1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Mammalian skeletal muscle comprises different fiber types, whose identity is first established during embryonic development by intrinsic myogenic control mechanisms and is later modulated by neural and hormonal factors. The relative proportion of the different fiber types varies strikingly between species, and in humans shows significant variability between individuals. Myosin heavy chain isoforms, whose complete inventory and expression pattern are now available, provide a useful marker for fiber types, both for the four major forms present in trunk and limb muscles and the minor forms present in head and neck muscles. However, muscle fiber diversity involves all functional muscle cell compartments, including membrane excitation, excitation-contraction coupling, contractile machinery, cytoskeleton scaffold, and energy supply systems. Variations within each compartment are limited by the need of matching fiber type properties between different compartments. Nerve activity is a major control mechanism of the fiber type profile, and multiple signaling pathways are implicated in activity-dependent changes of muscle fibers. The characterization of these pathways is raising increasing interest in clinical medicine, given the potentially beneficial effects of muscle fiber type switching in the prevention and treatment of metabolic diseases.

Fiber types in mammalian skeletal muscles.

Repeated, intense use of muscles leads to a decline in performance known as muscle fatigue. Many muscle properties change during fatigue including the action potential, extracellular and intracellular ions, and many intracellular metabolites. A range of mechanisms have been identified that contribute to the decline of performance. The traditional explanation, accumulation of intracellular lactate and hydrogen ions causing impaired function of the contractile proteins, is probably of limited importance in mammals. Alternative explanations that will be considered are the effects of ionic changes on the action potential, failure of SR Ca2+ release by various mechanisms, and the effects of reactive oxygen species. Many different activities lead to fatigue, and an important challenge is to identify the various mechanisms that contribute under different circumstances. Most of the mechanistic studies of fatigue are on isolated animal tissues, and another major challenge is to use the knowledge generated in these studies to identify the mechanisms of fatigue in intact animals and particularly in human diseases.

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Skeletal Muscle Fatigue: Cellular Mechanisms

Ca(2+) regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A(7)TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca(2+) binding sites on TnC, conformational changes resulting from Ca(2+) binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca(2+) binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1-2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca(2+)-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the "open" probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A(7)TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca(2+) binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca(2+) regulates the strong binding of M.ADP.P(i) to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca(2+) activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A(7)TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca(2+)]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca(2+) binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. (ABSTRACT TRUNCATED)

https://www.physiology.org/doi/pdf/10.1152/physrev.2000.80.2.853

Regulation of Contraction in Striated Muscle

A positive temperature coefficient is the term which has been used to indicate that an increase in solubility occurs as the temperature is raised, whereas a negative coefficient indicates a decrease in solubility with rise in temperature.

Effect of Temperature

1. Force responses from mechanically skinned fibres of rat skeletal muscles (extensor digitorum longus and soleus) were measured at different temperatures in the range 3-35 degrees C following sudden changes in Ca2+ concentration in the preparations. 2. At all temperatures there were characteristic differences between the slow- and fast-twitch muscle fibres with respect to the relative steady-state force-[Ca2+] relation: such as a lower [Ca2+] threshold for activation and a less steep force-pCa curve in slow-twitch muscle fibres. 3. At 3-5 degrees C the force changes in both types of muscle fibres lagged considerably behind the estimated changes in [Ca2+] within the preparations and this enabled us to perform a comparative analysis of the Ca2+ kinetics in the process of force development in both muscle fibre types. This analysis suggest that two and six Ca2+ ions are involved in the regulatory unit for contraction of slow- and fast-twitch muscle fibres respectively. 4. The rate of relaxation following a sudden decrease in [Ca2+] was much lower in the slow-twitch than in the fast-twitch muscle at 5 degrees C, suggesting that properties of the contractile apparatus could play an essential role in determining the rate of relaxation in vivo. 5. There was substantial variation in Ca2+ sensitivity between muscle fibres of the same type from different animals at each temperature. However the steepness of the force-[Ca2+] relation was essentially the same for all fibres of the same type. 6. A change in temperature from 5 to 25 degrees C had a statistically significant effect on the sensitivity of the fast-twitch muscle fibres, rendering them less sensitive to Ca2+ by a factor of 2. However a further increase in temperature from 25 to 35 degrees C did not have any statistically significant effect on the force-[Ca2+] relation in fast-twitch muscle fibres. 7. The effect of temperature on the Ca2+ sensitivity of slow-twitch muscle fibres was not statistically significant, mainly because of the large variation in sensitivity amongst these preparations at room temperature. 8. Two types of oscillatory processes not associated with intracellular membranes were observed in the force response of all slow-twitch muscle fibres when submaximally activated (less than 60% maximum force) at 25 and 35 degrees C, but never at 3-5 degrees C. The frequency of oscillations increased with temperature. 9. Maximum Ca2+-activated force in both muscle fibre types was greatly dependent upon temperature over the range 0-25 degrees C, but increased only slightly above 25 degrees C. 10. Experiments on the rigor state suggest that the number of possible actomyosin interacting sites diminishes considerably as temperature is decreased below 25 degrees C.

Calcium-activated force responses in fast- and slow-twitch skinned muscle fibres of the rat at different temperatures.

1. Steady-state force-pCa relations were determined for mechanically skinned fibres of fast- and slow-twitch rat skeletal muscle, extensor digitorum longus (e.d.l.) and soleus respectively, at varied sarcomere lengths and temperatures (3-35 degrees C).2. This relation was different for the two fibre types at all sarcomere lengths, with soleus fibres having lower Ca(2+) concentration threshold for activation and requiring a wider Ca(2+) concentration range to reach force saturation.3. An increase in sarcomere length within the range 2.2-3.6 mum reversibly shifted the steady-state force-pCa curves for both fast- and slow-twitch fibres toward lower Ca(2+) without affecting the steepness of the curves.4. The results are consistent with the idea that the sensitivity of the contractile apparatus to Ca(2+) is increased with increasing sarcomere length.5. The change in apparent Ca(2+) sensitivity (measured as the change in pCa corresponding to 50% Ca-activated force (DeltapCa(50))) was approximately proportional to the change in sarcomere length (DeltaSL) at all temperatures for both types of muscle fibre.6. The proportionality coefficient (DeltapCa(50)/DeltaSL) was higher for slow-twitch fibres than for fast-twitch fibres by a factor of 1.5-2.0 at all temperatures investigated.7. The force-pCa relation was less affected by changes in sarcomere length at lower (3-5 degrees C) than at higher temperatures (22-35 degrees C).8. The sarcomere length-maximum force relation obtained with skinned fibres for sarcomere lengths between 2.10 and 4.05 mum was similar for both fibre types at all temperatures despite large temperature dependent variations in maximum Ca-activated force response. Maximum force decreased linearly to zero between ca. 2.8 and 3.95 mum; remained high and essentially constant between ca. 2.40 and 2.80 mum, and decreased significantly below 2.40 mum.9. Myofilament-generated tension oscillations produced by partially activated soleus skinned fibres are highly length dependent, disappearing completely when sarcomere length is increased above 3.15 mum.

Effects of sarcomere length on the force—pCa relation in fast‐ and slow‐twitch skinned muscle fibres from the rat

1. Mechanically skinned fast-twitch (FT) and slow-twitch (ST) muscle fibres of the rat were used to investigate the effects of fatigue-like changes in creatine phosphate (CP) and inorganic phosphate (P(i)) concentration on Ca(2+)-activation properties of the myofilaments as well as Ca2+ movements into and out of the sarcoplasmic reticulum (SR). 2. Decreasing CP from 50 mM to zero in FT fibres increased maximum Ca(2+)-activated tension (Tmax) by 16 +/- 2% and shifted the mid-point of the tension-pCa relation (pCa50) to the left by 0.28 +/- 0.03 pCa units. In ST fibres, a decrease of CP from 25 mM to zero increased Tmax by 9 +/- 1% and increased the pCa50 by 0.16 +/- 0.01 pCa units. The effect of CP on Tmax was suppressed in both fibre types by prior treatment with 0.3 mM FDNB (1-fluoro-2,4-dinitrobenzene), suggesting that these effects may occur via changes in creatine kinase activity. 3. Increases of P(i) in the range 0-50 mM reduced the pCa50 and Tmax in both fibre types. These effects were more pronounced in ST fibres than in FT fibres in absolute terms. However, normalization of the results to resting P(i) levels appropriate to both fibre types (1 mM for FT and 5 mM for ST fibres) revealed similar decreases in Tmax (approximately 39% at 25 mM P(i) and approximately 48% at 50 mM P(i)) and pCa50 (0.25 pCa units at 25-50 mM P(i)). The depressant action of P(i) on both parameters was considerably reduced when the rise in P(i) was accompanied by an equivalent reduction in [CP]. 4. Tension development in the presence of complex, fatigue-like milieu changes (40 mM P(i) for FT; 20 mM P(i) for ST) was decreased by 35-40% at a constant myoplasmic [Ca2+] of 6 microM in both fibre types. 5. SR Ca2+ loading at a myoplasmic [Ca2+] of 100 nM was found to increase abruptly when the [P(i)] during loading was increased to near 9 mM. At a myoplasmic [Ca2+] of 300 nM, the threshold P(i) for this effect dropped to approximately 3 mM. 6. Tension responses evoked by caffeine in the absence of P(i) were smaller and slower to peak if fibres were exposed to P(i) in a restricted myoplasmic Ca2+ pool after SR Ca2+ loading. This indicated that myoplasmic P(i) can decrease and prolong the rate of Ca2+ release from the SR.(ABSTRACT TRUNCATED AT 400 WORDS)

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1995.sp020504

Effects of creatine phosphate and P(i) on Ca2+ movements and tension development in rat skinned skeletal muscle fibres.

1. The effects on normal excitation-contraction (E-C) coupling of two important intracellular ions, H+ and Mg2+, were examined in skinned fibres from the extensor digitorum longus muscle of rat. 2. A single depolarization (2-3 s duration) in the presence of 1 mM Mg2+ (pH 7.1, 23 degrees C) released most of the available Ca2+ in the sarcoplasmic reticulum (SR), but a similar depolarization in the presence of 10 mM Mg2+ was unable to release almost any Ca2+. Thus, raised [Mg2+] potently inhibits depolarization-induced Ca2+ release in mammalian muscle. 3. Depolarization at pH 6.2 (1 mM Mg2+, 23 degrees C) induced a large force response, which was on average 78 +/- 2%, n = 6, of the depolarization-induced response at pH 7.1; this reduction resulted from a corresponding reduction in maximum Ca(2+)-activated force at pH 6.2. Similar results were obtained at 37 degrees C. Also, a single depolarization at pH 6.2 caused almost complete depletion of the releasable Ca2+ in the SR. Thus, low pH does not prevent depolarization-induced Ca2+ release in mammalian muscle. 4. Lowering the free [Mg2+] from 1 mM to 15 microM caused massive release of Ca2+, and depletion of the SR, at both pH 7.1 and 6.2, indicating that over this pH range, H+ did not readily substitute for Mg2+ at its inhibitory site on the Ca2+ release channel.(ABSTRACT TRUNCATED AT 250 WORDS)

Effects of intracellular pH and [Mg2+] on excitation-contraction coupling in skeletal muscle fibres of the rat.

1. Raising the intracellular [Ca2+] for 10 s at 23 degrees C abolished depolarization-induced force responses in mechanically skinned muscle fibres of toad and rat (half-maximal effect at 10 and 23 microM, respectively), without affecting the ability of caffeine or low [Mg2+] to open the ryanodine receptor (RyR)/Ca2+ release channels. Thus, excitation-contraction coupling was lost, even though the Ca2+ release channels were still functional. Coupling could not be restored in the duration of an experiment (up to 1 h). 2. The Ca(2+)-dependent uncoupling had a Q10 > 3.5, and was three times slower at pH 5.8 than at pH 7.1. Sr2+ caused similar uncoupling at twenty times higher concentration, but Mg2+, even at 10 mM, was ineffective. Uncoupling was not noticeably affected by removal of ATP or application of protein kinase or phosphatase inhibitors. 3. Confocal laser scanning microscopy showed that the transverse tubular system was sealed in its entirety in mechanically skinned fibres and that its integrity was maintained in uncoupled fibres. Electron microscopy revealed distorted or severed triad junctions and Z-line aberrations in uncoupled fibres. 4. Only when uncoupling was induced at a relatively slow rate (e.g. over 60 s with 2.5 microM Ca2+) could it be prevented by the protease inhibitor leupeptin (1 mM). Immunostaining of Western blots showed no evidence of proteolysis of the RyR, the alpha 1-subunit of dihydropyridine receptor (DHPR) or triadin in uncoupled fibres. 5. Fibres which, whilst intact, were stimulated repeatedly by potassium depolarization with simultaneous application of 30 mM caffeine showed reduced responsiveness after skinning to depolarization but not to caffeine. Rapid release of endogenous Ca2+, or raised [Ca2+] under conditions which minimized the loss of endogenous diffusible myoplasmic molecules from the skinned fibre, caused complete uncoupling. Taken together, these results suggest that Ca(2+)-dependent uncoupling can also occur in intact fibres. 6. This Ca(2+)-dependent loss of depolarization-induced Ca2+ release may play an important feedback role in muscle by stopping Ca2+ release in localized areas where it is excessive and may be responsible for long-lasting muscle fatigue after severe exercise, as well as contributing to muscle weakness in various dystrophies.

D G Stephenson

Papers

Calcium-activated force responses in fast- and slow-twitch skinned muscle fibres of the rat at different temperatures.

Effects of sarcomere length on the force—pCa relation in fast‐ and slow‐twitch skinned muscle fibres from the rat

Effects of creatine phosphate and P(i) on Ca2+ movements and tension development in rat skinned skeletal muscle fibres.

Effects of intracellular pH and [Mg2+] on excitation-contraction coupling in skeletal muscle fibres of the rat.

Raised intracellular [Ca2+] abolishes excitation‐contraction coupling in skeletal muscle fibres of rat and toad.