Initial force production before sag is enhanced by prior contraction followed by a 3-minute rest period in fast motor units of the rat medial gastrocnemius

Unfused tetanic contractions evoked in fast motor units exhibit extra-efficient force production at the onset of contraction, an effect called “boost”. Boost is diminished in subsequent contractions if there is a short rest period between contractions, but can be re-established with a longer period of rest. We tested the hypothesis that contractile activity and rest could enhance boost-related metrics. Two sets of 3 unfused tetani were evoked 3 min apart in fast fatigable (FF) and fast fatigue-resistant (FR) motor units of the rat medial gastrocnemius. The greatest changes occurred in the first unfused tetanic contractions. Relative to the first contraction in the first set, the first contraction in the second set exhibited higher peak force during boost in a subset of motor units (76% of FF and 48% of FR). Enhanced force during boost was influenced by interaction of slowing of twitch contraction time (up to 20% and 25%, for FF and FR motor units, respectively), half-relaxation time (up to 37% and 49% for FF and FR motor units, respectively), and potentiation of the first twitch (up to 13% and 5% for FF and FR motor units, respectively). Examination of twitches evoked between sets suggested opportunity for greater enhancement of boost with shorter intervening rest periods. The phenomenon of enhanced boost following motor unit activity may interest sports scientists.     

Changes in the time course of potentiated and fatigued contractions of fast motor units in rat muscle

The contraction and relaxation times of the twitches and the last contractions within 32 unfused tetani of FF and 27 unfused tetani of FR motor units in the rat medial gastrocnemius muscle were studied during prolonged activity. The pattern of the MU stimulation included single pulses (to evoke twitches) and series of three trains of stimuli at 40, 50 and 60 Hz (to evoke unfused tetani), repeated 30 times. The analysis concerned changes of force and time parameters at the beginning of activity, during the potentiation and then during the fatigue. It was found that changes of force during the potentiation and the fatigue were mainly accompanied by changes in the course of relaxation. The significant prolongation of the half-relaxation time during the potentiation of either twitches or unfused tetani was revealed in both types of fast MU. The twitch contraction time did not change markedly, whereas significantly shortened in the last contractions of unfused tetani during the potentiation. These changes of time parameters correlated to the increase of the fusion degree. During the fatigue, the time parameters shortened, however, changes of the half-relaxation times were remarkably higher. The shortening of relaxation was responsible for the decrease of the fusion degree. Changes of the fusion index exceeding 0.75 during the potentiation or decreasing below this value during the fatigue, were accompanied by respective appearance or disappearance of the biphasic relaxation.     

The rate of changes in tension within fused tetani of single motor units in rat medial gastrocnemius muscle.

The time course of fused tetani of three main types of motor units: slow (S), fast resistant (FR) and fast fatigable (FF) was studied in the rat medial gastrocnemius. The rate of tension generation and of the relaxation within a tetanus was measured under isometric conditions. These measurements were performed at three points during both the contraction and relaxation: the beginning, the middle and the end of the phase of changes in tension. Significant differences were found in the rate of tension changes between fast and slow units. Comparison of FF and FR units showed less pronounced differences in their rates of the contraction and the relaxation. Moreover, slow units showed significantly greater slowing of both the contraction and relaxation within a tetanus in relation to the speed of their twitch when compared to fast motor units. The rate of changes in tetanic tension correlated to twitch time parameters and to tension generated during twitch or tetanus. The results point out that the well known difference in the speed of twitch contraction between fast and slow units is also visible in their fused tetani.     

Monophasic and biphasic relaxation during motor unit tetanic contractions of variable fusion degree

The phenomenon of transition of the monophasic relaxation into biphasic course in the unfused tetanic contractions was studied on functionally isolated motor units of the rat medial gastrocnemius muscle. The sample consisted of 16 FF, 16 FR and 10 S MUs which were stimulated with the same, digitally controlled patterns. The new parameter--QRT/HRT ratio, was introduced as a convenient tool for the classification of the relaxation into monophasic or biphasic. Analysis of tetani evoked at increasing stimulation frequencies revealed similar relationships between the tetanic fusion degree and the shape of relaxation for all three types of motor units investigated. In each MU, the QRT/HRT ratio fell into two distinct ranges related to either monophasic (lower values) or biphasic (higher values) relaxation. The relationship was also found between the shape of relaxation and degree of tetanic fusion--the biphasic course appeared for better fused tetani when fusion index was over the mean of 0.8. Mechanisms of development of the biphasic relaxation were discussed with respect to importance of this parameter in force development and summation of successive contractions into tetanus. Moreover, it was pointed out that adequacy of mathematical modeling of motor unit contractions should benefit from the precise analysis of the mono- or biphasic course of relaxation.     

Tetanic depression in fast motor units of the cat gastrocnemius muscle.

Ability of muscle fibers to generate force is decreased when higher frequency of stimulation of motor units immediately follows lower frequency. This phenomenon called tetanic depression was found in rat medial gastrocnemius. However, it was not clear whether tetanic depression occurred only in rat muscle or it concerns all mammals. This study was conducted on motor units of cat medial gastrocnemius. Analyses were made at three successive trains of stimulation: 30 Hz, 20 and 30 Hz and again 30 Hz (the first pattern) or 40 Hz, 25 and 40 Hz and 40 Hz (the second pattern). In all fast units force generated within the middle tetanus was lower than force generated at the same, but constant frequency of stimulation applied earlier or later. The mean tetanic depression in 30 Hz tetani amounted to 10.9% for fast fatigable (FF) and 15.9% for fast resistant (FR) motor units, whereas in 40 Hz tetani mean values were 5.6% and 7.3% for FF and FR motor units, respectively. In slow motor units tetanic depression was not observed. These results proved the existence of tetanic depression in the feline muscle and indicated that its intensity depends on the fusion of tetanus. It has been concluded, that the tetanic depression is a general property of fast motor units in mammals.     

Changes in the properties of mechanomyographic signals and in the tension during the fatigue test of rat medial gastrocnemius muscle motor units

The influence of activity-related changes in tension on properties of the mechanomyogram (MMG) was investigated in fast fatigable, fast resistant and slow motor units (MUs). A standard fatigue test was used in which rhythmically repeated unfused tetani were evoked. The amplitudes of the rise in tension of the first and the last contraction within the unfused tetanus and the amplitudes of accompanying signals in MMG were calculated. For fast fatigable MUs a parallel decrease in the amplitudes of both analysed contractions and in the amplitudes of accompanying MMG signals during the fatigue test was observed. For majority of fast resistant MUs at the beginning of the fatigue test a potentiation occurred and this phenomenon increased the tension of the first contraction and of the peak tetanic tension. However, the potentiation coincided also with a decrease of the amplitude of the last contraction in the tension recording of an unfused tetanus. The MMG reflected both, the increase of amplitude of the first contraction and the decrease of the amplitude of the further contractions within the tetanus. The single twitch contraction evoked immediately before and after the fatigue test was additionally recorded. A decrease (fatigue) or an increase (potentiation) of the twitch tension after the fatigue test was reflected by a decrease or an increase in the amplitude of MMG, respectively. However, the fatigue failed to change significantly the time parameters of MMG. To conclude, fatigue and potentiation can occur during activity of fast MUs and both these phenomena involve changes in the amplitude of oscillations in tension of unfused tetani which are reflected in MMG.     

Interspecies differences of motor units properties in the medial gastrocnemius muscle of cat and rat

The purpose of the study was to analyze the interspecies differences of motor unit contractile properties in two most frequently studied mammals: cats and rats. A total sample of 166 motor units (79 in cats and 85 in rats) was investigated in the medial gastrocnemius muscle. Considerable differences were found in composition of the studied muscle. In cats, fast fatigable, fast resistant and slow units formed 68, 18 and 14% of the investigated population, whereas in rats 36, 52 and 12%, respectively. The contraction and relaxation times of motor units in the cat muscle were evidently longer than in the rat and the border values for fast/slow motor units division in these species were 44 and 20 ms, respectively. The mean values of twitch and tetanic forces appeared to be 7-8 times lower in rats, for fast, while 2-5 times for slow motor units. Also variability between the strongest and the weakest units within each type revealed differences 10-60 times in cats, whereas only 3.5-14 times in rats. The summation of twitches into tetanus for fast units was comparable in both species, but for S units was evidently more effective in the cat. In fast motor units' tetanic contractions evident interspecies differences concerned sag appearance and profiles of unfused tetani of FF and FR units. Differences in contractile properties described in the study may depend on the size, number and innervation ratio of motor units in the muscle of cat and rat, as well as their biochemical variability. Differences in composition of motor unit types and uneven mechanisms of force development may reflect biological adaptation to variable behaviour of cats and rats.     

Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units.

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.     

Relationship between the tension-time area and the frequency of stimulation in motor units of the rat medial gastrocnemius muscle.

The tension-time area is an estimation of the work performed by contracting motor units. The relationship between tension and frequency of stimulation and between tension-time area and frequency have been studied on 148 single motor units of the rat medial gastrocnemius muscle, under isometric conditions. Motor units were classified as fast fatigable (FF), fast resistant to fatigue (FR) or slow (S). Trains of stimuli of increasing frequency and constant duration were used. For all motor units a half of the maximum tetanic tension corresponded to lower frequencies compared to frequencies at a half of the maximum tension-time area. Moreover, the slopes of tension-frequency and area-frequency curves (change of tension or area per 1 Hz rise in frequency) were higher for slow than for fast motor units. The tension-time area per one pulse was calculated for different frequencies of stimulation. For slow units the maximum area per pulse corresponded to significantly lower frequencies than for fast ones, especially of FF type. However, for all three types of motor units this optimal frequency corresponded to sub-fused tetani with a tension of about 75% of the maximum tension, and with the fusion index slightly over 0.90. The absolute values of the maximum tension-time area per pulse revealed that in one contraction within the tetanus, slow units are generating greater work than FR units. The work performed by FF units is nearly two times larger than for S units, although the tension of slow units is over eight times lower. The presented results reveal that the contraction of slow motor units is much more effective than was suggested based on their low tension.     

Experimentally verified mathematical approach for the prediction of force developed by motor units at variable frequency stimulation patterns

During normal daily activity, muscle motor units (MUs) develop unfused tetanic contractions evoked by trains of motoneuronal firings at variable interpulse intervals (IPIs). The mechanical responses of a MU to successive impulses are not identical. The aim of this study was to develop a mathematical approach for the prediction of each response within the tetanus as well as the tetanic force itself. Experimental unfused tetani of fast and slow rat MUs, evoked by trains of stimuli at variable IPIs, were decomposed into series of twitch-shaped responses to successive stimuli using a previously described algorithm. The relationships between the parameters of the modeled twitches and the tetanic force level at which the next response begins were examined and regression equations were derived. Using these equations, profiles of force for the same and different stimulation patterns were mathematically predicted by summating modeled twitches. For comparison, force predictions were made by the summation of twitches equal to the first one. The recorded and the predicted tetanic forces were compared. The results revealed that it is possible to predict tetanic force with high accuracy by using regression equations. The force predicted in this way was much closer to the experimental record than the force obtained by the summation of equal twitches, especially for slow MUs. These findings are likely to have an impact on the development of realistic muscle models composed of MUs, and will assist our understanding of the significance of the neuronal code in motor control and the role of biophysical processes during MU contractions.     

Model-generated decomposition of unfused tetani of motor units evoked by random stimulation

Unfused tetani of motor units (MUs) evoked by stimulation at variable interpulse intervals at mean frequencies of 20, 25, 33, 40 and 50 Hz were studied using ten functionally isolated fast-type MUs from the medial gastrocnemius muscle of adult Wistar rats. A previously proposed algorithm and computer program for mathematical decomposition of unfused tetani into a series of twitches, representing responses to individual pulses, were used. Analysis of the parameters of the decomposed twitches showed considerable variability in force of successive contractions. These twitches were extremely variable with up to 2-fold higher forces and longer contraction times than a single twitch evoked by one stimulus. However, when the stimulation frequency was decreased, the decomposed twitches became similar to the single twitch with respect to amplitude and contraction time. It was found that the basic contractile parameters of decomposed twitches could be predicted with high accuracy on the basis of the tetanus force level at which the next contraction begins. This analysis of the parameters of decomposed twitches demonstrated that the contractile responses of the muscle fibers to successive action potentials generated by motoneurons are highly variable and depend on the previous MU state.     

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40 Hz unfused tetani, and 150 Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.     

Time-related changes of motor unit properties in the rat medial gastrocnemius muscle after spinal cord injury. I. Effects of total spinal cord transection

The contractile properties of motor units (MUs) were electrophysiologically investigated in the medial gastrocnemius (MG) muscle in 17 Wistar three-month-old female rats: 14, 30, 90 and 180 days after the total transection of the thoracic spinal cord and compared to those in intact (control) rats. A sag phenomenon, regularly observed in unfused tetani of fast units in intact animals at 40 Hz stimulation, almost completely disappeared in spinal rats. Therefore, the MUs of intact and spinal rats were classified as fast or slow types basing on 20 Hz tetanus index, the value of which was lower or equal 2.0 for fast and higher than 2.0 for slow MUs. The MUs composition of MG muscle changed with time after the spinal cord transection: an increasing proportion of fast fatigable (FF) units starting one month after injury and a disappearance of slow (S) units within the three months were observed. In all MUs investigated the twitch contraction and half-relaxation time were significantly prolonged after injury (p < 0.01, Mann–Whitney U-test). Moreover, a decrease of the fatigue index for fast resistant (FR) and slow MUs was observed in subsequent groups of spinal rats. No significant changes were found between twitch forces in all MU types of spinal animals (p > 0.05). However, due to a decrease of the maximal tetanic force, a significant rise of the twitch-to-tetanus ratio of all MUs in spinal rats was detected (p < 0.01). The considerable reduction of ability to potentiate the force was noticed for fast, especially FF type MUs. In conclusion, the spinal cord transection leads to changes in the proportion of the three MU types in rat MG muscle. The majority of changes in MUs’ contractile properties were developed progressively with time after the spinal cord injury. However, the most intensive alterations of twitch-time parameters were observed in rats one month after the transection.     

Estimation of the error between experimental tetanic force curves of MUs of rat medial gastrocnemius muscle and their models by summation of equal successive contractions

More accurate muscle models require appropriate modelling of individual twitches of motor units (MUs) and their unfused tetanic contractions. It was shown in our previous papers, using a few MUs, that modelling of unfused tetanic force curves by summation of equal twitches is not accurate, especially for slow MUs. The aim of this study was to evaluate this inaccuracy using a statistical number of MUs of the rat medial gastrocnemius muscle (15 of slow, 15 of fast resistant and 15 of fast fatigable type). Tetanic contractions were evoked by trains of 41 stimuli at random interpulse intervals and different mean frequencies, resembling discharge patterns observed during natural muscle activity. The tetanic curves were calculated by the summation of equal twitches according to the respective experimental patterns. The previously described 6-parameter analytical function for twitch modelling was used. Comparisons between the experimental and the modelled curves were made using two coefficients: the fit coefficient and the area coefficient. The errors between modelled and experimental tetanic forces were substantially different between the three MU types. The error was the most significant for slow MUs, which develop much higher forces in real contractions than could be predicted based on the summation of equal twitches, while the smallest error was observed for FF MUs – their recorded tetanic forces were similar to those predicted by modelling. The obtained results indicate the importance of the inclusion of the type-specific non-linearity in the summation of successive twitch-like contractions of MUs in order to increase the reliability of modelling skeletal muscle force.     

Variability of successive contractions subtracted from unfused tetanus of fast and slow motor units

Stimulation of motor units (MUs) with repeated pulses evokes tetanic contractions, which consist of overlapping mechanical responses. The summation of these responses into tetanus is a nonlinear process due to the dynamic changes in the amplitudes and time parameters of the successive components. In order to study these changes, two MUs (one fast and one slow) of rat medial gastrocnemius muscle were stimulated with a progressively increasing number of pulses, from one (i = 1) to sixteen (i = 16) at a frequency of 15 Hz for the slow MU and 60 Hz for the fast MU. The individual responses were calculated by subtracting the (i)th from the (i + 1)th tetanus recording. The contractions obtained following subtraction were modeled using a novel 6-parameter analytical function. The main conclusions of this study are (1) the newly presented analytical function is able to precisely describe the variable shape of all subtracted experimental contractions; (2) the shapes of successive contractions are variable and the subtracted contractions differ from the individual twitches; (3) as the pulse number increases, the parameters of the subtracted contractions change in a different manner for the slow and fast MUs: for the slow MU, the maximal forces and the time parameters increase considerably up to the 4th response, after which they remain nearly constant or show only a slight increase; for the fast MU, the maximal forces and durations also increase, whereas the remaining time parameters initially increase and then maintain a constant level or decrease, which explains the sag phenomenon visible in the unfused tetanus of fast MUs.     

A commentary on muscle unit properties in cat hindlimb muscles

A broad survey of muscle unit properties in 14 muscles of the cat hind limb is presented which emphasizes some general features of unit properties in mammalian muscles. A more detailed analysis of muscle unit properties in three muscles of the posterior compartment of the lower leg is then presented using Burke's tetrapartite (FF, FI or F (Int.), FR, and S) unit classification scheme. Our data on the properties of motor units in cat tibialis posterior (TP) have been compared to those generated by Burke and colleagues on units in flexor digitorum longus (FDL) and medial gastrocnemius (MG). In all three muscles, twitch contraction time was distinctly slower for type S units and specific tension outputs were substantially greater for type FF units than for type S units. The innervation ratios of type FR units were slightly lower than for type S units but the specific tension of the FR units was closer to FF units than to type S units. The FF units controlled 70–74% of the cumulative force output of each muscles, indicating a substantial capacity for powerful rapid contractions of all three of these muscles despite their differences in “size,” action, and force generation. Distinctive features of the three muscles included differences in the unit types' force producing capabilities and in the relative representation of “nonfatigable” type FR and S units in each muscle. In particular, TP is endowed with some unusually powerful type FF units and a high percentage (42%) of type S units. In contrast, FDL has units that develop relatively little force and an unusually high representation (56%) of type FR units. The possible relationships between these muscle features and their presumed role in posture and locomotion is discussed.     

Axonal conduction velocity of motor units of rat's medial gastrocnemius muscle

Axonal conduction velocity and its relations to different contractile properties of motor units of medial gastrocnemius muscle were investigated in nine Wistar rats anaesthetized with pentobarbitone. Functionally isolated motor units were identified as slow (S), fast resistant (FR) and fast fatigable (FF). Axons of S motor units conducted significantly more slowly than of fast units, while there was considerable overlap between conduction velocities measured for FR and FF types. The mean values of conduction velocity were 50.9 m/s for S, 68.9 m/s for FR and 71.3 m/s for FF type motor units. Strong and significant negative correlation between conduction velocity and contraction time as well as half-relaxation time was demonstrated. However, only a weak correlation between conduction velocity and twitch tension, tetanic tension or fatigue index was found. The multiple regression analysis revealed that the major factor to determine conduction velocity was contraction time.     

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.     

Chronic stimulation modifies the isotonic shortening velocity of denervated rat slow-twitch muscle

Rat soleus muscles were denervated and stimulated in vivo for periods of up to 104 days. Stimuli used were trains of 1 ms pulses at 100 Hz delivered for periods of 1 s; trains were repeated every 10-100 s. In a majority of animals the tension of the muscles was maintained at about 10% of normal, equivalent to muscles denervated but unstimulated for 20 days. At the longest periods the stimulated muscles developed ten times more tension than ones that were denervated but not stimulated. In denervated and denervated-stimulated muscles twitch contraction and relaxation times were prolonged, compared with controls, for up to 3 weeks. Thereafter both sets showed a speeding of the isometric twitch that was greater in the stimulated muscles. At the longest periods the twitch was as short as that of a denervated fast muscle. Stimulation did not affect contralateral denervated muscles. Twitch: tetanus ratios remained high despite stimulation, and muscles showed little post-tetanic potentiation. Tension developed more rapidly in the tetani of the stimulated muscles, even allowing for larger final values. Maximum velocity of shortening was increased in many of the stimulated muscles, and there was a proportional flattening of the force-velocity curve, i.e. a/P0 increased. Maximum velocity and a/P0 increased reciprocally with twitch time to peak, so that those muscles that had twitches most changed by stimulation also had their isotonic properties modified to the greatest extent. Even at the longest period of stimulation, twitch time course and tetanic tension were not converted to those of normal fast muscle.     

Interspecies differences in the force-frequency relationship of the medial gastrocnemius motor units.

Single, functionally isolated motor units were studied in the medial gastrocnemius (MG) muscle of cats and rats. Axons of their motoneurons were stimulated with trains of pulses at frequencies increasing from 1 to 150 Hz and forces developed by muscle fibers were measured and force-frequency curves were compared between species. The following observations were made: (1) the most steep parts of curves (related to unfused tetani of motor units) begun at lower frequencies of stimulations in all types of feline motor units, (2) for fast motor units, the same relative values of force of unfused tetani were achieved at significantly lower frequencies of stimulations in the cat than in the rat. Twitch time parameters of both species influenced the course of force-frequency curves. It was showed that the contraction times of feline units varied in the wide range (21-81 ms), and these units reached 60% of the maximum force at stimulation frequencies between 10 and 38 Hz. On the other hand, contraction times of rat units ranged from 10 to 34 ms, whereas stimulation frequencies necessary to reach 60% of the maximum force varied considerably, from 12 to 65 Hz. The correlations between the above parameters were found for motor units of each species. However, the regression lines drown for the collected population of cat and rat units did not form linear continuity. Thus it seems that interspecies differences in the twitch contraction times do not fully explain different force-frequency relationships in mammalian skeletal muscles.