Transport in a molecular motor system

Michel Chipot; Stuart Hastings; David Kinderlehrer

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 6, page 1011-1034
  • ISSN: 0764-583X

Abstract

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Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

How to cite

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Chipot, Michel, Hastings, Stuart, and Kinderlehrer, David. "Transport in a molecular motor system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.6 (2004): 1011-1034. <http://eudml.org/doc/245184>.

@article{Chipot2004,
abstract = {Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.},
author = {Chipot, Michel, Hastings, Stuart, Kinderlehrer, David},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Fokker-Planck; weakly coupled system; molecular motor; brownian rachet; transport; nonequilibrium systems; fluctuations},
language = {eng},
number = {6},
pages = {1011-1034},
publisher = {EDP-Sciences},
title = {Transport in a molecular motor system},
url = {http://eudml.org/doc/245184},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Chipot, Michel
AU - Hastings, Stuart
AU - Kinderlehrer, David
TI - Transport in a molecular motor system
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 6
SP - 1011
EP - 1034
AB - Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
LA - eng
KW - Fokker-Planck; weakly coupled system; molecular motor; brownian rachet; transport; nonequilibrium systems; fluctuations
UR - http://eudml.org/doc/245184
ER -

References

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  1. [1] A. Ajdari and J. Prost, Mouvement induit par un potentiel périodique de basse symétrie : diélectrophorèse pulse. C. R. Acad. Sci. Paris II 315 (1992) 1653. 
  2. [2] R.D. Astumian, Thermodynamics and kinetics of a Brownian motor. Science 276 (1997) 917–922. 
  3. [3] J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. Zbl0968.76069
  4. [4] M. Chipot, D. Kinderlehrer and M. Kowalczyk, A variational principle for molecular motors. Meccanica 38 (2003) 505–518. Zbl1032.92005
  5. [5] C. Doering, B. Ermentrout and G. Oster, Rotary DNA motors. Biophys. J. 69 (1995) 2256–2267. 
  6. [6] J. Dolbeault, D. Kinderlehrer and M. Kowalczyk, Remarks about the flashing rachet, in Proc. PASI 2003 (to appear). Zbl1064.35065MR2091497
  7. [7] D.D. Hackney, The kinetic cycles of myosin, kinesin, and dynein. Ann. Rev. Physiol. 58 (1996) 731–750. 
  8. [8] S. Hastings and D. Kinderlehrer, Remarks about diffusion mediated transport: thinking about motion in small systems. (to appear). Zbl1099.35005MR2159989
  9. [9] J. Howard, Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Inc. (2001). 
  10. [10] A.F. Huxley, Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7 (1957) 255–318. 
  11. [11] R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. Zbl0915.35120
  12. [12] D. Kinderlehrer and M. Kowalczyk, Diffusion-mediated transport and the flashing ratchet. Arch. Rat. Mech. Anal. 161 (2002) 149–179. Zbl1065.76183
  13. [13] D. Kinderlehrer and N. Walkington, Approximation of parabolic equations based upon Wasserstein’s variational principle. ESAIM: M2AN 33 (1999) 837–852. Zbl0936.65121
  14. [14] J.S. Muldowney, Compound matrices and ordinary differential equations. Rocky Mountain J. Math. 20 (1990) 857–872. Zbl0725.34049
  15. [15] Y. Okada and N. Hirokawa, A processive single-headed motor: kinesin superfamily protein KIF1A. Science 283 (1999) 19. 
  16. [16] Y. Okada and N. Hirokawa, Mechanism of the single headed processivity: diffusional anchoring between the K-loop of kinesin and the C terminus of tubulin, in Proc. Nat. Acad. Sciences 7 (2000) 640–645. 
  17. [17] F. Otto, Dynamics of labyrinthine pattern formation: a mean field theory. Arch. Rat. Mech. Anal. 141 (1998) 63–103. Zbl0905.35068
  18. [18] F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. PDE 26 (2001) 101–174. Zbl0984.35089
  19. [19] P. Palffy-Muhoray, T. Kosa and E. Weinan, Dynamics of a light driven molecular motor. Mol. Cryst. Liq. Cryst. 375 (2002) 577–591. 
  20. [20] A. Parmeggiani, F. Jülicher, A. Ajdari and J. Prost, Energy transduction of isothermal ratchets: generic aspects and specific examples close and far from equilibrium. Phys. Rev. E 60 (1999) 2127–2140. 
  21. [21] C.S. Peskin, G.B. Ermentrout and G.F. Oster, The correlation ratchet: a novel mechanism for generating directed motion by ATP hydrolysis, in Cell Mechanics and Cellular Engineering, V.C Mow et al. Eds., Springer, New York (1995). 
  22. [22] M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, N.J. (1967). Zbl0153.13602MR219861
  23. [23] P. Reimann, Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361 (2002) 57–265. Zbl1001.82097
  24. [24] M. Schliwa, Molecular Motors. Wiley-VCH Verlag, Wennheim (2003). 
  25. [25] B. Schwarz, Totally positive differential systems. Pacific J. Math. 32 (1970) 203–230. Zbl0193.04501
  26. [26] A. Tudorascu, A one phase Stefan problem via Monge-Kantorovich theory. CNA Report 03-CNA-007. 
  27. [27] R.D. Vale and R.A. Milligan, The way things move: looking under the hood of motor proteins. Science 288 (2000) 88–95. 
  28. [28] C. Villani, Topics in optimal transportation, Providence. AMS Graduate Studies in Mathematics 58 (2003). Zbl1106.90001MR1964483
  29. [29] E. Zeidler, Nonlinear functional analysis and its applications. I Springer, New York (1986). Zbl0583.47050MR816732

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