Transport in a molecular motor system
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1011-1034.

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.

DOI : 10.1051/m2an:2004048
Classification : 34D23, 35K50, 35K57, 92C37, 92C45
Mots-clés : Fokker-Planck, weakly coupled system, molecular motor, brownian rachet, transport 
@article{M2AN_2004__38_6_1011_0,
     author = {Chipot, Michel and Hastings, Stuart and Kinderlehrer, David},
     title = {Transport in a molecular motor system},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1011--1034},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {6},
     year = {2004},
     doi = {10.1051/m2an:2004048},
     mrnumber = {2108942},
     zbl = {1077.35060},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an:2004048/}
}
TY  - JOUR
AU  - Chipot, Michel
AU  - Hastings, Stuart
AU  - Kinderlehrer, David
TI  - Transport in a molecular motor system
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2004
SP  - 1011
EP  - 1034
VL  - 38
IS  - 6
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/m2an:2004048/
DO  - 10.1051/m2an:2004048
LA  - en
ID  - M2AN_2004__38_6_1011_0
ER  - 
%0 Journal Article
%A Chipot, Michel
%A Hastings, Stuart
%A Kinderlehrer, David
%T Transport in a molecular motor system
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2004
%P 1011-1034
%V 38
%N 6
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/m2an:2004048/
%R 10.1051/m2an:2004048
%G en
%F M2AN_2004__38_6_1011_0
Chipot, Michel; Hastings, Stuart; Kinderlehrer, David. Transport in a molecular motor system. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1011-1034. doi : 10.1051/m2an:2004048. http://archive.numdam.org/articles/10.1051/m2an:2004048/

[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] R.D. Astumian, Thermodynamics and kinetics of a Brownian motor. Science 276 (1997) 917-922.

[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. | Zbl

[4] M. Chipot, D. Kinderlehrer and M. Kowalczyk, A variational principle for molecular motors. Meccanica 38 (2003) 505-518. | Zbl

[5] C. Doering, B. Ermentrout and G. Oster, Rotary DNA motors. Biophys. J. 69 (1995) 2256-2267.

[6] J. Dolbeault, D. Kinderlehrer and M. Kowalczyk, Remarks about the flashing rachet, in Proc. PASI 2003 (to appear). | MR | Zbl

[7] D.D. Hackney, The kinetic cycles of myosin, kinesin, and dynein. Ann. Rev. Physiol. 58 (1996) 731-750.

[8] S. Hastings and D. Kinderlehrer, Remarks about diffusion mediated transport: thinking about motion in small systems. (to appear). | MR | Zbl

[9] J. Howard, Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Inc. (2001).

[10] A.F. Huxley, Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7 (1957) 255-318.

[11] R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17. | Zbl

[12] D. Kinderlehrer and M. Kowalczyk, Diffusion-mediated transport and the flashing ratchet. Arch. Rat. Mech. Anal. 161 (2002) 149-179. | Zbl

[13] D. Kinderlehrer and N. Walkington, Approximation of parabolic equations based upon Wasserstein's variational principle. ESAIM: M2AN 33 (1999) 837-852. | Numdam | Zbl

[14] J.S. Muldowney, Compound matrices and ordinary differential equations. Rocky Mountain J. Math. 20 (1990) 857-872. | Zbl

[15] Y. Okada and N. Hirokawa, A processive single-headed motor: kinesin superfamily protein KIF1A. Science 283 (1999) 19.

[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] F. Otto, Dynamics of labyrinthine pattern formation: a mean field theory. Arch. Rat. Mech. Anal. 141 (1998) 63-103. | Zbl

[18] F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. PDE 26 (2001) 101-174. | Zbl

[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] 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] 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] M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, N.J. (1967). | MR | Zbl

[23] P. Reimann, Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361 (2002) 57-265. | Zbl

[24] M. Schliwa, Molecular Motors. Wiley-VCH Verlag, Wennheim (2003).

[25] B. Schwarz, Totally positive differential systems. Pacific J. Math. 32 (1970) 203-230. | Zbl

[26] A. Tudorascu, A one phase Stefan problem via Monge-Kantorovich theory. CNA Report 03-CNA-007.

[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] C. Villani, Topics in optimal transportation, Providence. AMS Graduate Studies in Mathematics 58 (2003). | MR | Zbl

[29] E. Zeidler, Nonlinear functional analysis and its applications. I Springer, New York (1986). | MR | Zbl

Cité par Sources :