Finite element modelling of contracting skeletal muscle

To describe the mechanical behaviour of biological tissues and transport processes in biological tissues, conservation laws such as conservation of mass, momentum and energy play a central role. Mathematically these are cast into the form of partial differential equations. Because of nonlinear material behaviour, inhomogeneous properties and usually a complex geometry, it is impossible to find closed-form analytical solutions for these sets of equations. The objective of the finite element method is to find approximate solutions for these problems. The concepts of the finite element method are explained on a finite element continuum model of skeletal muscle. In this case, the momentum equations have to be solved with an extra constraint, because the material behaves as nearly incompressible. The material behaviour consists of a highly nonlinear passive part and an active part. The latter is described with a two-state Huxley model. This means that an extra nonlinear partial differential equation has to be solved. The problems and solutions involved with this procedure are explained. The model is used to describe the mechanical behaviour of a tibialis anterior of a rat. The results have been compared with experimentally determined strains at the surface of the muscle. Qualitatively there is good agreement between measured and calculated strains, but the measured strains were higher.     

Structural features of cross-bridges in isometrically contracting skeletal muscle

Two-dimensional x-ray diffraction was used to investigate structural features of cross-bridges that generate force in isometrically contracting skeletal muscle. Diffraction patterns were recorded from arrays of single, chemically skinned rabbit psoas muscle fibers during isometric force generation, under relaxation, and in rigor. In isometric contraction, a rather prominent intensification of the actin layer lines at 5.9 and 5.1 nm and of the first actin layer line at 37 nm was found compared with those under relaxing conditions. Surprisingly, during isometric contraction, the intensity profile of the 5.9-nm actin layer line was shifted toward the meridian, but the resulting intensity profile was different from that observed in rigor. We particularly addressed the question whether the differences seen between rigor and active contraction might be due to a rigor-like configuration of both myosin heads in the absence of nucleotide (rigor), whereas during active contraction only one head of each myosin molecule is in a rigor-like configuration and the second head is weakly bound. To investigate this question, we created different mixtures of weak binding myosin heads and rigor-like actomyosin complexes by titrating MgATPgammaS at saturating [Ca2+] into arrays of single muscle fibers. The resulting diffraction patterns were different in several respects from patterns recorded under isometric contraction, particularly in the intensity distribution along the 5.9-nm actin layer line. This result indicates that cross-bridges present during isometric force generation are not simply a mixture of weakly bound and single-headed rigor-like complexes but are rather distinctly different from the rigor-like cross-bridge. Experiments with myosin-S1 and truncated S1 (motor domain) support the idea that for a force generating cross-bridge, disorder due to elastic distortion might involve a larger part of the myosin head than for a nucleotide free, rigor cross-bridge.     

The T-SR junction in contracting single skeletal muscle fibers

The junction between the T system and sarcoplasmic reticulum (SR) of frog skeletal muscle was examined in resting and contracting muscles. Pillars, defined as pairs of electron-opaque lines bounding an electron- lucent interior, were seen spanning the gap between T membrane and SR. Feet, defined previously in images of heavily stained preparations, appear with electron-opaque interiors and as such are distinct from the pillars studied here. Amorphous material was often present in the gap between T membrane and SR. Sometimes the amorphous material appeared as a thin line parallel to the membranes; sometimes it seemed loosely organized at the sites where feet have been reported. Resting single fibers contained 39 +/- 14.3 (mean +/- SD; n = 9 fibers) pillars/micrometer2 of tubule membrane. Single fibers, activated by a potassium-rich solution at 4 degrees C, contained 66 +/- 12.9 pillars/micrometer2 (n = 8) but fibers contracting in response to 2 mM caffeine contained 33 +/- 8.6/micrometer2 (n = 5). Pillar formation occurs when fibers are activated electrically, but not when calcium is released directly from the SR; and so we postulate that pillar formation is a step in excitation-contraction coupling.     

Increase in electromyogram low-frequency power in nonfatigued contracting skeletal muscle

We studied the relationship between changing elbow joint angle and the power spectral density of the biceps brachii muscle electromyogram (EMG) during submaximal isometric contractions. For this purpose, we recorded the EMG of the biceps brachii muscle with surface electrodes in 13 subjects. Each subject held a 2.8-kg weight and contracted the biceps isometrically for 30 s at one of two lengths. The length of the muscle was changed by flexing the forearm toward the upper arm to form an angle of 135 degrees (L1) or 45 degrees (L2). We found that the mean centroid frequency (fc) of the EMG power spectral density was 26% lower at L1 than at L2 (P less than 0.01). For each subject there was no significant change in fc during the isometric contraction at either angle. In addition, in nine subjects who sustained fatiguing contractions of the biceps with a 6-kg load, fc decreased by 15% (P less than 0.025). These data suggest that a change in the length at which a muscle contracts isometrically can alter or induce indirectly an alteration in the frequency content of its EMG. This finding may have important implications for the assessment of respiratory muscle EMG especially during loaded breathing.     

Effects of arterial hypotension on microvascular oxygen exchange in contracting skeletal muscle.

In healthy animals under normotensive conditions (N), contracting skeletal muscle perfusion is regulated to maintain microvascular O2 pressures (PmvO2) at levels commensurate with O2 demands. Hypovolemic hypotension (H) impairs muscle contractile function; we tested whether this condition would alter the matching of O2 delivery (Qo2) to O2 utilization (Vo2), as determined by PmvO2 at the onset of muscle contractions. PmvO2 in the spinotrapezius muscles of seven female Sprague-Dawley rats (280+/-6 g) was measured every 2 s across the transition from rest to 1-Hz twitch contractions. Measurements were made under N (mean arterial pressure, 97+/-4 mmHg) and H (induced by arterial section; mean arterial pressure, 58+/-3 mmHg, P<0.05) conditions; PmvO2 profiles were modeled using a multicomponent exponential fitted with independent time delays. Hypotension reduced muscle blood flow at rest (24+/-8 vs. 6+/-1 ml-1.min-1.100 g-1 for N and H, respectively; P<0.05) and during contractions (74+/-20 vs. 22+/-4 ml-1.min-1.100 g-1 for N and H, respectively; P<0.05). H significantly decreased resting PmvO2 and steady-state contracting PmvO2(19.4+/-2.4 vs. 8.7+/-1.6 Torr for N and H, respectively, P<0.05). At the onset of contractions, H reduced the time delay (11.8+/-1.7 vs. 5.9+/-0.9 s for N and H, respectively, P<0.05) before the fall in PmvO2 and accelerated the rate of PmvO2 decrease (time constant, 12.6+/-1.4 vs. 7.3+/-0.9 s for N and H, respectively, P<0.05). Muscle Vo2 was reduced by 71% at rest and 64% with contractions in H vs. N, and O2 extraction during H averaged 78% at rest and 94% during contractions vs. 51 and 78% in N. These results demonstrate that H constrains the increase of skeletal muscle Qo2 relative to that of Vo2 at the onset of contractions, leading to a decreased PmvO2. According to Fick's law, this scenario will decrease blood-myocyte O2 flux, thereby slowing Vo2 kinetics and exacerbating the O2 deficit generated at exercise onset.     

X-ray study of myosin heads in contracting frog skeletal muscle

Using synchrotron radiation, the behaviour of the diffuse X-ray scatter was investigated in the relaxed and active phases of auxotonic and isometric contractions. Muscles were stimulated tetanically for 0.75 of a second, leaving intervals of three minutes between successive contractions. In isometric contractions the scatter is very asymmetric, which means that the myosin heads have a strongly preferred orientation. During tension rise the scatter expands in the meridional direction and contracts in the equatorial direction, the maximal local intensity change being about 20%. The shape change indicates that on average the myosin heads become oriented more perpendicularly to the fibre axis. The distribution of orientations at peak tension is quite different from that we found previously in X-ray scattering data from rigor muscles. In auxotonic contractions where muscles shorten against an increasing tension the scatter is practically circularly symmetrical. This suggests that during shortening the myosin heads go evenly through a wide range of orientations. It is concluded that the results from both the auxotonic and isometric experiments provide strong support for the rotating myosin head model. In isometric contractions the transition between the relaxed phase and peak tension is accompanied by an overall increase in scattering intensity of about 10%: this corresponds to a relative increase in the fraction of disordered myosin heads by almost 30%.     

Effect of epinephrine on net lactate uptake by contracting skeletal muscle.

The purpose of this study was to determine the effect of epinephrine on net lactate (La(-)) uptake at constant elevated blood La(-) concentration and steady level metabolic rate (O(2) uptake) in the canine gastrocnemius-plantaris muscle in situ. Infusion of La(-)/lactic acid (pH 3.5) established a mean arterial blood La(-) concentration of ~10 mM while normal blood-gas and pH status were maintained as the gastrocnemius-plantaris was stimulated with tetanic trains at a rate of one contraction every 4 s. After steady-state control measures, epinephrine was infused for 35 min at rates that produced a high physiological concentration with (Pro; n = 6) and without (Epi; n = 6) beta-adrenergic-receptor blockade via propranolol. Net La(-) uptake values during the control conditions were not significantly different between trials (Epi: 0.756 +/- 0.043; Pro: 0.703 +/- 0.061 mmol. kg(-1). min(-1)). Steady level O(2) uptake averaged approximately 69.5 ml. kg(-1). min(-1) for both control conditions and did not significantly change over the course of the experiments in either set of trials. Epi experiments resulted in a significantly reduced net La(-) uptake (0.346 +/- 0.088 mmol. kg(-1). min(-1) after 5 min of infusion) compared with control value at all sample times measured. However, net La(-) uptake was not significantly different from control at any time during Pro (0.609 +/- 0.052 mmol. kg(-1). min(-1) after 5 min of infusion). When the change from the respective control values for net La(-) uptake was compared across time for both series of experiments, Epi resulted in a significantly greater change from control than did Pro. This study suggests that epinephrine can have a profound effect on net La(-) uptake by contracting muscle and that these effects are elicited through beta-adrenergic-receptor stimulation.     

Bradykinin release from contracting skeletal muscle of the cat

Results of previous studies from our laboratory suggest that bradykinin has a role in the exercise pressor reflex elicited by static muscle contraction. The purpose of this study was to quantify the release of bradykinin from contracting skeletal muscle. In 18 cats, blood samples were withdrawn directly from the venous effluent of the triceps surae muscles immediately before and after 30 s of static contraction producing peak muscle tensions of 33, 50, and 100% of maximum electrically stimulated contraction. Contractions producing muscle tensions of 50 and 100% of maximum increased muscle venous bradykinin levels by 27 +/- 9 and 19 +/- 10 pg/ml, respectively. Conversely, 33% maximum contraction did not alter muscle venous bradykinin concentrations. However, when captopril was administered to slow the degradation of bradykinin, muscle venous bradykinin increased from 68 +/- 15 pg/ml at rest to 106 +/- 18 after contractions of 33% of maximum. When muscle ischemia was induced by 2 min of arterial occlusion before and during 30 s of 33% of maximum contraction, muscle venous bradykinin increased by 15 +/- 5 pg/ml. In addition, contraction-induced changes in muscle venous pH and lactate strongly correlated with bradykinin concentrations (r = 0.80 and 0.83, respectively). These data demonstrate that static contraction of relatively high intensity evokes the release of bradykinin from skeletal muscle and that ischemia, decreased pH, and increased lactate are strongly correlated with this release.     

Lactate metabolism in resting and contracting canine skeletal muscle with elevated lactate concentration.

This study was undertaken to quantitatively account for the metabolic disposal of lactate in skeletal muscle exposed to an elevated lactate concentration during rest and mild-intensity contractions. The gastrocnemius plantaris muscle group (GP) was isolated in situ in seven anesthetized dogs. In two experiments, the muscles were perfused with an artificial perfusate with a blood lactate concentration of ~9 mM while normal blood gas/pH status was maintained with [U-(14)C]lactate included to follow lactate metabolism. Lactate uptake and metabolic disposal were measured during two consecutive 40-min periods, during which the muscles rested or contracted at 1.25 Hz. Oxygen consumption averaged 10.1 +/- 2.0 micromol. 100 g(-1). min(-1) (2.26 +/- 0.45 ml. kg(-1). min(-1)) at rest and 143.3 +/- 16.2 micromol. 100 g(-1). min(-1) (32.1 +/- 3.63 ml. kg(-1). min(-1)) during contractions. Lactate uptake was positive during both conditions, increasing from 10.5 micromol. 100 g(-1). min(-1) at rest to 25.0 micromol. 100 g(-1). min(-1) during contractions. Oxidation and glycogen synthesis represented minor pathways for lactate disposal during rest at only 6 and 15%, respectively, of the [(14)C]lactate removed by the muscle. The majority of the [(14)C]lactate removed by the muscle at rest was recovered in the muscle extracts, suggesting that quiescent muscle serves as a site of passive storage for lactate carbon during high-lactate conditions. During contractions, oxidation was the dominant means for lactate disposal at >80% of the [(14)C]lactate removed by the muscle. These results suggest that oxidation is a limited means for lactate disposal in resting canine GP exposed to elevated lactate concentrations due to the muscle's low resting metabolic rate.     

Correlation between mechanical and enzymatic events in contracting skeletal muscle fiber

The conventional hypothesis of muscle contraction postulates that the interaction between actin and myosin involves tight coupling between the power stroke and hydrolysis of ATP. However, some in vitro experiments suggested that hydrolysis of a single molecule of ATP caused multiple mechanical cycles. To test whether the tight coupling is present in contracting muscle, we simultaneously followed mechanical and enzymatic events in a small population of cross-bridges of glycerinated rabbit psoas fibers. Such small population behaves as a single cross-bridge when muscle contraction is initiated by a sudden release of caged ATP. Mechanical events were measured by changes of orientation of probes bound to the regulatory domain of myosin. Enzymatic events were simultaneously measured from the same cross-bridge population by the release of fluorescent ADP from the active site. If the conventional view were true, ADP desorption would occur simultaneously with dissociation of cross-bridges from thin filaments and would be followed by cross-bridge rebinding to thin filaments. Such sequence of events was indeed observed in contracting muscle fibers, suggesting that mechanical and enzymatic events are tightly coupled in vivo.     

High glycogen levels enhance glycogen breakdown in isolated contracting skeletal muscle

The influence of supranormal muscle glycogen levels on glycogen breakdown in contracting muscle was investigated. Rats either rested or swam for 3 h and subsequently had their isolated hindquarters perfused after 21 h with access to food. Muscle glycogen concentrations were measured before and after 15 min of intermittent electrical muscle stimulation. Before stimulation, glycogen was higher in rats that swam on the preceding day (supercompensated rats) compared with controls. During muscle contractions, glycogen breakdown in fast-twitch red and white fibers was larger in supercompensated hindquarters than in controls, and glycogenolysis correlated significantly with precontraction glycogen concentrations. In slow-twitch fibers, electrical stimulation did not elicit glycogenolysis in either group. Glucose uptake and lactate release were decreased and increased, respectively, in supercompensated hindquarters compared with controls. O2 uptake, release of tyrosine and glycerol, and tension development were similar in the two groups. In conclusion, during muscle contractions, increased muscle glycogen levels lead to increased breakdown of glycogen and release of lactate and decreased uptake of glucose by mechanisms exerted within the muscle cells. Intramuscular lipolysis and net protein breakdown are unaffected. There seems to be no close linkage between needs and mobilization of fuel within the working muscle.     

Glucose ingestion blunts hormone-sensitive lipase activity in contracting human skeletal muscle

To examine the effect of attenuated epinephrine and elevated insulin on intramuscular hormone sensitivity lipase activity (HSLa) during exercise, seven men performed 120 min of semirecumbent cycling (60% peak pulmonary oxygen uptake) on two occasions while ingesting either 250 ml of a 6.4% carbohydrate (GLU) or sweet placebo (CON) beverage at the onset of, and at 15 min intervals throughout, exercise. Muscle biopsies obtained before and immediately after exercise were analyzed for HSLa. Blood samples were simultaneously obtained from a brachial artery and a femoral vein before and during exercise, and leg blood flow was measured by thermodilution in the femoral vein. Net leg glycerol and lactate release and net leg glucose and free fatty acid (FFA) uptake were calculated from these measures. Insulin and epinephrine were also measured in arterial blood before and throughout exercise. During GLU, insulin was elevated (120 min: CON, 11.4 +/- 2.4, GLU, 35.3 +/- 6.9 pM, P < 0.05) and epinephrine suppressed (120 min: CON, 6.1 +/- 2.5, GLU, 2.1 +/- 0.9 nM; P < 0.05) compared with CON. Carbohydrate feeding also resulted in suppressed (P < 0.05) HSLa relative to CON (120 min: CON, 1.71 +/- 0.18, GLU, 1.27 +/- 0.16 mmol.min-1.kg dry mass-1). There were no differences in leg lactate or glycerol release when trials were compared, but leg FFA uptake was lower (120 min: CON, 0.29 +/- 0.06, GLU, 0.82 +/- 0.09 mmol/min) and leg glucose uptake higher (120 min: CON, 3.16 +/- 0.59, GLU, 1.37 +/- 0.37 mmol/min) in GLU compared with CON. These results demonstrate that circulating insulin and epinephrine play a role in HSLa in contracting skeletal muscle.     

Direct modeling of X-ray diffraction pattern from contracting skeletal muscle

A direct modeling approach was used to quantitatively interpret the two-dimensional x-ray diffraction patterns obtained from contracting mammalian skeletal muscle. The dependence of the calculated layer line intensities on the number of myosin heads bound to the thin filaments, on the conformation of these heads and on their mode of attachment to actin, was studied systematically. Results of modeling are compared to experimental data collected from permeabilized fibers from rabbit skeletal muscle contracting at 5°C and 30°C and developing low and high isometric tension, respectively. The results of the modeling show that: i), the intensity of the first actin layer line is independent of the tilt of the light chain domains of myosin heads and can be used as a measure of the fraction of myosin heads stereospecifically attached to actin; ii), during isometric contraction at near physiological temperature, the fraction of these heads is ∼40% and the light chain domains of the majority of them are more perpendicular to the filament axis than in rigor; and iii), at low temperature, when isometric tension is low, a majority of the attached myosin heads are bound to actin nonstereospecifically whereas at high temperature and tension they are bound stereospecifically.     

Energy metabolism in relation to oxygen supply in contracting rat skeletal muscle

The regulation of the energy metabolism in contracting skeletal muscle is under close control, and several regulating factors have been reported. The aim of this study was to investigate the importance of the oxygen supply as a limiting factor for muscle performance during contractions and recovery from contractions. To perform well-controlled standardized experiments on contracting skeletal muscle, the perfused rat hind limb model was developed. The 31P NMR technique was adapted to the rat hind limb model. This enabled continuous nondestructive monitoring of the energy state at various levels of muscular activity. Significant correlations were found between oxygen delivery and oxygen consumption, lactate release, and glucose uptake, respectively. An increased degree of fatigue was observed at lower oxygen deliveries. In both soleus and gastrocnemius muscles, oxygen delivery correlated with the intramuscular concentrations of phosphocreatine (PCr), lactate, and glycogen. The 31P NMR experiments showed a correlation between oxygen delivery and the steady-state level of PCr/inorganic phosphate (Pi) during the contraction period. The rate of recovery in PCr/Pi after the contraction was also dependent on oxygen delivery. The results demonstrate a causal relationship between oxygen supply and energy state in contracting as well as recovering skeletal muscles.