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A comparison of the tension response to rapid lengthening or shortening steps in isometrically contracting… Dusik, Laureen Anne 1984

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A COMPARISON OF THE TENSION RESPONSE TO RAPID LENGTHENING OR SHORTENING STEPS IN ISOMETRICALLY CONTRACTING FROG SKELETAL MUSCLE By LAUREEN ANNE DUSIK B.SC, The University of Winnipeg, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Anatomy We accept t h i s thesis as conforming to the reauired standard THE UNIVERSITY OF BRITISH COLUMBIA October 1984 © Laureen Anne Dusik, 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Anatomy The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 October 12, 1984 ABSTRACT Rapid length steps of i s o m e t r i c a l l y contracting single s k e l e t a l muscle f i b r e s , or whole muscle, provide a measure of the e l a s t i c properties of a structure believed to be an i n t e g r a l part of the myosin cross-bridge. The experiments to be described were designed to compare the e l a s t i c properties of th i s structure when measured with small amplitude (2-6 nm/h-s), rapid (1ms or 500 ps duration) lengthening steps versus shortening steps. A l l the experiments were c a r r i e d out at 0°-4°C, using small bundles (2-20 f i b r e s ) or single f i b r e s from frog semitendinosus muscle. The preparation was given a rapid stretch or release at various times during the isometric twitch and tetanus. During the i n i t i a l development of tension i n an isometric twitch and tetanus, the s t i f f n e s s was always seen to be r i s i n g faster than the force. During the relaxation phase of the isometric twitch, the s t i f f n e s s was observed to lag the tension. During the relaxation phase of an isometric tetanus p r i o r to the 'shoulder', the change i n s t i f f n e s s was seen to lag the tension change. Following the shoulder, there was a rapid f a l l i n s t i f f n e s s which corresponded to a s i m i l a r decline in tension. In a l l instances, when s t i f f n e s s values at a given force, and measured with a rapid release, were compared to those obtained with s t r e t c h , rapid lengthening produced a co n s i s t e n t l y higher s t i f f n e s s than a shortening step. The differ e n c e was most pronounced during the lat e r i s i n g phase of tension, maximum tension, and the early relaxation phase of the twitch or tetanus. Several suggestions are discussed to explain t h i s observed difference i n s t i f f n e s s between stret c h and release. These include the p o s s i b i l i t i e s that the instantaneous e l a s t i c i t y of the cross-bridge may be non-linear during stretch, and detachment of cross-bridges occurs during release but not s t r e t c h . - i i i -TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES i v ACKNOWLEDGEMENTS v i I. INTRODUCTION 1 II. REVIEW OF LITERATURE 7 V i s c o - e l a s t i c models 8 Introduction of a c o n t r a c t i l e element: H i l l ' s model 8 C r i t i c a l test of H i l l ' s model 12 S l i d i n g filaments and cross-bridges 13 (a) X-ray d i f f r a c t i o n 17 (b) Biochemistry 23 (c) Tension-length curve 23 (d) Speed of shortening at zero tension 25 A l t e r n a t i v e models 26 Cross-bridge mechanics 27 (a) V e l o c i t y transients 27 (b) Tension transients 28 Revised two-component model of contraction: Huxley and Simmons' model 30 S t i f f n e s s 32 I I I . METHODS 34 Muscle preparation 35 Experimental apparatus 36 (a) The Ling Shaker system 37 (b) The Cambridge Dual Mode Servo-System 39 Sarcomere length measurements 43 Experimental procedure 46 Technical considerations and corrections 52 (a) Force transducer response 52 (b) Series e l a s t i c i t y 54 (c) Fibre i n e r t i a and f r i c t i o n 56 IV. RESULTS 60 Twitch 64 Tetanus 68 (a) Rising phase 68 (b) Plateau 68 (c) Relaxation phase 75 V. DISCUSSION 80 S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the isometric twitch and tetanus 81 Stretch versus release 85 VI. REFERENCES 96 - i v -LIST OF FIGURES Page •1. Summary of muscle mechanics terminology 3 2. Block diagram of experimental apparatus 38 3. Response of Shaker system 40 4. Response of Cambridge system 42 5. Cambridge servo-system 44 6. Photomicroscopy 47 7. Tension and length changes at plateau of isometric, tetanus 50 8. Tension transients corrected for force transducer response 55 9. Tension transients corrected for i n e r t i a 57 10. Tension responses to two durations of length step at plateau of isometric tetanus 62 11. T l and T2 curves at plateau of isometric tetanus 63 12. Isometric twitch and tetanus with s t r e t c h superimposed on twitch and tetanus with release 65 13. Comparison of tension to s t i f f n e s s during isometric twitch i n single f i b r e s 66 14. Comparison of tension to s t i f f n e s s during r i s i n g phase of isometric twitch - 67 15. Comparison of tension to s t i f f n e s s during peak of isometric twitch 69 16. Comparison of tension to s t i f f n e s s during relaxation phase of isometric twitch 70 17. Comparison of tension to s t i f f n e s s during isometric twitch in muscle bundles 71 18. Comparison of tension to s t i f f n e s s during r i s i n g phase of isometric tetanus 72 19. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during r i s i n g phase of isometric tetanus 73 20. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during plateau of isometric tetanus 74 - v -21. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during r e l a x a t i o n phase of isometric tetanus 76 22. Comparison of tension to s t i f f n e s s during r e l a x a t i o n phase of isometric tetanus in single f i b r e s 77 23. Comparison of tension to s t i f f n e s s during r e l a x a t i o n phase of isometric tetanus in muscle bundles 79 24. Basic free energy p r o f i l e for Eisenberg-Hill-Chen model of s k e l e t a l muscle contraction 88 25. D i s t r i b u t i o n of cross-bridges among attached states during isometric contraction and immediately following a rapid length step 91 - v i -ACKNOWLEDGEMENTS The author would l i k e to express appreciation to Dr. B.H. Bressler for his guidance and encouragement throughout t h i s research project; to Ursula Dole, Edie Goble, and Miriam Hurley, for technical assistance; to the committee members, Dr. M.R. Menard, Dr. V. Palaty, and Dr. P.C. Vaughan for t h e i r advice and assistance; and to Kirk D i e t r i c h and Bert Mueller for preparation of the figure s . Special thanks are extended to Dr. Menard for assistance with the technical corrections. This project was completed while the author was in receipt of a Pre-Doctoral Fellowship from the Muscular Dystrophy Association of Canada. The cost of th i s project was defrayed from a Medical Research Council of Canada grant to Dr. B.H. Bressler. - 1 -I. INTRODUCTION - 2 -The tension produced by a contracting s k e l e t a l muscle i s thought to be the sum of the tensions produced by a number of i d e n t i c a l , independent force generators (Huxley and Simmons, 1971b). The tension generator i s the head (subfragment 1 or S-l) of the myosin molecule (figure l a , b ) . It i s thought to attach to a binding s i t e on the a c t i n filament and undergo a series of r o t a t i o n s . This r e s u l t s in the production of tension and s l i d i n g of the ac t i n filaments towards the center of the sarcomere. The tension i s transmitted from S-l to the myosin filament backbone through subfragment 2 (S-2). It was proposed that cross-bridges behaved as independent force generators because tension was observed to decrease l i n e a r l y with filament overlap as the muscle i s stretched beyond i t s rest length (Gordon, Huxley and J u l i a n , 1966) (figure l c ) . If a sarcomere i s stretched beyond i t s r e s t i n g length, the amount of overlap between the act i n and myosin filaments decreases. Thus the number of cross-bridges which can be formed decreases, and th i s accounts for the observed decrease i n tension. S i m i l a r l y , s t i f f n e s s (Huxley and Simmons, 1971a, Bressler and Clinch, 1974, Ford, Huxley and Simmons, 1981) was shown to decrease proportionately with decreased filament overlap and decreased tension, suggesting i t i s also a property of the cross-bridges. S t i f f n e s s , the tension required to cause a unit change in muscle length, i s determined by measuring the tension response of i s o m e t r i c a l l y contracting muscle to small rapid length steps (that i s , more rapid than the maximum v e l o c i t y of shortening of the muscle). A rapid shortening step r e s u l t s in a simultaneous decrease of tension which i s believed to be due to unloading of an undamped e l a s t i c component in the cross-bridges (Huxley and Simmons, 1970a) (see figure 7). This i s followed by recovery of the - 3 -Figure 1. Summary of muscle mechanics terminology. ( a ) I l l u s t r a t i o n of the arrangement of myofilaments i n the fundamental c o n t r a c t i l e unit of the muscle, the sarcomere. The diagram on the l e f t shows maximum filament overlap. The A bands contain the thick (myosin) filaments, covered with projections (the cross-bridges), and overlapping, i n t e r d i g i t a t i n g thin (actin) filaments. The I band consists of the thin filaments only. The H zone i s the central part of the A band between the ends of the two sets of thin filaments. The M l i n e i s due to thickenings i n the centre of the thick filaments. The diagram on the r i g h t shows decreased filament overlap. ( b ) I l l u s t r a t i o n showing a force generator, or cross-bridge, which consists of the S-l and S-2 portions of a myosin molecule. Curved arrow represents r o t a t i o n of bound force generator. Arrow on l e f t represents d i r e c t i o n of s l i d i n g of ac t i n filaments (modified from Huxley and Simmons, 1971b). (c)Relationship between tension generated by i s o m e t r i c a l l y contracting s k e l e t a l muscle and sarcomere length. A sarcomere length of 2.0-2.25 um corresponds to re s t length (or maximum filament overlap) (modified from Gordon, Huxley and J u l i a n , 1966). (d)Plots of the r e l a t i o n s h i p between the instantaneous change in tension which occurs when an i s o m e t r i c a l l y contracting muscle i s given a quick release or stretch (Tl) versus the amplitude of the applied length change (in nm per hal f sarcomere), at maximum filament overlap ( s o l i d l i n e ) and at reduced filament overlap (broken l i n e ) . Tension i s plotted r e l a t i v e to the maximum isometric tension at maximum overlap i n both cases (modified from Huxley and Simmons, 1971a). - 4 -H-zone Z line n z lln« III11IIIIIHIIIIIIIII1II l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l iniiiiiniMiiiiiiiiiii i i i i i i i i i i i i i i i i i i ini i i -I-b( 1H1111111 f l 111111 i 1111 M and— \m A-bond •(•*-!-b< ind — maximum filament overlap H-zone 1 •] l l l l l l l l l l l l l l l l l l l l l l l l ' l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l lr l l l l l l l l l l l l l l l l l l l l l l lt M decreased filament overlap b c - 5 -Sarcomere spacing ( jjm) d Amplitude of length change (nm/h-s) tension to a value approximating that preceding the length change, which would be expected since the small length change causes l i t t l e or no change in the number of cross-bridges which can form (Huxley and Simmons, 1971b). The recovery of tension involves a r e o r i e n t a t i o n and r o t a t i o n of the cross-bridges as they proceed through t h e i r cycle and stretch out the e l a s t i c element to i t s pre-step length. The instantaneous change in tension r e s u l t i n g from rapid releases and stretches, measured during the plateau of an isometric tetanus, can be plotted versus the amplitude of the step length change to give a 'Tl curve'. T l curves can be constructed for various degrees of filament overlap. The T l curve obtained when the overlap i s small i s a scaled down version of the T l curve at maximal overlap (figure Id) (Huxley and Simmons, 1971a, Ford et a l , 1981). This indicates that the T l curve represents the c h a r a c t e r i s t i c s of the instantaneous e l a s t i c i t y of a formed, tension generating cross-bridge. The object of this research project was to further characterize the instantaneous e l a s t i c i t y of i s o m e t r i c a l l y contracting muscle by comparing the s t i f f n e s s measured with a rapid release to that measured with a rapid stre t c h throughout the time course of the isometric twitch and tetanus in frog s k e l e t a l muscle at r e s t i n g length (maximal filament overlap). It was found that s t i f f n e s s correlated with tension throughout the time course of the twitch and tetanus. However, stretch gave a higher absolute value of tension change than release for the same amplitude of length change and thus a higher s t i f f n e s s value. Several possible explanations for these r e s u l t s are discussed. The implications of these findings for the nature of the instantaneous e l a s t i c i t y are not yet c l e a r . - 7 -II. REVIEW OF THE LITERATURE - 8 -V i s c o - e l a s t i c models Before the introduction of the s l i d i n g filament theory (H.E. Huxley and Hanson, 1954, A.F. Huxley and Niedergerke, 1954) a considerable amount of mechanical data had been obtained for s k e l e t a l muscle. The e a r l i e s t mechanical models of muscle contraction consisted of one or more e l a s t i c elements arranged in such a way that the model could simulate the mechanical properties of muscle but they were not correlated with any actual structure within the muscle. The e a r l i e s t model was based on the work of Weber (1846) which suggested that when muscle was activated i t behaved l i k e a stretched spring. This basic idea was found to be i n s u f f i c i e n t to explain the apparent v i s c o - e l a s t i c behavior of muscle. It was refined by introducing viscous forces, which caused damping of the spring ( B l i x , 1893, H i l l , 1922, Gasser and H i l l , 1924) and by adding an undamped spring in series (a series e l a s t i c component) (Levin and Wyman, 1927). In 1935, Fenn and Marsh found that t h e i r f o r c e - v e l o c i t y r e l a t i o n s h i p could not be explained by the v i s c o - e l a s t i c model. Using i s o t o n i c a l l y contracting muscle, they measured the shortening speed against d i f f e r e n t loads. They observed that force decreased exponentially with increased shortening v e l o c i t y , whereas i t should decrease l i n e a r l y i f the v i s c o - e l a s t i c model were correct. Introduction of a c o n t r a c t i l e element: H i l l ' s model Improved mechanical and thermal measurements of s k e l e t a l muscle by A.V. H i l l (1938) led to the proposal of a new model. H i l l measured heat production during i s o t o n i c contractions under various conditions and confirmed Fenn 1 s (1924) r e s u l t s that extra heat (which H i l l defined as the shortening heat) i s produced i f the muscle i s allowed to shorten. - 9 -H i l l showed that as the muscle shortened a distance, x, extra heat, ax, is released (where 'a' i s a constant of p r o p o r t i o n a l i t y between heat and shortening). The work done in l i f t i n g a load, P, i s Px so that the extra energy released i s Px + ax = (P + a)x. It follows that the rate of extra energy release i s therefore (P + a)dx/dt. = (P + a)v, where v i s the v e l o c i t y of shortening. H i l l found experimentally that the rate of extra energy release depended l i n e a r l y on the load (P) on the muscle, increased as P decreased, was zero when P = Po, the isometric force, and had i t s maximum value when P = zero. Therefore (P + a)v = b(Po - P), where b i s a constant r e f l e c t i n g the absolute rate of energy l i b e r a t i o n . This equation can be rearranged so that only constants are on the r i g h t side, in which form i t i s c a l l e d H i l l ' s c h a r a c t e r i s t i c equation : (P + a)(v + b) = (Po - a)b. This r e l a t i o n s h i p also predicts the f o r c e - v e l o c i t y r e l a t i o n s h i p . H i l l found that mechanical experiments used to test his equation f i t the r e l a t i o n s h i p , and the values of a and b agreed well with those obtained in thermal experiments. H i l l concluded that a new mechanical model was needed to explain h i s data. He proposed that active muscle could s t i l l be represented as a two-component system, but suggested that i t consisted of an undamped e l a s t i c element in s e r i e s with a c o n t r a c t i l e element whose properties were determined by his c h a r a c t e r i s t i c equation. He also stated that, although there must be v i s c o - e l a s t i c and presumably purely viscous elements as well in r e s t i n g muscle, th e i r role in active muscle should be r e l a t i v e l y small. The requirement of an undamped e l a s t i c element, or series e l a s t i c component (SEC), in the new mechanical model arose from the work of Levin and Wyman (1927), which showed an instantaneous tension change in - 10 -response to a rapid length change in activated muscle. The i n t e r p r e t a t i o n of such an instantaneous response in terms of a passive s p r i n g - l i k e mechanical element i s compelling, and i t has been retained in current models. H i l l ' s model d i f f e r e d from the previous v i s c o - e l a s t i c models i n that the c o n t r a c t i l e component (CC) was a c t i v e , with mechanical changes determining the amount of energy i t l i b e r a t e d . Stimulation of the muscle caused the rapid build-up of the active properties of the CC, r e s u l t i n g either in shortening, or in tension development i f shortening i s hindered in any manner. In relaxed muscle the CC contributed n e g l i g i b l e force. However, i f r e s t i n g muscle i s greatly stretched i t w i l l produce tension. H i l l (1950) accounted for t h i s by adding the p a r a l l e l e l a s t i c component (PEC) to h i s model. The length-tension r e l a t i o n s h i p for the PEC was determined experimentally for relaxed muscle. The PEC does not come into play at normal body length (lo) and can therefore be ignored in experiments at l o . The PEC was thought to be made up mainly of the connective tissue sheaths (epimysium, perimysium and endomysium) of the muscle (Banus and Z e t l i n , 1938) and possibly the sarcolemma at sarcomere lengths greater than 3.0 pm (Casella, 1950, Natori, 1954, Podolsky, 1964, Rapoport, 1972). The SEC i s conceived to be the part of the muscle preparation which behaves l i k e a purely passive, non-linear spring with properites that are unaffected by the state of a c t i v a t i o n of the muscle. It i s characterized by a length-tension (tension-extension) curve. This r e l a t i o n s h i p can be obtained by applying rapid length changes to muscle and measuring the resultant tension change, or by applying rapid tension changes and measuring the resultant length changes. The SEC of a muscle preparation is both external and i n t e r n a l . The external component i s that found in the connections between the muscle and the experimental apparatus. H i l l (1938) recognized t h i s and attempted to reduce the external component by using fine jewelry chains rather than thread to connect the muscle to the apparatus. This was important because length changes i n the SEC are d i f f i c u l t to d i s t i n g u i s h from length changes in the CC. One must use r i g i d connections to reduce the SEC, or length clamp a c e n t r a l region of the muscle preparation, by using a device such as a spot follower (Gordon, Huxley and J u l i a n , 1966), to eliminate i t . The i n t e r n a l SEC i s found i n the tendons and in the muscle i t s e l f (Jewell and Wilkie, 1958). H i l l ' s model can be used to explain a great deal of mechanical and thermal data from s k e l e t a l muscle (Aidley, 1971). The r i s e i n tension during an isometric tetanus can be q u a l i t a t i v e l y predicted. At rest the muscle produces no tension, as the SEC i s slack and the CC i s i n a c t i v e . When the muscle i s stimulated, the CC w i l l s t a r t to shorten at i t s maximum v e l o c i t y since the tension i s i n i t i a l l y zero. Since the ends of the muscle are fi x e d , the shortening of the CC causes extension of the SEC. Tension w i l l s t a r t to r i s e in accordance with the tension-extension curve of the SEC. As tension increases, the v e l o c i t y of shortening w i l l decrease i n accordance with the f o r c e - v e l o c i t y r e l a t i o n s h i p of the CC, and therefore the SEC w i l l be extended more slowly and tension w i l l r i s e less quickly. This series of events w i l l continue u n t i l the maximum isometric tension, Po, i s reached at which point the v e l o c i t y of shortening w i l l be zero and the SEC w i l l be f u l l y extended. The model can also explain the quick release r e s u l t s of Gasser and H i l l (1924) using large amplitude releases. A quick release causes immediate shortening of the SEC, which r e s u l t s i n a drop i n tension. The new lower tension value w i l l determine the new faster v e l o c i t y at which the CC w i l l shorten and re-extend the SEC, which w i l l r e s u l t in the - I n -tension r i s i n g to i t s maximum isometric value at the new, shorter length. The model also explains after-loaded i s o t o n i c contractions. In th i s s i t u a t i o n the SEC i s at a constant length and tension during shortening, and therefore the v e l o c i t y of shortening of the muscle i s that of the CC. The load on the muscle i s then reduced to a new steady value, so that the tension in the SEC i s reduced to a new steady value. This r e s u l t s i n an immediate shortening of the SEC to a new constant length and the muscle shortens at a new v e l o c i t y determined by the fo r c e - v e l o c i t y r e l a t i o n s h i p of the CC. C r i t i c a l test of H i l l ' s model Jewell and Wilkie (1958) tested H i l l ' s two component model experimentally by measuring the f o r c e - v e l o c i t y curve of the CC and the tension-extension curve of the SEC at l o , where the PEC would not contribute to tension. This data was then used to predict the r i s e of tension in an isometric contraction from the following r e l a t i o n s : (1) dP/dt = (dP/dx) (dx/dt) = (dP/dx) v where v i s taken from the fo r c e - v e l o c i t y curve and dP/dx i s the slope of the tension-extension curve, and (2) t =^ J [1/(V) (dP/dx)] x dP where Pt i s the tension at time t a f t e r stimulation i s i n i t i a t e d . They measured the i n i t i a l development of isometric tension, and the redevelopment of tension following a rapid release of amplitude s u f f i c i e n t to drop the tension to zero, given at the maximum isometric tetanic tension in the same muscle. They then compared the predicted development of tension to the measured development and redevelopment. It took the muscle longer to reach a given tension than predicted by the two-component model, about 80% longer than expected for i n i t i a l development and about 50% longer than expected for redevelopment - 13 -following a release. Three p o s s i b i l i t i e s for this disagreement were suggested: there might have been errors in t h e i r f o r c e - v e l o c i t y curve; there might have been errors in t h e i r tension-extension curve; or muscle might not be c o r r e c t l y represented by H i l l ' s two component model. S l i d i n g filaments and cross-bridges H i l l proposed h i s two-component model in 1938, before the s t r u c t u r a l changes which occur during contraction of the muscle were known. Actin and myosin were found to be the major proteins present in muscle (Straub, 1943) and i t was suggested that contraction might be due to the shortening of continuous actomyosin filaments (see Huxley, 1974). However, the H i l l model did not describe a s t r u c t u r a l basis for the c o n t r a c t i l e element. In the 1950's l i g h t microscopic studies of the s t r i a t i o n pattern of s k e l e t a l muscle provided such a s t r u c t u r a l basis. Using interference microscopy to observe i s o l a t e d muscle f i b r e s , A.F. Huxley and Niedergerke (1954) showed that during stretching or contraction of the f i b r e s , the length of the A band remained constant. Using phase contrast to observe is o l a t e d m y o f i b r i l s , H.E. Huxley and Hanson (1954) showed that during contraction the distance between the Z l i n e and the edge of the H zone remained constant whereas the width of the I band and H zone shortened. The r e s u l t s of these two studies implied that the length of the myofilaments remained constant. In addition, A.F. Huxley and Niedergerke (1954) observed that contraction bands developed in the centre of the A band and at the Z l i n e at short sarcomere lengths, implying l o c a l i z e d f o l d i n g of the ends of the I band filaments. The observations of these two groups, taken in conjunction with (1) low-angle X-ray d i f f r a c t i o n studies (H.E. Huxley, 1953) showing an hexagonal double-array of - 14 -filaments, (2) electron micrographs of transversely sectioned s k e l e t a l muscle, showing each m y o f i b r i l consisted of an overlapping, double array of thick and thin filaments (H.E. Huxley, 1952), (3) the discovery that myosin i s l o c a l i z e d in the A bands by s e l e c t i v e protein extraction (Hasselbach, 1953, Hanson and H.E. Huxley, 1953), and (4) the observation that tension generated by i s o m e t r i c a l l y contracting frog muscle was maximal at body length and decreased at shorter or longer muscle lengths, becoming zero at approximately one-half and twice body length, with the decrease in tension at longer muscle lengths being l i n e a r l y r e l a t e d to the muscle length (Ramsey and Street, 1940), led to the following proposal. It was suggested that the s t r i a t i o n pattern of s k e l e t a l muscle was due to two sets of overlapping, i n t e r d i g i t a t i n g filaments, and contraction resulted from the s l i d i n g of one set of filaments r e l a t i v e to the other without any appreciable change in length of either set of filaments. Page and H.E. Huxley (1963) l a t e r confirmed that the filament lengths remain constant at d i f f e r e n t muscle lengths by electron microscopy of muscles fixed i n r e s t i n g condition and while contracting i s o m e t r i c a l l y . In addition, Harman (1954) confirmed these observations using cine-photography with the phase contrast microscope to record contraction and r e l a x a t i o n of m y o f i b r i l s . He observed that shortening occurred by o b l i t e r a t i o n of the I bands while the length of the A bands remained constant. Furthermore, the contraction bands i n the centre of the A band were observed in electron micrographs showing the ends of the I filaments s l i d i n g past each other r e s u l t i n g in a region of double overlap (H.E. Huxley, 1964). Electron micrographs of thin sections of m y o f i b r i l s (H.E. Huxley and Hanson, 1954, Hanson and H.E. Huxley, 1955 and H.E. Huxley, 1957) - 15 -confirmed that the m y o f i b r i l s contained two sets of i n t e r d i g i t a t i n g filaments of d i f f e r e n t diameter (figure l a ) . The thin filaments were attached to the Z li n e s and extended through the I bands into the A bands. The thick filaments were l o c a l i z e d i n the A bands. The H zone was the central part of the A band between the ends of the two sets of thin filaments. The M l i n e was observed to be due to thickenings i n the centre of the thick filaments. The suggestion of s l i d i n g filments raised the question of how such a system would work. A.F.Huxley (1957) suggested the existence within each overlap zone of some type of i n t e r a c t i o n s i t e s between the myofilaments, or mechanical l i n k s , which could "make and break". These links would be responsible for the generation of force between the filaments necessary for s l i d i n g . In Huxley's model, a 'side-piece', e l a s t i c a l l y connected to the myosin filament, was proposed to have at least two states; (1) attached to a s i t e on an a c t i n monomer of the a c t i n filament and (2) detached from the a c t i n s i t e . During contraction, the side-piece would go through i t s states c y c l i c a l l y . Attachment and detachment were assumed to be biochemical reactions and the t r a n s i t i o n between states was con t r o l l e d by p r o b a b i l i t i e s per unit time. The side-pieces were proposed to move randomly back and for t h by thermal a g i t a t i o n (Brownian motion) which caused the side-pieces to enter a strained state. The range of motion of the side-pieces was less than the distance between the act i n s i t e s . Attachment occurred i n this strained state with a moderate rate constant. This must be so to explain the decrease in the rate of energy release at high shortening speeds ( H i l l , 1938). In addition attachment was r e v e r s i b l e and no ATP was hydrolyzed i f the side-piece was unable to complete the working part of i t s cycle . This explained the decrease in energy release during s t r e t c h (Fenn, 1924, H i l l , 1938). As soon as attachment occurred the e l a s t i c connection produced a force in the d i r e c t i o n of shortening. Detachment occurred with the binding of ATP. The rate of detachment was slow when the side-piece was in a po s i t i o n such that i t exerted p o s i t i v e tension. The detachment rate was rapid when i t was in a pos i t i o n where i t was unstrained or compressed, and r e s i s t e d shortening. This would occur when shortening took place which allowed the side-piece to complete the working part of i t s cycle. In addition the difference in rate of detachment explained the increased energy release when shortening occurs (Fenn, 1924). The side-pieces c y c l i c a l l y produced interfilament shear forces which caused the a c t i n filament to s l i d e past the myosin filament. This resulted i n sarcomere shortening and c o n t r a c t i l e force. S l i d i n g of the filaments caused the attachment s i t e on the a c t i n filament to move past the s i t e of o r i g i n of the side-piece on the myosin filament, r e s u l t i n g i n d i s t o r t i o n of the side-piece. This d i s t o r t i o n influenced the force produced by the side-piece and the p r o b a b i l i t i e s per unit time of i t s subsequent changes i n state. The t o t a l contribution from a l l other attached side-pieces and the external load on the muscle determined whether s l i d i n g occurred. Soon a f t e r the proposal of A.F. Huxley's model, H.E. Huxley (1957) observed projections emerging from the thick filaments in high magnification electron micrographs of s k e l e t a l muscle. These projections, or cross-bridges, were suggested to be the side-pieces involved i n c y c l i c attachment and force production. Many l i n e s of evidence supported and elaborated on Huxley's model: (a) X-ray d i f f r a c t i o n showed the appropriate arrangement of molecules, (b) biochemistry showed the energy transduction mechanism, the ATPase, and (c) the d e t a i l e d tension-length curve supported the idea of independent force generators as did the speed of shortening at zero tension (d). a) X-ray d i f f r a c t i o n The X-ray d i f f r a c t i o n technique may be used to obtain accurate measurements of the spacing between repeating structures in an object which i s made up of regularly-spaced molecules or macromolecular sub-assemblies, as i s s k e l e t a l muscle. As in microscopy, X-rays are scattered by an object. However, unlike microscopy, X-rays cannot be re-focussed to produce an image of the object. Therefore in order to obtain an object's image the X-ray d i f f r a c t i o n pattern (the pattern produced by the scattered or d i f f r a c t e d X-ray beam) must be mathematically reconstructed (Aidley, 1971, Bagshaw, 1982). The spots and l i n e s making up a d i f f r a c t i o n pattern are r e f e r r e d to as r e f l e c t i o n s . Meridional r e f l e c t i o n s are produced by a x i a l l y repeating structures in the muscle while equatorial r e f l e c t i o n s are produced by transversely repeating structures. Off-meridional r e f l e c t i o n s are produced by structures repeating in a manner other than a x i a l l y or transversely, such as h e l i c a l l y repeating structures. Layer l i n e s are off-meridional r e f l e c t i o n s appearing as a series of l i n e s p a r a l l e l to the equator of the d i f f r a c t i o n pattern (Aidley, 1971). The r e l a t i v e i n t e n s i t i e s of the r e f l e c t i o n s in a d i f f r a c t i o n pattern provide information about the d i s t r i b u t i o n of mass between the corresponding structures. Cnanges in r e f l e c t i o n i n t e n s i t i e s indicate a movement of mass. Low-angle X-ray d i f f r a c t i o n produces a pattern in which the - 18 -d i f f r a c t e d X-rays diverge l i t t l e from t h e i r o r i g i n a l path. These patterns provide information about structures which repeat over r e l a t i v e l y large distances, such as the p e r i o d i c i t i e s of the myofilaments and the cross-bridges. Wide-angle X-ray d i f f r a c t i o n patterns provide information about structures repeating over r e l a t i v e l y small distances, mainly the a l p h a - h e l i c a l myosin rod. Low-angle X-ray d i f f r a c t i o n accurately measures the distance between repeating structures within the range of r e s o l u t i o n of the electron microscope. However X-ray d i f f r a c t i o n cannot provide d i r e c t information as to the i d e n t i t y of the structures measured. Conversely, electron microscopy can i d e n t i f y structures, but the accuracy of size measurements i s decreased due to such problems as tissue shrinkage and d i s t o r t i o n caused by f i x i n g , sectioning and s t a i n i n g procedures. When these two techniques are used in conjunction accurate information can be obtained about the u l t r a s t r u c t u r e of muscle which i s consistent with the independent force generator (cross-bridge) theory. Low-angle X-ray d i f f r a c t i o n studies of relaxed s k e l e t a l muscle by H.E. Huxley and Brown (1967) showed a meridional spot at 14.3 nm and layer l i n e s at 42.9 nm. The 14.3 nm a x i a l l y repeating structure corresponded well with the p e r i o d i c i t y of the cross-bridges observed in electron micrographs (H.E. Huxley, 1957). The d i f f r a c t i o n pattern would indicate that cross-bridges are arranged on an X-stranded h e l i c a l myosin molecule with an a x i a l repeat of 14.3 nm and a pi t c h of 42.9 X nm (Bagshaw, 1982). Huxley and Brown (1967) o r i g i n a l l y suggested pairs of cross-bridges emerged opposite each other from the (1-stranded) myosin filaments, with each successive pair of cross-bridges rotated 120° to the preceding pair so that there was a true repeat of cross-bridge pairs every 42.9 nm. However, the majority of the recent evidence supports X = 3 for vertebrate s k e l e t a l muscle (Squire, 1981) so that the preferred cross-bridge p o s i t i o n would be three cross-bridges emerging every 14.3 nm with a p i t c h of 128.7 (3 x 42.9) nm. In addition, 'forbidden' meridional r e f l e c t i o n s occur, which indicates that the spacing of the cross-bridges i s not completely regular. Negatively-stained electron micrographs of i s o l a t e d a c t i n filaments (Hanson and Lowy, 1963) showed these filaments to consist of two h e l i c a l strands of globular repeating a c t i n monomers. However, the p i t c h of the h e l i x and the number of monomers per turn were uncertain, and were postulated to be 35 or 41 nm for the p i t c h and 13 or 15 for the number of monomers. Using low-angle X-ray d i f f r a c t i o n , H.E. Huxley and Brown (1967) observed a meridional spot at 2.7 nm and layer l i n e s at 5.1, 5.9, and 37 nm. The meridional spot indicated an a x i a l distance of 2.7 nm between monomers. The two layer l i n e s are believed to a r i s e from the pitches of a right-handed and a left-handed p r i m i t i v e h e l i x . The two pr i m i t i v e h e l i c e s form the double non-primitive h e l i x which has a p i t c h of 74 nm (2 x 37) and a cross-over at 37 nm, which gives the 37 nm layer l i n e . The number of monomers per turn i s thus 13.5. Low-angle X-ray d i f f r a c t i o n studies of relaxed muscle also have shown two main equatorial r e f l e c t i o n s , the 1.0 and the 1.1 r e f l e c t i o n s . These r e f l e c t i o n s a r i s e from d i f f r a c t i o n planes of the hexagonally arranged myofilaments. The 1.0 d i f f r a c t i o n plane contains only myosin filaments while the 1.1 plane contains a c t i n and myosin filaments. The r e l a t i v e i n t e n s i t i e s of these r e f l e c t i o n s indicate the po s i t i o n of the cross-bridges in a muscle state (H.E. Huxley, 1968, Haselgrove and Huxley, 1973). The 1.0/1.1 i n t e n s i t y r a t i o gives a high value i n the relaxed state of about 2.5 (Haselgrove and Huxley, 1973). X-ray d i f f r a c t i o n studies have confirmed the find i n g from - 20 -microscopic studies (A.F. Huxley and Neidergerke, 1954, H.E. Huxley and Hanson, 1954, Harman, 1954) of the i n e x t e n s i b i l i t y of the myofilaments. I f the filament length changed at d i f f e r e n t sarcomere lengths or during contraction, the a x i a l distance between the repeating structures would change. The p e r i o d i c i t y of the meridional r e f l e c t i o n s from low-angle d i f f r a c t i o n patterns (H.E. Huxley, 1953) and the high-angle pattern (Astbury, 1947) of r e s t i n g muscles were found to be independent of the length of the muscle. During isometric contractions, H.E. Huxley and Brown (1967) found a s l i g h t increase of about 1% in the a x i a l spacing of the myosin filaments whereas there was no s i g n i f i c a n t change in the a x i a l spacing of the a c t i n monomers. In addition Haselgrove and Huxley (1973) found that the 1.0/1.1 i n t e n s i t y r a t i o of muscles allowed to a c t i v e l y shorten to a pre~set sarcomere length just before X-ray exposure was the same as that for the f i n a l sarcomere length and was independent of the immediate h i s t o r y of the muscle. Low-angle X-ray d i f f r a c t i o n studies have shown that in relaxed muscle the p o s i t i o n of the cross-bridges i s determined by t h e i r attachment to the myosin filament backbone. Studies of frog muscle in the r i g o r state (absence of ATP) (H.E. Huxley and Brown, 1967, H.E. Huxley, 1968, Haselgrove and Huxley, 1973, Haselgrove, 1975) have shown that in r i g o r the myosin cross-bridges move towards, and presumable attach to, the a c t i n filaments, as the cross-bridges take on the spacing of the a c t i n filaments. The 42.9 nm myosin layer l i n e decreases in i n t e n s i t y while the 5^1, 5.9 and 37 nm a c t i n layer l i n e s increase in i n t e n s i t y in r i g o r as compared to the relaxed state. The r e l a t i v e i n t e n s i t i e s of the equatorial r e f l e c t i o n s change during r i g o r , the 1.0 r e f l e c t i o n decreases while the 1.1 r e f l e c t i o n increases so that the 1.0/1.1 i n t e n s i t y r a t i o thus decreases in r i g o r to a value of about 0.2 - 21 -to 0.3 (Haselgrove and Huxley, 1973). These studies indicate that cross-bridges have moved away from t h e i r myosin-centered, relaxed positions to become actin-centered, l a b e l i n g the exteriors of the a c t i n filaments (H.E. Huxley and Brown, 1967, Reedy, 1967, M i l l e r and Tregear, 1972, Haselgrove Stewart and Huxley, 1976) and taking on the h e l i c a l c h a r a c t e r i s t i c s of the a c t i n filaments (Bagshaw, 1982). This conclusion was supported by electron micrographs of transverse sections of relaxed and r i g o r muscles (H.E. Huxley, 1968). However, the 14.3 nm meridional myosin r e f l e c t i o n decreases only s l i g h t l y . This observation, taken in conjunction with the i n t e n s i t y changes in the equatorial r e f l e c t i o n s , indicates that cross-bridges may bind to a c t i n "by a r a d i a l movement accompanied by a slewing about the azimuth, rather than extensive a x i a l movement" (Bagshaw, 1982). A.F. Huxley (1957) suggested that force generation i s mediated v i a the cross-bridges. This would imply that cross-bridges may move during contraction. The difference in the X-ray d i f f r a c t i o n data between the relaxed and r i g o r states in frog muscle would indicate that cross-bridge movement does occur. Further support has been obtained by Reedy, Holmes and Tregear (1965) studying glycerol-extracted insect f l i g h t muscle. They found s i m i l a r differences in t h e i r X-ray d i f f r a c t i o n patterns in the relaxed and r i g o r states as was observed in vertebrate muscle. In addition they observed that t h e i r electron micrographs d i f f e r e d in these two muscle states. In r e s t i n g muscle, the cross-bridges were oriented 90° from the myosin filament backbone, while in r i g o r , the cross-bridges were attached to the a c t i n filaments, and were oriented at an angle of 45° from the myosin backbone. Reedy et a l interpreted the r i g o r p o s i t i o n to correspond to the end of the working cycle of the cross-bridge. They proposed that the cross-bridge attached to a c t i n and moved from the 90° to the 45 (r i g o r ) p o s i t i o n , during which the a c t i n filament i s pushed towards the centre of the sarcomere. Furthermore, electron micrographs of vertebrate myosin S-l labeled a c t i n filaments produced i n r i g o r conditions have shown that cross-bridges attach to a c t i n monomers in well defined positions (H.E. Huxley, 1963, Moore, Huxley and DeRosier, 1970). This idea has been widely accepted and incorporated into contraction models, although there i s no d i r e c t evidence that the cross-bridges do ex i s t in these angles at the s t a r t and end of t h e i r working stroke. Based on the independent force generator theory, cross-bridges should attach to a c t i n during contraction and i t might be expected that s i m i l a r X-ray d i f f r a c t i o n patterns to those i n r i g o r would be obtained. During isometric contraction the 42.9 nm myosin layer l i n e decreases to about 30% of that in r e s t i n g muscle and the 14.3 nm meridional r e f l e c t i o n decreases to about 66% of that in r e s t i n g muscle (H.E. Huxley and Brown, 1967). The 1.0/1.1 i n t e n s i t y r a t i o of the equatorial r e f l e c t i o n s increases during contraction and was very s i m i l a r to the r a t i o i n r i g o r (Matsubara, Yagi and Hashizume, 1975). Contracting vertebrate and molluscan muscles give a s i g n i f i c a n t (although just marginally) increase i n i n t e n s i t y of the 5.9 nm a c t i n layer l i n e (Haselgrove, 1975, Vibert, Haselgrove, Lowy and Poulsen, 1972, Lowy, 1972) supporting the idea that attachment to a c t i n does occur. These r e s u l t s indicate that the cross-bridges move from t h e i r h e l i c a l l y ordered state about the myosin filament backbone during contraction. The equatorial r e f l e c t i o n changes would suggest that a s i g n i f i c a n t number of cross-bridges are attached with a wide d i s t r i b u t i o n i n t h e i r angular d i s t r i b u t i o n . The X-ray d i f f r a c t i o n data show that there i s some lo n g i t u d i n a l movement (or rotating) of the cross-bridges and that a s i g n i f i c a n t amount of r a d i a l movement occurs. - 23 -b) Biochemistry By 1945, i t was known that the energy released from ATP hydrolysis powered contraction and that myosin was an ATPase (see A.F. Huxley, 1980). In the 1960's i t was found that the mysoin S - l , the cross-bridge, has one a c t i n binding s i t e and one ATP binding s i t e (Young, 1967). Since the myosin cross-bridge i s an ATPase and i t s a c t i v i t y i s increased by the presence of a c t i n (Eisenberg and Moos, 1968, 1970), i t would appear that the cross-bridges are intimately involved in converting the chemical energy of ATP into mechanical work. X-ray d i f f r a c t i o n and electron microscopic studies have shown that the i n t e r a c t i o n of a c t i n , myosin S-l and ATP involved conformational changes in the proteins which r e s u l t s in s l i d i n g of the myofilaments (see section a). Rapid-reaction k i n e t i c studies (see Eisenberg and Greene, 1980) have shown that the i n t e r a c t i o n of a c t i n and myosin involved several intermediate steps, which indicated that the cross-bridges i n t e r a c t c y c l i c a l l y with a c t i n . However, in muscle, the chemical reaction sequence would be influenced by mechanical constraints as the cross-bridge must move r e l a t i v e to a c t i n for the reaction to proceed. Models of muscle contraction based on biochemical and mechanical data have been presented by Eisenberg and h i s co-workers (Eisenberg and H i l l , 1978, Eisenberg, H i l l and Chen, 1980, Eisenberg and Greene, 1980) (see dis c u s s i o n ) . c) Tension-length curve Gordon, Huxley and J u l i a n (1966) re-investigated the r e l a t i o n s h i p between tension and length (fi g u r e l c ) observed by Ramsey and Street (1940) i n frog s i n g l e f i b r e s . The c e n t r a l region of the f i b r e was held at a constant length by a feedback c i r c u i t while i t s tension was - 24 -measured. This was done to remove sarcomere length non-uniformity which occurs at the ends of the f i b r e s (A.F. Huxley and Peachey, 1961) and to remove external (series e l a s t i c ) compliance in the experimental apparatus and tendons. Their tension-length curve was found to correspond well with myofilament lengths obtained by Page and H.E. Huxley (1963); myosin filament, 1.6 pm, i t s bare zone, .15-.2 um, a c t i n filament, 1.0 pm, and the Z l i n e , .05 um. At a sarcomere length of 3.6 pm, where there would be no overlap of a c t i n and myosin filaments, a small amount of tension i s produced, probably as a r e s u l t of a small amount of scatter in the sarcomere lengths of the c e n t r a l portion of the f i b r e . Between no filament overlap (3.6 pm) and maximal overlap (2.25 pm) there i s a l i n e a r increase in the number of cross-bridges formed and in the tension generated. At sarcomere lengths of 2.05 to 2.25 pm, where the a c t i n filaments would be moving into the c e n t r a l zone of the myosin filaments, which i s devoid of cross-bridges, the tension generated remains constant, producing the plateau of the tension-length curve. These regions of the curve support the idea that tension generation i s mediated v i a a set of independent force generators, the cross-bridges, evenly d i s t r i b u t e d throughout the A band. At shorter sarcomere lengths, less than 2.05 pm, the tension decreases. Two possible mechanisms have been suggested. One p o s s i b i l i t y i s that mechanical interference occurs when the ends of the a c t i n filaments s l i d e into the opposite h a l f of the sarcomere and i n t e r f e r e with tension generation, and when the ends of the myosin filaments come into contact with the Z l i n e (at a sarcomere length of 1.65 pm). The other p o s s i b i l i t y i s that the e x c i t a t i o n - c o n t r a c t i o n coupling mechanism of the inner part of the f i b r e f a i l s at short sarcomere lengths (Taylor and Rudel, 1970, Rudel and Taylor, 1971). It - 25 -may be that both of these mechanisms determine the shape of the tension-length curve at short sarcomere lengths. This experiment supports the hypothesis that the cross-bridges are responsible for contraction, as the degree of tension generated was proportional to the amount of overlap between the filaments and thus the number of formed cross-bridges. Further support for the hypothesis was obtained in experiments of a c t i v e l y shortening muscle. It was shown that a f i b r e passively set to a long sarcomere length and then stimulated to contract against a l i g h t load shortened to the appropriate sarcomere length on the tension-length curve for that load (Edman, 1966, Gordon, Huxley and J u l i a n , 1966). It was also shown that when a f i b r e a c t i v e l y shortened from a long to a short sarcomere length and was then held at the shorter length, i t developed (within 10%) the same amount of tension as a f i b r e pre-set to the shorter length (see Simmons and Jewell, 1974). These experiments show that the myofilaments s l i d e in both a c t i v e l y and passively shortening muscle. d) Speed of shortening at zero tension Resistance to shortening of a contracting muscle may be due to an externally applied load, a viscous resistance to r e l a t i v e s l i d i n g of the myofilaments, or to l i m i t a t i o n s of the cross-bridge c y c l i n g speed (A.F. Huxley, 1980). The e f f e c t s of v i s c o s i t y are n e g l i g i b l e (Huxley, 1980). Therefore, when the external load on a muscle i s zero, the speed of shortening i s l i m i t e d only by the cross-bridges. The resistance to shortening that must be overcome, and the tension generated by the muscle, w i l l be proportional to the number of active cross-bridges, so the shortening v e l o c i t y of the muscle should be independent of the number of active cross-bridges and the amount of overlap between the filaments. - 26 -The speed of shortening that decreases the net power output (and thus the tension generated) of any cross-bridge to zero w i l l be i d e n t i c a l and independent of the number of active cross-bridges in the same h a l f sarcomere. It has been shown (A.F. Huxley and J u l i a n , 1964, Gordon et a l , 1966) that the speed of active shortening of frog muscle under a very l i g h t load from a number of d i f f e r e n t o r i g i n a l sarcomere lengths was v i r t u a l l y constant. A l t e r n a t i v e models The studies discussed i n sections a to d support a model of muscle contraction in which the length of the a c t i n and myosin filaments remain v i r t u a l l y constant as the sarcomeres shorten and i n which shortening i s produced, and tension generated, by myosin cross-bridges i n t e r a c t i n g independently with a c t i n s i t e s , that i s , acting as independent force generators. A l t e r n a t i v e models of muscle contraction e x i s t , two main categories being the l a t e r a l expansion theories and the e l e c t r o s t a t i c a t t r a c t i o n theories (see Huxley, 1980). The l a t e r a l expansion theories propose that a l a t e r a l repulsion between the myofilaments produces, force, which i s converted to shortening by some constraint which ensures that each sarcomere remains isovolumic. However, a skinned f i b r e (a f i b r e whose sarcomlemma has been removed) does not behave isovolumically (Matsubara and E l l i o t t , 1972) yet i t generates tension l e v e l s comparable to those generated by i n t a c t f i b r e s . The e l e c t r o s t a t i c a t t r a c t i o n theories propose that the a c t i n and myosin filaments are oppositely charged and the a c t i n filaments are drawn towards the centre of the sarcomere by the r e s u l t i n g e l e c t r o s t a t i c force. However, i f i t i s assumed that the charges on myosin are found on the cross-bridges, then filament overlap w i l l be complete at sarcomere - 27 -lengths between 2.0 and 2.2 um and would not proceed further. Therefore at these sarcomere lengths the tension produced would be zero, which disagrees with the tension-length curve (Gordon et a l , 1966). Although other theories e x i s t , the independent force generator model i s supported by the weight of the experimental evidence. Cross-bridge mechanics The properties of an average cross-bridge can be studied by examining the response of i s o m e t r i c a l l y contracting muscle to rapid tension or length changes, which produce a v e l o c i t y transient, or a tension transient r e s p e c t i v e l y . Experiments with improved time r e s o l u t i o n , as compared to experiments before the 1960's, have shown that the response of muscle to rapid changes of tension (load) or length are more complicated than those predicted by H i l l ' s two-component model and Huxley's (1957) model. a) V e l o c i t y transients Experiments by Podolsky (1960, Civan and Podolsky, 1966) showed the more complicated response following a rapid change in load in frog s i n g l e f i b r e s and bundles. The muscle preparation was allowed to develop i t s maximal isometric tetanic tension (Po), and was then quickly released and allowed to shorten under a constant load which was less than Po. The time course of the change in length of the muscle preparation was recorded during the load change. It was found that an i n i t i a l rapid shortening occurred, as would be predicted from the SEC. However, the > i n i t i a l shortening was followed by a complex sequence of changes in the shortening speed, the v e l o c i t y t ransient. This was contrary to the p r e d i c t i o n by H i l l ' s two-component model of a constant shortening speed - 28 -following the i n i t i a l shortening. I n i t i a l l y , the shortening speed was much faster than the steady-state speed for the same load. This showed that the f o r c e - v e l o c i t y r e l a t i o n i s not instantaneously obeyed when the load changes. The shortening speed then declined to a low value or reversed i t s d i r e c t i o n , and then returned to i t s steady-state value, sometimes with a damped o s c i l l a t i o n . This non-steady shortening was suggested to be due to the c y c l i c i n t e r a c t i o n of the cross-bridges with the a c t i n s i t e s (Civan and Podolsky, 1966). The time period necessary to a t t a i n steady shortening was found to have a large temperature c o e f f i c i e n t which suggested a chemical process was responsible for the observed response rather than a physical process. They further suggested a time-dependent compliance within the sarcomere, probably within the cross-bridges. b) Tension transients Experiments by A.F. Huxley and h i s co-workers (Armstrong, Huxley and J u l i a n , 1966, Huxley and Simmons, 1970a, 1971a,b) showed the complicated response following a rapid change in length in frog single f i b r e s . Length changes were used by these investigators rather than load changes because they found the e l e c t r o n i c s of the feedback system were less complicated, and better time res o l u t i o n could be attained in the former type of experiments. Huxley and co-workers found that the i n i t i a l tension change occurred simultaneously with the length change, as would be predicted by H i l l ' s two-component model. However, the i n i t i a l tension change was followed by a complex tension recovery, the tension transient. This was contrary to the nearly exponential recovery predicted by H i l l ' s model. The tension transient contained an a d d i t i o n a l rapid component (phase 2) which had not - 29 -been previously observed because of technical l i m i t a t i o n s . The tension transient was observed to be composed of four phases (Huxley and Simmons, 1970a). The f i r s t phase was the i n i t i a l rapid change i n tension occurring simultaneously with the length change. This was followed by a quick recovery of tension (phase 2) to a l e v e l approaching that p r i o r to the length change. The recovery then dramatically slowed and sometimes reversed (phase3). F i n a l l y , tension reached a l e v e l approximating i t s o r i g i n a l pre-length change l e v e l (phase 4). The rate of phase 2 was shown to be slow for stretches (lengthening steps) but increased r a p i d l y with the amplitude of releases (shortening steps) (Huxley and Simmons, 1971b). Huxley and Simmons (1971a) plotted the values of T l , the extreme tension value reached during the length change, and T2, the tension value immediately following the rapid recover, against the amplitude of length change to obtain T l and T2 curves. T l and T2 curves were measured at maximal filament overlap, 2.2pm, and at decreased filament overlap, 3.2pm. Based on the r a t i o of the isometric tension (Gordon et a l , 1966), they then calculated T l and T2 curves at a sarcomere length of 3.2 pm, which were found to f i t the experimental points. Since the magnitude of the T l and T2 values were found to scale in proportion to the overlap between the a c t i n and myosin filaments and thus the number of formed cross-bridges, Huxley and Simmons proposed that the cross-bridges are the structures responsible for the instantaneous e l a s t i c i t y as well as the early recovery of the tension transient, assuming a l l other structures i n the sarcomere are e f f e c t i v e l y r i g i d . If these curves were due to any other series e l a s t i c i t y r e s i d i n g elsewhere i n the sarcomere (for example i n the Z l i n e or the non-overlap regions of the filaments) the T l curve would have then had a slope that was independent of tension - 30 -(Huxley and Simmons, 1973). Recently, Ford, Huxley and Simmons (1981) have determined that the cross-bridges contain "at least 80% and probably well over 90%" of the measured instantaneous e l a s t i c i t y i n frog single f i b r e s . They indicated that the filamentary compliance would have "only small or n e g l i g i b l e e f f e c t s on the amplitude or time course of tension changes". Bressler and Clinch (1974) confirmed the findings of Huxley and Simmons at sarcomere lengths longer than r e s t i n g length in whole muscle. In addition, Bressler and Clinch (1975) showed that s t i f f n e s s was correlated with tension at sarcomere lengths shorter than r e s t i n g length. This was recently confirmed i n single f i b r e s by J u l i a n and Morgan (1981b). These studies ruled out a s i g n i f i c a n t contribution of the unbound portion of the a c t i n filaments to the measured instantaneous e l a s t i c i t y . Revised two-component model of contraction : Huxley and Simmons' model The response of i s o m e t r i c a l l y contracting s k e l e t a l muscle to rapid changes of length and load led to the proposal of a revised two-component model of muscle contraction in which the cross-bridge contains an instantaneous e l a s t i c i t y i n series with a c o n t r a c t i l e element (Huxley and Simmons, 1971b). This model i s an advance over that of H i l l i n that the s t r u c t u r a l and chemical basis of these elements i s known in some d e t a i l . Huxley and Simmons (1971b) explained t h e i r r e s u l t s using the i l l u s t r a t i o n of a 'rocking' cross-bridge in which the head of the myosin molecule contained the active c o n t r a c t i l e element and the S-2 portion between the head and myosin filament backbone contained the e l a s t i c element ( f i g u r e l b ) . They pointed out that t h i s was only one p o s s i b i l i t y as to the location of these two components. Huxley and Simmons proposed that there are two attached states, with the second state having less p o t e n t i a l energy than the f i r s t , and in each state a d i f f e r e n t angle i s formed between the myosin head and the a c t i n s i t e . In the isometric state, each cross-bridge spends an equal amount of time in each attached state as a r e s u l t of the p o t e n t i a l energy differences between the two states causing forward movement (from state 1 to state 2), and the tension in the e l a s t i c element causing backward movement (from state 2 to state 1). Thus the 'average' p o s i t i o n of a cross-bridge i s half-way between these two attached states. In the isometric state, i t i s not necessary for the filaments to s l i d e r e l a t i v e to each other to develop force, as the e l a s t i c i t y of the cross-bridge allows i t to rotate about the a c t i n s i t e and develop tension, which w i l l then be transmitted to the myosin filament through the e l a s t i c element. In order to move forward the cross-bridge needs a c t i v a t i o n energy to move from the state i t i s i n , and to perform the work required to s t r e t c h the e l a s t i c component s u f f i c i e n t l y to allow i t to move to the next state. The higher the tension, the greater the a c t i v a t i o n energy required and the greater the rate of movement to the next state. This model can account for the observed difference in the rate of the rapid early recovery phase (phase 2) of the tension transient. When is o m e t r i c a l l y contracting muscle i s r a p i d l y shortened the e l a s t i c element w i l l shorten before the c o n t r a c t i l e element can change i t s angle with respect to the a c t i n s i t e . Thus the tension in the e l a s t i c element w i l l decrease instantaneously. This allows the c o n t r a c t i l e element of the cross-bridge to move into the higher tension state (2) which restretches the e l a s t i c element and returns tension to i t s pre-length change l e v e l . A large amplitude of release, r e s u l t s in a large drop in the tension in the e l a s t i c element. This decreases the amount of a c t i v a t i o n energy - 32 -required for the forward movement of the c o n t r a c t i l e element which r e s u l t s i n a more rapid early recovery phase. As i n Huxley's 1957 model, the t r a n s i t i o n between the attached states depends on thermal a g i t a t i o n and i s thus r e l a t i v e l y slow. As a r e s u l t , the two attached state model predicts low values for the force and work per cross-bridge (Huxley and Simons, 1971b). Therefore, Huxley and Simmons suggested that at least three attached states would be required to explain p h y s i o l o g i c a l data. S t i f f n e s s X-ray d i f f r a c t i o n studies (H.E. Huxley and Brown, 1967) as well as mechanical studies (Ford, Huxley and Simmons, 1981) have shown that the compliance of the myofilaments i s very small. Ford et a l (1981) proposed that filament compliance would have only small or n e g l i g i b l e e f f e c t s on the amplitude or time course of tension t r a n s i e n t s . If i t i s assumed that the instantaneous e l a s t i c i t y of the cross-bridge, r e f l e c t e d by phase 1 of the tension transient, i s independent of the force-generating mechanism (Huxley and Simmons, 1971b), then the s t i f f n e s s associated with i t can be studied. S t i f f n e s s i s defined as the change in tension r e s u l t i n g from a given change in length during a quick length step, that i s , i t i s the slope of the T l curve. If the dependence of the amplitude of phase 1 on the amount of overlap between the myofilaments indicates the cross-bridge contains an undamped e l a s t i c i t y (Huxley and Simmons, 1971a), then s t i f f n e s s provides a measure of the number of formed cross-bridges. The recovery of tension i s assumed to occur independently of the changes in the instantaneous e l a s t i c i t y and begins before the length change i s complete (Huxley and Simmons, 1971b). This r e s u l t s i n - 33 -truncation of T l , that i s , an underestimation of the tension change. Therefore to obtain the true T l , truncation must be taken into account (see dis c u s s i o n ) . Because of the arrangement of the experimental apparatus, the length change involves the apparatus, the tendons and connections to the apparatus, and the muscle i t s e l f . The length change does not occur simultaneously in a l l sarcomeres, as i t must be propagated from the end where i t originates to the other end where i t i s recorded. This i s taken into account by multiple segment models (Ford et a l , 1977, 1981, Gott, 1979). S t i f f n e s s behavior can be tested against these models of the cross-bridge. - 34 -I I I . METHODS - 35 -A l l experiments were c a r r i e d out using single f i b r e s or small f i b r e bundles of the semitendinosus muscle from the frog, Rana pipiens or Rana temporaria. The experiments are conceptually simple, but are subject to ce r t a i n complex and subtle technical interferences. Therefore the methods w i l l be described in d e t a i l , and the relevant technical considerations w i l l be discussed. Muscle preparation Frogs were k i l l e d by a blow to the head. The head was quickly removed and the spinal cord was pithed. The legs were removed from the body and pinned onto a parafin d i s s e c t i n g board so that the cut surface was facing down. The legs were kept moist throughout the d i s s e c t i o n by r i n s i n g with cooled, unbuffered Ringer's s o l u t i o n . The leg to be dissected was skinned from the region of the p e l v i s to just past the knee. The loc a t i o n of the semitendinosus muscle could be approximated by observing the two proximal tendons and the d i s t a l tendon through the overlying muscle which was i n i t i a l l y removed. Subsequently one head of semitendinosus was i s o l a t e d and removed from the thigh as follows. A f t e r i s o l a t i n g the tendons, s u r g i c a l s i l k (5-0) was t i e d onto one proximal tendon and onto the d i s t a l tendon. The proximal tendon was cut and the muscle was gently l i f t e d and dissected away from the surrounding connective tissue and i t s neurovascular supply. Near the d i s t a l end the two heads of the muscle i n s e r t into a common tendon so the head not being used was c a r e f u l l y dissected away. The d i s t a l tendon was freed and the muscle was quickly transferred to a perspex d i s s e c t i n g dish, f i l l e d with cooled, unbuffered Ringer's s o l u t i o n . The threads on each tendon were looped around s t a i n l e s s s t e e l hooks at each end of the f l o o r of the di s s e c t i n g dish and the length of the muscle was adjusted to just past - 36 -slack length. The threads were secured to the rim of the di s s e c t i n g dish with p l a s t i c i n e . The remainder of the d i s s e c t i o n was done with the aid of a Zeiss d i s s e c t i n g microscope and dark f i e l d i l l u m i n a t i o n . The remaining nerve stump was located and about one-half to three-quarters of the muscle was dissected away from this region by either s t a r t i n g at one tendon and cutti n g along the long axis of the muscle, or by making an i n c i s i o n i n the middle of the muscle, peeling and cutting away the f i b r e s towards the tendons. Thus, the f i b r e s to be used were on the side of the muscle opposite to the point of entry of the nerve. Damaged f i b r e s were removed u n t i l the preparation was clean. Damaged f i b r e s could be distinguished from l i v i n g f i b r e s by opaque swellings at the s i t e of injury or by opacity of the whole f i b r e . L i v i n g f i b r e s looked c l e a r under the d i s s e c t i n g microscope. Fibres were removed one at a time or in small bundles by c a r e f u l l y taking hold of them with fi n e (#5) s t a i n l e s s s t e e l forceps, making a small i n c i s i o n , peeling them towards the tendons and c u t t i n g them away with fine s c i s s o r s . This was continued u n t i l the muscle preparation was the desired s i z e . To untwist the muscle or to remove damaged f i b r e s more r e a d i l y , the preparation could be rotated i n the d i s s e c t i n g dish by twisting the threads at one end. When the di s s e c t i o n was complete the muscle preparation was stored overnight at 5° C. The following day any f i b r e s that appeared damaged were removed. Usually single f i b r e preparations were used the same day as the d i s s e c t i o n . Experimental apparatus Two s l i g h t l y d i f f e r e n t experimental arrangements were used during the course of t h i s work. In both systems the muscle preparation was attached to a motor at one end and a force transducer at the other end - 37 -( f i g u r e 2). The motor was used to maintain the muscle preparation i n the isometric state or to give rapid length changes during a contraction. In the i n i t i a l s eries of experiments, a Ling shaker (model 201) was used as the servo-motor and this was subsequently replaced for a l l the single f i b r e experiments by a Cambridge model 300S servo-system. In addition, an RCA 5734 force transducer (1.2 KHz resonant frequency) was used with the shaker system and a model 404 capacitive type force transducer (2 KHz resonant frequency) was used with the Cambridge system. The analog outputs of both the motor and the force transducer could be displayed on two oscilloscopes (Tektronics D13 Dual Beam Storage Scope and the D i g i t a l N i c o l e t 3091) and photographed for l a t e r a n a l y s i s . A d i g i t a l timer (Digitimer D4030) triggered the stimulator (Medical Systems Corp. 2533), the function generator (Exact, model 330), the o s c i l l o s c o p e s , and the analog to d i g i t a l converter at pre-set times during a contraction. a) The Ling Shaker system The Shaker system was used for the i n i t i a l experiments on small muscle bundles. After d i s s e c t i o n , the tendons of small muscle bundles (2-20 f i b r e s ) were r e t i e d with 5-0 s i l k thread very close to the myotendinous junction to reduce stray series compliance. The preparation was subsequently transferred to the experimental chamber which consisted of two pieces of perspex each containing a transverse array of platinum wire electrodes at 1mm i n t e r v a l s . The arrangement of the electrodes permitted a l l - o v e r transverse stimulation of the f i b r e s . The thread on one end of the preparation was firmly t i e d to a wire s t i r r u p , which was glued to the anode pin of an RCA 5734 force transducer (1.2 KHz resonant frequency). The other end was t i e d to a s t r a i g h t annealed s t a i n l e s s s t e e l wire which was firmly connected to an aluminum rod (the moving arm) sum function generator oscilloscope Figure 2. Block, diagram of the experimental apparatus. The m stands for muscle preparation. The length feedback loop i s shown by the length transducer (AL) and the two a m p l i f i e r s . X stands for the analog to d i g i t a l converter and Dec Writer in the Shaker system, or the Nicolet d i g i t a l oscilloscope in the Cambridge system. See text for d e t a i l s . - 39 -extending from the moving element of the Ling Shaker (model 201). A l u c i t e block attached to the mounting plate of the Shaker contained a short brass tube through which the moving arm passed. The brass tube l i m i t e d any non-axial movements of the Shaker's moving arm. A glass chamber was placed over the perspex block and the whole apparatus was then set v e r t i c a l l y i n a 40L Dewar f l a s k containing constantly aerated ice and water mixture. This maintained the preparation at less than l c C. The glass chamber was f i l l e d with buffered Ringers s o l u t i o n and bubbled with 100% oxygen throughout the experiment. The composition of the Ringer's solution was (mM): NaCl, 115.0, KC1, 2.5, CaCl, 1.8, Na 2HP0 4, 2.1, NaH 2P0 4, 0.9 at pH = 7.1. Temperature was monitored throughout the experiment using a thermistor probe inserted into the chamber and l y i n g i n close proximity to the preparation. Figure 3 shows the response of the Shaker to a step input. The response i s c r i t i c a l l y damped and i s complete within 1.0 ms. This was the duration of the step length change used i n a l l experiments done with the Shaker system. The s t i f f n e s s of the system was 10.2 g/um. b) The Cambridge Dual Mode Servo-System The Cambridge system was primarily used for single f i b r e experiments. Two methods of attachment to the motor and force transducer were used in t h i s experimental set-up. In the bundle experiments and some single f i b r e experiments, a needle was used to make a small hole in the tendons close to the myotendinous junction. The muscle preparation was then transferred into the experimental chamber using a small piece of l o n g i t u d i n a l l y sectioned p l a s t i c tubing. The tendons were positioned so that the wires attached to the force transducer and motor went through the pre-made holes. The tendons d i s t a l to the holes were then t i e d - 40 -Figure 3. Response of the Shaker system (upper trace) to step inputs from the function generator (lower trace): (a) release (b) s t r e t c h . Responses are c r i t i c a l l y damped and complete within 1 ms. Time scale 1.0 ms per d i v i s i o n . Output of Shaker 33.5 mv per d i v i s i o n . - 41 -securely with 10-0 monofilament nylon thread onto the wires. In the remainder of the single f i b r e experiments aluminum f o i l clamps were used (Ford, Huxley and Simmons, 1977). The clamps were T-shaped with a hole in the t a i l of the T. Under 40x magnification, the two arms of the T were folded over and firm l y clamped onto the tendon of the f i b r e close to the myotendinous junction. The preparation was then transferred to the experimental set-up and the hole in the t a i l of the T-shaped clamp was placed over the wires connected to the force transducer and the motor. The sides of the t a i l of the clamp were then firm l y squeezed around the hook in the wires to ensure that the clamps would not move during the course of the experiment. The experimental chamber i n t h i s set-up was h o r i z o n t a l l y oriented. The chamber was made of hardened aluminum, coated with t e f l o n . It consisted of two plates between which were sandwiched two thermoelectric modules used to maintained the chamber at a constant pre-set temperature. The temperature for most experiments was less than 1° C however in some of the l a t e r experiments the temperature was 3-4°C. The chamber contained a double glazed f l o o r which allowed l i g h t to pass through the muscle f i b r e so that sarcomere length could be measured by laser d i f f r a c t i o n or photomicroscopy (described below). The sides of the chamber contained two platinum plate electrodes which allowed maximal transverse stimulation along the whole length of the muscle preparation. Figure 4 shows the response of the Cambridge servo motor to a step input. The response was c r i t i c a l l y damped and complete within 500 us. The shortest step duration possible with no overshoot was 350 us however, 500 us was used as the resonant frequency of the force transducer was only 2 KHz. The s t i f f n e s s of the servo system was 50.0 g/pm. The force transducer and motor were mounted on micromanipulators - 42 -a Figure 4. Response of the Cambridge system (upper trace) to step inputs from the function generator (lower trace) (a) release (b) s t r e t c h . Responses are c r i t i c a l l y damped and complete within 500 ps. Time scale 500 us per d i v i s i o n . Output of motor 67.1 mv per d i v i s i o n . - 43 -which were used for f i n e adjustment of f i b r e length and p o s i t i o n . The whole system (micromanipulators and experimental chamber) was mounted on the stage of a L e i t z microscope (figure 5). The microscope had been modified so that sarcomere length can be measured by laser d i f f r a c t i o n or photomicroscopy. Sarcomere length measurements As the functional unit of s t r i a t e d muscle, the sarcomere consists of a l t e r n a t i n g A-bands and I-bands of d i s s i m i l a r r e f r a c t i v e i n d i c e s , and are i n constant r e g i s t e r , they act as a phase d i f f r a c t i o n grating, so that when laser l i g h t was shone through muscle a d i f f r a c t i o n pattern i s observed. The distance from the zero to the f i r s t order i n t e n s i t y maxima of the d i f f r a c t i o n pattern represented the sarcomere length. A 5mW Helium-Neon laser was r i g i d l y mounted to the l i g h t port of the microscope base (fig u r e 5). The beam was then deflected v i a a mirror, through the glass f l o o r of the experimental chamber, and onto the muscle f i b r e . The resultant f i r s t and zero order of the d i f f r a c t i o n pattern were c o l l e c t e d i n a 4x convex lens, passed through the nosepiece of. the microscope and was then condensed v i a a c y l i n d r i c a l lens. The zero order was focussed onto a phototransistor and the f i r s t order onto a photodiode array ( F a i r c h i l d CCD 143 High Speed Linear Image Sensor) con s i s t i n g of 1024 elements. The output of t h i s sensor was then analyzed by a computer which compared the distance from the zero order to the mean po s i t i o n of the f i r s t order and gave a d i g i t a l readout of the s t a t i c sarcomere length. This system i s a modification of that of Iwazumi and Pollack (1979). For photomicroscopy, the laser sensor attachment was removed from the microscope and replaced by the photography attachment (fig u r e 6a). - 44 -Figure 5. The Cambridge servo-system. The force transducer and motor are mounted on brass plates attached to micromanipulators (3-way p o s i t i o n e r s ) . This arrangement allows fi n e adjustment of f i b r e length and p o s i t i o n . The micromanipulators and experimental chamber are mounted on a large brass p l a t e . This plate s i t s on the microscope stage and can be moved in the X and Y planes so as to scan the length and width of the f i b r e when measuring sarcomere length. The plate i s removable so that f i b r e s may be attached to the motor and force transducer with the aid of the d i s s e c t i n g microscope. Ice water i s c i r c u l a t e d through ports on ei t h e r side of the experimental chamber, acting as a heat sink. The temperature i s monitored by a c a l i b r a t e d thermistor probe mounted just outside the chamber (represented as large black dot). The laser d i f f r a c t i o n attachment i s shown in this figure (see sarcomere length measurement section for d e t a i l s ) . I l l u s t r a t i o n by Bruce Stewart (Biomedical Communications, UBC). - 45 -- 46 -Light from a f i b r e optic source (Volpi, 150 H) was r e f l e c t e d by a mirror mounted below the stage. The muscle was observed and the image focussed through the viewer and a lOx objective lens. Five areas of the f i b r e were photographed: the motor end, between the motor and centre, the centre, between the centre and the force transducer, and the force transducer end. In addition a c a l i b r a t e d d i f f r a c t i o n grating was photographed. Sarcomere spacing was obtained from p r i n t s of the various areas of the f i b r e ( f i g u r e 6b) by d i r e c t comparison with a p r i n t of the d i f f r a c t i o n grating. The sarcomere spacing of the f i b r e was taken as the average of the sarcomere spacings of the f i v e areas photographed. Experimental procedure Small f i b r e bundles or single f i b r e s were prepared and mounted for stimulation and isometric tension recording as described above. Throughout an experiment the preparation was stimulated at regular 90 second i n t e r v a l s with a regime con s i s t i n g of 3 twitches followed by a tetanus. The stimulus was a supramaximal square wave of 1 ms duration. The optimum stimulus voltage was determined by noting the voltage which produced the maximum twitch tension and adding 1 v o l t to th i s value. The frequency and duration of stimulation for tet a n i were determined in each experiment so as to obtain a fused isometric tetanus. A l l experiments were c a r r i e d out at l o , the length at which the maximum isometric twitch was recorded. At the end of every experiment, the t o t a l length of the muscle preparation between the knots securing the tendons was measured with fin e c a l i p e r s . Throughout the experiment representative twitches and t e t a n i were recorded in order to ensure that there was no s i g n i f i c a n t decline i n isometric tension. - 47 -- 48 -Figure 6. Modification of the Cambridge system for photomicroscopy. (a)Same as figure 5 except the laser d i f f r a c t i o n attachment has been replaced by the photomicroscopy attachment. (b)Representative photograph of c e n t r a l segment of a f i b r e . Experiment of August 4, 1983, sarcomere length, 2.15 pm. I l l u s t r a t i o n in (a) by Bruce Stewart (Biomedical Communications, UBC). - 49 -The instantaneous s t i f f n e s s measurements were obtained with two d i f f e r e n t methods. In experiments using the Shaker system tension-extension curves were obtained by imposing a length step (1 ms duration) on an i s o m e t r i c a l l y contracting muscle at 25, 50, or 100 ms time i n t e r v a l s throughout a twitch or a tetanus. The corresponding analog outputs of the length and tension transducers were d i g i t i z e d i n an ana l o g - t o - d i g i t a l converter at the rate of 50 us/address. Force values were then normalized with respect to the maximum tetanic force (Po) and the changes i n length were expressed as a f r a c t i o n a l change of the body length ( l o ) . P l o t t i n g force against the change i n length produced a tension-extension curve. The l i n e a r i t y of a portion of th i s curve (Bressler and Clinch, 1974) permitted the use of l i n e a r regression of the points from 0.4Po to Po for releases and from Po to T l (the extreme tension value reached) for stretches, and use the slope of the l i n e as a measure of the instantaneous s t i f f n e s s of the muscle. In experiments using the Cambridge servo-system the length change was complete i n 500 us and therefore the A-D converter did not provide s u f f i c i e n t r e s o l u t i o n to record the points d i r e c t l y . For these experiments s t i f f n e s s values were obtained by comparing the r a t i o of the tension change ( A P ) to the length change ( A l ) as read from the oscilloscope records (figure 7). In addition i t was possible to read values d i r e c t l y from the Nicolet d i g i t a l o s c i l l o s c o p e when i t became av a i l a b l e . A l l s t i f f n e s s values were expressed in terms of the maximum s t i f f n e s s measured at the plateau of an isometric tetanus. The amplitude of the length changes throughout the experiments were less than 6 nm/half-sarcomere, or less than 0.5% of the length of the muscle preparation. Small amplitudes were chosen so as not to move the f i b r e along i t s tension-length curve during the shortening or lengthening - 50 -Figure 7. Representative f i l m records of tension and length changes at the plateau of an isometric tetanus (a) on a slow time scale, 100 ms between upper row of time dots and (b) on an expanded time scale, 1 ms per d i v i s i o n . In (a) length i s the upper trace and tension i s the lower trace, while in (b) tension i s the upper trace and length i s the lower trace. The various tension and length values read from f i l m records are : Pr, s, the tension value immediately preceding the tension change, T l , the extreme tension value, AP, the change in tension, T2, the rapid early recovery tension l e v e l and A l , the amplitude of length change. The tension values were normalized with respect to Po and the length values were normalized with respect to l o . S t i f f n e s s (S) was calculated as the change in tension for a given change in length, AP/Al or A P / ( A l / l o ) . S values were normalized with respect to So, s t i f f n e s s values obtained at the l a s t shock of a tetanus with releases of the same amplitude. The length change was converted to nanometers/half-sarcomere (nm/h-s) by multi p l y i n g A l / l o by the sarcomere length /half-sarcomere (nm). - 52 -step. Small amplitudes of length change are desirable when comparing the difference in instantaneous s t i f f n e s s measured with release versus s t r e t c h . The rate constant of the rapid early recovery phase (phase 2) of the tension transient increases as the amplitude of the release increases. With s t r e t c h , t h i s rate constant decreases as the amplitude of the length change increases (Huxley and Simmons, 1971b). T h e o r e t i c a l l y , t h i s would r e s u l t in an underestimation of the instantaneous tension response (phase l ) to a release as the rapid early recovery phase would be taking place at a faster rate than in a s t r e t c h and would truncate part of phase 1 (see Discussion). Technical considerations and corrections The information that was desired from the mechanical experiments described in t h i s thesis was the e l a s t i c properties for an average, yet i d e a l cross-bridge, that i s , the r e l a t i o n s h i p between tension and length. However, several complicating factors existed due to dynamic e f f e c t s of the experimental system. These factors were (a) the inherent response c h a r a c t e r i s t i c s of the force transducer, (b) series e l a s t i c compliance in the tendons and attachments to the motor and force transducer, and (c) f i b r e i n e r t i a and f r i c t i o n forces retarding the movement of the f i b r e . a)Force transducer response It was necessary to determine to what extent the tension s i g n a l r e f l e c t e d the actual behavior of the muscle and how much was due to the inherent c h a r a c t e r i s t i c s of the transducer i t s e l f . This may be determined by measuring the response time and damping of the force transducer during rapid length changes by a technique o r i g i n a l l y - 53 -described by Ford, Huxley and Simmons (1977). A small piece of 10-0 monofilament nylon thread with a loop at each end was attached to the wire hooks on the motor arm and force transducer. A large release was then given to the thread so that i t went slack and the loop l o s t contact with the transducer hook. From a time just before the f i r s t minimum in the output s i g n a l , the force transducer was completely unloaded and should have performed a damped o s c i l l a t i o n at i t s natural frequency about the l e v e l corresponding to zero tension. The o s c i l l a t i o n s should have decayed exponentially with a s p e c i f i c time constant. However, complications in determining the resonant frequency and damping time constant arose due to a superimposed resonance of a d i f f e r e n t frequency believed to be due to the glass c a p i l l a r y tube which extended from the moving part of the force transducer and contained the wire to which muscle preparations were attached. Since the force transducer response during free o s c i l l a t i o n appeared to be the sum of a damped sinusoidal o s c i l l a t i o n due to the c a p i l l a r y tube and another damped sinusoidal o s c i l l a t i o n due to the moving part of the force transducer i t s e l f , the damped o s c i l l a t i o n due to the c a p i l l a r y tube was subtracted from the transducer s i g n a l . An exponentially decaying sinusoidal o s c i l l a t i o n with the same frequency as that of the c a p i l l a r y tube was calculated and subtracted. The subtracted record s t i l l appeared to be composed of more than one o s c i l l a t i o n so a second o s c i l l a t i o n was calculated based on parameters from the difference record. This o s c i l l a t i o n was then subtracted from the difference record. This correction routine resulted in a f i n a l record with a resonant frequency of 2 KHz. The damping time constant could not be determined and was assumed to be 3 periods (Ford et a l , 1977), or 1500 us. Representative tension records have been corrected for the force - 54 -transducer response using the equation of Ford et a l (1977) : Tc = [X - 2(mt/kt)X] + [(bt/kt)Y + (mt/kt)Y] + [-(bt/kt)Z + (mt/kt)Z] ( h ) 2 2h ( h ) 2 2h ( h ) 2 where mt/kt = l / [ ( 2 p i v ) 2 + ( 1 / t ) 2 ] and bt/kt = (2/t) x (mt/kt) . The values in these equations are : Tc i s corrected tension, X i s the tension point to be corrected, Y i s the tension point following X, Z i s the tension point preceding X, h i s the time i n t e r v a l between tension points, v i s the resonant frequency of the force transducer and t i s the transducer's damping time constant. Figure 8 shows a corrected record of a s t r e t c h and a release. Note that the correction changed both records in the same d i r e c t i o n and did not eliminate the difference in tension change observed with s t r e t c h versus release. b)Series e l a s t i c i t y It was necessary to determine to what extent the tension response r e f l e c t e d the actual response of the muscle and how much was due to the tendons and the attachment of the muscle to the motor and the force transducer. Since the attachments were not i d e a l l y r i g i d t his led to the problem that the applied length change was equal to the length change of the tendons and attachments plus the length change of the muscle. The amount of length change due to the tendons and attachments was minimized in the experiments reported on in this thesis by using s t i f f attachments and reducing the amount of tendon present by placing the attachments very close to the myotendinous junction. This reduced stray series compliance. Other investigators (eg. Gordon, Huxley and J u l i a n , 1966) eliminated series compliance in t h e i r preparations using segment length clamps. However, i t i s possible to measure the compliance and correct 155 150 145 J l 4 0 I 135 130 125 120 * A a A D * Uncorrected a Corrected • ft • H. H J I I L i . J I b 190 r 185 180 -- 175 h > E - 0 . 4 0 0.4 0.8 1.2 1.6 2.0 2.4 Time from Start of Tension Change (ms) 170 -c a> 165 160 -155 150 • ^Uncorrected ^Corrected a 6 A • B fi * J I I L J -0 .4 0 0.4 0.8 1.2 1.6 2.0 2.4 Time from Start of Tension Change (ms) Figure 8. Representative tension transients corrected for response of force transducer (a) release (b) s t r e t c h . Records from experiment of July 26, 1983. - 56 -for i t . When th i s was done by Bressler and Clinch (1974), compliance was found to be n e g l i g i b l e in t h e i r preparations. Although a contribution from the attachments and tendons can not be ruled out in the preparations used in this study, t h e i r contribution to the r e s u l t s obtained was believed to be minimal. c)Fibre i n e r t i a and f r i c t i o n It was necessary to determine to what extent the tension changes measured by the force transducer were due to changes in the muscle and how much was due to the e f f e c t s of i n e r t i a and f r i c t i o n a l forces. The e f f e c t of i n e r t i a was that i t took a c e r t a i n amount of time for the applied length change to be propagated down the f i b r e . Consequently, the motor end of the preparation received the length change and produced a tension change before a s i m i l a r segment near the force transducer responded, so that the tension signal from the force transducer was the sum of the tension changes along the length of the f i b r e . The e f f e c t of f r i c t i o n was to oppose the force produced by the cross-bridges by drag due to the surrounding f l u i d and i n t e r n a l v i s c o s i t y of the f i b r e . When a length change was applied to the f i b r e , f l u i d drag opposed the i n i t i a l movement of the f i b r e . The continuing motion of the f i b r e during the length change caused the f l u i d adjacent to the f i b r e to move with i t . When the length change ceased and the f i b r e stopped moving, i t was dragged towards the force transducer by the continuing movement of the f l u i d . When the muscle was stimulated, the filaments had to displace water as they i n t e r d i g i t a t e d and the i n t e r n a l v i s c o s i t y of the f i b r e r esulted in the production of f r i c t i o n a l forces. Tension records may be corrected for the e f f e c t s of i n e r t i a and f r i c t i o n using the equations of Ford et a l (1977). These investigators 155 150 145 l l 4 0 c o "55 § "35 \— 130 125 120 - 0 * * A * Uncorrected a Corrected A * A A A b 190 185 J L_ I I l i I 180 ~ 175 > E g 170 Ui c I-4 0 0.4 0.8 1.2 1.6 2.0 2.4 Time from Start of Tension Change (ms) 165 160 155 150 * Uncorrected D Corrected A A A A A A A A A A i J I L J I I -0.4 0 0.4 0.8 1.2 1.6 2.0 2.4 Time from Start of Tension Change (ms) Figure 9. Representative tension transients corrected for i n e r t i a (a)release (b)stretch. Records from experiment of July 26, 1983. - 58 -found that when they corrected tension records for the e f f e c t s of f r i c t i o n , the largest correction value obtained was about 0.5% of the t o t a l tension change. Since most of t h e i r f r i c t i o n a l forces were due to f l u i d drag from markers on the surface of t h e i r f i b r e s and these were not used in this study, f r i c t i o n would have had a smaller e f f e c t in our preparations and therefore t h i s correction was not performed. Representative tension records were corrected for the e f f e c t of i n e r t i a using the equation: A T = ( p i / d ) 2 Wf Nt (Ys/6) (1 + 2c) s i n (pi/d x t) where AT i s the change i n tension due to i n e r t i a , d i s the duration of the length change, Wf i s the weight of the f i b r e , Nt i s the t o t a l number of sarcomeres in the f i b r e , Ys i s the change of length per half-sarcomere at the end of the length step, c i s the tendon compliance as a f r a c t i o n of the f i b r e compliance, and t i s time. The value used for c was taken from Ford et a l (1977) as i t was not measured i n any experiments. It was found that the i n e r t i a l c o r rection had l i t t l e e f f e c t on tension records (fig u r e 9). Furthermore, the correction had the same e f f e c t on records of releases and stretches and did not eliminate the difference in tension change between stretches and releases. In e r t i a would have less of an e f f e c t in shorter muscle preparations, as the propagation time for an applied length change would be shorter. In order to determine whether i n e r t i a would a f f e c t the r e s u l t s of t h i s study, the experimental protocol was repeated on a t i b i a l i s a nterior f i b r e , as these f i b r e s are approximately one-half the length of semitendinosus f i b r e s . It was found that the difference i n s t i f f n e s s measured with a s t r e t c h versus a release was s t i l l present in the shorter t i b i a l i s a nterior f i b r e s . In summary, the p o t e n t i a l complicating technical factors in t h i s - 59 -experimental apparatus and preparation have been i d e n t i f i e d and characterized. In p a r t i c u l a r , no d i f f e r e n t i a l e f f e c t of these factors on the measured s t i f f n e s s in stretches versus releases has been found. - 60 -IV. RESULTS - 61 -In figure 10 are o r i g i n a l records from experiments both in small muscle bundles and single semitendinosus f i b r e s which were given length steps complete in 1 ms (figure 10a) or 500 us (figure 10b). In (a) the lower trace i s tension and the upper trace i s length while i n (b) the lower trace i s length and the upper trace i s tension. The c h a r a c t e r i s t i c tension transients f i r s t observed by Armstrong, Huxley and J u l i a n (1966) may be seen. The tension response consists of four phases (Huxley and Simmons, 1970a) : a) phase 1, a rapid change in tension to an extreme l e v e l , T l , that occurs simultaneously with the length change, b) phase 2, a rapid i n i t i a l recovery in tension to an apparent plateau, T2, c) phase 3, a slowing or even reve r s a l of the tension recovery and d) phase 4, a f i n a l slow recovery of tension. In figure 11 are t y p i c a l T l and T2 curves obtained from a semitendinosus f i b r e measured from records s i m i l a r to those in figure 10. The T l curve i s obtained by p l o t t i n g the extreme tension reached during the i n i t i a l length step, expressed as a f r a c t i o n of the maximum tetanic tension. Extrapolation of the l i n e a r portion of this curve to the abscissa provides a t h e o r e t i c a l measure of the size of length step that would be required to reduce the tension to zero from the plateau of an isometric tetanus. The value of 6.5 nm/half-sarcomere (nm/h-s) compares favourably with the published values of 8nm/h-s for semitendinosus f i b r e s using 1 ms length steps (Huxley and Simmons, 1971a,b) or 4 nm/h-s for t i b i a l i s a nterior f i b r e s with steps complete in 200 ps (Ford et a l , 1977). Previous work by Huxley and Simmons (1971a) and Bressler and Clinch (1974, 1975) has shown that the slope of the T l curve provides an estimate of the s t i f f n e s s of an e l a s t i c structure within the sarcomeres, most l i k e l y , the cross-bridges. The T2 curve i s obtained by p l o t t i n g the tension l e v e l reached Figure 10. O r i g i n a l records of tension responses to step length changes complete in (a) 1 ms and (b) 500 ps. Length changes given at l a s t shock of tetanus. In (a) length i s upper trace and tension i s lower trace while in (b) length i s lower trace and tension i s upper trace. Tension baseline i s indicated by arrow. Experiments of (a)December 10, 1981 and (b)January 24, 1984. Figure 11. Curves of T l , extreme tension, and T2, tension approached during early recovery phase, obtained with length steps of various amplitudes. Both T l and T2 are expressed as fracti o n s of To, the maximum isometric tetanic tension. Experiment of June 24, 1983, sarcomere length, 2.2 um. - 64 -immediately following the i n i t i a l rapid recovery phase, once again, expressed as a f r a c t i o n of the maximum tetanic tension. This curve may be seen to be highly non-linear. This i s due to the fact that the rate constant of the i n i t i a l recovery phase varies with the amplitude of the length step, being slow for stretches and becoming faster as the si z e of the release increases (see d i s c u s s i o n ) . O r i g i n a l records of a t y p i c a l experiment designed to measure the d i f f e r e n c e i s s t i f f n e s s between stret c h and release are shown i n figure 12. Tension records with a rapid release have been superimposed on (a) a twitch and (b) a tetanus with a rapid s t r e t c h . In both records, the upper trace i s length and the lower trace i s tension. The upper row of time dots at the bottom of the records are 100 ms apart. The length change i s expressed in nanometers/half-sarcomere (nm/h-s). Near the peak of the twitch, the s t r e t c h produced a tension change that was 7.5% greater than the release. At the plateau of an isometric tetanus there was a 10.1% difference in the tension change between stret c h and release. Twitch Figure 13 i s a comparison of the pooled s t i f f n e s s to tension r e l a t i o n s h i p throughout the isometric twitch obtained with 4 d i f f e r e n t amplitudes of length change i n 15 single f i b r e s . Irrespective of the amplitude of the length change, a rapid s t r e t c h produced a c o n s i s t e n t l y higher s t i f f n e s s value than a release. In order to determine whether the difference in the measured s t i f f n e s s between stret c h and release varied in d i f f e r e n t phases of the twitch, the tension immediately preceding the length step was compared to the s t i f f n e s s values during the r i s i n g phase (fig u r e 14), peak (0.95 -- 65 -a * 3 .7 Figure 12. O r i g i n a l records of (a) an isometric twitch with a rapid stretch superimposed on a twitch with a rapid release and (b) an isometric tetanus with a rapid stretch superimposed on a tetanus with a rapid release. The time of the length change was (a) 150 ms a f t e r stimulation and (b) at the l a s t shock of the tetanus. The amplitude of the length change i s expressed in nm/h-s. Experiment of January 18, 1984, sarcomere length 2.27 pm, temperature 3.1°C. - 66 -0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Relative Tension Figure 13. Comparison of tension during the isometric twitch to stiffness values obtained with 4 amplitudes of length step for 15 single fibres. A l l values are expressed as a fraction of the corresponding maximum values obtained at the plateau of an isometric tetanus. The solid line represents a 1:1 correlation between stiffness and tension. - 67 -3nm/h-s 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Relative Tension Figure 14. A comparison of tension values during the r i s i n g phase of the isometric twitch to s t i f f n e s s values obtained with 4 amplitudes of length change. A l l values expressed as f r a c t i o n of the maximum values at the plateau of an isometric tetanus. - 68 -1.0 Pr,s/Pt) (fi g u r e 15) and relaxation phase (figure 16) for the 4 amplitudes seen in figure 13. It may be seen that the largest difference i n s t i f f n e s s measured with s t r e t c h versus release occurred during the late r i s i n g phase of tension, the peak and early in the relaxation phase. The s t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the twitch was also investigated using muscle bundle preparations ranging in size from 2 to 20 f i b r e s . Similar r e s u l t s to those in figure 13 are seen in figure 17. Tetanus a) Rising phase Figure 18 i s a comparison of the s t i f f n e s s to tension r e l a t i o n s h i p during the i n i t i a l development of tension in an isometric tetanus obtained with 2 amplitudes of length change in 4 muscle bundles (a) and 2 single f i b r e s (b). As in the twitch, a rapid stretch resulted in a higher s t i f f n e s s value than a release. Figure 19 i s a comparison of the s t i f f n e s s - t e n s i o n r e l a t i o n s h i p to time during the i n i t i a l development of isometric tetanic tension from a representative experiment. In may be seen that s t i f f n e s s follows the time course of tension however, i t increases f a s t e r than tension during this phase of the tetanus. This supports previous studies by Bressler and Clinch (1974) and Cecchi, G r i f f i t h s , and Taylor (1982, 1984) using releases or sinusoidal o s c i l l a t i o n s r e s p e c t i v e l y to measure s t i f f n e s s . b) Plateau Figure 20 i s a comparison of during the plateau of an isometric length change in 1 single f i b r e i the s t i f f n e s s to tension r e l a t i o n s h i p tetanus obtained with 1 amplitude of ixperiment. In may be seen that the - 69 -3 nm/h-s •Stretch oRelease 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Relative Tension Figure 15. A comparison of tension values during the peak of the isometric twitch to s t i f f n e s s values obtained with 4 amplitudes of length change. A l l values are expressed as a f r a c t i o n of the maximum values at the plateau of an isometric tetanus. - 70 -2 nm/h-s 3 nm/h-s 2 1.2 r- 4 nm/h-s L I 5nm/h-s J I • S t r e t c h oRelease I I 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Relative T e n s i o n Figure 16. A comparison of tension values during the relaxation phase of the isometric twitch to s t i f f n e s s values obtained with 4 amplitudes of length change. A l l values are expressed as a f r a c t i o n of the maximum values at the plateau of an isometric tetanus. Relative Tension Figure 17. A comparison of tension immediately preceding the length change to s t i f f n e s s values obtained with 3 amplitudes of length step for 17 f i b r e bundles during the isometric twitch. A l l values are expressed as a fraction of the corresponding maximum values obtained at the plateau of an isometric tetanus. - 72 -4 nm/h-s CO CO CD c (7) CD > o cc •Stretch Release 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Relative T e n s i o n Figure 18. A comparison of tension during the r i s i n g phase of the isometric tetanus to s t i f f n e s s values obtained with (a)2 amplitudes of length change for 4 muscle bundles and (b)2 amplitudes of length change for 2 single f i b r e s . A l l values are expressed as a f r a c t i o n of the maximum values obtained at the plateau of an isometric tetanus. - 73 -0 0.1 0.2 0.3 0.4 Time (s) Figure 19. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the r i s i n g phase of an isometric tetanus. Tension values are those immediately preceding the length change. Amplitude of length changes was 2nm/h-s. Experiment of October 24, 1983, sarcomere length 2.2 um. - 74 -0) 1-2 r-10 h c o 35 0.8 h c/> c 0) 0.6 h J2 0.4 0.2 •Stretch oRelease ATension _ l -, 1.2 -M.0 A 0.8 A 0.6 -J 0.4 A 0.2 0 0.2 0.4 0.6 0.8 1.0 Time (s) (D C (0 > o cc Figure 20. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the plateau of an isometric tetanus. Tension values are from a representative tetanus. The amplitude of the length changes was 2nm/h-s. Experiment of October 24, 1983, sarcomere length 2.2 pm. - 75 -s t i f f n e s s and tension values remain constant during the plateau. In addition, s t i f f n e s s measured with stretch i s higher than that measured with release. c) Relaxation phase Figure 21 i s a comparison of the s t i f f n e s s - t e n s i o n r e l a t i o n s h i p to time during the relaxation phase of the isometric tetanus from a representative experiment. It may be seen that s t i f f n e s s follows the time course of the decline in tension, however i t does not decrease as r a p i d l y as tension (Dusik and Bressler, 1984). This agrees with recent r e s u l t s of Cecchi, G r i f f i t h s and Taylor (1984) and Shoenberg and Wells, (1984). The former group used single t i b i a l i s a nterior f i b r e s and high frequency sinusoidal o s c i l l a t i o n s to measure s t i f f n e s s , while the l a t t e r group used semitendinosus muscle bundles and a transmission time technique to measure s t i f f n e s s . For a short time following the l a s t shock, tension and s t i f f n e s s remain at the plateau values. During the i n i t i a l stage of relaxation p r i o r to the tension shoulder, the decline in s t i f f n e s s lags the tension change. Following the shoulder, both s t i f f n e s s and tension f a l l p r e c i p i t o u s l y . The difference between s t i f f n e s s values obtained with a stretch and s t i f f n e s s values obtained with a release i s most pronounced during the plateau and the early phase of r e l a x a t i o n . The magnitude of t h i s difference in s t i f f n e s s begins to decrease in the region of the shoulder and continues to decrease as r e l a x a t i o n proceeds. Figure 22 i s a comparison of the pooled s t i f f n e s s to tension r e l a t i o n s h i p during the relaxation phase of the isometric tetanus obtained with 3 amplitudes of length change in 10 single f i b r e s . Again, i t may be seen that a rapid stretch produced a consistently higher - 76 -1.2 1.0 c o "35 0.8 4> 0.6 .2 0.4 DC 0.2 I •Stretch Release ATension i i 1 1 - i 1.2 1.0 co 0.8 £ 0.6 CO CD > 0.4 0) CC 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) Figure 21. S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the relaxation phase of an isometric tetanus. Tension values are those immediately preceding the length change. Time i s measured from the l a s t shock of the stimulus t r a i n . The amplitude of the length changes was 2nm/h-s. Experiment of October 24, 1983, sarcomere length 2.2 um. Relative Tension Figure 22. A comparison of tension during the relaxation phase of the isometric tetanus to s t i f f n e s s values obtained with 3 amplitudes of length step for 10 single f i b r e s . A l l values are expressed as a f r a c t i o n of the maximum values obtained at the plateau of an isometric tetanus. - 78 -s t i f f n e s s value than a release. As in the twitch, i t may be seen that the largest d i f f e r e n c e i n s t i f f n e s s measured with stre t c h versus release occurred during the late r i s i n g phase of tension, the plateau, and early i n the relaxation phase of the tetanus (figures 19 to 22). The s t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the relaxation phase of the tetanus was also investigated using muscle bundle preparations ranging in size from 2 to 20 f i b r e s . Similar r e s u l t s were seen in these preparations (fi g u r e 23) as in single f i b r e s (figure 22). 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 R e l a t i v e T e n s i o n Figure 23. A comparison of tension during the relaxation phase of the isometric tetanus to s t i f f n e s s values obtained with 2 amplitudes of length change for 4 muscle bundles. A l l values are expressed as a f r a c t i o n of the maximum values obtained at the plateau of an isometric tetanus. - 80 -DISCUSSION - 81 -S t i f f n e s s - t e n s i o n r e l a t i o n s h i p during the isometric twitch and tetanus This study has shown that r e l a t i v e s t i f f n e s s values are greater than r e l a t i v e tension values throughout the isometric twitch and during the r i s i n g and r e l a x a t i o n phases of the isometric tetanus. Both the s t i f f n e s s and the tension are proportional to the number of attached cross-bridges. An independent measurement of the number of attached cross-bridges i s provided by X-ray d i f f r a c t i o n . Low-angle equatorial X-ray r e f l e c t i o n s are derived from the hexagonal array of the myofilaments, and the i n t e n s i t y r a t i o changes of these r e f l e c t i o n s have been interpreted to indicate the r e - d i s t r i b u t i o n / or movement of mass between the myosin and a c t i n filaments, that i s , cross-bridge formation (see introduction). Changes in the i n t e n s i t y r a t i o of these equatorial r e f l e c t i o n s during the isometric twitch and tetanus have been shown to precede tension during the r i s i n g phase (H.E. Huxley, 1979, Matsubara and Yagi, 1978), peak at approximately the same time as tension, and then lag tension during the relaxation phase (Yagi, Ito, Nakajima, Izumi, and Matsubara, 1977, Matsubara and Yagi, 1978). That i s , the time course of the i n t e n s i t y r a t i o changes of the equatorial r e f l e c t i o n s i s quite s i m i l a r to the time course of s t i f f n e s s changes during the isometric twitch and tetanus. S t i f f n e s s measurements indicate the number of attached cross-bridges. Thus the r e s u l t s of two independent experimental approaches suggest that cross-bridges move towards and attach to a c t i n before tension i s generated. The d i f f e r e n c e in the time course between s t i f f n e s s and tension ( r i s i n g phase : twitch - Bressler and Dusik, 1983, Shoenberg and Wells, 1984 , tetanus - Bressler and Clinch, 1974, Mason and Hasan, 1980 Cecchi, G r i f f i t h s and Taylor, 1982, 1984, Ambrogi-Lorenzini, Colomo and Lombardi, 1983 , r e l a x a t i o n phase : twitch - Bressler and Dusik, 1983, Shoenberg - 82 -and Wells, 1984, Stein and Parmiggiani, 1979, tetanus - Dusik and Bressler, 1984, Shoenberg and Wells, 1984, Cecchi et a l , 1984) may be explained in a number of ways. The r i s i n g phase w i l l be discussed f i r s t . It may be that attachment of the cross-bridges to the a c t i n s i t e s i s a two step process in which the f i r s t step i s r a p i d l y r e v e r s i b l e and tension i s generated only a f t e r both steps have occurred (A.F. Huxley, 1973). Another p o s s i b i l i t y i s that following attachment, the next chemical step in the cross-bridge cycle must occur before tension i s generated, with t h i s step having a r e l a t i v e l y slow rate constant (H.E. Huxley, 1979, Cecchi et a l , 1982, 1984). A l t e r n a t i v e l y , the d i f f e r e n c e between s t i f f n e s s and tension may be due to sarcomere shortening during the r i s i n g phase (Mason and Hasan, 1980, Ambrogi-Lorenzini et a l , 1983, Shoenberg and Wells, 1984). Huxley and Simmons (1971a, 1973) found that s t i f f n e s s increased p r o p o r t i o n a l l y with tension during the r i s i n g phase of the isometric tetanus, while the other investigators c i t e d above found s t i f f n e s s increased faster than tension. The r e s u l t s of Huxley and Simmons may d i f f e r from those of other investigators as t h e i r experiments were done using a length clamp. Ambrogi-Lorenzini et a l (1983) have pointed out that with fixed-end experimental conditions, a small amount of series compliance and i n e r t i a l a r t e f a c t s may contribute to the observed difference between s t i f f n e s s and tension, p a r t i c u l a r l y at low tension l e v e l s . The difference between s t i f f n e s s and tension during the r e l a x a t i o n phase may be explained by various p o s s i b i l i t i e s . The relaxation process may r e s u l t in a hindrance of the t r a n s i t i o n to the force producing state by cross-bridges which have just attached (see below). Other p o s s i b i l i t i e s include increased detachment of force producing cross-bridges r e l a t i v e to non force producing cross-bridges, detachment - 83 -followed by rapid re-attachment of some cross-bridges, t r a n s i t i o n of force producing cross-bridges to a non force producing state, or t r a n s i t i o n of force producing cross-bridges to a state generating r e l a t i v e l y less tension during relaxation than at the plateau (see Cecchi et a l , 1984). As was suggested for the r i s i n g phase, a r e l a t i v e l y slow t r a n s i t i o n between attachment and force generation i n the cross-bridge cycle i s assumed to occur during relaxation in these p o s s i b i l i t i e s . F i n a l l y , factors independent of the cross-bridge reaction mechanism such as inhomogeneities in the sarcomere length and/or an e f f e c t of calcium ions (Ca++) may account .for the observed diff e r e n c e between s t i f f n e s s and tension. It has been shown that the shoulder of the tension record marks the beginning of changes in sarcomere length (Huxley and Simmons, 1970b, 1973, J u l i a n and Morgan, 1979, Edman and F l i t n e y , 1977, 1982). Sarcomere shortening and lengthening occur in d i f f e r e n t regions of the r e l a x i n g muscle f i b r e following the shoulder, and become maximal when tension nears zero (Edman and F l i t n e y , 1977, 1982). The r e s t i n g sarcomere length i s not re-established u n t i l a f t e r tension has disappeared (Edman and F l i t n e y , 1982). This may explain why the i n t e n s i t y r a t i o changes of the equatorial X-ray r e f l e c t i o n s do not return to t h e i r r e s t i n g pattern u n t i l well a f t e r tension had reached zero (Yagi et a l 1977, Matsubara and Yagi, 1978, H.E. Huxley, 1979). The pattern of sarcomere length changes appears to be s i m i l a r during relaxation of twitches and t e t a n i (Edman and F l i t n e y , 1977). Blinks, Rudel and Taylor (1978) found that the sarcoplasmic Ca++ concentration, measured with aequorin, decreased r a p i d l y during r e l a x a t i o n of the twitch and tetanus and preceded the decline in tension. However, two l a t e r studies, using a much higher gain on the - 84 -aequorin s i g n a l , obtained d i f f e r e n t r e s u l t s . Ashley and Lignon (1981) found that during the twitch there was a prolonged phase to the decay of the aequorin response which continued u n t i l tension reached zero. Furthermore, Cannell (1982) found that the decrease in the aequorin s i g n a l during the tetanus i s reduced or reversed at the tension shoulder and a small increase i n the si g n a l remained a f t e r tension had reached zero. He suggested this might be due to shortening sarcomeres. A l l e n and Kurihara (1982) and Ridgway and Gordon(l984) measured Ca++ transients with aequorin following slow (5-6 ms), large (up to 6% lo) length changes. Length changes of th i s amplitude would move the sarcomeres along t h e i r tension-length curve. These investigators found that following a s t r e t c h , there was no change (Allen and Kurhara, 1982) or a small decrease (Ridgway and Gordon, 1984) in the aequorin s i g n a l whereas following a release the aequorin signal increased. Ridgway and Gordon (1984) suggested that following sarcomere lengthening the sarcoplasmic Ca++ concentration decreases due to Ca++ uptake by the filaments and following sarcomere shortening the sarcoplasmic Ca++ concentration increases due to Ca++ release from the filaments. This would agree with Cannell's suggestion and indicates that following the tension shoulder the increased rate of tension and s t i f f n e s s decline w i l l be due, i n part at l e a s t , to sarcomere shortening and lengthening and the accompanying Ca++ changes that these changes i n sarcomere length bring about. The difference between s t i f f n e s s and tension during relaxation may be the r e s u l t of hindrance of the t r a n s i t i o n to the force producing state of cross-bridges which have just attached. Biochemical in v i t r o studies by Chalovich and Eisenberg (1982) have suggested that the troponin-tropomyosin complex does not block the binding of myosin to a c t i n , but acts by blocking the rot a t i o n of myosin on a c t i n (or the - 85 -t r a n s i t i o n to the force generating s t a t e ) , increasing the a c t i v a t i o n energy for this t r a n s i t i o n and decreasing the cross-bridge c y c l i n g rate. I f the r o t a t i o n of the cross-bridges i s blocked or slowed, less tension w i l l be generated per cross-bridge than i f i t were allowed to complete i t s c y c l e . However, s t i f f n e s s measurements indicate the number of attached cross-bridges, whether or not they are generating tension. This would r e s u l t in a more rapid decline of tension values than s t i f f n e s s values during the relaxation phase. Stretch versus release This study has shown that a rapid stretch produced a c o n s i s t e n t l y higher s t i f f n e s s value than a rapid release throughout the time course of the isometric twitch and tetanus. One possible explanation for these r e s u l t s may be attained from the Eisenberg, H i l l and Chen (1980) model of muscle contraction. This model of contraction r e l a t e s in v i t r o biochemical studies to in vivo p h y s i o l o g i c a l studies. In order to develop a complete cross-bridge model of muscle contraction, the p h y s i o l o g i c a l property of cross-bridge e l a s t i c i t y had to be combined with the biochemical states. One of the main differences between t h i s model and the model of Huxley and Simmons (1971b) i s that in the l a t t e r the cross-bridge contains a tension generator and an independent e l a s t i c element. This e l a s t i c element i s "completely independent of any chemical changes in state occurring elsewhere in the attached cross-bridge". In the Eisenberg et a l model the e l a s t i c properties of the cross-bridges and chemical state changes are intimately r e l a t e d so that changes in state are d i r e c t l y r e l a t e d to changes in e l a s t i c i t y . Furthermore, each of the attached states has i n d i v i d u a l e l a s t i c and chemical properties. The biochemical basis for the model was the actomyosin cycle of - 86 -Chock, Chock and Eisenberg (1976). In th i s cycle, actomyosin i s r a p i d l y d i s s o c i a t e d by ATP which i s then hydrolyzed on the myosin head to ADP and inorganic phosphate ( P i ) . Next, a conformational change must occur i n the myosin head, from a r e f r a c t o r y to a non-refractory state, before i t can re-bind to a c t i n . This i s the r a t e - l i m i t i n g step i n the cyc l e . Subsequently myosin, with bound ADP and P i , binds to a c t i n . This i s followed by the r e l a t i v e l y quick release of P i , and then ADP, and the return to the beginning of the cyc l e . It was assumed that two unattached states, the r e f r a c t o r y and non-refractory states, and two attached states A-M-ADP-Pi (A i s a c t i n , M i s myosin) and A-M-ADP occurred in s i g n i f i c a n t concentrations in vivo and that the other states in the cycle were transient intermediates. A-M-ADP-Pi (or state 1) was assumed to be the 90°state and A-M-ADP (or state 2) was assumed to be the 45°state. The 90° and 45° states were based on s t r u c t u r a l studies (Reedy, 1967, Reedy, Holmes and Tregear, 1965) of glycerol-extracted insect f l i g h t muscle which showed that i n relaxed muscle the detached cross-bridges were oriented at a 90° angle from the myosin filament while i n r i g o r the attached cross-bridges were oriented at a 45°angle. In the Eisenberg et a l model the cross-bridges do not exi s t s o l e l y at 90°or 45°angles. These are the preferred angles for the attached states. The cross-bridges can rotate to a larger angle where they w i l l exert p o s i t i v e force or to a smaller angle where they w i l l exert negative force. "The key point i n this model i s that the e l a s t i c properties of the cross-bridge states do not determine the rate constants between these states. Therefore the rate constants between the 90° and 45° states do not depend on thermal (Brownian) motion to st r e t c h an e l a s t i c element as i n the Huxley-Simmons model". The binding of ATP was assumed to have no e f f e c t on the angle of attachment so that work done by a cross-bridge was a r e s u l t of myosin - 87 -binding to a c t i n . In biochemical studies, each biochemical state has s p e c i f i c thermodynamic properties and i s defined as a thermodynamic state. It w i l l always e x i s t at i t s minimum free energy l e v e l (Eisenberg and H i l l , 1978). In p h y s i o l o g i c a l studies, however, the thermodynamic properties and free energy l e v e l s of an attached cross-bridge state w i l l vary because of the e l a s t i c i t y of the cross-bridge. Therefore "a biochemical thermodynamic state i s a p h y s i o l o g i c a l cross-bridge state at a s p e c i f i c value of x", the a x i a l p o s i t i o n of the a c t i n binding s i t e r e l a t i v e to the attached cross-bridge. The free energy p r o f i l e in figure 24 shows the basic free energy of the four cross-bridge states in the Eisenberg et a l model as a function of x. The free energy p r o f i l e s r e l a t e the chemical parameter of free energy to the p h y s i o l o g i c a l parameters of the p o s i t i o n of the attached cross-bridge and the mechanical force. The free energy p r o f i l e s of the unattached states are independent of the position of the a c t i n binding s i t e s and therefore independent of x. The free energy p r o f i l e s of attached cross-bridge states w i l l be dependent on x because of the cross-bridge e l a s t i c i t y . The parabolic shape of state 1 and 2 free energy curves i s based on the isometric tension transient data of Ford, Huxley and Simmons (1977) which showed that the corrected experimental curve for the e l a s t i c i t y of the cross-bridge ( T l curve) i s l i n e a r . Force development depends on the presence of a gradient of free energy as a function of the a x i a l position of a cross-bridge r e l a t i v e to i t s rest p o s i t i o n i n that state (Eisenberg and H i l l , 1978). Thus, the slope of the free energy curve for an attached state, at any value of x, i s equal to the force exerted by that cross-bridge state at that value of x. Zero force i s generated at the bottom of the free energy curve. "Because cross-bridge states are at t h e i r minimum free energy l e v e l s in s o l u t i o n , - 38 -J I 0 (45°) 8 ( 9 0 ° ) X (nm) Figure 24. Basic free energy p r o f i l e for the Eisenberg-Hill-Chen cross-bridge model. The ordinate shows the r e l a t i v e basic free energy for the cross-bridge states. "The p r o f i l e repeats i n d e f i n i t e l y above and below, with one ATP being hydrolyzed during each c y c l e . " The abscissa shows the a x i a l p o s i t i o n of the a c t i n binding s i t e r e l a t i v e to the attached cross-bridge, x, with reference to i t s po s i t i o n when state 2 i s at i t s minimum free energy. The angle of attachment at X=0 i s 45°and at x=8 i s 90°. (Modified from Eisenberg et a l , 1980). - 89 -the r e l a t i v e v e r t i c a l positions of the minimum of the free energy curves are based on the equilibrium constants between cross-bridge states in so l u t i o n " . F i n a l l y , " t h e basic free energy drop for 1 complete cycle i s equal to the free energy of the hydrolysis of 1 ATP molecule which i s about 12 kcal/mole i n vivo (Kushmerick and Davies, 1969, and Curtin et a l , 1974 in Eisenberg and H i l l , 1978)". As there are four states i n th i s model there are four pairs of rate constants. "The r a t i o of the forward and reverse rate constants between any two states i s determined by the free energy difference between the two states (Eisenberg and H i l l , 1978). Like the free energy curves themselves, the values of these rate constants were chosen to be consistent with both biochemical and ph y s i o l o g i c a l data". In the isometric state there w i l l be a d i s t r i b u t i o n of cross-bridges among the various cross-bridge states as a function of x (figure 25a). This d i s t r i b u t i o n i s due to the difference i n the a x i a l repeat distance of the two sets of myofilaments (H.E. Huxley, 1969), and the assumption that during steady isometric contraction no a x i a l displacement of the filaments occurs. Therefore, cross-bridges w i l l be attached to a c t i n binding s i t e s over a range of angles but each i n d i v i d u a l cross-bridge w i l l be attached only at the angle where i t i s able to attach to an a c t i n binding s i t e and w i l l go through i t s cycle at that angle. I f a cross-bridge i s attached at an angle greater than 90° , the free energy of state 2 w i l l be much higher than that of state 1 so that few cross-bridges w i l l be capable of changing states. Thus these cross-bridges w i l l neither complete t h e i r cycle nor hydrolyze ATP. Instead, an equilibrium w i l l occur between the unattached states and state 1. If a cross-bridge i s attached at an angle less than 90° the free energy of state 2 w i l l be lower than that of state 1 so these - 90 -cross-bridges w i l l cycle and hydrolyze ATP. Figure 25 shows the cross-bridge d i s t r i b u t i o n in the isometric state (a) and immediately following a small amplitude release (b) and stretch ( c ) . Eisenberg and H i l l (1978) assumed that the tension transients were completely due to cross-bridges, and primarily to a rapid change of attached states. It can be seen that the cross-bridge d i s t r i b u t i o n i s s h i f t e d simultaneously with the length change and that the cross-bridges have been forced to rotate to angles at which they exert a d i f f e r e n t amount of tension than in the isometric state. As stated above the steeper the slope of the free energy curve the higher the tension generated. During a release the cross-bridges in state 1 have been forced to rotate to angles where they produce l i t t l e tension, no tension (bottom of curve) or negative tension (negative slope). The cross-bridges i n state 2 have been forced to rotate to angles at which they exert less force than in the isometric state. During a stre t c h the cross-bridges i n both states have been forced to rotate to angles where they produce more tension than during the isometric state. Re - d i s t r i b u t i o n during the length change r e s u l t s in cross-bridges at each angle being forced into an inappropriate state for that angle. The recovery phase of the tension transient i s due to "readjustment to the appropriate d i s t r i b u t i o n for each angle". The difference i n the rate of recovery between stre t c h and release i s due to the t r a n s i t i o n between states following the length change. Following a release the t r a n s i t i o n from the 90° state to the 45° state occurs r a p i d l y as the rate of t h i s t r a n s i t i o n increases as the cross-bridge angle decreases below 90° Following a s t r e t c h the t r a n s i t i o n from the 45° state to the 90° state occurs r e l a t i v e l y slowly as the rate of this reverse t r a n s i t i o n remains nearly constant as the cross-bridge angle increases above 90° Thus - 91 -Figure 25. D i s t r i b u t i o n of cross-bridges among the attached cross-bridge states as a function of x. The slopes of the free energy curves equal the tension generated by a cross-bridge state at a s p e c i f i c value of x. The thick l i n e indicates the states a cross-bridge w i l l occupy at each value of x under s p e c i f i c conditions. ( a ) D i s t r i b u t i o n of cross-bridges during isometric contraction. ( b ) D i s t r i b u t i o n of cross-bridges immediately following a small amplitude, rapid release. The arrows indicate the r e - d i s t r i b u t i o n of cross-bridges to the appropriate state « for each value of x responsible for tension recovery. ( c ) D i s t r i b u t i o n of cross-bridges immediately following a small amplitude rapid s t r e t c h . Arrows as in (b). (Modified from Eisenberg and H i l l , 1978). - 92 -a 0 ( 4 5 ° ) 8 ( 9 0 ° ) X (nm) C 0 ( 4 5 * ) 8 ( 9 0 » ) X (nm) Eisenberg and H i l l (1978) and Eisenberg et a l (1980) explained the isometric tension transient as a t r a n s i t i o n between two attached states, as did Huxley and Simmons (1971b). However, in the Eisenberg et a l model, the t r a n s i t i o n between states was accounted for "without postulating an independent e l a s t i c element in the cross-bridge". Thus the Eisenberg-Hill-Chen model can account for the decrease i n tension following a rapid release and the increase in tension following a rapid s t r e t c h . It may also account for the higher s t i f f n e s s values obtained with a s t r e t c h as follows. Recent studies in which s t i f f n e s s has been measured during the rapid tension recovery using quick length steps (Ford et a l , 1974) or sinusoidal o s c i l l a t i o n s throughout the tension transient ( J u l i a n and Morgan, 1981a, Cecchi et a l , 1981, 1982, 1984) have shown that s t i f f n e s s decreases following a small (le s s than 1% lo) rapid release but does not change s i g n i f i c a n t l y during a small, rapid s t r e t c h . This would suggest that some of the bound cross-bridges detach during a release but stay on during a s t r e t c h . If i s i t assumed that cross-bridges may be c y c l i n g at a faster rate than the time course of the length changes used to measure s t i f f n e s s (Guth, Kuhn, Tsuchiya and Ruegg, 1981, Ford et a l , 1977), i t may be that during release the cross-bridges in state 2 being forced down t h e i r energy well are responsible for the decrease in s t i f f n e s s . The cross-bridges in state 1 being forced into a negative force generating mode w i l l r e s i s t further change which may cause some truncation of the tension response. In addition cross-bridges w i l l be detaching during the release, most l i k e l y cross-bridges near the bottom of the state 2 free energy curve as these bridges w i l l be forced to an angle where detachment i s favored. During stretch cross-bridges w i l l stay on and are forced into higher tension generating angles, r e s u l t i n g in higher s t i f f n e s s values. - 94 -It i s also possible that truncation of the tension transient with releases contributes to the r e s u l t s obtained. Huxley and Simmons (1971b) have shown that the rate of the rapid recovery phase in frog semitendinosus f i b r e s decreases as the amplitude of stretches increases, and increases as the amplitude of the release increases. However, Abbott and Steiger (1977) have found i n glycerinated rabbit psoas f i b r e s that the rate of the rapid recovery increased as the amplitude of length change increased up to 2 nm/h-s and then remained constant for both stretches and releases. The difference i n r e s u l t s between these studies has been suggested to be due to the d i f f e r e n t muscle preparations used, the difference in speed of length step, and differences i n experimental apparatus and methodology (Abbott and Steiger, 1977, A.F. Huxley, 1980). The r e s u l t s of Huxley and Simmons would indicate that the e f f e c t of truncation of the instantaneous tension change due to rapid recovery would be smallest when comparing stretch and release at small length changes while the r e s u l t s of Abbott and Steiger would indicate the truncation would have the same e f f e c t on stretches and releases at any amplitude of length change. In any event, the difference i n s t i f f n e s s between stretch and release i s s t i l l evident at small amplitudes of length change. This suggests that truncation due to rapid recovery cannot f u l l y explain the re s u l t s of this study. Furthermore i t has been found that the rapid early recovery of tension following a release i s s i g n i f i c a n t l y slowed by hypertonic solution (Vaughan, Bressler, Dusik and Trotter, 1983) which would reduce the e f f e c t of truncation. It has been observed that the s t i f f n e s s measured with stretch i s higher than that measured during release i n hypertonic solution (Bressler and Dusik, unpublished r e s u l t s ) . This would again suggest that truncation cannot f u l l y explain - 95 -the r e s u l t s obtained in this study. Another possible explanation for the r e s u l t s of t h i s study i s that the instantaneous e l a s t i c i t y i s non-linear. Ford et al(1977, 1981) found that using computer simulation they could reproduce the tension response to releases but not to stretches. From t h i s they concluded that the instantaneous e l a s t i c i t y i s non-linear in stretches, i t s tension-extension curve being concave upwards. At present i t i s not possible to t e l l which of these explanations best f i t s the data. Many complex and subtle technical considerations were i d e n t i f i e d and characterised during t h i s study, and improved technical features, such as correction for truncation and faster length steps made possible by computer-assisted data c o l l e c t i o n with a Nicolet d i g i t a l o s c i l l o s c o p e linked to an Apple He, have been developed. Experiments using these improved techniques are being conducted to determine which of these p o s s i b i l i t i e s i s responsible for the r e s u l t s obtained. - 96 -VI. REFERENCE - 97 -Abbott, R.H., and Steiger, G.J. 1977. Temperature and amplitude dependence of tension transients i n glycerinated s k e l e t a l and insect f i b r i l l a r muscle. J. Physiol. 266: 13-42. Aidl e y , D.J. 1971. The Physiology of Excitable C e l l s . Cambridge University Press: London. A l l e n , D.G., and Kurihara, S. 1982. The e f f e c t s of muscle length on i n t r a c e l l u l a r calcium transients in mammalian cardiac muscle. J . P h y s i o l . 327: 79-94. Ambrogi-Lorenzini, C , Colomo, F., and Lombardi,V. 1983. Development of f o r c e - v e l o c i t y r e l a t i o n , s t i f f n e s s and isometric tension in frog s i n g l e muscle f i b r e s . J . Mus. Res. C e l l M o t i l . 4: 177-189. Armstrong, C.F., Huxley, A.F., and J u l i a n , F.J. 1966. O s c i l l a t o r y responses i n frog s k e l e t a l muscle f i b r e s . J . P h y s i o l . 186: 26-27P. Ashley, C.C, and Lignon, J. 1981. Aequorin responses during r e l a x a t i o n of tension of single muscle f i b r e s stimulated by voltage clamp. J. Physiol. 318: 10-11P. Astbury, W.T. 1947. On the structure of b i o l o g i c a l f i b r e s and the problem of muscle. Proc. R. Soc. Lond. 134: 303-328. Bagshaw, C.R. 1982. Muscle Contraction. Chapman and H a l l Ltd: London. Banus, M.G., and Z e t l i n , A.M. 1938. The r e l a t i o n of isometric tension to length in s k e l e t a l muscle. J. C e l l Comp. Physiol. 12: 403-420. Blinks, J.R., Rudel, R., and Taylor, S.R. 1978. Calcium transients i n i s o l a t e d amphibian s k e l e t a l muscle f i b r e s : detection with aequorin. J. Physiol. 277: 291-323. B l i x , M. 1893. Die Lange und die Spannung des Muskels. Skand. Arch. Physiol. 4: 399-409. Bressler, B.H., and Clinch, N.F. 1974. The compliance of contracting s k e l e t a l muscle. J. P h y s i o l . 237: 477-493. Bressler, B.H., and Clinch, N.F. 1975. Cross bridges as the major source of compliance i n contracting s k e l e t a l muscle. Nature 256: 221-222. Bres s l e r , B.H., and Dusik, L.A. 1983. Is the instantaneous e l a s t i c i t y of contracting s k e l e t a l muscle non-linear? Biophys. J . 41: 34a. Cannell, M.B. 1982. I n t r a c e l l u l a r calcium during r e l a x a t i o n i n frog single muscle f i b r e s . J. Physiol. 326: 70P. Casella, C. 1950. T e n s i l e force in s t r i a t e d muscle, i s o l a t e d f i b r e and sarcolemma. Acta. P h y s i o l . Scand. 21: 380-401. Cecchi, G., G r i f f i t h s , P.J., and Taylor, S.R. 1982. High-frequency s t i f f n e s s measurements of i s o l a t e d frog s k e l e t a l muscle f i b r e s . J . P h y s i o l . 324: 22-23P. - 98 -Cecchi, G., G r i f f i t h s , P.J., and Taylor, S.R. 1982. Muscular contraction: k i n e t i c s of crossbridge attachment studied by high-frequency s t i f f n e s s measurements. Science 217: 70-72. Cecchi, G., G r i f f i t h s , P.J., and Taylor, S.R. 1 9 8 4 . The k i n e t i c s of cross-bridge attachment and detachment studied by high frequency s t i f f n e s s measurements. In C o n t r a c t i l e Mechanisms in Muscle. ed. Sugi, H. and Pollack, G.H. Plenum Press: New York. Chalovich, J.M., and Eisenberg, E. 1982. I n h i b i t i o n of actomyosin ATPase a c t i v i t y by troponin-tropomyosin without blocking the binding of myosin to a c t i n . J. B i o l . Chem. 257: 2432-2437. Chock, S.P., Chock, P.B., and Eisenberg, E. 1976. Pre-steady-state k i n e t i c evidence for a c y c l i c i n t e r a c t i o n of myosin S-l with a c t i n during the hydrolysis of ATP. Biochemistry 15: 3 2 4 4 - 3 2 5 3 . Civan, M.M., and Podolsky, R.J. 1966. Contraction k i n e t i c s of s t r i a t e d muscle f i b r e s following quick changes in load. J. Physiol. 184: 511-534. Dusik, L.A., and Bressler, B.H. 1984. S t i f f n e s s measurements during the relaxation phase of the isometric tetanus. Biophys. J . 45: 347a. Edman, K.A.P. 1966. The r e l a t i o n between sarcomere length and active tension in i s o l a t e d semitendinosus f i b r e s of the frog. J . P h y s i o l . 183: 407-417. Edman, K.A.P., and F l i t n e y , F.W. 1977. Non-uniform behaviour of sarcomeres during isometric relaxation of s k e l e t a l muscle. J . P h y s i o l . 276: 15-16P. Edman, K.A.P., and F l i t n e y , F.W. 1982. Laser d i f f r a c t i o n studies of sarcomere dynamics during 'isometric' relaxation in i s o l a t e d muscle f i b r e s of the frog. J . P h y s i o l . 329: 1-20. Eisenberg, E., and Greene, L.E. 1980. The r e l a t i o n of muscle biochemistry to muscle physiology. Ann. Rev. P h y s i o l . 42: 293-309. Eisenberg, E., and H i l l , T.L. 1978. A cross-bridge model of muscle contraction. Prog. Biophys. Mol. B i o l . 33: 55-82. Eisenberg, E., H i l l , T.L., and Chen, Y. 1980. Cross-bridge model of muscle contraction - quantitative a n a l y s i s . Biophys. J . 29: 195-227. Eisenberg, E., and Moos, C. 1968. Adenosine triphosphate a c t i v i t y of acto-heavy meromyosin: a k i n e t i c analysis of a c t i n a c t i v a t i o n . Biochemistry 7: 1486-1489. Eisenberg, E., and Moos, C. 1970. A c t i n a c t i v a t i o n of heavy-meromyosin adenosine triphosphatase. J . B i o l . Chem. 245: 2451-2456. Fenn, W.O. 1924. The r e l a t i o n between the work performed and the energy li b e r a t e d in muscular contraction. J . Physiol. 58: 373-395. - 99 -Fenn, W.O., and Marsh, B.S. 1935. Muscular force at d i f f e r e n t speeds of shortening. J. P h y s i o l . 85: 277-297. Ford, L.E., Huxley, A.F., and Simmons, R.M. 1974. Mechanism of e a r l y tension recovery a f t e r a quick release i n tetanized muscle f i b r e s . J. P hysiol. 240: 42-43P. Ford, L.E.,' Huxley, A.F., and Simmons, R.M. 1977. Tension responses to sudden length change in stimulated frog muscle f i b r e s near slack length. J. P h y s i o l . 269: 441-515. Ford, L.E., Huxley, A.F., and Simmons, R.M. 1981. The r e l a t i o n between s t i f f n e s s and filament overlap i n stimulated frog muscle f i b r e s . J. Physiol. 311: 219-249. Gasser, H.S., and H i l l , A.V. 1924. The dynamics of muscular contraction. Proc. R. Soc. B 96: 398-437. Gordon, A.M., Huxley, A.F., and J u l i a n , F.J. 1966. The v a r i a t i o n i n isometric tension with sarcomere length in vertebrate muscle f i b r e s . J . P hysiol. 184: 170-192. Gott, A.H. 1979. Mul t i p l e segment analysis of muscle data. In Cross-bridge Mechanism in Muscle Contraction. ed. Sugi, H. and Pollack, G.H. Un i v e r s i t y Park Press: Baltimore. Guth, K., Kuhn, H.J., Tsuchiya, T., and Ruegg, J.C. 1981. Length dependent state of a c t i v a t i o n - length change dependent k i n e t i c s of cross-bridges in skinned insect f l i g h t muscle. Biophys. Struct. Mech. 7: 139-169. Hanson, J . , and Huxley, H.E. 1953. Structural basis of the c r o s s - s t r i a t i o n s i n muscle. Nature 172: 530-532. Hanson, J., and Huxley, H.E. 1955. The s t r u c t u r a l basis of contraction in s t r i a t e d muscle. Symp. Soc. Exp. B i o l . 9: 228-264. Hanson, J . , and Lowy, J . 1963. The structure of F-actin and of a c t i n filaments i s o l a t e d from muscle. J. Mol. B i o l . 6: 46-60. Harman, J.W. 1954. Contractions of s k e l e t a l muscle m y o f i b r i l s by phase microscopy. Fedn. Proc. 13: 430. Haselgrove, J.C. 1975. X-ray evidence for conformational changes i n the myosin filaments of vertebrate s t r i a t e d muscle. J. Mol. B i o l . 92: 113-143. Haselgrove, J . C , and Huxley, H.E. 1973. X-ray evidence for r a d i a l cross-bridge movement and for the s l i d i n g filament model i n a c t i v e l y contracting s k e l e t a l muscle. J . Mol. B i o l . 77: 549-568. Haselgrove, J . C , Stewart, M., and Huxley, H.E. 1976. Cross-bridge movement during muscle contraction. Nature 261: 606-608. - LOO -Hasselbach, W. 1953. Elektronenmikroskopische untersuchungen an M u s k e l f i b r i l l e n b e i t o t a l e r und p a r t i e l l e r extraktion des L-myosins. Z. Naturforsch 8b: 449-454. H i l l , A.V. 1922. The maximum work and mechanical e f f i c i e n c y of human muscles and t h e i r most economical speed. J. Physiol. 56: 19-41. H i l l , A.V. 1938. The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. B 126: 136-195. H i l l , A.V. 1950. Mechanics of the c o n t r a c t i l e element of muscle. Nature 166: 415-419. Huxley, A.F. 1957. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7: 255-318. Huxley, A.F. 1973. A note suggesting that the cross-bridge attachment during muscle contraction may take place i n two stages. Proc. Roy. Soc. B 183: 83-86. Huxley, A.F. 1974. Muscular contraction. J. Ph y s i o l . 243: 1-43. Huxley, A.F. 1980. Reflections on Muscle. Princeton University Press: Princeton, New Jersey. Huxley, A.F., and J u l i a n , F.J. 1964. Speed of unloaded shortening i n frog s t r i a t e d muscle f i b r e s . J. Physiol. 177: 60-61P. H u x l e y A . F . , and Niedergerke, R. 1954. Interference microscopy of l i v i n g muscle f i b r e s . Nature 173: 971-973. Huxley, A.F., and Peachey, L.D. 1961. The maximum length for contraction in vertebrate s t r i a t e d muscle. J. Physiol. 156: 150-165. Huxley, A.F., and Simmons, R.M. 1970a. A quick phase i n the s e r i e s - e l a s t i c component of s t r i a t e d muscle, demonstrated in i s o l a t e d f i b r e s from the frog. J . Physiol. 208: 52-53P. Huxley, A.F., and Simmons, R.M. 1970b. Rapid 'give' and the tension 'shoulder' i n the relaxation of frog muscle f i b r e s . J . Ph y s i o l . 210: 32-33P. Huxley, A.F., and Simmons, R.M. 1971a. Mechanical properties of cross-bridges of frog s t r i a t e d muscle. J. Physiol. 218: 60-61P. Huxley, A.F., and Simmons, R.M. 1971b. Proposed mechanism of force generation i n s t r i a t e d muscle. Nature 233: 533-538. Huxley, A.F., and Simmons, R.M. 1973. Mechanical transients and the o r i g i n of muscular force. Cold Spring Harbour Symp. Quant. B i o l . 37: 669-680. Huxley, H.E. 1952. X-ray analysis and the problem of muscle. Proc. Roy. Soc. B 141: 59-62. - 101 -Huxley, H.E. 1953. Electron microscopic studies on the organization of the filaments i n s t r i a t e d muscle. Biochem. Biophys. Acta 12: 387-394. Huxley, H.E. 1957. The double array of filaments i n c r o s s - s t r i a t e d muscle. J. Biophys. Biochem. Cytol. 3: 631-648. Huxley, H.E. 1964. St r u c t u r a l arrangements and the c o n t r a c t i l e mechanism in s t r i a t e d muscle. Proc. Roy. Soc. B 160: 442-448. Huxley, H.E. 1968. St r u c t u r a l differences between r e s t i n g and r i g o r muscle; evidence from i n t e n s i t y changes in the low angle equatorial X-ray diagram. J. Mol. B i o l . 37: 507-520. Huxley, H.E. 1969. The mechanism of muscular contraction. Science 164: 1356-1366. Huxley, H.E. 1979. Time resolved X-ray d i f f r a c t i o n studies on muscle. In Cross-bridge Mechanism i n Muscle Contraction. ed. Sugi, H. and Pollack, G.H. Uni v e r s i t y Park Press: Baltimore. Huxley, H.E., and Brown, W. 1967. The low-angle X-ray diagram of vertebrate s t r i a t e d muscle and i t s behaviour during contraction and r i g o r . J. Mol. B i o l . 30: 383-434. Huxley, H.E., and Hanson, J . 1954. Changes i n the c r o s s - s t r i a t i o n of muscle during contraction and stretch and t h e i r s t r u c t u r a l i n t e r p r e t a t i o n . Nature 173: 973-976. Iwazumi, T., and Pollack G.H. 1979. On-line measurement of sarcomere length from d i f f r a c t i o n patterns i n muscle. IEEE Trans. Biomed. Eng. 26: 86-93. Jewell, B.R., and Wilkie, D.R. 1958. An analysis of the mechanical components in frog's s t r i a t e d muscle. J. Physiol. 143: 515-540. J u l i a n , F.J., and Morgan, D.L. 1979. Intersarcomere dynamics during fixed-end tetanic contractions of frog muscle f i b r e s . J. P h y s i o l . 293: 365-378. J u l i a n , F.J., and Morgan, D.L. 1981a. Va r i a t i o n of muscle s t i f f n e s s with tension during tension transients and constant v e l o c i t y shortening i n the frog. J. Ph y s i o l . 319: 193-203. J u l i a n , F.J., and Morgan, D.L. 1981b. Tension, s t i f f n e s s , unloaded shortening speed and potentiation of frog muscle f i b r e s at sarcomere lengths below optimum. J . Physiol. 319: 205-217. Levin, A., and Wyman, J. 1927. The viscous e l a s t i c properties of muscle. Proc. Roy. Soc. B 101: 218-243. Mason, P., and Hasan, H. 1980. Muscle cross-bridge action i n e x c i t a t i o n and r e l a x a t i o n . Experientia 36: 949-950. - 102 -Matsubara, I., and E l l i o t t , G.F. 1972. X-ray d i f f r a c t i o n studies on skinned single f i b r e s of frog s k e l e t a l muscle. J . Mol. B i o l . 72: 657-669. Matsubara, I., and Yagi, N. 1978. A time-resolved X-ray d i f f r a c t i o n study of muscle during twitch. J. Physiol. 278: 297-307. Matsubara, I., Yagi, N., and Hashizume, H. 1975. Use of an X-ray t e l e v i s i o n for d i f f r a c t i o n of the frog s t r i a t e d muscle. Nature 255: 728-729. M i l l e r , A., and Tregear, R.T. 1972. The structure of insect f l i g h t muscle i n the presence and absence of ATP. J . Mol. B i o l . 70: 85-104. Moore, P.B., Huxley, H.E., and DeRosier, D.J. 1970. 3-D reconstruction of F-actin thin filaments and decorated thin filaments. J. Mol. B i o l . 50: 279-295. Natori, R. 1954. The property and contraction process of i s o l a t e d m y o f i b r i l s . J i k e i k a j i Med. J . 1: 119-126. Page, S.G., and Huxley, H.E. 1963. Filament lengths i n s t r i a t e d muscle. J. C e l l B i o l . 19: 369-390. Podolsky, R.J. 1960. K i n e t i c s of muscular contraction : the approach to the steady state. Nature 188: 666-668. Podolsky, R.J. 1964. The maximum sarcomere length for contraction of is o l a t e d m y o f i b r i l s . J. Physiol. 170: 110-123. Ramsey, R.W.,,and Street, S.F. 1940. The isometric length-tension diagram of i s o l a t e d s k e l e t a l muscle f i b r e s of the frog. J . C e l l Comp. Phy s i o l . 15: 11-34. Rapoport, S.I. 1972. Mechanical properties of the sarcolemma and myoplasm i n frog muscle as a function of sarcomere length. J. Gen Phys i o l . 59: 559-585. Reedy, M.K. 1967. Cross-bridges and periods i n insect f l i g h t muscle. Am. Zool. 7: 465-481. Reedy, M.K., Holmes, K.C., and Tregear, R.T. 1965. Induced changes i n ori e n t a t i o n of the cross-bridges of glycerinated insect f l i g h t muscle. Nature 207: 1276-1280. Ridgway, E.B., and Gordon, A.M. 1984. Muscle calcium transient - e f f e c t of post-stimulus length changes i n single f i b e r s . J . Gen. Physiol. 83: 75-103. Rudel, R., and Taylor, S.R. 1971. St r i a t e d muscle f i b r e s : f a c i l i t a t i o n of contraction at short lengths by ca f f e i n e . Science 172: 387-388. - 103 -Shoenberg, M., and Wells, J.B. 1984. S t i f f n e s s , force, and sarcomere shortening during a twitch in frog semitendinosus muscle bundles Biophys. J. 45: 389-397. Simmons, R.M., and Jewell, B.R. 1974. Mechanics and models of muscular contraction. In Recent Advances in Physiology. ed. Linden, R.J C h u r c h i l l - L i v i n g s t o n : Edinburgh. Squire, J . 1981. The S t r u c t u r a l Basis of Muscular Contraction. Plenum Press: New York. Stein, R.B., and Parmiggiani, F. 1979. The s t i f f n e s s of slow-twitch muscle lags behind twitch tension : implications for c o n t r a c t u mechanisms and behavior. Can. J . Physiol. Pharmacol. 57: 1189-1192. Straub, F.B. 1943. A c t i n . Stud. Inst. Med. Chem. Univ. Szeged. 2: 3-15. Taylor, S.R., and Rudel, R. 1970. S t r i a t e d muscle f i b r e s : i n a c t i v a t i o n of contraction induced by shortening. Science 167: 882-884. Vaughan, P.C., Bressler, B.H., Dusik, L.A., and T r o t t e r , M.J. 1983. Hypertonicity and force development in frog s k e l e t a l muscle f i b r e s Can. J . P h y s i o l . Pharmacol. 61: 847-856. Vibe r t , P.J., Haselgrove, J . C , Lowy, J., and Poulsen, F.R. 1972. Structural changes in actin-containing filaments of muscle. J . Mol B i o l . 71: 757-767. Weber, E. 1846. Muskeibewegung. Handwortenbuch der Physiol, p . l . Yagi, N., Ito, M.H., Nakajima, H., Izumi, T., and Matsubara, I. 1977. Return of myosin heads to thick filaments a f t e r muscle contraction Science 197: 685-687. Young, D.M. 1967. Studies on the s t r u c t u r a l basis of the i n t e r a c t i o n between myosin and a c t i n . Proc. Natl. Acad. S c i . USA. 58 2393-2400. 

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