Skip to main content
PMC home page
Proceedings of the Royal Society B: Biological Sciences logoLink to Proceedings of the Royal Society B: Biological Sciences
. 2001 Oct 22;268(1481):2113–2122. doi: 10.1098/rspb.2001.1764

Molecular motors: thermodynamics and the random walk.

N Thomas 1, Y Imafuku 1, K Tawada 1
PMCID: PMC1088855  PMID: 11600075

Abstract

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.

Full Text

The Full Text of this article is available as a PDF (208.6 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Astumian R. D., Derényi I. A chemically reversible Brownian motor: application to kinesin and Ncd. Biophys J. 1999 Aug;77(2):993–1002. doi: 10.1016/S0006-3495(99)76950-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Astumian R. D. Thermodynamics and kinetics of a Brownian motor. Science. 1997 May 9;276(5314):917–922. doi: 10.1126/science.276.5314.917. [DOI] [PubMed] [Google Scholar]
  3. Block S. M., Goldstein L. S., Schnapp B. J. Bead movement by single kinesin molecules studied with optical tweezers. Nature. 1990 Nov 22;348(6299):348–352. doi: 10.1038/348348a0. [DOI] [PubMed] [Google Scholar]
  4. 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]
  5. Coy D. L., Wagenbach M., Howard J. Kinesin takes one 8-nm step for each ATP that it hydrolyzes. J Biol Chem. 1999 Feb 5;274(6):3667–3671. doi: 10.1074/jbc.274.6.3667. [DOI] [PubMed] [Google Scholar]
  6. Duke T., Leibler S. Motor protein mechanics: a stochastic model with minimal mechanochemical coupling. Biophys J. 1996 Sep;71(3):1235–1247. doi: 10.1016/S0006-3495(96)79323-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Hackney D. D. Evidence for alternating head catalysis by kinesin during microtubule-stimulated ATP hydrolysis. Proc Natl Acad Sci U S A. 1994 Jul 19;91(15):6865–6869. doi: 10.1073/pnas.91.15.6865. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Hackney D. D. Highly processive microtubule-stimulated ATP hydrolysis by dimeric kinesin head domains. Nature. 1995 Oct 5;377(6548):448–450. doi: 10.1038/377448a0. [DOI] [PubMed] [Google Scholar]
  9. Hancock W. O., Howard J. Kinesin's processivity results from mechanical and chemical coordination between the ATP hydrolysis cycles of the two motor domains. Proc Natl Acad Sci U S A. 1999 Nov 9;96(23):13147–13152. doi: 10.1073/pnas.96.23.13147. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hill T. L. Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. Prog Biophys Mol Biol. 1974;28:267–340. doi: 10.1016/0079-6107(74)90020-0. [DOI] [PubMed] [Google Scholar]
  11. Hirokawa N. Kinesin and dynein superfamily proteins and the mechanism of organelle transport. Science. 1998 Jan 23;279(5350):519–526. doi: 10.1126/science.279.5350.519. [DOI] [PubMed] [Google Scholar]
  12. Hodge T., Cope M. J. A myosin family tree. J Cell Sci. 2000 Oct;113(Pt 19):3353–3354. doi: 10.1242/jcs.113.19.3353. [DOI] [PubMed] [Google Scholar]
  13. Howard J., Hudspeth A. J., Vale R. D. Movement of microtubules by single kinesin molecules. Nature. 1989 Nov 9;342(6246):154–158. doi: 10.1038/342154a0. [DOI] [PubMed] [Google Scholar]
  14. Hua W., Young E. C., Fleming M. L., Gelles J. Coupling of kinesin steps to ATP hydrolysis. Nature. 1997 Jul 24;388(6640):390–393. doi: 10.1038/41118. [DOI] [PubMed] [Google Scholar]
  15. Huxley A. F., Simmons R. M. Proposed mechanism of force generation in striated muscle. Nature. 1971 Oct 22;233(5321):533–538. doi: 10.1038/233533a0. [DOI] [PubMed] [Google Scholar]
  16. Huxley H. E. The mechanism of muscular contraction. Science. 1969 Jun 20;164(3886):1356–1365. doi: 10.1126/science.164.3886.1356. [DOI] [PubMed] [Google Scholar]
  17. Kim A. J., Endow S. A. A kinesin family tree. J Cell Sci. 2000 Nov;113(Pt 21):3681–3682. doi: 10.1242/jcs.113.21.3681. [DOI] [PubMed] [Google Scholar]
  18. Lymn R. W., Taylor E. W. Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry. 1971 Dec 7;10(25):4617–4624. doi: 10.1021/bi00801a004. [DOI] [PubMed] [Google Scholar]
  19. Mehta A. D., Rock R. S., Rief M., Spudich J. A., Mooseker M. S., Cheney R. E. Myosin-V is a processive actin-based motor. Nature. 1999 Aug 5;400(6744):590–593. doi: 10.1038/23072. [DOI] [PubMed] [Google Scholar]
  20. Rice S., Lin A. W., Safer D., Hart C. L., Naber N., Carragher B. O., Cain S. M., Pechatnikova E., Wilson-Kubalek E. M., Whittaker M. A structural change in the kinesin motor protein that drives motility. Nature. 1999 Dec 16;402(6763):778–784. doi: 10.1038/45483. [DOI] [PubMed] [Google Scholar]
  21. Rief M., Rock R. S., Mehta A. D., Mooseker M. S., Cheney R. E., Spudich J. A. Myosin-V stepping kinetics: a molecular model for processivity. Proc Natl Acad Sci U S A. 2000 Aug 15;97(17):9482–9486. doi: 10.1073/pnas.97.17.9482. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Schnitzer M. J., Block S. M. Kinesin hydrolyses one ATP per 8-nm step. Nature. 1997 Jul 24;388(6640):386–390. doi: 10.1038/41111. [DOI] [PubMed] [Google Scholar]
  23. Schnitzer M. J., Visscher K., Block S. M. Force production by single kinesin motors. Nat Cell Biol. 2000 Oct;2(10):718–723. doi: 10.1038/35036345. [DOI] [PubMed] [Google Scholar]
  24. Susalka S. J., Hancock W. O., Pfister K. K. Distinct cytoplasmic dynein complexes are transported by different mechanisms in axons. Biochim Biophys Acta. 2000 Mar 17;1496(1):76–88. doi: 10.1016/s0167-4889(00)00010-0. [DOI] [PubMed] [Google Scholar]
  25. Svoboda K., Mitra P. P., Block S. M. Fluctuation analysis of motor protein movement and single enzyme kinetics. Proc Natl Acad Sci U S A. 1994 Dec 6;91(25):11782–11786. doi: 10.1073/pnas.91.25.11782. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Svoboda K., Schmidt C. F., Schnapp B. J., Block S. M. Direct observation of kinesin stepping by optical trapping interferometry. Nature. 1993 Oct 21;365(6448):721–727. doi: 10.1038/365721a0. [DOI] [PubMed] [Google Scholar]
  27. Vale R. D., Funatsu T., Pierce D. W., Romberg L., Harada Y., Yanagida T. Direct observation of single kinesin molecules moving along microtubules. Nature. 1996 Apr 4;380(6573):451–453. doi: 10.1038/380451a0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Vale R. D., Milligan R. A. The way things move: looking under the hood of molecular motor proteins. Science. 2000 Apr 7;288(5463):88–95. doi: 10.1126/science.288.5463.88. [DOI] [PubMed] [Google Scholar]
  29. Vale R. D., Oosawa F. Protein motors and Maxwell's demons: does mechanochemical transduction involve a thermal ratchet? Adv Biophys. 1990;26:97–134. doi: 10.1016/0065-227x(90)90009-i. [DOI] [PubMed] [Google Scholar]
  30. Walker M. L., Burgess S. A., Sellers J. R., Wang F., Hammer J. A., 3rd, Trinick J., Knight P. J. Two-headed binding of a processive myosin to F-actin. Nature. 2000 Jun 15;405(6788):804–807. doi: 10.1038/35015592. [DOI] [PubMed] [Google Scholar]
  31. Weber J., Senior A. E. Catalytic mechanism of F1-ATPase. Biochim Biophys Acta. 1997 Mar 28;1319(1):19–58. doi: 10.1016/s0005-2728(96)00121-1. [DOI] [PubMed] [Google Scholar]
  32. Yasuda R., Noji H., Yoshida M., Kinosita K., Jr, Itoh H. Resolution of distinct rotational substeps by submillisecond kinetic analysis of F1-ATPase. Nature. 2001 Apr 19;410(6831):898–904. doi: 10.1038/35073513. [DOI] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary data file
PB012113s01.pdf (109.5KB, pdf)

Articles from Proceedings of the Royal Society B: Biological Sciences are provided here courtesy of The Royal Society

RESOURCES