Single-molecule stochastic times in a reversible bimolecular reaction

Journal of Chemical Physics

Volumn 137, Issue 8, 2012, Pages

  Keller, Peter ^a,b   Valleriani, Angelo ^a  

^a MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES   (Germany)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE TREATMENT; BIMOLECULAR REACTION; DETAILED BALANCE; LAW OF MASS ACTION; MOLECULAR MOTORS; PROBABILITY DENSITIES; REVERSIBLE REACTION; SINGLE-MOLECULE; STOCHASTIC FLUCTUATION; WAITING-TIME;

STOCHASTIC SYSTEMS;

MOLECULES;

ADENOSINE TRIPHOSPHATE; KINESIN; MOLECULAR MOTOR;

ARTICLE; CHEMISTRY; METABOLISM; MOLECULAR DYNAMICS; STATISTICS; TIME;

ADENOSINE TRIPHOSPHATE; KINESIN; MOLECULAR DYNAMICS SIMULATION; MOLECULAR MOTOR PROTEINS; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 84865777621     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4747337     Document Type: Article

References (32)

1. J. Yu, J. Xiao, X. J. Ren, K. Q. Lao, and X. S. Xie, Probing gene expression in live cells, one protein molecule at a time., Science 311, 1600-1603 (2006). 10.1126/science.1119623
2. Y. Taniguchi, P. J. Choi, G. W. Li, H. Y. Chen, M. Babu, J. Hearn, A. Emili, and X. S. Xie, Quantifying E-coli proteome and transcriptome with single-molecule sensitivity in single cells., Science 329, 533-538 (2010). 10.1126/science.1188308
3. H. H. McAdams and A. Arkin, Its a noisy business! Genetic regulation at the nanomolar scale., Trends Genet. 15, 65-69 (1999). 10.1016/S0168-9525(98) 01659-X (Pubitemid 29136643)
4. C. A. Gomez-Uribe, G. C. Verghese, and A. R. Tzafriri, Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics., J. Chem. Phys. 129, 244112 (2008). 10.1063/1.3050350
5. D. T. Gillespie, Stochastic simulation of chemical kinetics., Annu. Rev. Phys. Chem. 58, 35-55 (2007). 10.1146/annurev.physchem.58.032806.104637 (Pubitemid 46877584)
6. D. A. McQuarrie, Stochastic approach to chemical kinetics., J. Appl. Probab. 4, 413 (1967). 10.2307/3212214
7. D. T. Gillespie, General method for numerically simulating stochastic time evolution of coupled chemical-reactions., J. Comput. Phys. 22, 403-434 (1976). 10.1016/0021-9991(76)90041-3 (Pubitemid 8008311)
8. D. T. Gillespie, A rigorous derivation of the chemical master equation., Physica A 188, 404-425 (1992). 10.1016/0378-4371(92)90283-V
9. E. Doka and G. Lente, Stochastic mapping of the Michaelis-Menten mechanism., J. Chem. Phys. 136, 054111 (2012). 10.1063/1.3681942
10. C. V. Rao and A. P. Arkin, Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm., J. Chem. Phys. 118, 4999-5010 (2003). 10.1063/1.1545446
11. I. J. Laurenzi, An analytical solution of the stochastic master equation for reversible bimolecular reaction kinetics., J. Chem. Phys. 113, 3315-3322 (2000). 10.1063/1.1287273
12. Y. Cao, D. T. Gillespie, and L. R. Petzold, The slow-scale stochastic simulation algorithm., J. Chem. Phys. 122, 014116 (2005). 10.1063/1.1824902 (Pubitemid 41047759)
13. S. N. Xie, Single-molecule approach to enzymology., Single Mol. 2, 229-236 (2001). 10.1002/1438-5171(200112)2:4229::AID-SIMO229>3.0.CO;2-9
14. S. C. Kou, B. J. Cherayil, W. Min, B. P. English, and X. S. Xie, Single-molecule Michaelis-Menten equations., J. Phys. Chem. B 109, 19068-19081 (2005). 10.1021/jp051490q (Pubitemid 41541103)
15. B. P. English, W. Min, A. M. van Oijen, K. T. Lee, G. B. Luo, H. Y. Sun, B. J. Cherayil, S. C. Kou, and X. S. Xie, Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited., Nat. Chem. Biol. 2, 87-94 (2006). 10.1038/nchembio759
16. G. Bel, B. Munsky, and I. Nemenman, The simplicity of completion time distributions for common complex biochemical processes., Phys. Biol. 7, 016003 (2010). 10.1088/1478-3975/7/1/016003
17. R. Grima, An effective rate equation approach to reaction kinetics in small volumes: Theory and application to biochemical reactions in nonequilibrium steady-state conditions., J. Chem. Phys. 133, 035101 (2010). 10.1063/1.3454685
18. S. Klumpp, Y. Chai, and R. Lipowsky, Effects of the chemomechanical stepping cycle on the traffic of molecular motors., Phys. Rev. E 78, 041909 (2008). 10.1103/PhysRevE.78.041909
19. N. J. Carter and R. A. Cross, Mechanics of the kinesin step., Nature (London) 435, 308-312 (2005). 10.1038/nature03528 (Pubitemid 40745535)
20. S. Liepelt and R. Lipowsky, Kinesins network of chemomechanical motor cycles., Phys. Rev. Lett. 98, 258102 (2007). 10.1103/PhysRevLett.98.258102 (Pubitemid 47139922)
21. A. Valleriani, S. Liepelt, and R. Lipowsky, Dwell time distributions for kinesins mechanical steps., Europhys. Lett. 82, 28011 (2008). 10.1209/0295-5075/82/28011
22. A. Garai and D. Chowdhury, Stochastic kinetics of a single-headed motor protein: Dwell time distribution of KIF1A., Europhys. Lett. 93, 58004 (2011). 10.1209/0295-5075/93/58004
23. V. Bierbaum and R. Lipowsky, Chemomechanical coupling and motor cycles of Myosin V., Biophys. J. 100, 1747-1755 (2011). 10.1016/j.bpj.2011.02.012
24. H. J. Dong, L. Nilsson, and C. G. Kurland, Co-variation of tRNA abundance and codon usage in Escherichia coli at different growth rates., J. Mol. Biol. 260, 649-663 (1996). 10.1006/jmbi.1996.0428 (Pubitemid 26270960)
25. G. Zhang, I. Fedyunin, O. Miekley, A. Valleriani, A. Moura, and Z. Ignatova, Global and local depletion of ternary complex limits translational elongation., Nucleic Acids Res. 38, 4778-4787 (2010). 10.1093/nar/gkq196
26. A. T. Bharucha-Reid, Elements of the Theory of Markov Processes and Their Applications (Dover, Mineola, NY, 1997).
27. H. M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, 3rd ed. (Academic, San Diego, 1998).
28. E. A. van Doorn and A. I. Zeifman, Birth-death processes with killing., Stat. Probab. Lett. 72, 33-42 (2005). 10.1016/j.spl.2004.11.020 (Pubitemid 40317367)
29. E. A. Van Doorn and A. I. Zeifman, Extinction probability in a birth-death process with killing., J. Appl. Probab. 42, 185-198 (2005). 10.1239/jap/1110381380 (Pubitemid 40653653)
30. P. J. Brockwell, The extinction time of a general birth and death process with catastrophes., J. Appl. Probab. 23, 851-858 (1986). 10.2307/3214459
31. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (Dover, New York, 1994).
32. T. L. Hill, Free Energy Transduction and Biochemical Cycle Kinetics (Dover, Mineola, NY, 2005).