Dissecting muscle power output

The following review examines in somewhat greater detail those factors that affect force and therefore power output during cyclic contraction of muscle.

The muscles chosen to illustrate concepts are two crustacean muscles, the flagellum abductor (FA) and a respiratory muscle, scaphognathite levator muscle L2B, from the green crab Carcinus maenas. Information on the innervation pattern, ultrastructure and contractile properties of these muscles can be found in Josephson and Stokes (1987, 1994) and Stokes and Josephson (1992). These crustacean muscles were selected as examples not because they are unusual in any obvious way, but because I have worked with them and they are the muscles with which I am most familiar. In fact, in their mechanical properties during tetanic stimulation, the FA and muscle L2B are quite like more commonly studied frog and mammalian muscles.

It has long been known that there is an optimum muscle length for force production. Since the classic work of Gordon et al. (1966), the decline in force with stretch beyond the optimum length has been attributed to a reduction in the amount of overlap between thick and thin filaments and therefore a decrease in the number of potentially active cross-bridges. The reduction in force with shortening below the optimum length is thought to be due to hindrance between thin filaments when these meet in the middle of the sarcomere, to overlap between thin filaments and cross-bridges of inappropriate polarity when the thin filaments slide beyond the middle of the sarcomere and to compressive forces produced when the thick filaments reach the Z-line.

The study of length–tension relationships by Gordon et al. (1966) was performed with isolated segments along single muscle fibers. Sarcomeres within a short fiber segment were expected to be of similar length and filament overlap. The resulting length–tension diagram was made up of a series of linear segments. This diagram has now become commonplace in all modern texts dealing with muscle contraction. However, in real muscle, the length–tension curve is more bell-shaped than polygonal (Fig. 2). The deviation between the length–tension behavior expected from the Gordon–Huxley–Julian model and that of whole muscles presumably results from inhomogeneities among the sarcomeres of whole muscles and possibly from inhomogeneities in the lengths of thick and thin filaments in individual sarcomeres (Edman and Reggiani, 1987). If either sarcomeres or filaments are not all of similar length, there will be dispersion in the values of overall muscle length at which individual thin filaments during shortening first reach the central bare zone of a sarcomere, at which they begin to overlap with thin filaments from the opposing Z-line or at which they encounter oppositely oriented cross-bridges, dispersion that will result in gradual rather than sharp transitions at critical points along the length–tension curve.

In most behaviors involving cyclic muscle activity, the participating muscles spend about as much time lengthening as they do shortening. There is an abundance of data on the force–velocity properties of shortening muscle but a paucity of such information for lengthening muscles. Several force–velocity curves for lengthening muscle have been published (see, for examples, Fig. 2.21 in Woledge et al., 1985). However, in most relevant studies, there is not a single-valued relationship between force and lengthening velocity. Rather, muscle force rises continuously during isovelocity stretch, and velocity changes continuously during isotonic lengthening (Fig. 4; literature surveyed in Josephson and Stokes, 1999a). A common pattern among skeletal muscle is for force to rise continuously but at a declining rate during stretch at low velocity and to rise to a yield point during high-velocity stretch, following which force may continue to rise but at a lower slope, or be reasonably constant, or sometimes fall even though stretch is continued (see, for example, Sugi and Tsuchiya, 1988; Malamud et al., 1996; Sandercock and Heckman, 1997). At the end of stretch, force declines gradually and can remain above the isometric level expected at the stretched length for many seconds (see Edman and Tsuchiya, 1996, and references therein). The enhanced force following stretch is probably due in part to the increased heterogeneity in sarcomere length along a fiber that develops during the stretch (Edman and Tsuchiya, 1996). Since force varies continually during isovelocity stretch, to predict the force in a lengthening muscle requires knowledge of the time since the onset of stretch as well as the stretch velocity. The force–velocity relationship of lengthening muscle is not a planar curve; rather, it is a surface with time of stretch as a third axis (Fig. 5).

The capacity of a muscle to generate force and do work rises rapidly following stimulation and then falls during relaxation. Despite its obvious importance and the many studies devoted to it, the development of an appropriate measure of muscle activation which might be used to quantify the changing capacity of a muscle to develop force and to do work following stimulation has been an elusive goal (for a review, see Ford, 1991). Techniques have been developed for measuring variation in cytoplasmic Ca²⁺ concentration and in instantaneous stiffness of muscle associated with activation, but Ca²⁺ concentration and stiffness are only indirectly related to the capacity to generate force and to do work. Some measure of the changing position and possibly shape of force–velocity curves following stimulation is needed, but what this measure might be is not obvious. Ford (1991) suggests using maximum power, determined from force–velocity curves, as a measure of muscle activation. But to reach the force at which power is maximal early in a contraction requires stretching the muscle and introduces the possibility of stretch activation as well as the complexities in the force–velocity relationship associated with stretch described above. The many early studies on the time course of the ‘active state’ in frog muscle suggest that activation rises abruptly and decays exponentially following a short plateau (e.g. Hill, 1949; Jewell and Wilkie, 1960). We used the shortening velocity at a fixed, light load to characterize activation during the twitch of a locust flight muscle (Malamud and Josephson, 1991) and concluded that, here too, activation following stimulation rose rapidly to a maximum, reached 2–3 ms after the end latent period, and then, after a brief plateau, decayed approximately exponentially. The general shape of the activation versus time curve in the locust muscle was similar to that in frog muscle but on a faster time scale. This pattern, a rapid rise followed by exponential decay, may be the common one among skeletal muscles.

It seems to be a general feature of muscle that relaxation becomes slower as muscle length increases (e.g. Hartree and Hill, 1921; Close, 1972; Malamud, 1989; see also Fig. 4). The increase in relaxation time has been attributed to an increase in the Ca²⁺ affinity of myofilaments with increasing muscle length (Stephenson and Wendt, 1984). In intact organisms, an increase in contractile duration with increase in muscle length should partially compensate for the decline in force as a muscle is stretched into the descending limb of the length–tension curve. If a muscle becomes stretched because of load or increased activity in antagonistic muscles, its contractions become longer and the time-average of its force becomes greater than would be the case were activation not length-dependent.

Another feature modifying muscle force, which appears to be common among skeletal muscles, is a depression of the capacity to develop tension following active shortening. In frog muscle fibers (Granzier and Pollack, 1989) and in crab muscles (Josephson and Stokes, 1999b), the extent of the depression increases with increasing distance of shortening (Fig. 6) and is inversely related to the velocity of shortening (Fig. 7). The reduced capacity to develop force following shortening is frequently described as ‘shortening deactivation’. However, it is not simply the amount of shortening that determines the degree of depression, since the latter also varies with the velocity of shortening and therefore with the force during shortening and the work done. Granzier and Pollack (1989) found that in frog muscle the magnitude of force depression following shortening is closely correlated with the work done during shortening, and the same is true in crab muscle (Fig. 8). Hence, the deactivation associated with shortening is better described as ‘work-dependent deactivation’ than as ‘shortening deactivation’.

The force generated by cross-bridges is transmitted to the load through myofilaments, Z-lines and tendons or apodemes, all of which are to some extent compliant. The compliant elements interposed between the force generators and the load are described collectively as the series elastic component (SEC). Stretch of the SEC is generally found to be a non-linear function of stress. The presence of series elasticity allows some internal sliding of filaments and shortening of sarcomeres when the muscle as a whole is held at constant length in an ‘isometric’ contraction. Length changes in the SEC are in series with and additive to those of the contractile elements. The length change and velocity of the contractile component may be greater than or less than that of the muscle as a whole depending on whether force is rising and the SEC is becoming stretched or force is falling and the SEC is shortening. Force–velocity relationships for the contractile component derived from isotonic contractions in which force and SEC length are constant will not apply exactly to the usual conditions of muscle use in vivo during which force changes continuously and, therefore, so does SEC length. The consequences of series elasticity on work and power output of muscle are well illustrated in a recent paper by Curtin et al. (1998).

The factors listed in Fig. 1, and perhaps others yet to be discovered, determine the work output during length change. These, then, are the elements that might be included in a model of mechanical power production by muscle. Some may be quantitatively insignificant in particular cases, but it seems prudent to consider them all if postulated models of muscle power are to be accurate reflections of real muscle performance. Some of the components of Fig. 1 are well-studied, in particular force–velocity relationships and length–tension relationships, the others less so. But being well-studied is not the same as being well-understood. The length–tension relationship in small muscle segments may not show a sharp transition between a plateau and the descending limb, even though theory predicts it should (Edman and Reggiani, 1987). Force–velocity relationships may have an odd and unexplained concavity at the high-force end (Edman, 1988). But, in general, the determinants of force and work output seem sufficiently if not exactly understood that they could be included in a model of work output.

Several recent studies have examined the extent to which the force during muscle stimulation and movement patterns simulating those of normal activity can be predicted from the force–velocity and length–tension properties of the muscle and usually a postulated time course for the state of muscle activation (Caiozzo and Baldwin, 1997; Sandercock and Heckman, 1997; Askew and Marsh, 1998; Curtin et al., 1998; Williams et al., 1998). In general, the predicted force matched measured force reasonably well early in contractions, but there tended to be deviation late in a cycle, especially during relaxation following shortening. None of the studies directly incorporated work-dependent deactivation, realistic views of the force–velocity relationships during muscle lengthening or enhanced force following lengthening, although the paper by Askew and Marsh (1998) did calculate the time course of activation in general as the ratio between the muscle force actually measured and that expected from muscle velocity and length. I think it highly likely that incorporating work-dependent deactivation and more accurate representations of the force–velocity properties of lengthening muscle would substantially improve the theoretical muscle models as predictors of real muscle behavior. The early study of Weis-Fogh and Alexander (1977) provided a framework for considering the potential work output of muscle; the task now is to add and shape details so as to make the structure increasingly realistic.

This work was supported by NSF research grant IBN-9603187.