The following is an abstract of the article discussed in the subsequent letter:
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ABSTRACT |
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Karatzaferi, Christina, Kathryn H. Myburgh, Marc K. Chinn, Kathleen
Franks-Skiba, and Roger Cooke. Effect of an ADP analog on isometric force and ATPase activity of
active muscle fibers. Am J Physiol 284: C816-C825, 2003.The role played by ADP in modulating cross-bridge function has
been difficult to study, because it is hard to buffer ADP concentration
in skinned muscle preparations. To solve this, we used an analog of
ADP, spin-labeled ADP (SL-ADP). SL-ADP binds tightly to myosin but is a
very poor substrate for creatine kinase or pyruvate kinase. Thus ATP
can be regenerated, allowing well-defined concentrations of both ATP
and SL-ADP. We measured isometric ATPase rate and isometric tension as
a function of both [SL-ADP], 0.1-2 mM, and [ATP],
0.05-0.5 mM, in skinned rabbit psoas muscle, simulating fresh or
fatigued states. Saturating levels of SL-ADP increased isometric
tension (by P'), the absolute value of P' being nearly constant,
~0.04 N/mm2, in variable ATP levels, pH 7. Tension
decreased (50-60%) at pH 6, but upon addition of SL-ADP, P' was
still ~0.04 N/mm2. The ATPase was inhibited competitively
by SL-ADP with an inhibition constant, Ki, of
~240 and 280 µM at pH 7 and 6, respectively. Isometric force and
ATPase activity could both be fit by a simple model of cross-bridge kinetics.
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LETTER |
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To the Editor: The data and analysis presented by Karatzaferi et al. (6) support a new paradigm for muscle contraction, which if correct demands a fundamental reassessment of decades' worth of muscle mechanics studies. At issue is how mechanics and chemistry are coupled in muscle.
The conventional model of the past 40 years (4, 5) has mechanics and chemistry coupled within individual cross bridges, with ATP, ADP, and Pi concentrations formally expressed as functions of a mechanical parameter (the molecular strain, x) of an isolated cross bridge. In contrast, by expressing [ADP] as a function of a mechanical parameter of the muscle system (the macroscopic muscle force, PSL-ADP), Eq. 1 in Karatzaferi et al. implicitly couples mechanics and chemistry at the level of an ensemble of cross bridges. Equations of this form have been legitimized only within the context of a thermodynamic muscle model (2, 3): a model originally developed to account for the first direct measurements of mechanochemical coupling in muscle (1). By demonstrating that Eq. 1 accurately describes their data, where conventional models fail, Karatzaferi et al. provide additional experimental support for a thermodynamic muscle model (2), not, as stated, "a molecular explanation for [it]".
The conventional model of mechanochemical coupling uses rational mechanics to describe muscle force as a sum of well-defined myosin cross-bridge forces. In contrast, a thermodynamic model describes muscle force as an emergent property of a dynamic actin-myosin network, within which the force of a given cross bridge stochastically fluctuates due to force-generating transitions of neighboring cross bridges that are transmitted through compliant linkages. The "molecular explanation" for a thermodynamic muscle model is that, through these intermolecular interactions, the mechanics and chemistry of a given cross bridge are mixed up with the mechanics and chemistry of its neighbors.
The above competing descriptions of muscle force (molecular reductionist vs. thermodynamic) are mutually exclusive. As Gibbs points out, "If we wish to find in rational mechanics an a priori foundation for the principles of thermodynamics, we must seek mechanical definitions of temperature and entropy" (3a). Thus the thermodynamic muscle model (2, 3) supported by Karatzaferi et al. represents a fundamental shift in our understanding of muscle mechanics. In essence, if this model is correct, then one must conclude that the successes of conventional muscle models are superficial, resulting from strain (x)-dependent rate constants that were artificially tuned to make individual myosin cross bridges mimic the emergent properties (P) of dynamic actin-myosin networks in muscle. Although it remains to be determined which model most accurately describes muscle mechanics, growing support for a thermodynamic model of muscle (2, 3) from studies like that presented in Karatzaferi et al. suggests that this paradigm shift and its profound implications for our understanding of muscle contraction warrant careful consideration.
Josh E. Baker Department of Molecular Physiology and Biophysics University of Vermont Burlington, VT 05405 E-mail: jbaker{at}physiology.med.uvm.edu |
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REFERENCES |
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1.
Baker, JE,
LaConte LE,
Brust-Mascher II,
and
Thomas DD.
Mechanochemical coupling in spin-labeled, active, isometric muscle.
Biophys J
77:
2657-2664,
1999
2.
Baker, JE,
and
Thomas DD.
A thermodynamic muscle model and a chemical basis for A. V. Hill's muscle equation.
J Muscle Res Cell Motil
21:
335-344,
2000[ISI][Medline].
3.
Baker, JE,
and
Thomas DD.
Thermodynamics and kinetics of a molecular motor ensemble.
Biophys J
79:
1731-1736,
2000
3a.
Gibbs, JW.
Elementary Principles in Statistical Mechanics. New Haven, CT: Yale University Press, 1902, p. 165.
4.
Hill, TL.
Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I.
Prog Biophys Mol Biol
28:
267-340,
1974[Medline].
5.
Huxley, AF.
Muscle structure and theories of contraction.
Prog Biophys
7:
255-317,
1957[ISI].
6.
Karatzaferi, C,
Myburgh KH,
Chinn MK,
Franks-Skiba K,
and
Cooke R.
The effect of an ADP analog on isometric force and ATPase activity of active muscle fibers.
Am J Physiol Cell Physiol
284:
C816-C825,
2002[ISI].
To the Editor: We agree that our model provides
support for the approach taken by Baker and colleagues.
Reversal of the power stroke of a single myosin head would require the
input of energy required by other heads and transmitted through the
filament network. In this way, the properties of the muscle are the
result of a collection of interacting motors. These conclusions arise
from the fit of a model to the data. More direct experimental proof of
this concept would be helpful.
REPLY
Roger Cooke, Christina Karatzaferi Department of Biochemistry and Biophysics Cardiovascular Research Institute University of California San Francisco, CA 94143 E-mail: cooke{at}cgl.ucsf.edu |
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FOOTNOTES |
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10.1152/ajpcell.00597.2002
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