Asymptotics of a Brownian ratchet for protein translocation

Stochastic Processes and their Applications

Volumn 120, Issue 6, 2010, Pages 901-925

  Depperschmidt, Andrej ^a   Pfaffelhuber, Peter ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Brownian motion; Cumulative process; Protein translocation; Ratchet mechanism; Reflected Brownian motion

Indexed keywords

ASYMPTOTIC VARIANCE; ASYMPTOTICS; BROWNIAN MOTION; BROWNIAN RATCHET; IN-CELL; PROTEIN TRANSLOCATION; RATCHET MECHANISMS; RATE OF CHANGE; REFLECTED BROWNIAN MOTION; REFLECTION BOUNDARIES; REFLECTION POINTS;

ASYMPTOTIC ANALYSIS; PROTEINS;

BROWNIAN MOVEMENT;

EID: 77950594964     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2010.01.018     Document Type: Article

References (22)

1. Abdolvahab R.H., Roshani F., Nourmohammad A., Sahimi M., and Tabar M.R. Analytical and numerical studies of sequence dependence of passage times for translocation of heterobiopolymers through nanopores. J. Chem. Phys. 129 (2008) 235102-235102-8
2. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (1972), Dover Publications, New York (10. print., with corr. ed.)
3. Ambjornsson T., Lomholt M.A., and Metzler R. Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins. J. Phys. Condens. Matter 17 47 (2005) S3945-S3964 (Sp. Iss. SI)
4. Borodin A.N., and Salminen P. Handbook of Brownian Motion-Facts and Formulae. second ed. (2002), Birkhäuser Verlag
5. Budhiraja A., and Fricks J. Molecular motors, Brownian ratchets, and reflected diffusions. Discrete Contin. Dyn. Syst. B 6 4 (2006) 711-734
6. Doob J.L. Renewal theory from the point of view of the theory of probability. Trans. Amer. Math. Soc. 63 (1948) 422-438
7. Elston T.C. The Brownian ratchet and power stroke models for posttranslational protein translocation into the endoplasmic reticulum. Biophys. J. 82 (2002) 1239-1253
8. Feynman R., Leighton R., and Sands M. The Feynman Lectures on Physics (1963), Addison-Wesley
9. Fitzsimmons P., and Pitman J. Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process. Stochastic Processes Appl. 79 1 (1999) 117-134
10. Janson S. Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas. Probab. Surv. 4 (2007) 80-145
11. Kac M. On the average of a certain Wiener functionals and a related limit result in calculus of probability. Trans. Amer. Math. Soc. 59 (1946) 401-414
12. Liebermeister W., Rapoport T.A., and Heinrich R. Ratcheting in post-translational protein translocation: A mathematical model. J. Mol. Biol. 305 (2001) 643-656
13. Liggett T.M. Interacting Particle Systems (1985), Springer-Verlag
14. Matlack K.E., Misselwitz B., Plath K., and Rapoport T.A. BiP acts as a molecular ratchet during posttranslational transport of prepro-alpha factor across the ER membrane. Cell 97 (1999) 553-564
15. Peskin C.S., Odell G.M., and Oster G.F. Cellular motions and thermal fluctuations: The Brownian ratchet. Biophys. J. 65 (1993) 316-324
16. Revuz D. Markov Chains. second ed. (1984), American Elsevier, North-Holland
17. Roginsky A.L. A central limit theorem for cumulative processes. Adv. Appl. Probab. 26 (1994) 104-121
18. Simon S.M., Peskin C.S., and Oster G.F. What drives the translocation of proteins?. Proc. Natl. Acad. Sci. USA 89 (1992) 3770-3774
19. Smith W.L. Regenerative stochastic processes. Proc. R. Soc. Lond. Ser. A. 232 (1955) 6-31
20. van der Hofstad R. The constants in the central limit theorem for the one-dimensional Edwards model. J. Statist. Phys. 90 5-6 (1998) 1295-1310
21. van der Hofstad R., den Hollander F., and König W. Central limit theorem for the Edwards model. Ann. Probab. 25 2 (1997) 573-597
22. Westwater J. On Edwards model for polymer chains. In: Albeverio S., and Blanchard P. (Eds). Trends and Developments in the Eighties. Bielefeld Encounters in Mathematical Physics IV/V (1985), World Scientific, Singapore