Force-velocity Relation and Contractility in Striated Muscles

Transcription

1 Japanese Journal of Physiology, 34,1-17, 1984 MINIRE VIEW Force-velocity Relation and Contractility in Striated Muscles Hidenobu MASHIMA Department of Physiology, School of Medicine, Juntendo University, Bunkyo-ku, Tokyo, 113 Japan This review deals with the contractility of striated muscles as made evident in the force and the shortening velocities in various contractions. The contractility, that is, the capability of contraction, can be expressed using two parameters. One is the maximum tension during isometric contraction and the other, the maximum shortening velocity during isotonic contraction under zero load. Shortening velocity is a function of load, which is equal to the muscle tension during isotonic contraction, and the maximum tension, Tm, can be obtained from the full isometric tetanic contraction at the optimal muscle length, Lm. Therefore, the most important way of ascertaining contractility is to determine the relation between tension and velocity, i.e., the force-velocity relation, at the initial length of Lm. Figure 1 is a three-dimensional illustration of contractility, in which force-velocity curves (a, b, and c) are depicted on the T -v plane and a tension-length curve (dl, descending limb; d2, ascending limb) is on the T -L plane. The curve a is a typical force-velocity curve obtained at Lm where the isometric tension, Tm, is true maximum tension, and the shortening velocity under zero load, vm, is true maximum velocity. In the curve b the isometric tension, Tb, is smaller than Tm, because the muscle is not fully but partially activated. In the curve c, the muscle is fully activated, but the isometric tension, To, is also smaller than Tm, because the initial length, Lo, is different from Lm. Whether the maximum shortening velocities obtained under various conditions, such as represented by curves b and c, are equal or not and the nature of the theoretical explanation of the force-velocity curve from the viewpoint of the recently constructed crossbridge model are the main concerns of this review. A. FORCE-VELOCITY RELATION OF SKELETAL MUSCLES 1. Hill's characteristic equation The force-velocity relation of skeletal muscle at Lm was described by HILL [22] for the isotonic shortening of the frog sartorius muscle in terms of a simple hyperbolic "characteristic equation," (T+a)(v+b)=b(Tm+a)=const., (1) where T is the load equal to the tension during isotonic shortening, v is the shorten- 1

2 2 H. MASHIMA V Fig. 1. Three-dimensional illustration of contractility L, muscle length; T, developed tension; v, shortening velocity; Lm, optimal length; Lo, initial length other than Lm; Tm, maximum tension at Lm; Tb, partially activated tension at Lm; To, maximum tension at Lo; vm, maximum velocity at Lm; v0, maximum velocity at L0. a, b, c, force-velocity curves at Tm, Tb, To, respectively; dl (descending limb), d2 (ascending limb), tensionlength curve; e1, e2, maximum velocity-length curve. ing velocity, Tm is the maximum isometric tension, and a and b are the dynamic constants. According to Hill, if T(g) is the load lifted and x (cm) is the shortening distance, shortening heat is ax (g. cm). The shortening heat appeared as if it were derived from the work done against a viscous resistance of a(g). Thus the total energy liberation, in excess of isometric contraction, is (Ta)x. The rate of extra energy liberation, therefore, is (T+a)dx/dt, or (T+a)v. Hill confirmed experimentally that (T+a)v was a linear function of (Tm-T ). Thus the equation (T+a)v=b(Tm-T) (2) was introduced, where b is a constant defining the rate of energy liberation. Equation (1) can be obtained from Eq. (2). Substituting T=0 in these equations, we obtain the maximum velocity under no load, vm=btm/a. Since Hill's equation was confirmed as being able to be fitted with not more than a few per cent error to high precision force-velocity data from tetanized skeletal muscle [29], it has been widely used to describe the force-velocity behavior of contracting muscles, not only of skeletal muscles but also of cardiac muscles, although some investigators pointed out that in some muscles the data depart from a hyperbola in the high-force region of the curve [14]. Japanese Journal of Physiology

3 FORCE-VELOCITY RELATION OF MUSCLE 3 2. Factors affecting the force-velocity relation a) Active state. Since the studies of HILL [22] and WILKIE [58], it has been generally accepted in the field of muscle mechanics that the skeletal muscle contains an active contractile component (CC) capable of generating tension in series with a noncontractile series elastic component (SEC), as shown in Fig. 2 (a). The CC of stimulated muscle is brought into an "active state," which was defined by HILL [23] as the tension developed when the CC was neither lengthening nor shortening. Making quick stretches at various instances after stimulus, HILL [23] measured a resistance to stretch and demonstrated an abrupt development of the active state in the frog sartorius muscle. It was subsequently believed for a long time that the muscle enters the fully active state immediately after a stimulus. However, it has become evident that it takes some time until the active state reaches its full extent. BAHLER et al. [5] defined the active state as a force-generating capability of the CC and determined the whole course of the active state during isometric twitch and found that the active state did not reach maximum a value but only 92% of it at 17.5 C, in rat gracilis anticus muscle. MASHIMA et al. [38] also determined the time-course of the active state by both analytical and experimental methods in frog semitendinosus muscle and comfirmed that the active state never reached its full extent in a single twitch but only 70-80% of it at 15 C and that two or three stimuli were necessary for the active state to fully develop and form a plateau. b) Method of velocity measurement. From the above evidence, it is obvious that the shortening velocity measured in the early part of the contraction must be underestimated because of the immaturity of the active state. When velocity is measured by the afterload method, the muscle begins to shorten with a short Fig. 2. (a) Two-component model, (b) sliding filament model, (c) cross-bridge model and mechanical equivalent. A, thin filament; M, thick filament; CC, contractile component; SEC, series elastic component; f, force; fq, viscous force-loss; e, elastic part of a single cross-bridge. Vol. 34, No. 1, 1984

4 4 H. MASHIMA latency under a small load, although it does so after a longer delay from a stimulus under a large load. Therefore, the force-velocity data determined by the afterload method may be underestimated as the load becomes smaller. In order to avoid this disadvantage, the quick release method has been widely adopted, in which the muscle begins to shorten under any load at the same instant of the active state being present. To minimize the oscillatory movement of the lever at the instant of quick release, various techniques such as controlled or damped quick release were devised [29, 37, 43]. Another important factor is the linearity of the shortening curve. The shortening curve is linear only in the early part of the contraction, even if the active state has reached the plateau. Supposing the velocity is decreasing, the length of the SEC must be decreasing by negative acceleration. As the measured velocity is a sum of the velocities of CC and SEC, this does not mean the velocity of the CC, as far as the shortening curve i s not linear. c) Mode of stimulation. For electrical stimulation, clamps at both ends of the muscle are often used as stimulating electrodes. In this case, the action potential generated at the cathodal end propagates to the other end. Taking the propagation velocity as 4 m/sec and the muscle length as 4 cm, it takes 10 msec before the whole muscle is activated. Therefore, this type of stimulation is not adequate for measuring shortening velocity of the muscle. To minimize the propagation problem, HILL [22] used a multielectrode assembly or grid stimulation, that is, several platinum wire electrodes are embedded in the surface of the insulator plate at 2 mm intervals, cathodes and anodes alternatively. Although the propagation distance decreases to 2 mm by use of this device, some tensionloss due to friction must occur, because the muscle contacts the electrodes. Transverse field stimulation by massive electrodes is free from both propagation and friction problems. A pair of platinum foil electrodes are placed at both sides of the muscle in the solution bath [14, 37]. The muscle is away from the surface of the electrode and stimulated by electric current field between both electrodes. According to MASHIMA et al. [37], long lasting tetanus-like contraction was achieved in muscle rendered inexcitable by excess potassium (10-12 mm). By applying Hz AC transverse field stimulation, the strength of this tetanuslike contraction was increased with increasing field intensity. The change in membrane potential in the inexcitable muscle under AC stimulation was also observed and it was confirmed that the amount of depolarization increased with an increase in the field intensity [40]. Thus it became possible to obtain partially activated tetani of various intensities by using AC field stimulation in the excess potassium solution. Furthermore, no difference was observed between the forcevelocity curves obtained with normal tetanus and tetanus-like contraction evoked by a field stimulation [14]. Japanese Journal of Physiology

5 FORCE-VELOCITY RELATION OF MUSCLE 5 3. Sliding filament theory of contraction Since about 1953, the sliding filament concept has been evolved independently and more or less simultaneously by H. E. HUXLEY's electron microscopic and X-ray diffraction studies [27, 28] and A. F. HUXLEY's physiological studies [18, 25, 26]. It is now widely accepted as a result of the evidence that has accumulated since that time. According to this theory, the force of contraction is developed by the cross-bridges in the overlap of thick and thin filaments and active shortening is caused by movement of the cross-bridges, which causes one filament to slide along the other. The half sarcomere is a structural unit of the striated muscle fiber and the number of cross-bridges was estimated as 0.55 x 1013/cm2 for half sarcomere [28]. It was confirmed that the contractile force was proportional to the length of overlap region as shown in Fig. 3, curve 1, that is, the number of cross-bridges participating in the sliding motion, and that the shortening velocity under no load, v0, was independent of the length of overlap region or muscle length (i.e., vo=vm), at least at the descending limb of the tension-length diagram [18] (see Fig. 1, curve d1 and e1). Now, the CC is considered to reside in the overlap region as illustrated in Fig. 2 (b). As for the SEC, HUXLEY and SIMMONs [26] suggested from the results of high-speed quick-release experiments that nearly all SEC resided in the crossbridges as illustrated in Fig. 2 (c), e. SUGI [54] indicated, however, that the SEC may largely originate from some structures in each sarcomere other than the crossbridges. After all, these elasticities can be summarized as SEC in Fig. 2(b). According to HUXLEY [25], the force-velocity relation can be expressed by the following equation, JQII.uIIICIC ICll~lll l/uiiij Fig. 3. Tension-length curves for various muscles. 1, skeletal muscle; 2, skeletal muscle (final creep tension); 3, cardiac muscle (twitch); 4, cardiac muscle (tetanus); 5, cardiac muscle (maximally activated skinned fiber). In the descending limb, a length change means a change in the overlap length between A and M, but in the ascending limb it does not (see top figures). A, thin filament; M, thick filament. Vol. 34. No

6 6 H. MASHIMA T=C1 1_ Cv (1_e-c2/v)(l+C3v), (3) 2 where C1, C2, and C3 are the constants including the rate constants of a crossbridge, f and g, for the reactions which attach and detach the connecting links between the sites of thick and thin filaments. At first sight, Eq. (3) is very different from Hill's equation (1), but the deviation of T -v plots of Eq. (3) from hyperbola was not much greater than the experimental error of the observations on which Hill based his relationships [25]. 4. Generalization of Hill's equation Hill's equation (1) is formed only under the condition that the isometric tension is Tm. But the isometric tension is a function of muscle length and activation, as shown in Fig. l (To and Tb). As for the effect of activation, JEWELL and WILKIE [30] examined the force-velocity curves at various times after a single shock in frog sartorius muscle and pointed out that all curves could have been fitted by Hill's equation. Recently, similar results were obtained in frog single muscle fiber [4, 8], Fig. 4. Force-velocity curves obtained at various contractile forces at Lm in frog semitendinosus muscle. Filled circle, determined by isotonic shortening; open circle, determined by isotonic lengthening; triangle, determined by isovelocity stretching; 10 C [37]. Japanese Journal of Physiology

7 FORCE-VELOCITY RELATION OF MUSCLE 7 and it was suggested that the force-velocity relation represented the level of activation at any time during isometric contraction [8]. MASHIMA et al. [37] determined the force-velocity curves for the partially activated tetani of various intensities under the same initial length as seen in Fig. 4 (curves 1-6), and found that all curves determined at the isometric tension, Tb (Tb <_ Tm), were fitted by Hill's equation. Thus, Hill's equation (1) was generalized to all isometric tensions under the same initial length. A new equation was formulated as follows : or (T+ka)(v+b)=b(Tb+ka), (4) (T+ka)v=b(Tb-T), (5) where k= Tb/Tm, a and b are the dynamic constants at Tm. Comparing Eq. (1) and Eq. (4), it is obvious that b does not alter but a alters to ka. Only when Tb= Tm, does Eq. (4) become Eq. (1). The maximum velocity under no load becomes btb/ka=btm/a=vm, which is apparently independent of Tb. Equation (4) can be rewritten as follows : Fo=(Tb-T )= T b (Tm+a) vb. (6) m v~ F9 is the difference between isometric force before movement and isotonic force during movement, that is, a viscous-like force-loss induced by a movement at the velocity v. Equation (6) shows that this force-loss is not only a function of velocity but also is proportional to the isometric tension, Tb. Supposing each cross-bridge has a proper force, f, and viscous force-loss which is a function of velocity, fo(v), as shown in Fig. 2(c), and N is the number of active cross-bridges, then the total force becomes Nf (=Tb) and the total force-loss becomes Nfo (=Fo). That is why Fo is proportional to Tb. Both are in proportion to the number of participating cross-bridges. The velocity of isotonic lengthening induced by loads larger than the isometric tension was also determined [37]. The lengthening velocity, -v, was plotted against the load as shown in Fig. 4 (curves 7-16). These curves were also hyperbolic and formulated as follows : (T-2Tb-ka')(v-b')=b'(Tb+ka'), (7) where k=tb/tm, a' and b' are the dynamic constants in lengthening. The effect of length on the force-velocity relation was also examined when the initial length, Lo, was between Lm, and it was confirmed that all curves satisfied the following equation, (T+ka)(v+b)=b(T0+ka), (8) where k=to/tm, To is the isometric tension at Lo (see Fig. 1, curve c). Comparing Eq. (8) with Eq. (1), it is obvious that the constant a alters to ka when the length Vol. 34, No. 1, 1984

8 8 H. MASHIMA is altered from Lm to L, and the maximum velocity under no load, v, is equal to vm within this range of muscle length. EDMAN [13] also demonstrated that vo was constant at a sarcomere length between um but that it decreased below 1.65,um. 5. Modeling of the muscular contraction Although many kinetic models have been developed in order to explain gross filament sliding from local molecular events, few of them have dealt with the molecular mechanism of Hill's characteristic equation [1, 11]. In particular, AKAZAWA's model [1] successfully explains not only Hill's constants in the steadystate contraction but also the dynamic and energetic properties of isometric and isotonic twitches. Four states (except for the resting state) were considered in the cross-bridge cycle: state 1) is an activation phase of a site on the thin filament through the binding of Ca ion to troponin, state 2) is a force-generating phase by the action of the cross-bridge attached to the thin filament, state 3) is a sliding phase by movement of the cross-bridge, and state 4) is a detachment phase of the cross-bridge. The rate constants of transfer between these states are Kl (state 1-~2), K2 (state 2--3), K3 (state 3-~4), and K4 (state 4--~ 1). It was assumed that K2=a +a1v, where v is the sliding velocity and a and al are constants. Thus, the kinetic equations connecting these states were obtained, and under steady state conditions the following force-velocity equation was introduced, ~'~ N~K v= K+a NfK -T, (9) al al K--a where N is the number of active cross-bridges at a tension of Tb, f and fo are the force and the viscous-like force of each cross-bridge, respectively, js is the viscosity constant of a cross-bridge (fo=j9v), and 1/K=1/Kl+l/K3+1/K4. Comparing Eq. (9) with Eq. (5), we obtain a- NmI9K, b= K+ao, and Tm= Nmf K (10) al al K--a0 where Nm is the value of N at Tm (Tb/Tm-N/Nm=k). These Eqs. (10) describe the interrelations between Hill's constants and the constants of kinetic analysis based on the cross-bridge model. B. FORCE-VELOCITY RELATION OF CARDIAC MUSCLES 1. Difficulties arising in velocity measurement Some difficulties arise in velocity measurement of cardiac muscle. Firstly, cardiac muscle contraction is always a twitch and no steady state can be observed. Secondly, the rate of rise of tension is much slower than that of skeletal muscle. As pointed out in the previous section (A-Z), linear shortening can hardly occur during a twitch. Thus the measured velocity may differ from true velocity Japanese Journal of Physiology

9 FORCE-VELOCITY RELATION OF MUSCLE 9 of the CC. The slow rate of rise of contraction means a slow onset of the active state. At room temperature (23 C) the active state in mammalian cardiac muscle reaches its peak about msec from the time of stimulation, and declines by % before isometric tension reaches its peak without showing a plateau [51]. This fact means that most velocities measured by the afterload method will be underestimated. Thirdly, the twitch tension can be dramatically augmented in cardiac muscle by such inotropic factors as stimulus rate, temperature, external sodium or calcium ion concentration, and humoral agents. Under these inotropic conditions, both the peak of the active state and the time to peak active state will largely alter. Thus it is difficult to constantly measure the velocity at the peak of the active state, even if the quick release method is adopted. Fourthly, fairly large internal shortening of the CC has been pointed out for cardiac muscle [50]. Furthermore, owing to the lack of a tendon at one or both ends of the preparation, clamps used may damage the tissue. After all, estimated elongation of the SEC is more than 10 of the muscle length during isometric contraction, while it is less than 2 % in skeletal muscle [29]. If the CC shortens by 10%, the tension would reduce by 30-50%. This is why most tension-length curves for isolated cardiac muscle have a steep ascending limb [12] (see Fig. 3, curve 3). Fifthly, relatively high resting tension of cardiac muscle at Lm disturbs velocity measurement. A correction must be made by subtracting the resting tension at the instant of velocity measurement. Paying attention to these difficulties, the force-velocity curves were determined for the twitches in mammalian papillary muscle [15, 43, 44, 49] and even in isolated single cells from rat ventricle [l0]. Most of them were hyperbolic and true hyperbolic shape was obtained by the damped release technique [15], although some of them were rather curvilinear, especially when the afterload method was adopted [44] or in the single cell preparation [l0]. SONNENBLICK [49] suggested that the maximum velocity, v0, is independent of muscle length. BRUTSAERT et al. [7] also confirmed using load clamp technique that vo was constant between Lm in cat papillary muscle. NILssoN [43], however, found that vo as well as To decreased with decreasing muscle length, so that v0/t0 was almost independent of length. 2. Force-velocity relation of tetanized cardiac muscle If we could tetanize, cardiac muscle, most technical and theoretical difficulties should be eliminable. The first attempt to tetanize cardiac muscle was made by HENDERSON et al. [20] in rat papillary muscle. A train of electrical pulses at Hz was applied in the presence of mm external calcium and a low tetanic tension was obtained. FORMAN et al. [17] effected repetitive electrical pulses at 10 Hz in cat papillary muscle and found that smooth tetanus was obtained in the presence of both 10 mm caffeine and 10 mm calcium. Vol. 34, No. 1, 1984 In contrast with mammalian

10 10 H. MASHIMA muscle, frog ventricular muscle was easily tetanized without caffeine by AC transverse field stimulation at 10 Hz and 20 V/cm in the presence of 9 mm external calcium [35]. The tension of tetanus-like contraction thus obtained was double or more the maximum twitch tension and identical steady tension curves were obtained repeatedly for hours, although twitch tensions declined rather quickly. Barium-induced contracture was also used to obtain steady contraction in cardiac muscle [48] but it is difficult to repeat contraction and relaxation cycles in order to measure the isotonic shortening velocities at various loads. The force-velocity curves of tetanized cat papillary muscles were fitted by Hill's hyperbola and both the extrapolated maximum velocity, v0, and isometric tension, To, declined with decreasing muscle lengths between Lm [17]. In the tetanized frog ventricular muscle, the force-velocity curves were determined by the controlled quick release method, paying attention to minimizing internal shortening [35, 36]. MASHIMA [36] confirmed that the force-velocity curves obtained at initial lengths between Lm were fitted by Eq. (8) and vo=vm. Thus most force-velocity data were obtained at 0.9L, where the resting tension is very small. As a result, it was evident that all the Eqs. (4), (5), and (6) held in cardiac muscle at OLm and at mm external calcium concentration. That is, the maximum velocity, vm, does not alter regardless of the degree of activation. At muscle lengths shorter than 0.9Lm, however, the maximum velocity, v0, at length Lo, was decreased, as if some internal load had been added (see curve e2 in Fig. 1). The internal load which is defined as the difference between the external load and calculated load from Eq. (4) was in proportion to both the velocity of shortening and the decrease in muscle length [36]. 3. The maximum shortening velocity as an index of myocardial contractility SONNENBLICK [49, 50] suggested that the parameter of velocity as well as force must be stressed in describing the activity of cardiac muscle, because force and velocity may be altered independently. The Frank-Starling effect expressed by the tension-length relation was explained by a variation in the number of crossbridges formed between thick and thin myofilaments [18], while the inotropic response was considered to be a change in the rate of interaction of each crossbridge. As for the assessment of the contractile state of the ventricle, some hemodynamic variables such as cardiac output, stroke volume, intraventricular pressure, P, and dp/dt, etc., used to be measured. These variables, however, are easily affected by preload (resting muscle length) and afterload (muscle tension) during ejection, and therefore are not necessarily independent expressions of the inotropic state of cardiac muscle. The contractile state of the heart must be quantified in terms of ventricular muscle mechanics. MASON et al. [41] developed the method of measuring instantaneous velocity of the CC of wall muscle, vcc, in human ventricle by the following equation, assuming an ellipsoid for the shape of the ventricle, Japanese Journal of Physiology

11 FORCE-VELOCITY RELATION OF MUSCLE 11 vc0=(dp/dt)/kp, (11) where P is the isovolumic ventricular pressure. When K is 32, v0c is expressed in muscle length per second. The maximum velocity, vo (or Vmax), was approximated from a linear extrapolation of P-vCC plots to zero pressure, although the pressure-velocity curve was a slight hyperbola. As a result, increasing contractility on exercise raised vo from 1.19 to 1.58, but elevations of left ventricular enddiastolic or aortic diastolic pressure levels did not increase v0. Since vo is expressed in terms of muscle units and is free of variables of left ventricular loading and wall thickness, vo was considered to be a specific index of the inotropic state, which is sensitive to inotropic effects but insensitive to the length effect. As already described above, however, vo in tetanized cardiac muscle decreased with length in the range shorter than 0.9Lm (see Fig. 1, curve e2) [17, 36]. As the working range of cardiac muscle is in the ascending limb of the tension-length curve, vo must be length-dependent at these short muscle lengths. Anyhow, Mason's method was developed for clinical use, and thus precise determination of vo was difficult. 4. Length-dependency of the force and velocity in the ascending limb of the tensionlength curve Contrary to the traditional concept that the length and inotropic effects on myocardial contractility can be separated from one another, subsequent studies have suggested that the increase in force and velocity along the ascending limb of the tension-length curve is due not so much to an increase in myofilament overlap as to a length-dependent alteration in the amount of calcium activating the crossbridges [2, 16, 21, 31, 34]. As for the effect of internal calcium concentration on v0, PoDOLSKY and TEICHHOLZ [46] reported in the mechanically skinned fiber of frog skeletal muscle that the relative force-velocity relation was independent in the pca range between and that calcium does not influence v0. However, JULIAN and Moss [32] found in skinned fiber that vo was significantly influenced by calcium concentration, decreasing by about one half when the calcium concentration was reduced to give a steady tension of less than half-maximal. Although precise velocity measurements under small loads in these preparations are very difficult, these results suggest the possibility that calcium modifies not only the number of active cross-bridges but also the degree of activation in each cross-bridge. This suggestion is particularly important in the ascending limb of the curve representing the tension-length relation for cardiac muscle, where a decrease in tension with decreasing length cannot be explained by a decrease in overlap length. JEWELL and his coworkers [2, 21, 31] demonstrated evidence that the sensitivity of the contractile system to calcium increased with sarcomere length over the ascending limb of the tension-length relation curve. For example, in Fig. 3, curves 3-5 illustrate the cardiac tension-length relations at various activation levels. Curve Vol. 34, No. 1, 1984

12 12 H. MASHIMA 1 is a control curve of frog skeletal muscle determined by GORDON et al. [18]. Curve 3 is a traditional tension-length curve for cat papillary muscle [52] and curve 4 was obtained for tetanized frog ventricular muscle in high-calcium solution [35]. Curve 5 was obtained for skinned rat ventricular muscle under conditions of maximal activation [16]. As the degree of activation becomes higher, the maximum tension generated at a certain length becomes larger. Then it can be said that as long as calcium ion levels have not become fully saturated, higher calcium concentration or inotropic action may possibly activate interactions between regulatory and contractile proteins. C. NEW APPROACHES 1. Studies on sarcomere dynamics using the laser diffraction method Since the application of laser diffraction technique to the study of intact skeletal muscle fibers, it has been possible to measure sarcomere length changes of living cells with a resolution of 5 nm. With such resolution, the non-uniformity of sarcomeres during isometric contraction [9] and the stepwise shortening during isotonic contraction [47] have been pointed out. TER KEURS et al. [55] once argued that the descending limb of the tension-length curve for skeletal muscle should be like curve 2 in Fig. 3 rather than curve 1, when final tetanic tensions are measured. However, these large tensions can now be explained in relation to the non-uniform sarcomere lengths at the final creep state of tetanus. This technique was also applied to cardiac muscle. GORDON and POLLACK [19] measured the effect of calcium on the sarcomere length-tension curve in thin trabeculae from rat right ventricle and confirmed that the height of the curve was progressively depressed as extracellular calcium levels were reduced from 2.5 to 0.3 mm (similarly to curves 5 to 3 in Fig. 3). TER KEURS and WoHLFART [56] measured sarcomere shortening velocity by means of the isovelocity release technique. The force-velocity relation was hyperbolic and vo was not altered at external calcium concentration higher than 1.2 mm but it was decreased at below this concentration. KRUEGER and his coworkers [33, 34] found that in single unattached cardiac muscle cells enzymatically isolated from the ventricular tissue of adult rats, sarcomere length was 1.93 µm in unstimulated cells and 1.57,um at peak shortening and that the maximum velocity of sarcomere shortening was comparable to that observed in intact heart muscle preparations. They further developed the sarcomere length clamp technique and observed that the clamped sarcomeres generated larger and prolonged tension, suggesting the direct effect of sarcomere length on the activation of myofilaments. The sarcomere forcevelocity curves determined by the length clamp technique were hyperbolic in the shortening range but were dissociated from the hyperbola in the lengthening range [57]. Japanese Journal of Physiology

13 FORCE-VELOCITY RELATION OF MUSCLE Calcium transient during contraction The calcium-sensitive bioluminescent protein aequorin [6] or the metallochromic calcium indicator arsenazo III [42] has been used to detect the release and resequestration of calcium ions in the early phase of contraction. ALLEN and KURIHARA [3] injected aequorin into cells of rat and cat ventricular muscles and found that after an increase in muscle length the tension immediately increased but that the aequorin signal was initially unchanged and showed a slow increase. This fact suggests that the aequorin signal does not show the calcium concentration in the adjacent milieu of the myofilaments. Actually, the time-course of calcium concentration change near the myofilament calculated by MASHIMA and KASASAWA [39] using the revised model of cardiac muscle contraction showed some time delay and a slow falling phase, as compared with the aequorin signal. Recently, HoUSMANS et al. [24] demonstrated in cat papillary muscle that the aequorin signal was prlonged by shortening. Attention must be paid to the possibility that shortening velocity may be fed back to the activation process in the determination of the sarcomere force-velocity relation. 3. Interrelation between the pressure-velocity relation of the ventricle and the forcevelocity relation of wall muscle Although many studies have been made on cardiac muscle mechanics and on ventricular performance, few attempts have been made to elucidate the interrelation between both frameworks. Recently, SUGA and SAGAWA [53] developed a technique of direct measurement of the lumen volume of the isolated dog ventricle by an intraventricular balloon method. Adapting this method to isolated rabbit ventricle, OKUYAMA [45] determined the relation between intraventricular pressure, P, and ejection velocity, V, and introduced the following equation, (P+A)(V +B)=B(P0+A), (12) where A and B are dynamic constants of the ventricle, Po is the maximum systolic pressure and V=dV/dt, V is the ventricular volume. Using the thick-walled spherical ventricular model and comparing Eq. (12) with Eq. (8) of the wall muscle, the following equations were obtained, ka=cpa, b=cob, TO=CpP0, (13) Cp=(V/Vw)[1~4/{1~CI~Vw/~)-1~3}3] C9=(6/2/3[(V+ w V)-2'3+ V-2/3], (14) T where V. is the volume of wall muscle. From these equations Hill's constants ka and b can be calculated from the ventricular constants A and B. It was shown that the ratio v0/t0 (=CVB/CpA) was insensitive to the ventricular volume or muscle length and sensitive to ventricular performance. These studies will offer a way to analyze ventricular performance on the basis of cardiac muscle mechanics. Vol. 34, No. 1, 1984

14 14 H. MASHIMA SUMMARY For skeletal muscle, the physiological meaning of Hill's hyperbolic forcevelocity equation and the factors affecting it, such as the active state, method of velocity measurement and mode of stimulation, have been discussed. After the development of the sliding filament theory, Hill's equation was generalized to all partially activated isometric tensions and the meaning of Hill's dynamic constants was interpreted from the kinetic analysis of the cross-bridge cycle. In cardiac muscle, determination of the precise force-velocity relation was almost impossible, but most difficulties were overcome by tetanizing the cardiac muscle. As a result, the force-velocity properties of cardiac muscle were confirmed to be very similar to those of skeletal muscle. The maximum shortening velocity under no load, v0, was once used as an index of myocardial contractility which is insensitive to muscle length, but it is now believed that at least at shorter lengths, vo may vary with muscle length and degree of activation. As new approaches, studies on sarcomere dynamics by the laser diffraction method, observation of calcium transient and pressure-velocity measurement in whole ventricle have been introduced. Key Words: force-velocity relation, muscle force, (Vma$), contractility, cross-bridge cycle. maximum shortening velocity REFERENCES 1. AKAZAWA, K., YAMAMOTO, M., FUJII, K., and MASHIMA, H. (1976) A mechanochemical model for the steady and transient contractions of the skeletal muscle. Jpn. J. Physiol., 26: ALLEN, D. G., JEWELL, B. R., and MURRAY, J. W. (1974) The contribution of activation processes to the length-tension relation of cardiac muscle. Nature, 248: ALLEN, D. G. and KURIHARA, S. (1982) The effects of muscle length on intracellular calcium transients in mammalian cardiac muscle. J. Physiol. (Lond.), 327: AMBROGI-LORENZINI, C., COLOMO, F., and LOMBARDI, V. (1983) Development of forcevelocity relation, stiffness and isometric tension in frog single muscle fibres. J. Musc. Res. Cell Motility, 4: BAHLER, A. S., FALES, J. T., and ZIERLER, K. L. (1967) The active state of mammalian skeletal muscle. J. Gen. Physiol., 50: BLINKS, J. R. (1973) Calcium transients in striated muscle cells. Eur. J. Cardiol.,1: BRUTSAERT, D. L., CLAES, V. A., and SONNENBLICK, E. H. (1971) Effects of abrupt load alterations on force-velocity-length and time relations during isotonic contractions of heart muscle: Load clamping. J. Physiol. (Loud.), 216: CECCHI, G., CoLoMo, F., LOMBARDI, V., and PIAZZESI, G. (1979) Development of activation and rise of tension in an isometric tetanus. Pflugers Arch., 381: CLEWORTH, D. R. and EDMAN, K. A. P. (1972) Changes in sarcomere length during isometric tension development in frog skeletal muscle. J. Physiol. (Loud.), 227: DE CLERCK, N. M., CLAES, V. A., and BRUTSAERT, D. L. (1977) Force velocity relations of single cardiac muscle cells. J. Gen. Physiol., 69: Japanese Journal of Physiology

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17 FORCE-VELOCITY RELATION OF MUSCLE 17 maximal velocity of sarcomere shortening in rat trabeculae. J. Physiol. (Loud.), 330: 41 P. 57. Tsu7IOKA, K., KRUEGER, J. W., and SONNENSLICK, F. H. (1983) Contraction and relaxation dynamics of cardiac sarcomere observed by laser diffraction method. Jpn. J. Med. Electron. Biol. Eng., 21: WILKIE, D. R. (1950) The relation between force and velocity in human muscle. J. Physiol. (Lond.),110: Vol. 34, No. 1, 1984