Tension generation by threads of contractile proteins

Threads of contractile proteins were formed via extrusion and their isometric tensions and isotonic contraction velocities were measured. We obtained reproducible data by using a new and sensitive tensiometer. The force-velocity curves of actomyosin threads were similar to those of muscle, with isometric tensions of the order of 10g/cm2 and maximum contraction velocites of the order of 10(-2) lengths/s. The data could be fitted by Hill's equation. Addition of tropomyosin and troponin to the threads increased isometric tension and maximum contraction velocity. Threads which contained troponin and tropomyosin required Ca++ for contraction and the dependence of their isometric tension on the level of free Ca++ was like that of muscle. The dependence of tension or of contraction velocity upon temperature or upon ionic strength is similar for actomyosin threads and muscle fibers. In contrast, the dependence of most parameters which are characteristic of the actomyosin interaction in solution (or suspension) upon these variables is not similar to the dependence of the muscle fiber parameters. The conclusion we have drawn from these results is that the mechanism of tension generation in the threads is similar to the mechanism that exists in muscle. Because the protein composition of the thread system can be manipulated readily and because the tensions and velocities of the threads can be related directly to the physiological parameters of muscle fibers, the threads provide a powerful method for studying contractile proteins.     

Model of muscle-tendon interaction during frog semitendinosis fixed-end contractions.

A structural model was developed to explain sarcomere shortening at the expense of tendon lengthening in the frog semitendinosis (ST) muscle-tendon system. The model was based on the data of Lieber et al. [Am. J. Physiol. 261, C86-C92 (1991)], who determined the relationship between the sarcomere length, tendon load (as a fraction of maximum isometric tension) and tendon, bone-tendon junction (BTJ), and aponeurosis strain. The model was generated assuming a finite time-course of cross-bridge attachment [Huxley, Prog. Biophys. 7,255-318 (1957)], an ideal sarcomere length-tension relationship [Gordon et al., J. Physiol. 184, 170-192 (1966)] and an ideal force-velocity relationship [Katz, J. Physiol. 96, 45-64 (1939); Edman, J. Physiol. 291, 143-159 (1979)]. Functionally, sarcomeres operated on three distinct regions of the length-tension curve: (1) regions where the muscle force decreased as sarcomeres shortened (the shallow and steep ascending limbs); (2) regions where the muscle force increased as sarcomeres shortened and there was little passive tension (descending limb, where sarcomere length greater than or equal to 3.0 microns); and (3) regions where the muscle force increased as sarcomeres shortened and there was a significant passive tension (descending limb where sarcomere length greater than 3.0 microns). Using such a physiological model, it was found that the effect of tendon compliance was to 'skew' the sarcomere length-tension curve to the right and to increase the operating range of the muscle-tendon unit.(ABSTRACT TRUNCATED AT 250 WORDS)     

Correlation between active and passive isometric force and intramuscular pressure in the isolated rabbit tibialis anterior muscle

The purpose of this study was to quantify the relationship between intramuscular pressure (IMP) and muscle force during isometric muscle contraction of the rabbit tibialis anterior (TA) absent the effect of either bone or fascia. To quantify this relationship, length-tension experiments were performed on the isolated TA of the New Zealand White rabbit (mass=2.5+/-0.5kg, n=12). The knee was fixed in a custom jig, the distal tendon of the TA was attached to a servomotor, and a 360 microm fiber optic pressure transducer was inserted into the TA. The peroneal nerve was stimulated to define optimal length (L(0)). The length-tension curve was created using 40Hz isometric contractions with 2-min rest intervals between each contraction. Measurements began at L(0)-50%L(f) and progressed to L(0)+50%L(f), changing the length-tension in 5% L(f) increments after each contraction. Qualitatively, the length-tension curve for isometric contractions was mimicked by the length-pressure curve for both active and passive conditions. Linear regression was performed individually for each animal for the ascending and descending limb of the length-tension curve and for active and passive conditions. Pressure-force coefficients of determination ranged from 0.138-0.963 for the active ascending limb and 0.343-0.947 for the active descending limb. Passive pressure coefficients of determination ranged from 0.045-0.842 for the ascending limb and 0.672-0.982 for the descending limb. These data indicate that IMP measurement provide a fairly accurate index of relative muscle force, especially at muscle lengths longer than optimal.     

Force-velocity relationships in hypertensive arterial smooth muscle

Increased total peripheral resistance is the cardinal haemodynamic disorder in essential hypertension. This could be secondary to alterations in the mechanical properties of vascular smooth muscle. Adequate study has not been made of the force-velocity (F-V) relationship in hypertensive arterial smooth muscle. Increased shortening in arterial smooth muscle would result in greater narrowing of arteries. The objectives of this investigation were to see if there is (i) increased shortening or increased maximum change in muscle length (delta Lmax where L stands for muscle length), (ii) an increased maximum velocity of shortening (Vmax) measured in l omicron per second where l omicron is the optimal muscle length for tension development, and (iii) a difference in maximum isometric tension (P omicron) developed in spontaneously hypertensive rat (SHR; N = 6) compared with normotensive Wistar Kyoto rat (WKY;N = 5) caudal artery strips. An electromagnetic muscle lever was employed in recording force-velocity data. Analysis of these data revealed the following: (a) the SHR mean P omicron of 6.21 +/- 1.01 N/cm2 was not different from the mean WKY P omicron of 6.97 +/- 1.64 N/cm2 (p greater than 0.05); (b) the SHR preparations showed greater shortening for all loads imposed; (c) the SHR Vmax of 0.016 l omicron/s was greater than the WKY Vmax of 0.013 l omicron/s (p less than 0.05). This study provides evidence that while hypertensive arterial smooth muscle is not able to produce more force than normotensive arterial smooth muscle, it is capable of faster and greater shortening. The latter could result in increased narrowing of hypertensive arteries and increased blood pressure.     

Control of human eye movements: I. modelling of extraocular muscle

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

Control of human eye movements: III. dynamic characteristics of the eye tracking mechanism

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

A theory of contraction and a mathematical model of striated muscle

A theory of contraction and an associated model of striated muscle are presented, based on the assumption that chemical energy is being converted into electrical energy which, in turn, is being converted into mechanical energy and heat.The model, set up for the frog sartorius muscle, is able to predict the “rowing” motion of the cross-bridges, the force-velocity relation, the tension-length curve, the isometric force, all energy rates (heat and work rates), the metabolic rates and all known features of the stretched, stimulated muscle (no ATP-splitting, stretching tension higher than isometric tension, etc.). It also offers an alternative explanation for Hill's thermoelastic effect. The significance of Hill's force-velocity equation in the context of this theory is also discussed in detail.     

Validity of the Force-Velocity Relation for Muscle Contraction in the Length Region, l ≤ l0

Considerable attention has been directed to the characteristic force-velocity relation discovered by A. V. Hill in the study of muscle kinematics. Models of contractile process were tested on the basis of their compatibility with the Hill equation. However, almost all the isotonic data have been restricted to one length, l₀, the maximum length with almost no resting tension; the velocities measured are those initial values when the load begins to move. The force-velocity curve extrapolates to zero velocity for isometric tension, but only for the tension at that one length. Very few efforts have been made to study the profiles of the curves throughout the range of lengths over which shortening takes place. In examining the length region, l ≤ l₀, for an isotonically contracting muscle, not only is the force-velocity relation valid for the initial reference length, l₀, but also for any other length. The analysis in this report indicates that the constants a/P₀ and b/l₀ remain fixed throughout the length change of afterloaded isotonic shortening in the Rana pipiens sartorius muscles.     

Force-velocity shifts with repetitive isometric and isotonic contractions of canine gastrocnemius in situ.

The force-velocity (F-V) relationships of canine gastrocnemius-plantaris muscles at optimal muscle length in situ were studied before and after 10 min of repetitive isometric or isotonic tetanic contractions induced by electrical stimulation of the sciatic nerve (200-ms trains, 50 impulses/s, 1 contraction/s). F-V relationships and maximal velocity of shortening (Vmax) were determined by curve fitting with the Hill equation. Mean Vmax before fatigue was 3.8 +/- 0.2 (SE) average fiber lengths/s; mean maximal isometric tension (Po) was 508 +/- 15 g/g. With a significant decrease of force development during isometric contractions (-27 +/- 4%, P < 0.01, n = 5), Vmax was unchanged. However, with repetitive isotonic contractions at a low load (P/Po = 0.25, n = 5), a significant decrease in Vmax was observed (-21 +/- 2%, P < 0.01), whereas Po was unchanged. Isotonic contractions at an intermediate load (P/Po = 0.5, n = 4) resulted in significant decreases in both Vmax (-26 +/- 6%, P < 0.05) and Po (-12 +/- 2%, P < 0.01). These results show that repeated contractions of canine skeletal muscle produce specific changes in the F-V relationship that are dependent on the type of contractions being performed and indicate that decreases in other contractile properties, such as velocity development and shortening, can occur independently of changes in isometric tension.     

A study of inotropic mechanisms in the papillary muscle preparation

The length-tension diagram, the force-velocity relation, the characteristics of the series elasticity, and the duration of the active state have been studied on the papillary muscle preparation of the cat heart, and on other examples of cardiac muscle. Positive inotropic changes such as the staircase phenomenon and post-extrasystolic potentiation occur without lengthening, but frequently with shortening, of the duration of the active state. They are accompanied by an increased velocity of contraction, and may be caused either by an intensification of the active state or by an alteration of the force-velocity characteristics of the contractile component. The changes in the force-velocity relation point to an adaptation of the velocity-efficiency relation in dependence on the frequency of contraction.     

A dynamic model of smooth muscle contraction

A dynamic model of smooth muscle contraction is presented and is compared with the mechanical properties of vascular smooth muscle in the rat portal vein. The model is based on the sliding filament theory and the assumption that force is produced by cross-bridges extending from the myosin to the actin filaments. Thus, the fundamental aspects of the model are also potentially applicable to skeletal muscle. The main concept of the model is that the transfer of energy via the cross-bridges can be described as a 'friction clutch' mechanism. It is shown that a mathematical formulation of this concept gives rise to a model that agrees well with experimental observations on smooth muscle mechanics under isotonic as well as isometric conditions. It is noted that the model, without any ad hoc assumptions, displays a nonhyperbolic force-velocity relationship in its high-force portion and that it is able to maintain isometric force in conditions of reduced maximum contraction velocity. Both these findings are consistent with new experimental observations on smooth muscle mechanics cannot be accounted for by the classical Hill model.     

Contractile properties of bronchial smooth muscle with and without cartilage

The majority of in vitro studies on airway smooth muscle have used the trachealis (TSM) as a convenient substitute for muscle from airways that constitute the flow-limiting segment. The latter are technically difficult to work with. However, because the site of maximum resistance to airflow is at the third to seventh generations of the bronchial tree, the trachealis preparation is of limited value. Length-tension and force-velocity properties were therefore studied at optimal length (lo) of canine bronchial smooth muscle (BSM) from which cartilage had been carefully removed. Normalized maximum isometric tension or stress (Po x 10(4) N/m2) for BSM was 7.1 +/- 0.19 (SE), which was similar to that of BSM with cartilage (BSM+C, 6.8 +/- 0.21) but lower than for TSM (18.2 +/- 0.81). At length greater than lo, the BSM+C was stiffer than the BSM. The values of maximum shortening capacity (delta Lmax), obtained directly from isotonic shortening at a load equal to the resting tension at lo, were 0.76 lo +/- 0.03, 0.41 lo +/- 0.02, and 0.24 +/- 0.02 lo for TSM, BSM, and BSM+C, respectively. The BSM and BSM+C delta Lmaxs were different (P less than 0.05). Maximal shortening velocities (Vo) for BSM, elicited at 2, 4, and 8 s by quick release in the course of an isometric contraction were significantly higher than for the BSM+C. Vos showed gradual decreases in all three groups in the later phase of contraction, suggesting the operation of latch bridges.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mechanical properties of human bronchial smooth muscle in vitro.

The in vitro mechanical properties of smooth muscle strips from 10 human main stem bronchi obtained immediately after pneumonectomy were evaluated. Maximal active isometric and isotonic responses were obtained at varying lengths by use of electrical field stimulation (EFS). At the length (Lmax) producing maximal force (Pmax), resting tension was very high (60.0 +/- 8.8% Pmax). Maximal fractional muscle shortening was 25.0 +/- 9.0% at a length of 75% Lmax, whereas less shortening occurred at Lmax (12.2 +/- 2.7%). The addition of increasing elastic loads produced an exponential decrease in the shortening and velocity of shortening but increased tension generation of muscle strips stimulated by EFS. Morphometric analysis revealed that muscle accounted for 8.7 +/- 1.5% of the total cross-sectional tissue area. Evaluation of two human tracheal smooth muscle preparations revealed mechanics similar to the bronchial preparations. Passive tension at Lmax was 10-fold greater and maximal active shortening was threefold less than that previously demonstrated for porcine trachealis by us of the same apparatus. We attribute the limited shortening of human bronchial and tracheal smooth muscle to the larger load presumably provided by a connective tissue parallel elastic component within the evaluated tissues, which must be overcome for shortening to occur. We suggest that a decrease in airway wall elastance could increase smooth muscle shortening, leading to excessive responses to contractile agonists, as seen in airway hyperresponsiveness.     

Relationship between length-tension relation and 20,000 dalton myosin light chain phosphorylation in guinea-pig taenia caeci

1. Relationship between length-tension relation and phosphorylation of 20,000 dalton myosin light chain (LC20) in guinea-pig taenia caeci was investigated. 2. At in situ length (Lb), a good linear correlation was obtained between isometric tension and LC20 phosphorylation in high-K+-stimulated muscle. 3. In 100 mM K+-stimulated muscle, the active tension decreased at muscle lengths other than Lb, but no significant decrease in degree of LC20 phosphorylation was observed. 4. These results suggest that in guinea-pig taenia caeci, the major portion of the decrease in active tension at muscle lengths other than Lb is not due to a decrease in degree of activation.     

Prediction of the cardiac muscle force-velocity relation from its force-time and force-length relations

The force-velocity relation for cardiac muscle fibers can be calculated from a proposed constitutive law based on force-time and force-length data. The calculated force-velocity relation agrees quite well with the measured force-velocity relation obtained from a quick release of sarcomere controlled rat cardiac trabeculae. The theory confirms the measured linear relationship between maximal velocity of sarcomere shortening and sarcomere length. The implication is that the force-velocity relation is not an independent property, and therefore need not be explicitly included as a rheological element in the constitutive law.     

Evaluation of the sliding distance in shortening muscles and in polymerizing actin from Hill's force-velocity equation

The relationship derived earlier between the sliding distance, Deltal(m), and a/P(0), the characteristic parameter of Hill's force-velocity equation for muscle contraction, was re-formulated in order to get a more general relationship which can be applied also to other biological mechano-chemical energy converters: alpha x Deltal(m)=phi (0)(a/P(0))Deltal(m)=-Deltag where Deltag is the free energy change accompanying the hydrolysis of one ATP molecule while alpha and phi (0) are, respectively, the average forces developed by a myosin head-actin complex which are responsible for shortening and for isometric tension generation. These two molecular forces are different in magnitude and in nature and it is demonstrated that alpha , not phi (0), is the true contractile force. The values of alpha and of phi (0) have been calculated for three muscles. The equation has been successfully applied to actin polymerization-based motility. The value of Deltag in different muscles under different environmental conditions can be easily determined from this equation with the value of Deltal(m) derived experimentally.     

Continuum rheology of muscle contraction and its application to cardiac contractility.

A set of constitutive equations is proposed to describe the mechanics of contraction of skeletal and heart muscle. Fiber tension is assumed to depend on the degree of chemical activation, the stretch ratio, and the rate of stretching of the fibers. The time rate of change of activation is governed by a differential equation. The proposed constitutive equations are used to model the time courses of isotonic and isometric twitches during contraction and relaxation phases of the muscle response to stimulation. Various contractility indices of the left ventricle are considered next by using the proposed constitutive equations. The present analysis introduces a new interpretation of the index of contractility (dP/dt)/P used in cardiac literature. It is shown that this index may not be related at all to the maximum speed of shortening and that it may be dependent on both preload and afterload. The development of pressure during isovolumetric contraction of the left ventricle is shown to be governed by a differential equation describing the time rate of change of tension during isometric contraction of myocardium fibers.     

Changes in force-velocity properties of trachealis due to oscillatory strains.

The physically dynamic environment of the lung constantly modulates the mechanical properties of airway smooth muscle. In vitro experiments have shown that contractility of the muscle is compromised by oscillatory strains, perhaps through disruption of cross-bridge interaction and organization of the contractile filaments. To understand the mechanism by which oscillation affects contractility, functional changes of the muscle in terms of force-velocity relationship were assessed before and after imposition of length oscillation in both relaxed and activated states. The oscillation protocol was designed to reduce isometric force by 15-20%, followed by measurement of force-velocity properties. Maximal velocity and power changed by +8 and -14%, respectively, after oscillation applied in the relaxed state and changed by -15 and -25%, respectively, after oscillation applied during contraction. A simple model of reduced activation could not account for the results; neither could the results be explained satisfactorily by the current cross-bridge theory of contraction. The results, however, could be explained if the possibility of reorganization of the contractile filaments due to oscillatory strains was considered.     

Contractile properties of the shortening rat diaphragm in vitro

Diaphragmatic fatigue has been defined in terms of the failure of the muscle to continue to generate a given level of tension. Appropriate shortening of the diaphragm is, however, just as important for adequate ventilation. In this study we have examined in vitro the contractile properties of the rat diaphragm under afterloaded isotonic conditions and the effect of fatigue on the ability of the diaphragm to shorten. Shortening of the muscle strips was found to depend on size of afterload, frequency of stimulation, duration of stimulation, and initial length of the muscle. The afterloaded isotonic length-tension relationship coincided with the relationship between length and active isometric tension only for relatively small afterloads. Fatigue of the muscle strips, induced by isometric or afterloaded isotonic contractions, was associated with a decline in the extent of shortening as well as a decrease in active isometric tension. Ability to shorten and ability to develop isometric tension did not decrease to the same extent under all conditions. We conclude that active shortening, as well as active isometric tension, is decreased by muscular fatigue and that changes in these properties can be different depending on experimental conditions. The results suggest that the definition of diaphragmatic fatigue should be expanded to include the ability of the muscle to shorten by an appropriate amount. The results also suggest that measurement of isometric performance may not provide a complete estimate of the overall performance of the fatigued diaphragm.     

The effects of ADP and phosphate on the contraction of muscle fibers.

The products of MgATP hydrolysis bind to the nucleotide site of myosin and thus may be expected to inhibit the contraction of muscle fibers. We measured the effects of phosphate and MgADP on the isometric tensions and isotonic contraction velocities of glycerinated rabbit psoas muscle at 10 degrees C. Addition of phosphate decreased isometric force but did not affect the maximum velocity of shortening. To characterize the effects of ADP on fiber contractions, force-velocity curves were measured for fibers bathed in media containing various concentrations of MgATP (1.5-4 mM) and various concentrations of MgADP (1-4 mM). As the [MgADP]/[MgATP] ratio in the fiber increases, the maximum velocity achieved by the fiber decreases while the isometric tension increases. The inhibition of fiber velocities and the potentiation of fiber tension by MgADP is not altered by the presence of 12 mM phosphate. The concentration of both MgADP and MgATP within the fiber was calculated from the diffusion coefficient for nucleotides within the fiber, and the rate of MgADP production within the fiber. Using the calculated values for the nucleotide concentration inside the fiber, observed values of the maximum contraction velocity could be described, within experimental accuracy, by a model in which MgADP competed with MgATP and inhibited fiber velocity with an effective Ki of 0.2-0.3 mM. The average MgADP level generated by the fiber ATPase activity within the fiber was approximately 0.9 mM. In fatigued fibers MgADP and phosphate levels are known to be elevated, and tension and the maximum velocity of contraction are depressed. The results obtained here suggest that levels of MgADP in fatigued fibers play no role in these decreases in function, but the elevation of both phosphate and H+ is sufficient to account for much of the decrease in tension.