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VOLUME 83, NUMBER 25 PHYSICAL REVIEW LETTERS 20D ECEMBER 1999Comment on “Cooperative Molecular Motors”In a Letter published recently [1], Jülicher and Prostproposed a simple stochastical model for motor moleculesthat cooperate in large groups. In the case of muscle,it is well known that the interaction between actin and21myosin can lead to contraction if ATP and Ca arepresent [2]. A muscle fiber contains a large amount ofthese actin-myosin “motors,” and it thus seems natural toapply Jülicher and Prost’s model to the muscle fiber as away of studying some aspects of the fascinating behaviorof this system. The asymmetry of muscle fibers at thesarcomeric level has already been established, and one ofthe predictions of the stochastical model is that there is acritical point at which this system behaves as a liquid-vaporsystem; that is, velocity and external force are related by13jy2yj f 2 f at this point. The authors alsoc ext cpredict an instability of the system when ≠f ≠y , 0.ext FIG. 1. Qualitative comparison between the predictions of theThis instability is interpreted as a phase transition in which stochastical model (Ref. [1]) (solid line) and the experimentalthe system changes its direction of motion discontinuously results of Ref. [3] (hollow circles). The filled circle representsthe abnormal point at which the first and second derivatives ofwhen the external load exceeds the maximum load that they with respect to f are zero. The units of y ...
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VOLUME 83, NUMBER 25 PHYSICAL REVIEW LETTERS 20D ECEMBER 1999
Comment on “Cooperative Molecular Motors”
In a Letter published recently [1], Jülicher and Prost
proposed a simple stochastical model for motor molecules
that cooperate in large groups. In the case of muscle,
it is well known that the interaction between actin and
21myosin can lead to contraction if ATP and Ca are
present [2]. A muscle fiber contains a large amount of
these actin-myosin “motors,” and it thus seems natural to
apply Jülicher and Prost’s model to the muscle fiber as a
way of studying some aspects of the fascinating behavior
of this system. The asymmetry of muscle fibers at the
sarcomeric level has already been established, and one of
the predictions of the stochastical model is that there is a
critical point at which this system behaves as a liquid-vapor
system; that is, velocity and external force are related by
13jy2yj f 2 f at this point. The authors alsoc ext c
predict an instability of the system when ≠f ≠y , 0.ext FIG. 1. Qualitative comparison between the predictions of the
This instability is interpreted as a phase transition in which stochastical model (Ref. [1]) (solid line) and the experimental
the system changes its direction of motion discontinuously results of Ref. [3] (hollow circles). The filled circle represents
the abnormal point at which the first and second derivatives ofwhen the external load exceeds the maximum load that the
y with respect to f are zero. The units of y Ls wereextcollection of motors can carry. A similar instability occurs
defined in Ref. [3] as (muscle lengths).
for the reverse motion.
The aim of this Comment is to point out that such be- instabilities or unstable motion have not yet been observed
havior is not observed in muscle contraction, to judge from experimentally in muscle.
current experimental evidence. Experiments performed by
1 2 2 2Edman [3] about ten years ago support the idea that there J. L. Marı ´n, M. Huerta, J. Muñiz, and X. Trujillo
1is a flat region at which the velocity of muscle contraction Departamento de Investigación en Fı ´sica
Universidad de Sonorashows isometric (zero velocity) behavior under increasing
Apartado Postal 5-088, 83190 Hermosillo, Sonora, Mexicoload. Moreover, experiments by Stienen et al. [4], which
2Centro Universitario de Investigaciones Biomédicaswere performed by changing the concentration of inorganic
Universidad de Colimaphosphate, revealed similar behavior, but the curves are
Apartado Postal 11, 28000 Colima, Colima, Mexico
shifted for different phosphate concentrations. A similar
21result was found when Ca or ATP was changed above
Received 21 September 1998
physiological levels [5,6]. In this context, the predictions
PACS numbers: 87.19.Rr, 05.40.–a, 87.10.+e
of the model proposed by Jülicher and Prost do not seem
to be applicable to muscle contraction since, although the
[1] F. Jülicher and J. Prost, Phys. Rev. Lett. 75, 2618 (1995).experimental results of Refs. [3–5] can be interpreted as
[2] A. F. Huxley, Prog. Biophys. Biophys. Chem. 7, 255indicating an abnormal point for this phenomenon, the
(1957); see also G. H. Pollack, Muscle & Moleculesbehavior of the velocity around the point y 0, f c c
(Ebner & Sons, Seattle, 1990).
0.282, is very different from that predicted by these au-
[3] K. A. P. Edman, J. Physiol. (London) 404, 301 (1988).
thors. To illustrate this discrepancy, we depict in Fig. 1
[4] G. J. M. Stienen, P. G. A. Versteeg, Z. Papp, and
the qualitative prediction of Jülicher and Prost, as com- G. Elzinga, J. Physiol. (London) 451, 503 (1992).
pared with the experimental results of Ref. [3]. [5] E. Pate and R. Cooke, J. Muscle Res. Cell Motil. 10, 181
The main objection to the theory of Jülicher and Prost (1989).
rests on the fact that, on increasing the concentration [6] S. V. Brooks and J. A. Faulkner, Am. J. Physiol. 267, C507
of ATP above and far from physiological levels, such (1994).
0031-90079983(25)5403(1)$15.00 © 1999 The American Physical Society 5403

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