Ca2+ dependence of tension and ADP production in segments of chemically skinned muscle fibers

Levy, Ronald M.; Umazume, Yoshiki; Kushmerick, Martin J.

doi:10.1016/0005-2728(76)90091-8

Cited by 52 publications

(26 citation statements)

References 29 publications

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“…An elementary calculation shows that both activations generally rise much more steeply with increasing Z2 than does the corresponding analogue of the Langmuir adsorption isotherm, showing what is often referred to as "positive cooperativity." We also note thatJ' $ 1' and the ratio 41/J' generally increases with increasing Z2; i.e., the relative tension cost decreases with increasing activation, as is often but not always observed (10,11 [4] which was used instead of Eq. 3 for the calculation of Fig.…”

Section: The Modelmentioning

confidence: 67%

“…1B. That this approximation is reasonable is indicated by the qualitative similarity between measurements ofthe Ca2+ activation ofATPase in isometric fibers (10,11) and those in myofibrils (17).…”

Section: The Modelmentioning

confidence: 71%

“…As the concentration of Ca2' is raised, it is adsorbed onto troponin (1,8,9) and the reaction of crossbridges with actins is stimulated, resulting in increases in the stationary-state isometric force and ATPase in fibers (9)(10)(11) and an increase in ATPase in myofibrils (10). To take into account the promotion of crossbridge reaction with actins by Ca2' adsorption to troponin, we assume that when a Ca2" site is occupied and a nearest-neighbor actin is reacting with a crossbridge, there is an attractive (<O) free energy of interaction w12.…”

Section: The Modelmentioning

confidence: 99%

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Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics.

Shiner¹,

Solaro

1982

Proc. Natl. Acad. Sci. U.S.A.

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We discuss the activation of thin-filament-regulated muscles by calcium ion in terms of a qualitative model based on nearest-neighbor lattice statistics. For the most part, the model takes into account only the essential features of the phenomenon-that there must be an interaction between calcium adsorption to troponin and crossbridge reaction with actin for calcium ion to activate contraction and that the relevant stationary states are nonequilibrium ones. Even so, the model predicts the following features which are seen experimentally but have generally not been considered in previous models: (i) the relative activations of stationary-state isometric force and ATPase are not equal; (ii) in general, neither activation of force nor that of ATPase is proportional to calcium adsorption to the activating sites; and (iii) the slopes of the relations between the activations and the logarithm of the calcium ion concentration generally depend on the necessary interaction between calcium ion adsorption and crossbridge reaction with actin. Thus, these relations show cooperative effects even if there is no interaction between calcium adsorption sites.There is significant understanding ofthe relations between the molecular events and their phenomenological manifestations in the activation of muscle contraction by calcium ion (1-4). Yet this understanding is not complete. Much of it is based on concepts from the theory of equilibrium systems and from other limiting cases, whereas contraction and its activation are distinctly nonequilibrium phenomena, even at the stationary state, and the limiting cases are so particular that they would not seem to obtain in muscle. We have recently begun to develop a model of cooperative systems with nonequilibrium stationary states (5), and in this paper we use this model to offer insights into these facets of the Ca2" activation process. We will attempt to show that some of the previous interpretations of this process have been based on untenable assumptions. We will also offer explanations for some puzzling aspects ofthe phenomenon, but we will not attempt to develop a complete quantitative model; our goal is qualitative rather then quantitative. We will consider only essential aspects of the phenomenon so that the model reflects its basic features. (Derivations of the approximations and details of other points are available upon request.) The model should thus be considered a paradigm for more accurate models. THE MODELWe picture the thin filament as a lattice of two classes of sites: those on troponin that adsorb Ca2" and the actins. Contraction is brought about by a cyclic reaction of projections of myosin from the thick filament, the crossbridges, with the actins and is powered by an ATPase located on the myosins (1-4). It is generally acknowledged that a crossbridge may exist in various states, both when it is reacting with an actin and when it is not reacting. However, because we are concerned with the activation of contraction, not the contraction itself, a two-state cros...

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Section: The Modelmentioning

confidence: 67%

Section: The Modelmentioning

confidence: 71%

Section: The Modelmentioning

confidence: 99%

See 1 more Smart Citation

Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics.

Shiner¹,

Solaro

1982

Proc. Natl. Acad. Sci. U.S.A.

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“…Assuming that k4 is roufhly equivalent to the hydrolysis rate constant, we estimate it to be -0.5-1 s-from studies on glycerinated muscle (Hayashi and Tonomura, 1968;Levy et al, 1976;Takashi and Putnam, 1979) . Using these values and taking k_ 1 to equal 30 s-', we obtain a range for the ratio k_1/k4 of 30-60.…”

Section: Discussionmentioning

confidence: 99%

Effect of cross-bridge kinetics on apparent Ca2+ sensitivity.

Brandt¹,

Cox²,

Kawai³

et al. 1982

The Journal of General Physiology

148

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Three different ways of shifting the pCa/tension curve on the pCa axis have been studied and related to changes in the rate constants of the crossbridge cycle. The curve midpoint shifts to higher pCa's wheel the substrate (Mg-ATP) is reduced from 5 to 0.25 mM, when the phosphate concentration is reduced from 7.5 mM to 0, and when the ionic strength is reduced from 0.200 to 0.120 . The Hill coefficients of the pCa/tension curve in our standard saline (5 mM substrate, 5 mM free ATP, 7.5 mM phosphate, ionic strength 0.200, 15°C) are between 5.1 and 5.6 and fall to 3.0 with the left shift of the curve brought about by reducing both substrate and phosphate. Left shifts of the curve produced by reduction in the ionic strength do not result in a lower Hill coefficient . Reducing either substrate or phosphate is associated with a reduction in the optimal frequency for oscillatory work, but reduction in ionic strength is not so associated . Maximum tension increases with the left shift of the curve brought about by reducing phosphate concentration or ionic strength, but tension decreases with the left shift of the curve accompanying substrate concentration reduction in a phosphate-free saline . We argue that one mechanism for the observed shift of the curve along the pCa axis is the relationship between the time a cross-bridge takes to complete a cycle and the time Ca 2+ stays bound to troponin C (TnC) . If the cycle rate is decreased, a smaller fraction of TnC sites must be occupied to keep a given fraction of cross-bridges active . To illustrate this concept, we present a simplified model of the cross-bridge cycle incorporating the kinetics of Ca binding to TnC.

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“…4, which shows actual data points (circles) superimposed on a family of hypothetical curves (lines). Each curve represents a different apparent pKd, corresponding to a given value of the ratio defined (33) than that for myofibrils.…”

Section: Discussionmentioning

confidence: 99%

Can the binding of Ca2+ to two regulatory sites on troponin C determine the steep pCa/tension relationship of skeletal muscle?

Brandt¹,

Cox²,

Kawai³

1980

Proc. Natl. Acad. Sci. U.S.A.

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The relationship between tension and Ca2+ concentration in single skinned muscle fibers has been determined with a high density of experimental points and the data have been fitted by a least squares method to the Hill equation. We find that the mean Hill coefficient for the slope of the tension/Ca2+ relationship is between 5 and 6, and the pKld is about 5.9. Because there are four Ca2+ binding sites on troponin C, and only two of these regulate hydrolysis of MgATP, we conclude that the regulation of tension by Ca2+ binding is greatly modified by other factors. One important factor is the time required for a cross-bridge to complete a cycle once initiated, relative to the time Ca2+ remains bound to troponin C. The pCa/tension relationship will shift to higher pCa values as the ratio of cross-bridge cycle time to the Ca2+ bound time increases. For example, the pCa/tension curve may progressively shift to the left with increase in tension because strain in the myofilament lattice progressively increases the cycle time. This left shift will produce a ta/tension relationship that is steeper than the actual Ca2 binding curve. The anticipated shift of the pCa/ tension curve with cycle time also bears on interpretations of earlier experiments on the "active state" and on the effects of Ca2+ on the maximal velocity of shortening.

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Ca2+ dependence of tension and ADP production in segments of chemically skinned muscle fibers

Cited by 52 publications

References 29 publications

Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics.

Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics.

Effect of cross-bridge kinetics on apparent Ca2+ sensitivity.

Can the binding of Ca2+ to two regulatory sites on troponin C determine the steep pCa/tension relationship of skeletal muscle?

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