. 6) accurately represent the L-F of single smooth muscle cells only if 1) after activation, changes in activated cell length reflect changes in contractile unit length, and 2) cell length alone is the major determinant of active isometric force in this protocol. The evidence that these conditions are met is as follows. Homogeneous shortening. In skeletal muscle, isometric force can be related directly to the length of the contractile unit, the sarcomere (1,9,30). Because the morphology of the smooth muscle contractile unit is still uncertain, length vs. force studies in smooth muscle tissue (see Ref. 16 for review) and in single cells (6, 11) have only been able to relate isometric force to overall muscle length. However, investigators have proposed that series arrays of contractile units attach at two places on the cell membrane and shorten to cause smooth muscle cell shortening (6). If so, changes in smooth muscle length following activation may indeed reflect changes in contractile unit length. Although the qualitative similarities between the L-F of smooth and skeletal muscle (15, 19) mav support this nronosal. no concrete proof exists.
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LENGTH
VSFORCE
The minimum requirement for interpreting changes in muscle length as indicators of changes in contractile unit length is that length changes applied to the activated cell must be homogeneously distributed along the cell length and not merely taken up in compliant end regions. The results of cell surface marker controls (Figs. 2 and 5) show that this is the case, in agreement with the results of previous studies in these single cells (28, 29). Shortening deactiuation. The L-F in skeletal muscle (1, 23) and in smooth muscle tissue (14,19) is commonly obtained by a series of activations at different muscle lengths. Because this was not possible in these single smooth muscle cells (see METHODS), a protocol that determines the L-F in the course of a single contraction (Fig. 3) was employed. Studies in smooth muscle tissue indicate that determining the L-F in this manner may not affect the result obtained (26). It is still important, however, to ascertain that the dynamic nature of the protocol used in this study does not govern the relationship between isometric force and cell length. Shortening itself may reduce subsequent isometric force generation both in skeletal muscle (5) and in smooth muscle tissue (10). In skeletal muscle this deactivation is long lasting (5) and not abolished by restretch (4). If shortening deactivation also exists in single smooth muscle cells, it could cause the reductions in isometric force seen at short lengths. However, the similarity between the L-F obtained here for single cells and that previously measured in smooth muscle tissue by a series of activations at various lengths (14, 19) suggests that the dynamic nature of the length vs. force protocol (Fig. 3) may not affect the force values obtained. Furthermore, once the cell is activated at Lcell, isometric force appears to be a unique function of cell length (Table 2). Therefore, a shortening deactivation with properties described above is not a major determinant of force in these smooth muscle cells. A short-lived shortening deactivation that is reversed by restretch could still play a role. Ascending Limb of the L-F The finding that all cells activated at Lcellhave similar L-F (Fig. 6) suggests that, when activated, these cells have similar contractile unit lengths as well. Furthermore, linear regression analysis of this relationship predicts that active force will be eliminated at 0.40 Lcell. This is similar to the value of 0.39 optimum length estimated for smooth muscle tissue (14). Therefore, setting cell length to L cell and then activating the cells apparently results in the contractile units of all cells being close to the optimum length for force generation. The decline in isometric force seen at short lengths may occur through a reduction in the number of attached cross bridges caused by excessive contractile filament overlap and steric hindrance of cross-bridge attachment (1, 9). Alternatively, isometric force could fall without a decrease in the number of attached cross bridges as the result of an internal load (9) or a decrease in the force per cross bridge (13, 18, 23). Therefore, cell elastic modulus was used to estimate the relative number of attached cross bridges (830). A proportional relationship between
IN SMOOTH
MUSCLE
cell elastic modulus and isometric force was observed (Fig. 9). Because this relationship is similar to the one previously reported for these cells during activation (28, 30) where cross-bridge recruitment predominates, we believe that a reduction in the number of attached cross bridges may be responsible for the fall in force along the ascending limb of the L-F. In tissue, this matter can be addressed by stiffness measurements as well as via energetic determinations, the assumption being that an attached cycling cross bridge will both possessstiffness and use ATP. At short muscle lengths where isometric force is reduced, both stiffness and high energy phosphate usage remain constant in taenia coli, suggesting no change in the number of attached cross bridges (19). In contrast, oxygen consumption (i.e., ATP consumption) falls with force along the ascending limb of the L-F in mesenteric vein (16). Similarly, stiffness has been found to fall (although more slowly than force) in rabbit mesotubarium (12, 13) and rat mesenteric resistance vessels (14). Interpretation of these tissue data is complicated by the presence of a significant connective tissue matrix, introducing a noncellular elasticity (14) that could mask cellular stiffness. Contractile filament misalignment with shortening could also cause force and elastic modulus to decrease at short lengths without a reduction in the number of attached cross bridges. This would occur because both force (3) and elastic modulus, which are measured along the long axis of the cell, are related to the actual force and elastic modulus by the cosine of the angle that the contractile units make with the axis of force measurement. As the cell shortens, contractile filament angles relative to the cell’s long axis could increase, causing force and elastic modulus to fall in parallel. However, when contractile filament orientation was measured by electron microscopy in relaxed smooth muscle tissue (2, 25) and estimated from cell surface marker movement in single smooth muscle cells (29), values of tl0” to the long axis of the cell were obtained. Assuming a 10” starting contractile filament angle, isovolumic shortening to 0.6 Lcell would increase the filament angle to 20” and cause only about a 5% reduction in isometric force, far less than the 68% reduction observed (Fig. 6). Thus contractile unit reorientation cannot be the sole factor responsible for the decline in isometric force along the ascending limb of the L-F. Effect of Stretching Relaxed Cells When skeletal muscle is stretched beyond its optimum length for force generation, the extent of thick and thin filament overlap is reduced and isometric force-generating capacity falls proportionally (9). Smooth muscle tissue also exhibits a descending limb for its L-F, similar to that seen in skeletal muscle (15). Even giant single smooth muscle cells isolated from a molluscan preparation show a decline in peak twitch force at long lengths (11) However, smooth muscle also demonstrates a plasticity in its L-F not seen in skeletal muscle. Mulvany and Warshaw (14) reported that when relaxed smooth muscle tissue is stretched beyond the leng$h for optimum force
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LENGTH
VS.
FORCE
generation, the peak of the L-F is shifted to a longer length. Furthermore, preliminary results obtained from single isolated toad stomach smooth muscle cells indicate a capacity to generate substantial force even when activated at two times rest length (7). These findings suggest that muscle length and contractile filament length may not always be tightly linked in relaxed smooth muscle, as is the case in skeletal muscle. In this study, when relaxed smooth muscle cells were stretched beyond their resting length (L&, subsequent maximum active isometric force did not decrease and, to our surprise, no descending limb of the L-F was observed. Rather, stretched cells produced a L-F similar to that observed at Lcell but shifted along the length axis by the amount of the stretch (Figs. 7 and 8). This result is consistent with the possibility that the L-F in these cells is characterized by a broad plateau and that the decline in force seen after reductions in cell length is the result of shortening deactivation. As discussed above, however, the presence of a shortening deactivation similar to that seen in skeletal muscle is not apparent in these cells. However, a novel short-acting shortening deactivation is not ruled out. It is intriguing to speculate that stretching relaxed single smooth muscle cells does not change the position of the contractile units on their L-F. As previously concluded by VanDijk et al. (24), a viscous element may exist in relaxed smooth muscle cells. If this viscous element is connected in series with the contractile element, it could allow changes in cell length to occur without corresponding changes in contractile unit length in relaxed cells. Then, upon activation, significant cytostructural changes may occur that tightly couple contractile unit length to cell length. This proposal predicts that stretching relaxed smooth muscle will not decrease the extent of thin and thick filament overlap as in skeletal muscle (9). Interestingly, this has been shown to be the case. Somlyo et al. (21) demonstrated that thick filaments were still surrounded by thin filaments (i.e., evidence for overlap) in transverse sections of mesenteric vein stretched to a length at which active force was zero. Regardless of the mechanism, the shift of the L-F with stretch reported here appears to be a basic property of single smooth muscle cells. However, definition of the manner in which this property presents itself in the tissue awaits further study. We thank Janet Desrosiers and Heather Spring for their technical assistance, Steven Work for his computer program development, and Trish Warshaw for the illustrations. This work was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant AR-34872. D. M. Warshaw is an Established Investigator of the American Heart Association. Address reprint requests to D. M. Warshaw. Received
29 May
1990; accepted
in final
form
2 January
1991.
REFERENCES
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AND R. L. MOSS. Factors influencing the ascending limb of the sarcomere length-tension relationship in rabbit skinned muscle fibers. J. Physiol. Lond. 390: 119-136, 1987. 2. ASHTON, F. T., A. V. SOMLYO, AND A. P. SOMLYO. The contractile apparatus of vascular smooth muscle: intermediate high voltage
IN
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electron microscopy. J. Mol. Biol. 98: 17-29, 1975. 3. BAGBY, R. M. Organization of contractile/cytoskeletal elements. In: Biochemistry of Smooth Muscle, edited by N. L. Stephens. Boca Raton, FL: CRC, 1983, vol. 1, p. l-84. 4. EDMAN, K. A. P. Depression of mechanical performance by active shortening during twitch and tetanus of vertebrate muscle fibers. Acta Physiol. Stand. 109: 15-26, 1980. 5. EKELUND, M. C., AND K. A. P. EDMAN. Shortening induced deactivation of skinned fibers of frog and mouse striated muscle. Acta Physiol. Stand. 116: 189-199, 1982. 6. FAY, F. S. Structural and Function Features of Isolated Smooth Muscle Cells. Cold Spring Harbor, NY: Cold Spring Harbor Laboratory, 1976, p. 185-201. 7. FAY, F. S., R. HOFFMAN, S. LECLAIR, AND P. MERRIAM. Preparation of individual smooth muscle cells from the stomach of Bufo marinus. Methods Enzymol. 85: 284-292, 1982. 8. FORD, L. E., A. F. HUXLEY, AND R. M. SIMMONS. The relation between stiffness and filament overlap in stimulated frog muscle fibers. J. Physiol. Lond. 311: 219-249, 1981. 9. GORDON, A. M., A. F. HUXLEY, AND F. J. JULIAN. The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. Lond. 184: 170-192, 1966. 10. GUNST, S. J. Effect of length history on contractile behavior on canine tracheal smooth muscle. Am. J. Physiol. 250 (Cell Physiol. 19): C146-C154,1986. 11. ISHI, N., AND K. TAKAHASHI. Length-tension relation of single smooth muscle cells isolated from the pedal retractor muscle of Mytilus edulis. J. Muscle Res. Cell Motil. 3: 25-38, 1982. 12. MEISS, R. A. Dynamic stiffness of rabbit mesotubarium smooth muscle: effect of isometric length. Am. J. Physiol. 234 (Cell Physiol. 3): C14-C26, 1978. R. A. The effect of tissue properties on smooth muscle 13. MEISS, mechanics. In: Frontiers in Smooth Muscle Research, edited by N. Sperelakis and J. D. Wood. New York: Liss, 1990, p. 435-449. 14. MULVANY, M. J., AND D. W. WARSHAW. The active tension-length curve of vascular smooth muscle related to its cellular components. J. Gen. Physiol. 74: 85-104, 1979. 15. MURPHY, R. A. The mechanics of vascular smooth muscle. In: Handbook of Physiology. The Cardiovascular System. Muscle Mechanics. Bethesda, MD: Am. Physiol. Sot., 1980, sect. 2, vol. II, chapt. 13, p. 325-351. 16. PAUL, R. J., AND J. W. PETERSON. Relation between length, isometric force, and 0, consumption rate in vascular smooth muscle. Am. J. Physiol. 228: 915-922, 1975. 17. PETERSON, J. W., AND R. J. PAUL. Effects of initial length and active shortening on vascular smooth muscle contractility. Am. J. Physiol. 227: 1019-1024, 1974. M., AND R. J. PODOLSKY. Length-force relation of 18. SCHOENBERG, calcium activated muscle fibers. Science Wash. DC 176: 52-54, 1972. 19. SIEGMAN, M. J.: T. M. BUTLER, AND S. U. MOOERS. Energetic, mechanical, and ultrastructural correlates of the length-tension relationship in smooth muscle. In: Smooth Muscle Contraction, edited by N. L. Stephens. New York: Dekker, 1984, p. 189-198. 20. SINGER, J. J., AND F. S. FAY. Detection of contraction of isolated smooth muscle cells in suspension. Am. J. Physiol. 232 (Cell Physiol. 1): C138-C143, 1977. 21. SOMLYO, A. P., A. V. SQMLYO, C. E. DEVINE, AND R. V. RICE. Aggregation of thick and thin filaments into ribbons in mammalian smooth muscle. Nature New Biol. 231: 243-246, 1971. A. V. Ultrastructure of vascular smooth muscle. In: 22. SOMLYO, Handbook of Physiology. The Cardiovascular System. Structure. Bethesda, MD: Am. Physiol. Sot., 1980, sect. 2, vol. II, chapt. 2, p. 33-67. 23. STEPHENSON, D. G., A. W. STEWART, AND G. J. WILSON. Dissociation of force from myofibrillar MgATPase and stiffness at short sarcomere lengths in rat and toad skeletal muscle. J. Physiol. Lond. 410: 351-366, 1989. A. M., P. A. WIERINGA, M. VAN DER MEER, AND J. D. 24. VANDIJK, LAIRD. Mechanics of resting isolated single vascular smooth muscle cells from bovine coronary artery. Am. J. Physiol. 246 (Cell Physiol. 15): C277-C287,1984. 25. WALMSLEY, J. G., AND R. A. MURPHY. Force-length dependence of arterial lamellar, smooth muscle, and myofilament orientations. Circ. Ph.ysiol. 22): H1141-H1147, Am. J. Phvsiol. 253 (Heart 1987.
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FORCE
26. WARSHAW, D.M. Direct Correlation Between Structure and Function in Arterial Resistance Vessels in Young And Old Spontaneously Hypertensive Rats (PhD thesis). Burlington: Univ. of Vermont, 1978. 27. WARSHAW, D. M. Force:velocity relationship in single isolated toad stomach smooth muscle cells. J. Gen. Physiol. 89: 771-789, 1987. 28. WARSHAW, D. W., AND F. S. FAY. Cross-bridge elasticity in single smooth muscle cells. J. Gen. Physiol. 82: 157-199, 1983. 29. WARSHAW, D. W., W. J. MCBRIDE, AND S. S. WORK. Corkscrew-
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like shortening in single smooth muscle cells. Science Wash. DC 236: 1457-1459, 1987. 30. WARSHAW, D. W., D. D. REES, AND F. S. FAY. Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells. J. Gen. Physiol. 91: 761-779, 1988. 31. WORK, S. S., AND D. M. WARSHAW. Detection of surface movements on single smooth muscle cells: digital video microscopy. Comput. Biol. Med. 18: 385-393, 1988.
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