Single-molecule enzymology à la Michaelis-Menten

FEBS Journal

Volumn 281, Issue 2, 2014, Pages 518-530

  Grima, Ramon ^a   Walter, Nils G ^b   Schnell, Santiago ^c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF MICHIGAN MEDICAL SCHOOL   (United States)

Author keywords

chemical master equation; deterministic rate equations; effective mesoscopic rate equations; initial rate; Michaelis Menten reaction mechanism; noise; parameter estimation; single molecule analysis; stochastic enzyme kinetics; stochastic simulations

Indexed keywords

BIOPOLYMER;

ANALYTIC METHOD; BIOCHEMISTRY; CATALYSIS; CHEMICAL MASTER EQUATION; DETERMINISTIC RATE EQUATION; ENZYME ANALYSIS; ENZYME KINETICS; ENZYME MECHANISM; ENZYME SUBSTRATE COMPLEX; FLUORESCENCE MICROSCOPY; FLUORESCENCE RESONANCE ENERGY TRANSFER; MATHEMATICAL PARAMETERS; MICHAELIS MENTEN KINETICS; PHYSICAL CHEMISTRY; PRIORITY JOURNAL; REVIEW; SIGNAL NOISE RATIO; SINGLE CELL ANALYSIS; SINGLE MOLECULE ANALYSIS; STOCHASTIC MODEL; VALIDATION PROCESS;

CHEMICAL MASTER EQUATION; DETERMINISTIC RATE EQUATIONS; EFFECTIVE MESOSCOPIC RATE EQUATIONS; INITIAL RATE; MICHAELIS-MENTEN REACTION MECHANISM; NOISE; PARAMETER ESTIMATION; SINGLE-MOLECULE ANALYSIS; STOCHASTIC ENZYME KINETICS; STOCHASTIC SIMULATIONS;

ALGORITHMS; BIOCATALYSIS; ENZYMES; KINETICS; MODELS, CHEMICAL; STOCHASTIC PROCESSES;

EID: 84892826516     PISSN: 1742464X     EISSN: 17424658     Source Type: Journal    
DOI: 10.1111/febs.12663     Document Type: Review

References (78)

1. Fersht A, (1999) Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. Freeman, New York.
2. Cornish-Bowden A, (2012) Fundamentals of Enzyme Kinetics, 4th edn. Wiley-VCH, Weinheim.
3. Henri V, (1902) Théorie générale de l'action de quelques diastases. CR Hebd Acad Sci 135, 916-919.
4. Henri V, (1903) Lois Générales De L'Action Des Diastases. Hermann, Paris.
5. Schnell S, Chappell MJ, Evans ND, &, Roussel MR, (2006) The mechanism distinguishability problem in biochemical kinetics: the single-enzyme, single-substrate reaction as a case study. CR Biol 329, 51-61.
6. Michaelis L, &, Menten ML, (1913) Die kinetik der invertinwirkung. Biochem Z 49, 333-369.
7. max estimates. Comment Theor Biol 8, 169-187.
8. Zimmerle CT, &, Frieden C, (1989) Analysis of progress curves by simulations generated by numerical integration. Biochem J 258, 381-387.
9. Duggleby RG, (1995) Analysis of enzyme progress curves by nonlinear-regression. Methods Enzymol 249, 61-90.
10. Marangoni AG, (2003) Enzyme Kinetics: A Modern Approach. Wiley-Interscience, Hoboken, NJ.
11. Turner TE, Schnell S, &, Burrage K, (2004) Stochastic approaches for modelling in vivo reactions. Comput Biol Chem 28, 165-178.
12. Grima R, &, Schnell S, (2008) Modelling reaction kinetics inside cells. Essays Biochem 45, 41-56.
13. Ishihama Y, Schmidt T, Rappsilber J, Mann M, Hartl FU, Kerner MJ, &, Frishman D, (2008) Protein abundance profiling of the Escherichia coli cytosol. BMC Genomics 9, 102.
14. Walter NG, Huang CY, Manzo AJ, &, Sobhy MA, (2008) Do-it-yourself guide: how to use the modern single-molecule toolkit. Nat Methods 5, 475-489.
15. Bartholomay AF, (1962) A stochastic approach to statistical kinetics with application to enzyme kinetics. Biochemistry 1, 223-230.
16. van Kampen NG, (2007) Stochastic Processes in Physics and Chemistry, 3rd edn. North-Holland, Amsterdam.
17. Xie XS, &, Trautman JK, (1998) Optical studies of single molecules at room temperature. Annu Rev Phys Chem 49, 441-480.
18. Grohmann D, Werner F, &, Tinnefeld P, (2013) Making connections-strategies for single molecule fluorescence biophysics. Curr Opin Chem Biol 17, 691-698.
19. Coelho M, Maghelli N, &, Tolic̈-Nørrelykke IM, (2013) Single-molecule imaging in vivo: the dancing building blocks of the cell. Integr Biol 5, 748-758.
20. Xia T, Li N, &, Fang X, (2013) Single-molecule fluorescence imaging in living cells. Annu Rev Phys Chem 64, 459-480.
21. Puchner EM, &, Gaub HE, (2012) Single-molecule mechanoenzymatics. Annu Rev Biophys 41, 497-518.
22. Elson EL, (2011) Fluorescence correlation spectroscopy: past, present, future. Biophys J 101, 2855-2870.
23. Harriman OLJ, &, Leake MC, (2011) Single molecule experimentation in biological physics: exploring the living component of soft condensed matter one molecule at a time. J Phys-Condens Matter 23, 503101.
24. Li GW, &, Xie XS, (2011) Central dogma at the single-molecule level in living cells. Nature 475, 308-315.
25. Feynman RP, (1961) Miniaturization. Reinhold, New York.
26. Walter NG, (2010) Single molecule tools: fluorescence based approaches Part A. Preface. Methods Enzymol 472, xxi-xxii.
27. Jain A, Liu R, Ramani B, Arauz E, Ishitsuka Y, Ragunathan K, Park J, Chen J, Xiang YK, &, Ha T, (2011) Probing cellular protein complexes using single-molecule pull-down. Nature 473, 484-488.
28. Hoskins AA, Gelles J, &, Moore MJ, (2011) New insights into the spliceosome by single molecule fluorescence microscopy. Curr Opin Chem Biol 15, 864-870.
29. English BP, Min W, van Oijen AM, Lee KT, Luo G, Sun H, Cherayil BJ, Kou SC, &, Xie XS, (2006) Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited. Nat Chem Biol 2, 87-94.
30. Ries J, &, Schwille P, (2012) Fluorescence correlation spectroscopy. BioEssays 34, 361-368.
31. Xie XS, Yu J, &, Yang WY, (2006) Living cells as test tubes. Science 312, 228-230.
32. Roy R, Hohng S, &, Ha T, (2008) A practical guide to single-molecule FRET. Nat Methods 5, 507-516.
33. Pitchiaya S, Androsavich JR, &, Walter NG, (2012) Intracellular single molecule microscopy reveals two kinetically distinct pathways for microRNA assembly. EMBO Rep 13, 709-715.
34. Jares-Erijman EA, &, Jovin TM, (2003) FRET imaging. Nat Biotechnol 21, 1387-1395.
35. Gillespie DT, (1992) A rigorous derivation of the chemical master equation. Phys A 188, 404-425.
36. Baras F, Pearson JE, &, Mansour MM, (1990) Microscopic simulation of chemical oscillations in homogeneous systems. J Chem Phys 93, 5747-5750.
37. Baras F, Mansour MM, &, Pearson JE, (1996) Microscopic simulation of chemical bistability in homogeneous systems. J Chem Phys 105, 8257-8261.
38. Grima R, (2010) Intrinsic biochemical noise in crowded intracellular conditions. J Chem Phys 132, 185102.
39. Kurtz TG, (1972) Relationship between stochastic and deterministic models for chemical reactions. J Chem Phys 57, 2976-2978.
40. Grima R, (2010) 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.
41. Komorowski M, Finkenstadt B, Harper CV, &, Rand DA, (2009) Bayesian inference of biochemical kinetic parameters using the linear noise approximation. BMC Bioinformatics 10, 343.
42. Roussel MR, &, Fraser SJ, (1991) Accurate steady-state approximations: implications for kinetics experiments and mechanism. J Phys Chem 95, 8762-8770.
43. Gillespie DT, (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58, 35-55.
44. Jachimowski CJ, McQuarrie DA, &, Russell ME, (1964) A stochastic approach to enzyme-substrate reactions. Biochemistry 3, 1732-1736.
45. Arányi P, &, Tõth J, (1977) A full stochastic description of the Michaelis-Menten reaction for small systems. Acta Biochim Biophys Acad Sci Hung 12, 375-388.
46. Schnell S, &, Mendoza C, (2004) The condition for pseudo-first-order kinetics in enzymatic reactions is independent of the initial enzyme concentration. Biophys Chem 107, 165-174.
47. Schnell S, (2013) Validity of the Michaelis-Menten equation-Steady-state, or reactant stationary assumption: that is the question. FEBS J, doi: 10.1111/febs.12564.
48. Schnell S, &, Mendoza C, (1997) Closed form solution for time-dependent enzyme kinetics. J Theor Biol 187, 207-212.
49. Schnell S, &, Maini PK, (2000) Enzyme kinetics at high enzyme concentration. Bull Math Biol 62, 483-499.
50. Hanson SM, &, Schnell S, (2008) Reactant stationary approximation in enzyme kinetics. J Phys Chem A 112, 8654-8658.
51. Ramaswamy R, González-Segredo N, Sbalzarini IF, &, Grima R, (2012) Discreteness-induced concentration inversion in mesoscopic chemical systems. Nat Commun 3, 779.
52. Kou SC, Cherayil BJ, Min W, English BP, &, Xie XS, (2005) Single-molecule Michaelis-Menten equations. J Phys Chem B 109, 19068-19081.
53. Qian H, (2008) Cooperativity and specificity in enzyme kinetics: a single-molecule time-based perspective. Biophys J 95, 10-17.
54. Munsky B, &, Khammash M, (2006) The finite state projection algorithm for the solution of the chemical master equation. J Chem Phys 124, 044104.
55. Rao CV, &, Arkin AP, (2003) Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J Chem Phys 118, 4999-5010.
56. Sanft KR, Gillespie DT, &, Petzold LR, (2011) Legitimacy of the stochastic Michaelis-Menten approximation. IET Syst Biol 5, 58-69.
57. Qian H, &, Bishop LM, (2010) The chemical master equation approach to nonequilibrium steady-state of open biochemical systems: linear single-molecule enzyme kinetics and nonlinear biochemical reaction networks. Int J Mol Sci 11, 3472-3500.
58. Grima R, (2009) Investigating the robustness of the classical enzyme kinetic equations in small intracellular compartments. BMC Syst Biol 3, 101.
59. Ge H, &, Qian H, (2013) Dissipation, generalized free energy, and a self-consistent nonequilibrium thermodynamics of chemically driven open subsystems. Phys Rev E 87, 062125.
60. Stefanini MO, McKane AJ, &, Newman TJ, (2005) Single enzyme pathways and substrate fluctuations. Nonlinearity 18, 1575-1595.
61. Qian H, (2012) Cooperativity in cellular biochemical processes: noise-enhanced sensitivity, fluctuating enzyme, bistability with nonlinear feedback, and other mechanisms for sigmoidal responses. Annu Rev Biophys 41, 179-204.
62. Darvey IG, &, Staff PJ, (1967) The application of the theory of Markov processes to the reversible one substrate-one intermediate-one product enzymic mechanism. J Theor Biol 14, 157-172.
63. Qian H, &, Elson EL, (2002) Single-molecule enzymology: stochastic Michaelis-Menten kinetics. Biophys Chem 101-102, 565-576.
64. Bar-Even A, Noor E, Savir Y, Liebermeister W, Davidi D, Tawfik DS, &, Milo R, (2011) The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters. Biochemistry 50, 4402-4410.
65. Tanaka S, Kerfeld CA, Sawaya MR, Cai F, Heinhorst S, Cannon GC, &, Yeates TO, (2008) Atomic-level models of the bacterial carboxysome shell. Science 319, 1083-1086.
66. Yeates TO, Crowley CS, &, Tanaka S, (2010) Bacterial microcompartment organelles: protein shell structure and evolution. Annu Rev Biophys 39, 185-205.
67. Thomas P, Matuschek H, &, Grima R, (2012) Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA. Paper presented at the 2012 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), pp. 1-5.
68. Xu L, &, Qu Z, (2012) Roles of protein ubiquitination and degradation kinetics in biological oscillations. PLoS ONE 7, e34616.
69. Kaern M, Elston TC, Blake WJ, &, Collins JJ, (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6, 451-464.
70. Taniguchi Y, Choi PJ, Li GW, Chen H, Babu M, Hearn J, Emili A, &, Xie XS, (2010) Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science 329, 533-538.
71. Shahrezaei V, &, Swain PS, (2008) Analytical distributions for stochastic gene expression. Proc Natl Acad Sci USA 105, 17256-17261.
72. Cai L, Friedman N, &, Xie XS, (2006) Stochastic protein expression in individual cells at the single molecule level. Nature 440, 358-362.
73. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, &, van Oudenaarden A, (2002) Regulation of noise in the expression of a single gene. Nat Genet 31, 69-73.
74. Anzenbacher P Jr, &, Palacios MA, (2009) Polymer nanofibre junctions of attolitre volume serve as zeptomole-scale chemical reactors. Nat Chem 1, 80-86.
75. Karlsson M, Davidson M, Karlsson R, Karlsson A, Bergenholtz J, Konkoli Z, Jesorka A, Lobovkina T, Hurtig J, Voinova M, et al,. (2004) Biomimetic nanoscale reactors and networks. Annu Rev Phys Chem 55, 613-649.
76. Boys RJ, Wilkinson DJ, &, Kirkwood TBL, (2008) Bayesian inference for a discretely observed stochastic kinetic model. Stat Comput 18, 125-135.
77. Moles CG, Mendes P, &, Banga JR, (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res 13, 2467-2474.
78. Samoilov MS, &, Arkin AP, (2006) Deviant effects in molecular reaction pathways. Nat Biotechnol 24, 1235-1240.