703
Journal of Physiology (1991), 441, pp. 703-718 Wl'ith 7 figures Printed in Great Britain
CHARACTERIZATION OF RADIAL FORCE AND RADIAL STIFFNESS IN Ca2l-ACTIVATED SKINNED FIBRES OF THE RABBIT PSOAS MUSCLE
By BERNHARD BRENNER* AND LEEPO C. YUt From the * University of Tiibingen, Tiubingen, Germany and the tNational Institutes of Health, Bethesda, MD 20892, USA
(Received 11 May 1990) SUMMARY
1. When chemically skinned muscle fibres are activated by Ca2" at an ionic strength of 170 mm, the spacing between the filaments has been shown to decrease with increasing force, suggesting that the cross-bridges can generate force not only in the axial but also in the radial direction. In the present study, radial force and radial stiffness of activated single skinned rabbit psoas fibres were studied by X-ray diffraction. The responses of the lattice spacing to changes in osmotic pressure by application of dextran T500, which is equivalent to force applied in the radial direction, was examined. The radial force generated by the attached cross-bridges was calculated, with the approximation that a negligible fraction of cross-bridges was attached in the relaxed muscle at the same ionic strength of 170 mM. 2. The active radial force was found to be a slightly non-linear function of lattice spacing, reaching zero at 34 nm. The radial force was compressive at lattice spacing greater than 34 nm and expansive at less than 34 nm. 3. The active axial force, on the other hand, was found to be much less affected by the application of dextran T500. Active axial force increased by 4% to a plateau at 4% dextran T500 and then decreased by 10% at 8% dextran T500. 4. While not under osmotic pressure, the radial force of the activated fibre was determined to be 400 pN (single thick filament)-'. This is of the same order of magnitude as the axial force. The radial stiffness was also comparable to the axial stiffness at 7 pN (thick filament)-' (0-1 nm)-1. 5. The radial elasticity of the fully activated fibre differs significantly from that of the fibre in rigor. The radial stiffness exhibited by fibres in rigor was approximately five times higher, at 30 pN (thick filament)-' (0-1 nm)-' and the point where the radial force reached zero was 38 nm. 6. In the activated state, the point at which radial force reaches zero is independent of the level of Ca2' activation, i.e. independent of the number of crossbridges attached to actin in the force-generating state. We suggest that the zero-force point is equivalent to the equilibrium point of a spring and is an intrinsic property of the radial elasticity of the cross-bridge. 7. It is concluded that activated and rigor cross-bridges exhibit a spring-like * Present address: University of Ulm, Ulm, Germany. t To whom correspondence should be addressed. M1S 8488
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property in the radial direction. Furthermore, the equilibrium point of the radial elasticity appears to depend on the physiological state of the cross-bridges. The significance of the large magnitude of radial elasticity and of the different equilibrium points is discussed. INTRODUCTION
A general concept of the cross-bridge theory of muscle contraction is that the kinetics of the cyclic cross-bridge action depend on the elastic deformation sustained by the attached myosin head (Huxley, 1957). Various forms of strain-dependent rate constants have been proposed for the cross-bridge cycle (Huxley, 1957; Podolsky & Nolan, 1973; Eisenberg & Hill, 1985). Recently, it was shown that the rate of relaxation of skinned psoas fibres from rigor depends on the initial stress in the fibre (Goldman, Hibberd & Trentham, 1984) and the rate of force decay for skinned psoas fibres bathed in ATP analogue-containing solutions was also found to depend on the amplitude of stress applied to the fibres (Schoenberg & Eisenberg, 1985). Hitherto, discussions and experimental findings have been mostly centred on the effects of axial strain on the rate constants. If elasticity of the cross-bridges in the radial direction, i.e. in the direction perpendicular to the fibre axis, is not negligible, radial strain is expected to affect the free energy of an attached cross-bridge and thus kinetics of all reaction steps involving such a state (Hill, 1974). Radial force has been shown to exist in activated skinned rabbit psoas fibres (Shapiro, Tawada & Podolsky, 1979; Brenner & Yu, 1985) and skinned mouse toe muscle (Matsubara, Umazume & Yagi, 1985). The radial forces were manifested in the shrinking of the myofilament lattice as a non-linear function of activation level (Brenner & Yu, 1985). As muscle goes into rigor, similar shrinkage was observed (Matsubara, Goldman & Simmons, 1984). The change in lattice spacing most likely originated from the attachment of force-generating cross-bridges since the change accompanied activation while experimental conditions such as the ionic strength, the temperature, and the sarcomere length were kept constant. In addition, preliminary results indicated that when fibres were stretched out of overlap, adding Ca2" did not affect the lattice spacing (B. Brenner and L. C. Yu, unpublished results). However, the radial elasticity of cross-bridges in the activated state has not yet been studied, nor has the magnitude of the active radial force been determined. In the present study radial force levels and radial elasticity of single chemically skinned rabbit psoas muscle fibres in various states, including the activated state, have been characterized. At the lattice spacing of 38-5 nm, radial force and radial stiffness of the activated fibre are found to be of the same order of magnitude as those in the axial direction. Furthermore, the radial elasticity appears to be a function of the cross-bridge state. METHODS
Fibre preparation Rabbits were anaesthetized with Ketamine (Ketaset, Fort Dodge Laboratories, IMC, IA, USA) at 10 mg (kg of body weight)-' and exsanguinated via the carotid artery. Single, chemically skinned psoas muscle fibres were used throughout this study. Fibres were skinned and dissected according to Brenner (1983; for further details see Yu & Brenner, 1989). Most of the experiments were performed at ionic strength (u) of 170 mm except for the relaxed state at It = 20 mm. Sarcomere
RADIAL ELASTICITY OF ACTIVATED MUISCLE
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length was 2-3-2-4 ,um, which was measured by laser light diffraction simultaneously with X-ray diffraction. Temperature was 5-7 'C. Solutions Relaxing solution (mM): 1 ATP, 3 MgCl2, 1 EGTA, 10 imidazole, 1 DTT (dithiothreitol; Sigma Chemical Co., St. Louis, MO, USA), pH 7 0, It = 20 mM; 150 KCl was added for ,u = 170 mM. Activating solution (mM): 1 ATP, 3 MgCl2, 1 Ca-EGTA, 10 phosphocreatine, 250-300 units (u) creatine phosphokinase (Sigma Chemical Co.), 10 caffeine, 10 imidazole, 1 DTT, 120 KCl, pH 70. Pre-activating solution contained the same composition as the activating solution except that Ca-EGTA was replaced by EGTA at the same concentration. Rigor solution (mM): 10 imidazole, 2-5 EGTA, 2-5 EDTA, 1 DTT, 159 KCl, pH 7-0. Before applying the rigor solution, the fibres were rinsed several times by solutions containing 20 imidazole, 5 EGTA, 15 EDTA, 1 DTT, 100 KCl, pH 7 0. Applied Osmotic Pressure The anhydroglucose polymer dextran T,500 (Pharmacia Fine Chemicals Inc., Uppsala, Sweden; weight-averaged molecular weightMw 470000; number-averaged molecular weightMn 170000) was added to solutions for applying osmotic pressure on the muscle fibres. Concentrations of dextran T500 ranging between 0 and 8 % (w/v) were used. Since slight variations were found among different batches of the supplies, osmotic pressure of some sample relaxing solutions (,u = 170 mM), containing up to 7 % (w/v) dextran T500, was determined directly by a micro-osmometer (Knauer Co., Wissenschaftkliche Gerate, K. G., Oberursel-Taunus, Germany), using a cellulose membrane with cut-off at molecular weight 20000 (Schleicher & Schuell, Germany). Matsubara et al. (1984), using 1251-labelled PVP (polyvinylpyrrolidone), estimated that 53 % of the skinned single fibre volume was accessible to PVP-40 whose number-averaged molecular weight (Mn) was 40000. Due to the presence of PVP inside the fibre, an 50 % correction was required to lower the estimates of the calculated osmotic pressure exerted by PVP-40. Presumably, a significant fraction of the PVP-40 is distributed below a molecular weight of 20 000 and yet the necessary correction to osmotic pressure was only 50 %. In our case, where the osmotic pressure was measured with a membrane cut-off at molecular weight of 20000, the correction to our data would be far less than 50 %. For order of magnitude estimates of applied radial force, such a correction would be insignificant. Six different batches of dextran T500 were used in the experiments. Osmotic pressures were measured directly on three batches. Osmotic pressure for solutions containing 8 % dextran T500 were obtained by extrapolation, since at such high concentration the resulting osmotic pressure went beyond the normal measuring capacity of the Knauer osmometer. The measured osmotic pressures varied by approximately 10 % among the three batches. The values of osmotic pressure data presented in the results are the averaged values of the three different batches of dextran T500. Different batches of dextran did not cause noticeable variations beyond normal experimental error in the results of measured lattice spacing. -
-
-
Calculations of radial forces per unit length of thick filament The radial forces generated by the attached cross-bridges were calculated from the applied osmotic pressure that was needed to compress the filament lattice of the relaxed muscle at It = 170 mm to the same spacing as brought by cross-bridge attachment. Our calculations of the radial force followed those presented by earlier works (Schoenberg, 1980; Matsubara et al. 1984; Rau, Lee & Parsegian, 1984). For a hexagonal lattice, the radial force, F, between the thick filaments and the thin filaments per unit length of thick filament is given by Fr = 2V3 Hdlo (1) H where is the applied osmotic pressure and d,o is the lattice spacing of the Bragg plane [1,0] of the filament lattice. In the Results, radial force is expressed in units of pN (single thick filament)-' with the thick filament assumed to be 1-6 ,um in length. Activation The activation procedure, in the presence and in the absence of dextran, followed that described earlier by Brenner (1983). The single skinned fibre segments were mounted between a force transducer and the lever tip of a modified moving-coil galvanometer while bathed in skinning 23
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solution. Fibres were then placed in a chamber of some 500 ,ul volume. Before introducing the activating solution, the fibres were first incubated in the pre-activating solution for about 15 min. In the absence of radial compression, a skinned psoas fibre can be continuously activated at , = 170 mm for up to 2 h without visible changes in sarcomere patterns during X-ray exposure by using a technique that cycles the fibre between the isometric state and lightly loaded isotonic shortening (Brenner, 1983). The frequencies of cycling used in this series of study varied between 0 3 and 0-1 s-1. As a result of using the cycling technique, there was no sarcomere shortening during the isometric phase even in the presence of dextran. While there was no visible deterioration in the sarcomere pattern, with 4% dextran added to the activating solution X-ray diffraction patterns obtained by a laboratory source showed deterioration after 10 min. -
Equatorial X-ray diffraction The data presented in this study were obtained in two series of experiments. Initially, X-raydiffraction patterns were recorded in the laboratory by using a conventional rotating anode X-ray generator (Elliott GX-6) and a single-wire position-sensitive X-ray detector (Yu & Brenner, 1989). However, the diffraction patterns from activated fibres under osmotic pressure ( > 4 % of dextran T500) deteriorated during the 10 min of X-ray exposure necessary with the laboratory source. Consequently, we could not obtain satisfactory X-ray-diffraction patterns above 4 % dextran. To shorten the exposure time, the intense X-ray source generated by synchrotron radiation at Deutsche Electronensynchrotron (DESY; Hamburg, Germany) was later used. The experiments were carried out on beam line X-33 of the European Molecular Biology Laboratory (EMBL) Outstation in Hamburg. The camera was modified for low-angle diffraction from a small specimen. The beam at the specimen was 300-350 ,um high by 3 mm wide. The specimen-to-detector distance was 3-9 m. Diffraction patterns were recorded on a multi-wire linear detector (Hendrix, 1985). The total intensity of the beam transmitted through the specimen holding chamber was recorded by an ionization chamber. This recorded intensity was used to normalize each diffraction pattern in order to compensate for the varying beam intensity in the storage ring. The improvement in beam intensity was better than 500-fold, compared to that of the conventional rotating anode source. The exposure time in the laboratory was at least 500 s; at DESY, generally 5 s. Experimental protocol X-ray-diffraction patterns from the fibre in relaxing solution at It = 20 mm and 170 mm were always recorded first. The protocol following these initial exposures depended on whether the fibre was activated or not. For static studies (i.e. rigor and relaxed state at ,u = 20 mM), a series of X-ray patterns were recorded with increasing concentrations of dextran. Once the highest concentration of dextran was reached, a control exposure without dextran was taken to ensure full reversibility. It was then followed by a series of exposures under another condition. A wait of approximately 5 min before X-ray exposure was found to be sufficient for dextran T500 to equilibrate. For activating conditions, diffraction patterns of relaxed muscle in pre-activating solution with dextran were always recorded before the activated patterns in dextran at the same concentration. At the higher dextran concentrations, frequently each diffraction pattern of the activated fibre was preceded and followed by relaxed patterns obtained under the same osmotic pressure. All the 'before' and 'after' control (relaxed) patterns were included as data for the relaxed state. X-ray exposure was started only after the force had reached steady level, which was within 2 min. Patterns were recorded only during the isometric phase of the mechanical cycling of the fibre (see Methods). At low concentrations of dextran ( < 4 %) each fibre was activated in solutions with at least two different concentrations of dextran. At higher concentrations, each fibre was activated at only one concentration of dextran. RESULTS
Response of relaxed fibres at ,a
170 mM to dextran solutions The response of the relaxed fibre at ,u = 170 mm to dextran solutions was first recorded to characterize the passive behaviour of a skinned rabbit psoas fibre. Since only a few cross-bridges (< 10%) are attached to actin under this condition =
RADIAL ELASTICITY OF ACTIVATED MUSCLE
707
(Schoenberg, 1988), the response to applied compression originates mainly from passive forces in the fibre other than forces of attached cross-bridges (e.g. cytoskeletal elements, electrostatic forces). We assume that under all conditions, a given filament separation is reached when the passive radial forces are balanced by possible radial 50
45
-
040
-
0
35
*i< 30
2400 1600 800 Applied radial force (pN (single thick filament)-1) Fig. 1. Response of single fibres to applied radial force by dextran T500 0, relaxed state at ,u = 170 mM; A, fully Ca2+-activated fibres at ,u = 170 mm. Error bars are S.E.M. Sarcomere length, 2-3-2A4,um. Temperature, 5 'C. Number of fibres used, 12. Radial force per unit length is calculated as 2/V3 H d,o, where 1 is the osmotic pressure of the dextran solutions. The unit pN (single thick filament)-' assumes the filament length to be 1-6 ,um. The values of the osmotic pressure used are averages of three batches of dextran solutions. Maximum concentration of dextran T500 used was 8% (w/v). Lines were obtained by a least-squares fit using the mathematical routine MLAB (Knott, 1979). The equation used for the relaxed state is a exp(bz) + c exp(cLz) + cons with x representing the applied radial force in units of pN (single thick filament)-'; a, b, c, d and cons being parameters. The best fit was found with a = 76-566, b = - 0-000606, c = 90 543, d = -0-005197, cons =279-79. The equation used for the activated state was aexp(bz)+cons, with a = 67-043, b = -0-00157, cons = 311-92. 0
forces of attached cross-bridges and/or the compressive force of dextran. It follows that the radial force exerted by dextran to compress the relaxed fibre at ,u = 170 mM to the same lattice spacings as those reached during activation or in rigor is equal to the radial force generated by the attached cross-bridges. Figure 1 (0) shows that the lattice spacing of the relaxed fibre is a monotonic decreasing function of the applied radial force. The data included both the 'before' and 'after' activation spacings. The data can be fitted closely by a function of one, or better two, exponentials. The latter is shown by the dashed line in Fig. 1. Lattice spacings of the activated fibres in dextran solutions The activated fibres were compressed by various concentrations of dextran T500. The data (A) in Fig. 1 are combined results that were obtained (1) by the laboratory X-ray source for 0-4 % dextran T500 solutions (applied radial force ranged between 0 and 400 pN (single thick filament)-') and (2) by using the synchrotron radiation at 23-2
B. BRENNER AND L. C. YU
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DESY for 0, 4, 6 and 8 % dextran T500 solutions (equivalent applied radial force: 0, 400, 1100 and 2180 pN (single thick filament)-'). The results show that application of dextran T500 to the fully Ca2+-activated fibre at ,u = 170 mm compresses the filament lattice to below 38 nm, and the response is non-linear. The data are fitted
G,10
a
oa 0 05-i L_
z
. . . 800 1600 2400 Applied radial force (pN (single thick filament)-1') Fig. 2. Active force in the axial direction under applied radial force. Force levels are normalized with respect to those in the absence of dextran. Average value for the force level in 0 % dextran was 1.0 kg cm-2. Error bars are S.E.M. For each concentration of dextran, at least twelve measurements were made. Five fibres were used. The order of application of dextran was random. 0
0.
.
by a single exponential function as shown by the continuous line in Fig. 1. The radial stiffness (inverse slope of the continuous line) found in the activated fibres is higher than that of the relaxed fibres over the entire range of concentrations used. At applied radial force of 880 pN (single thick filament)-1 and d1o = 34 nm, the two curves cross over each other. Thus, pre-compressing a relaxed fibre to 34 nm, activation will no longer change lattice spacing. At higher lattice spacing, activation decreases d10, while below 34 nm, it increases d1o0 This suggests that at d1o = 34 nm attached force-generating cross-bridges produce no radial force (zero-force point). At 4 % of dextran T500, the averages of lattice spacings obtained in the laboratory and at DESY were identical. However, the reflection peaks were sharper with the shorter exposure time used at DESY. This suggests that the order of the hexagonal filament array deteriorated with time under osmotic pressure. The average lattice spacing of the remaining ordered arrays, however, was unchanged. Active axial force is largely independent of concentrations of applied dextran T500 To determine whether the radial force exerted by cross-bridges is proportional to the axial force, the latter was also recorded at various concentrations of dextran T500. Figure 2 shows that between 0 and 8% w/v of dextran T500 (equivalent applied radial force: 0-2180 pN (single thick filament)-') the axial force level changed by no more than 10% while radial force decreased to zero under 1100 pN (single thick filament)-' applied radial force (6% dextran T500) and changed direction (Fig. 1).
RADIAL ELASTICITY OF ACTIVATED MUSCLE
709
Response of fibres in rigor to dextran solutions Changes in lattice spacing of the rigor fibres as a function of the applied radial force were recorded between 0 and 2500 pN (single thick filament)-1 (0-8 % dextran T500; Fig. 3). The rigor fibres are considerably less compliant. At 2500 pN (single thick 50 45 Z
E\ c='40 '_
CD
40.
Co
2 35
30 0
800
1600
2400
Applied radial force (pN (single thick filament)-1) Fig. 3. Response of fibres in rigor (@) to applied radial force as compared to that of the relaxed fibre (0). Ionic strength = 170 mm. Sarcomere length, 2-3-2-4 ,um. Temperature, 5 'C. Seven fibres were used. Error bars are S.E.M. The rigor data was fitted by a single exponential function aexp(bzx)+cons with a = 30-33, b = -0-00182, cons = 366-50. A double exponential function was used for the relaxed state, a exp(bx) + c exp(dx) + cons with a = 93.53, b = -0-001311, c = 67-78, d = -0-006165, cons = 302-88.
filament)-1 (8 % dextran T500), the lattice spacing changed only by 3 nm (from 39 to 36 nm). At an applied radial force of 430 pN (single thick filament)-1 (4% of T500 dextran) the lattice spacing of the fibre in the rigor state is the same as that in the relaxed state. As the concentration is increased, the rigor fibre expanded compared to the relaxed fibre. This phenomenon is similar to that observed in the active fibre except that the stiffness (inverse slope of the continuous line) is very much higher in the rigor solution, and the zero-force point of the rigor cross-bridges is at 38 nm instead of 34 nm.
Response of the relaxed fibre at low ionic strength to dextran solution In a relaxed fibre at ,u = 20 mm, at 5 °C, experimental evidence suggested that at least 60% of the cross-bridges are attached to actin in the weak-binding states (Brenner, Schoenberg, Chalovich, Greene & Eisenberg, 1982; Brenner, Yu & Podolsky, 1984; Yu & Brenner, 1989). The radial elasticity of these cross-bridges was investigated. Figure 4 shows that the response of the low ionic strength relaxed fibre is rather distinct from those of the active and the rigor fibres. At low applied radial force, i.e. for d10 above 36 nm, the two curves appear to be converging. However, for smaller d1o, the change in d4o is almost parallel to that of the relaxed fibre at , = 170 mm and no cross-over was found between the two sets of data.
B. BRENNER AND L. C. YU
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E CU. 40 CI)
Journal of Physiology (1991), 441, pp. 703-718 Wl'ith 7 figures Printed in Great Britain
CHARACTERIZATION OF RADIAL FORCE AND RADIAL STIFFNESS IN Ca2l-ACTIVATED SKINNED FIBRES OF THE RABBIT PSOAS MUSCLE
By BERNHARD BRENNER* AND LEEPO C. YUt From the * University of Tiibingen, Tiubingen, Germany and the tNational Institutes of Health, Bethesda, MD 20892, USA
(Received 11 May 1990) SUMMARY
1. When chemically skinned muscle fibres are activated by Ca2" at an ionic strength of 170 mm, the spacing between the filaments has been shown to decrease with increasing force, suggesting that the cross-bridges can generate force not only in the axial but also in the radial direction. In the present study, radial force and radial stiffness of activated single skinned rabbit psoas fibres were studied by X-ray diffraction. The responses of the lattice spacing to changes in osmotic pressure by application of dextran T500, which is equivalent to force applied in the radial direction, was examined. The radial force generated by the attached cross-bridges was calculated, with the approximation that a negligible fraction of cross-bridges was attached in the relaxed muscle at the same ionic strength of 170 mM. 2. The active radial force was found to be a slightly non-linear function of lattice spacing, reaching zero at 34 nm. The radial force was compressive at lattice spacing greater than 34 nm and expansive at less than 34 nm. 3. The active axial force, on the other hand, was found to be much less affected by the application of dextran T500. Active axial force increased by 4% to a plateau at 4% dextran T500 and then decreased by 10% at 8% dextran T500. 4. While not under osmotic pressure, the radial force of the activated fibre was determined to be 400 pN (single thick filament)-'. This is of the same order of magnitude as the axial force. The radial stiffness was also comparable to the axial stiffness at 7 pN (thick filament)-' (0-1 nm)-1. 5. The radial elasticity of the fully activated fibre differs significantly from that of the fibre in rigor. The radial stiffness exhibited by fibres in rigor was approximately five times higher, at 30 pN (thick filament)-' (0-1 nm)-' and the point where the radial force reached zero was 38 nm. 6. In the activated state, the point at which radial force reaches zero is independent of the level of Ca2' activation, i.e. independent of the number of crossbridges attached to actin in the force-generating state. We suggest that the zero-force point is equivalent to the equilibrium point of a spring and is an intrinsic property of the radial elasticity of the cross-bridge. 7. It is concluded that activated and rigor cross-bridges exhibit a spring-like * Present address: University of Ulm, Ulm, Germany. t To whom correspondence should be addressed. M1S 8488
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B. BRENNER ANVD L. C. YU
property in the radial direction. Furthermore, the equilibrium point of the radial elasticity appears to depend on the physiological state of the cross-bridges. The significance of the large magnitude of radial elasticity and of the different equilibrium points is discussed. INTRODUCTION
A general concept of the cross-bridge theory of muscle contraction is that the kinetics of the cyclic cross-bridge action depend on the elastic deformation sustained by the attached myosin head (Huxley, 1957). Various forms of strain-dependent rate constants have been proposed for the cross-bridge cycle (Huxley, 1957; Podolsky & Nolan, 1973; Eisenberg & Hill, 1985). Recently, it was shown that the rate of relaxation of skinned psoas fibres from rigor depends on the initial stress in the fibre (Goldman, Hibberd & Trentham, 1984) and the rate of force decay for skinned psoas fibres bathed in ATP analogue-containing solutions was also found to depend on the amplitude of stress applied to the fibres (Schoenberg & Eisenberg, 1985). Hitherto, discussions and experimental findings have been mostly centred on the effects of axial strain on the rate constants. If elasticity of the cross-bridges in the radial direction, i.e. in the direction perpendicular to the fibre axis, is not negligible, radial strain is expected to affect the free energy of an attached cross-bridge and thus kinetics of all reaction steps involving such a state (Hill, 1974). Radial force has been shown to exist in activated skinned rabbit psoas fibres (Shapiro, Tawada & Podolsky, 1979; Brenner & Yu, 1985) and skinned mouse toe muscle (Matsubara, Umazume & Yagi, 1985). The radial forces were manifested in the shrinking of the myofilament lattice as a non-linear function of activation level (Brenner & Yu, 1985). As muscle goes into rigor, similar shrinkage was observed (Matsubara, Goldman & Simmons, 1984). The change in lattice spacing most likely originated from the attachment of force-generating cross-bridges since the change accompanied activation while experimental conditions such as the ionic strength, the temperature, and the sarcomere length were kept constant. In addition, preliminary results indicated that when fibres were stretched out of overlap, adding Ca2" did not affect the lattice spacing (B. Brenner and L. C. Yu, unpublished results). However, the radial elasticity of cross-bridges in the activated state has not yet been studied, nor has the magnitude of the active radial force been determined. In the present study radial force levels and radial elasticity of single chemically skinned rabbit psoas muscle fibres in various states, including the activated state, have been characterized. At the lattice spacing of 38-5 nm, radial force and radial stiffness of the activated fibre are found to be of the same order of magnitude as those in the axial direction. Furthermore, the radial elasticity appears to be a function of the cross-bridge state. METHODS
Fibre preparation Rabbits were anaesthetized with Ketamine (Ketaset, Fort Dodge Laboratories, IMC, IA, USA) at 10 mg (kg of body weight)-' and exsanguinated via the carotid artery. Single, chemically skinned psoas muscle fibres were used throughout this study. Fibres were skinned and dissected according to Brenner (1983; for further details see Yu & Brenner, 1989). Most of the experiments were performed at ionic strength (u) of 170 mm except for the relaxed state at It = 20 mm. Sarcomere
RADIAL ELASTICITY OF ACTIVATED MUISCLE
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length was 2-3-2-4 ,um, which was measured by laser light diffraction simultaneously with X-ray diffraction. Temperature was 5-7 'C. Solutions Relaxing solution (mM): 1 ATP, 3 MgCl2, 1 EGTA, 10 imidazole, 1 DTT (dithiothreitol; Sigma Chemical Co., St. Louis, MO, USA), pH 7 0, It = 20 mM; 150 KCl was added for ,u = 170 mM. Activating solution (mM): 1 ATP, 3 MgCl2, 1 Ca-EGTA, 10 phosphocreatine, 250-300 units (u) creatine phosphokinase (Sigma Chemical Co.), 10 caffeine, 10 imidazole, 1 DTT, 120 KCl, pH 70. Pre-activating solution contained the same composition as the activating solution except that Ca-EGTA was replaced by EGTA at the same concentration. Rigor solution (mM): 10 imidazole, 2-5 EGTA, 2-5 EDTA, 1 DTT, 159 KCl, pH 7-0. Before applying the rigor solution, the fibres were rinsed several times by solutions containing 20 imidazole, 5 EGTA, 15 EDTA, 1 DTT, 100 KCl, pH 7 0. Applied Osmotic Pressure The anhydroglucose polymer dextran T,500 (Pharmacia Fine Chemicals Inc., Uppsala, Sweden; weight-averaged molecular weightMw 470000; number-averaged molecular weightMn 170000) was added to solutions for applying osmotic pressure on the muscle fibres. Concentrations of dextran T500 ranging between 0 and 8 % (w/v) were used. Since slight variations were found among different batches of the supplies, osmotic pressure of some sample relaxing solutions (,u = 170 mM), containing up to 7 % (w/v) dextran T500, was determined directly by a micro-osmometer (Knauer Co., Wissenschaftkliche Gerate, K. G., Oberursel-Taunus, Germany), using a cellulose membrane with cut-off at molecular weight 20000 (Schleicher & Schuell, Germany). Matsubara et al. (1984), using 1251-labelled PVP (polyvinylpyrrolidone), estimated that 53 % of the skinned single fibre volume was accessible to PVP-40 whose number-averaged molecular weight (Mn) was 40000. Due to the presence of PVP inside the fibre, an 50 % correction was required to lower the estimates of the calculated osmotic pressure exerted by PVP-40. Presumably, a significant fraction of the PVP-40 is distributed below a molecular weight of 20 000 and yet the necessary correction to osmotic pressure was only 50 %. In our case, where the osmotic pressure was measured with a membrane cut-off at molecular weight of 20000, the correction to our data would be far less than 50 %. For order of magnitude estimates of applied radial force, such a correction would be insignificant. Six different batches of dextran T500 were used in the experiments. Osmotic pressures were measured directly on three batches. Osmotic pressure for solutions containing 8 % dextran T500 were obtained by extrapolation, since at such high concentration the resulting osmotic pressure went beyond the normal measuring capacity of the Knauer osmometer. The measured osmotic pressures varied by approximately 10 % among the three batches. The values of osmotic pressure data presented in the results are the averaged values of the three different batches of dextran T500. Different batches of dextran did not cause noticeable variations beyond normal experimental error in the results of measured lattice spacing. -
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-
Calculations of radial forces per unit length of thick filament The radial forces generated by the attached cross-bridges were calculated from the applied osmotic pressure that was needed to compress the filament lattice of the relaxed muscle at It = 170 mm to the same spacing as brought by cross-bridge attachment. Our calculations of the radial force followed those presented by earlier works (Schoenberg, 1980; Matsubara et al. 1984; Rau, Lee & Parsegian, 1984). For a hexagonal lattice, the radial force, F, between the thick filaments and the thin filaments per unit length of thick filament is given by Fr = 2V3 Hdlo (1) H where is the applied osmotic pressure and d,o is the lattice spacing of the Bragg plane [1,0] of the filament lattice. In the Results, radial force is expressed in units of pN (single thick filament)-' with the thick filament assumed to be 1-6 ,um in length. Activation The activation procedure, in the presence and in the absence of dextran, followed that described earlier by Brenner (1983). The single skinned fibre segments were mounted between a force transducer and the lever tip of a modified moving-coil galvanometer while bathed in skinning 23
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B. BRENNER AND L. C YU
solution. Fibres were then placed in a chamber of some 500 ,ul volume. Before introducing the activating solution, the fibres were first incubated in the pre-activating solution for about 15 min. In the absence of radial compression, a skinned psoas fibre can be continuously activated at , = 170 mm for up to 2 h without visible changes in sarcomere patterns during X-ray exposure by using a technique that cycles the fibre between the isometric state and lightly loaded isotonic shortening (Brenner, 1983). The frequencies of cycling used in this series of study varied between 0 3 and 0-1 s-1. As a result of using the cycling technique, there was no sarcomere shortening during the isometric phase even in the presence of dextran. While there was no visible deterioration in the sarcomere pattern, with 4% dextran added to the activating solution X-ray diffraction patterns obtained by a laboratory source showed deterioration after 10 min. -
Equatorial X-ray diffraction The data presented in this study were obtained in two series of experiments. Initially, X-raydiffraction patterns were recorded in the laboratory by using a conventional rotating anode X-ray generator (Elliott GX-6) and a single-wire position-sensitive X-ray detector (Yu & Brenner, 1989). However, the diffraction patterns from activated fibres under osmotic pressure ( > 4 % of dextran T500) deteriorated during the 10 min of X-ray exposure necessary with the laboratory source. Consequently, we could not obtain satisfactory X-ray-diffraction patterns above 4 % dextran. To shorten the exposure time, the intense X-ray source generated by synchrotron radiation at Deutsche Electronensynchrotron (DESY; Hamburg, Germany) was later used. The experiments were carried out on beam line X-33 of the European Molecular Biology Laboratory (EMBL) Outstation in Hamburg. The camera was modified for low-angle diffraction from a small specimen. The beam at the specimen was 300-350 ,um high by 3 mm wide. The specimen-to-detector distance was 3-9 m. Diffraction patterns were recorded on a multi-wire linear detector (Hendrix, 1985). The total intensity of the beam transmitted through the specimen holding chamber was recorded by an ionization chamber. This recorded intensity was used to normalize each diffraction pattern in order to compensate for the varying beam intensity in the storage ring. The improvement in beam intensity was better than 500-fold, compared to that of the conventional rotating anode source. The exposure time in the laboratory was at least 500 s; at DESY, generally 5 s. Experimental protocol X-ray-diffraction patterns from the fibre in relaxing solution at It = 20 mm and 170 mm were always recorded first. The protocol following these initial exposures depended on whether the fibre was activated or not. For static studies (i.e. rigor and relaxed state at ,u = 20 mM), a series of X-ray patterns were recorded with increasing concentrations of dextran. Once the highest concentration of dextran was reached, a control exposure without dextran was taken to ensure full reversibility. It was then followed by a series of exposures under another condition. A wait of approximately 5 min before X-ray exposure was found to be sufficient for dextran T500 to equilibrate. For activating conditions, diffraction patterns of relaxed muscle in pre-activating solution with dextran were always recorded before the activated patterns in dextran at the same concentration. At the higher dextran concentrations, frequently each diffraction pattern of the activated fibre was preceded and followed by relaxed patterns obtained under the same osmotic pressure. All the 'before' and 'after' control (relaxed) patterns were included as data for the relaxed state. X-ray exposure was started only after the force had reached steady level, which was within 2 min. Patterns were recorded only during the isometric phase of the mechanical cycling of the fibre (see Methods). At low concentrations of dextran ( < 4 %) each fibre was activated in solutions with at least two different concentrations of dextran. At higher concentrations, each fibre was activated at only one concentration of dextran. RESULTS
Response of relaxed fibres at ,a
170 mM to dextran solutions The response of the relaxed fibre at ,u = 170 mm to dextran solutions was first recorded to characterize the passive behaviour of a skinned rabbit psoas fibre. Since only a few cross-bridges (< 10%) are attached to actin under this condition =
RADIAL ELASTICITY OF ACTIVATED MUSCLE
707
(Schoenberg, 1988), the response to applied compression originates mainly from passive forces in the fibre other than forces of attached cross-bridges (e.g. cytoskeletal elements, electrostatic forces). We assume that under all conditions, a given filament separation is reached when the passive radial forces are balanced by possible radial 50
45
-
040
-
0
35
*i< 30
2400 1600 800 Applied radial force (pN (single thick filament)-1) Fig. 1. Response of single fibres to applied radial force by dextran T500 0, relaxed state at ,u = 170 mM; A, fully Ca2+-activated fibres at ,u = 170 mm. Error bars are S.E.M. Sarcomere length, 2-3-2A4,um. Temperature, 5 'C. Number of fibres used, 12. Radial force per unit length is calculated as 2/V3 H d,o, where 1 is the osmotic pressure of the dextran solutions. The unit pN (single thick filament)-' assumes the filament length to be 1-6 ,um. The values of the osmotic pressure used are averages of three batches of dextran solutions. Maximum concentration of dextran T500 used was 8% (w/v). Lines were obtained by a least-squares fit using the mathematical routine MLAB (Knott, 1979). The equation used for the relaxed state is a exp(bz) + c exp(cLz) + cons with x representing the applied radial force in units of pN (single thick filament)-'; a, b, c, d and cons being parameters. The best fit was found with a = 76-566, b = - 0-000606, c = 90 543, d = -0-005197, cons =279-79. The equation used for the activated state was aexp(bz)+cons, with a = 67-043, b = -0-00157, cons = 311-92. 0
forces of attached cross-bridges and/or the compressive force of dextran. It follows that the radial force exerted by dextran to compress the relaxed fibre at ,u = 170 mM to the same lattice spacings as those reached during activation or in rigor is equal to the radial force generated by the attached cross-bridges. Figure 1 (0) shows that the lattice spacing of the relaxed fibre is a monotonic decreasing function of the applied radial force. The data included both the 'before' and 'after' activation spacings. The data can be fitted closely by a function of one, or better two, exponentials. The latter is shown by the dashed line in Fig. 1. Lattice spacings of the activated fibres in dextran solutions The activated fibres were compressed by various concentrations of dextran T500. The data (A) in Fig. 1 are combined results that were obtained (1) by the laboratory X-ray source for 0-4 % dextran T500 solutions (applied radial force ranged between 0 and 400 pN (single thick filament)-') and (2) by using the synchrotron radiation at 23-2
B. BRENNER AND L. C. YU
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DESY for 0, 4, 6 and 8 % dextran T500 solutions (equivalent applied radial force: 0, 400, 1100 and 2180 pN (single thick filament)-'). The results show that application of dextran T500 to the fully Ca2+-activated fibre at ,u = 170 mm compresses the filament lattice to below 38 nm, and the response is non-linear. The data are fitted
G,10
a
oa 0 05-i L_
z
. . . 800 1600 2400 Applied radial force (pN (single thick filament)-1') Fig. 2. Active force in the axial direction under applied radial force. Force levels are normalized with respect to those in the absence of dextran. Average value for the force level in 0 % dextran was 1.0 kg cm-2. Error bars are S.E.M. For each concentration of dextran, at least twelve measurements were made. Five fibres were used. The order of application of dextran was random. 0
0.
.
by a single exponential function as shown by the continuous line in Fig. 1. The radial stiffness (inverse slope of the continuous line) found in the activated fibres is higher than that of the relaxed fibres over the entire range of concentrations used. At applied radial force of 880 pN (single thick filament)-1 and d1o = 34 nm, the two curves cross over each other. Thus, pre-compressing a relaxed fibre to 34 nm, activation will no longer change lattice spacing. At higher lattice spacing, activation decreases d10, while below 34 nm, it increases d1o0 This suggests that at d1o = 34 nm attached force-generating cross-bridges produce no radial force (zero-force point). At 4 % of dextran T500, the averages of lattice spacings obtained in the laboratory and at DESY were identical. However, the reflection peaks were sharper with the shorter exposure time used at DESY. This suggests that the order of the hexagonal filament array deteriorated with time under osmotic pressure. The average lattice spacing of the remaining ordered arrays, however, was unchanged. Active axial force is largely independent of concentrations of applied dextran T500 To determine whether the radial force exerted by cross-bridges is proportional to the axial force, the latter was also recorded at various concentrations of dextran T500. Figure 2 shows that between 0 and 8% w/v of dextran T500 (equivalent applied radial force: 0-2180 pN (single thick filament)-') the axial force level changed by no more than 10% while radial force decreased to zero under 1100 pN (single thick filament)-' applied radial force (6% dextran T500) and changed direction (Fig. 1).
RADIAL ELASTICITY OF ACTIVATED MUSCLE
709
Response of fibres in rigor to dextran solutions Changes in lattice spacing of the rigor fibres as a function of the applied radial force were recorded between 0 and 2500 pN (single thick filament)-1 (0-8 % dextran T500; Fig. 3). The rigor fibres are considerably less compliant. At 2500 pN (single thick 50 45 Z
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CD
40.
Co
2 35
30 0
800
1600
2400
Applied radial force (pN (single thick filament)-1) Fig. 3. Response of fibres in rigor (@) to applied radial force as compared to that of the relaxed fibre (0). Ionic strength = 170 mm. Sarcomere length, 2-3-2-4 ,um. Temperature, 5 'C. Seven fibres were used. Error bars are S.E.M. The rigor data was fitted by a single exponential function aexp(bzx)+cons with a = 30-33, b = -0-00182, cons = 366-50. A double exponential function was used for the relaxed state, a exp(bx) + c exp(dx) + cons with a = 93.53, b = -0-001311, c = 67-78, d = -0-006165, cons = 302-88.
filament)-1 (8 % dextran T500), the lattice spacing changed only by 3 nm (from 39 to 36 nm). At an applied radial force of 430 pN (single thick filament)-1 (4% of T500 dextran) the lattice spacing of the fibre in the rigor state is the same as that in the relaxed state. As the concentration is increased, the rigor fibre expanded compared to the relaxed fibre. This phenomenon is similar to that observed in the active fibre except that the stiffness (inverse slope of the continuous line) is very much higher in the rigor solution, and the zero-force point of the rigor cross-bridges is at 38 nm instead of 34 nm.
Response of the relaxed fibre at low ionic strength to dextran solution In a relaxed fibre at ,u = 20 mm, at 5 °C, experimental evidence suggested that at least 60% of the cross-bridges are attached to actin in the weak-binding states (Brenner, Schoenberg, Chalovich, Greene & Eisenberg, 1982; Brenner, Yu & Podolsky, 1984; Yu & Brenner, 1989). The radial elasticity of these cross-bridges was investigated. Figure 4 shows that the response of the low ionic strength relaxed fibre is rather distinct from those of the active and the rigor fibres. At low applied radial force, i.e. for d10 above 36 nm, the two curves appear to be converging. However, for smaller d1o, the change in d4o is almost parallel to that of the relaxed fibre at , = 170 mm and no cross-over was found between the two sets of data.
B. BRENNER AND L. C. YU
710
E CU. 40 CI)
