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. 2001 Sep;81(3):1234–1244. doi: 10.1016/S0006-3495(01)75781-5

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: curvature as an indicator of the torque.

D A Cherepanov 1, W Junge 1
PMCID: PMC1301605  PMID: 11509340

Abstract

ATP synthase (F-ATPase) operates as an electrochemical-to-mechanical-to-chemical energy transducer with an astounding 360 degrees rotary motion of subunits epsilongammac(10-14) (rotor) against delta(alphabeta)(3)ab(2) (stator). The enzyme's torque as a function of the angular reaction coordinate in relation to ATP-synthesis/hydrolysis, internal elasticity, and external load has remained an important issue. Fluorescent actin filaments of micrometer length have been used to detect the rotation as driven by ATP hydrolysis. We evaluated the viscoelastic dynamics of actin filaments under the influence of enzyme-generated torque, stochastic Langevin force, and viscous drag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (approximately 100 ms), power strokes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretical background for the alternative use of the filament as a spring balance. The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Pertinent experiments were analyzed in the companion paper.

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Selected References

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  1. Abrahams J. P., Leslie A. G., Lutter R., Walker J. E. Structure at 2.8 A resolution of F1-ATPase from bovine heart mitochondria. Nature. 1994 Aug 25;370(6491):621–628. doi: 10.1038/370621a0. [DOI] [PubMed] [Google Scholar]
  2. Adachi K., Yasuda R., Noji H., Itoh H., Harada Y., Yoshida M., Kinosita K., Jr Stepping rotation of F1-ATPase visualized through angle-resolved single-fluorophore imaging. Proc Natl Acad Sci U S A. 2000 Jun 20;97(13):7243–7247. doi: 10.1073/pnas.120174297. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Boyer P. D. The ATP synthase--a splendid molecular machine. Annu Rev Biochem. 1997;66:717–749. doi: 10.1146/annurev.biochem.66.1.717. [DOI] [PubMed] [Google Scholar]
  4. Cherepanov D. A., Mulkidjanian A. Y., Junge W. Transient accumulation of elastic energy in proton translocating ATP synthase. FEBS Lett. 1999 Apr 16;449(1):1–6. doi: 10.1016/s0014-5793(99)00386-5. [DOI] [PubMed] [Google Scholar]
  5. Duncan T. M., Zhou Y., Bulygin V. V., Hutcheon M. L., Cross R. L. Probing interactions of the Escherichia coli F0F1 ATP synthase beta and gamma subunits with disulphide cross-links. Biochem Soc Trans. 1995 Nov;23(4):736–741. doi: 10.1042/bst0230736. [DOI] [PubMed] [Google Scholar]
  6. Gittes F., Mickey B., Nettleton J., Howard J. Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J Cell Biol. 1993 Feb;120(4):923–934. doi: 10.1083/jcb.120.4.923. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Hunt A. J., Gittes F., Howard J. The force exerted by a single kinesin molecule against a viscous load. Biophys J. 1994 Aug;67(2):766–781. doi: 10.1016/S0006-3495(94)80537-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Häsler K., Engelbrecht S., Junge W. Three-stepped rotation of subunits gamma and epsilon in single molecules of F-ATPase as revealed by polarized, confocal fluorometry. FEBS Lett. 1998 Apr 24;426(3):301–304. doi: 10.1016/s0014-5793(98)00358-5. [DOI] [PubMed] [Google Scholar]
  9. Isambert H., Venier P., Maggs A. C., Fattoum A., Kassab R., Pantaloni D., Carlier M. F. Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J Biol Chem. 1995 May 12;270(19):11437–11444. doi: 10.1074/jbc.270.19.11437. [DOI] [PubMed] [Google Scholar]
  10. Jones P. C., Fillingame R. H. Genetic fusions of subunit c in the F0 sector of H+-transporting ATP synthase. Functional dimers and trimers and determination of stoichiometry by cross-linking analysis. J Biol Chem. 1998 Nov 6;273(45):29701–29705. doi: 10.1074/jbc.273.45.29701. [DOI] [PubMed] [Google Scholar]
  11. Junge W., Lill H., Engelbrecht S. ATP synthase: an electrochemical transducer with rotatory mechanics. Trends Biochem Sci. 1997 Nov;22(11):420–423. doi: 10.1016/s0968-0004(97)01129-8. [DOI] [PubMed] [Google Scholar]
  12. Kinosita K., Jr, Yasuda R., Noji H., Ishiwata S., Yoshida M. F1-ATPase: a rotary motor made of a single molecule. Cell. 1998 Apr 3;93(1):21–24. doi: 10.1016/s0092-8674(00)81142-3. [DOI] [PubMed] [Google Scholar]
  13. Leslie A. G., Abrahams J. P., Braig K., Lutter R., Menz R. I., Orriss G. L., van Raaij M. J., Walker J. E. The structure of bovine mitochondrial F1-ATPase: an example of rotary catalysis. Biochem Soc Trans. 1999 Feb;27(2):37–42. doi: 10.1042/bst0270037. [DOI] [PubMed] [Google Scholar]
  14. Mendelson R., Morris E. P. The structure of the acto-myosin subfragment 1 complex: results of searches using data from electron microscopy and x-ray crystallography. Proc Natl Acad Sci U S A. 1997 Aug 5;94(16):8533–8538. doi: 10.1073/pnas.94.16.8533. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Noji H., Yasuda R., Yoshida M., Kinosita K., Jr Direct observation of the rotation of F1-ATPase. Nature. 1997 Mar 20;386(6622):299–302. doi: 10.1038/386299a0. [DOI] [PubMed] [Google Scholar]
  16. Omote H., Sambonmatsu N., Saito K., Sambongi Y., Iwamoto-Kihara A., Yanagida T., Wada Y., Futai M. The gamma-subunit rotation and torque generation in F1-ATPase from wild-type or uncoupled mutant Escherichia coli. Proc Natl Acad Sci U S A. 1999 Jul 6;96(14):7780–7784. doi: 10.1073/pnas.96.14.7780. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Oster G., Wang H. ATP synthase: two motors, two fuels. Structure. 1999 Apr 15;7(4):R67–R72. doi: 10.1016/s0969-2126(99)80046-x. [DOI] [PubMed] [Google Scholar]
  18. Panke O, Rumberg B. Kinetic modeling of rotary CF0F1-ATP synthase: storage of elastic energy during energy transduction . Biochim Biophys Acta. 1999 Jun 30;1412(2):118–128. doi: 10.1016/s0005-2728(99)00059-6. [DOI] [PubMed] [Google Scholar]
  19. Pänke O., Cherepanov D. A., Gumbiowski K., Engelbrecht S., Junge W. Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: angular torque profile of the enzyme. Biophys J. 2001 Sep;81(3):1220–1233. doi: 10.1016/S0006-3495(01)75780-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Pänke O., Gumbiowski K., Junge W., Engelbrecht S. F-ATPase: specific observation of the rotating c subunit oligomer of EF(o)EF(1). FEBS Lett. 2000 Apr 21;472(1):34–38. doi: 10.1016/s0014-5793(00)01436-8. [DOI] [PubMed] [Google Scholar]
  21. Sabbert D., Engelbrecht S., Junge W. Functional and idling rotatory motion within F1-ATPase. Proc Natl Acad Sci U S A. 1997 Apr 29;94(9):4401–4405. doi: 10.1073/pnas.94.9.4401. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Sabbert D., Engelbrecht S., Junge W. Intersubunit rotation in active F-ATPase. Nature. 1996 Jun 13;381(6583):623–625. doi: 10.1038/381623a0. [DOI] [PubMed] [Google Scholar]
  23. Sabbert D., Junge W. Stepped versus continuous rotatory motors at the molecular scale. Proc Natl Acad Sci U S A. 1997 Mar 18;94(6):2312–2317. doi: 10.1073/pnas.94.6.2312. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Sambongi Y., Iko Y., Tanabe M., Omote H., Iwamoto-Kihara A., Ueda I., Yanagida T., Wada Y., Futai M. Mechanical rotation of the c subunit oligomer in ATP synthase (F0F1): direct observation. Science. 1999 Nov 26;286(5445):1722–1724. doi: 10.1126/science.286.5445.1722. [DOI] [PubMed] [Google Scholar]
  25. Seelert H., Poetsch A., Dencher N. A., Engel A., Stahlberg H., Müller D. J. Structural biology. Proton-powered turbine of a plant motor. Nature. 2000 May 25;405(6785):418–419. doi: 10.1038/35013148. [DOI] [PubMed] [Google Scholar]
  26. Stock D., Leslie A. G., Walker J. E. Molecular architecture of the rotary motor in ATP synthase. Science. 1999 Nov 26;286(5445):1700–1705. doi: 10.1126/science.286.5445.1700. [DOI] [PubMed] [Google Scholar]
  27. Tsunoda S. P., Aggeler R., Noji H., Kinosita K., Jr, Yoshida M., Capaldi R. A. Observations of rotation within the F(o)F(1)-ATP synthase: deciding between rotation of the F(o)c subunit ring and artifact. FEBS Lett. 2000 Mar 31;470(3):244–248. doi: 10.1016/s0014-5793(00)01336-3. [DOI] [PubMed] [Google Scholar]
  28. Yanagida T., Nakase M., Nishiyama K., Oosawa F. Direct observation of motion of single F-actin filaments in the presence of myosin. Nature. 1984 Jan 5;307(5946):58–60. doi: 10.1038/307058a0. [DOI] [PubMed] [Google Scholar]
  29. Yasuda R., Miyata H., Kinosita K., Jr Direct measurement of the torsional rigidity of single actin filaments. J Mol Biol. 1996 Oct 25;263(2):227–236. doi: 10.1006/jmbi.1996.0571. [DOI] [PubMed] [Google Scholar]
  30. Yasuda R., Noji H., Kinosita K., Jr, Yoshida M. F1-ATPase is a highly efficient molecular motor that rotates with discrete 120 degree steps. Cell. 1998 Jun 26;93(7):1117–1124. doi: 10.1016/s0092-8674(00)81456-7. [DOI] [PubMed] [Google Scholar]

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