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Correlation analysis of enzymatic reaction of a single protein molecule. (English) Zbl 1254.92034

Summary: New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme molecules behave fundamentally differently from what classical models predict. A stochastic network model was previously proposed to explain the experimental discovery. This paper conducts detailed theoretical and data analyses of the stochastic network model, focusing on the correlation structure of the successive reaction times of a single enzyme molecule. We investigate the correlation of experimental fluorescence intensity and the correlation of enzymatic reaction times, and examine the role of substrate concentration in enzymatic reactions. Our study shows that the stochastic network model is capable of explaining the experimental data in depth.

MSC:

92C42 Systems biology, networks
92C05 Biophysics
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C40 Biochemistry, molecular biology
62P10 Applications of statistics to biology and medical sciences; meta analysis
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References:

[1] Albery, W. J. and Knowles, J. R. (1976). Free-energy profile of the reaction catalyzed by triosephosphate isomerase. Biochemistry 15 5627-5631.
[2] Asbury, C. L., Fehr, A. N. and Block, S. M. (2003). Kinesin moves by an asymmetric hand-over-hand mechanism. Science 302 2130-2134.
[3] Atkins, P. and de Paula, J. (2002). Physical Chemistry , 7th ed. Freeman, New York.
[4] Dorland, W. A. (2003). Dorland’s Illustrated Medical Dictionary , 30th ed. Saunders, Philadelphia.
[5] English, B., Min, W., van Oijen, A. M., Lee, K. T., Luo, G., Sun, H., Cherayil, B. J., Kou, S. C. and Xie, X. S. (2006). Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited. Nature Chem. Biol. 2 87-94.
[6] Flomembom, O. et al. (2005). Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules. Proc. Natl. Acad. Sci. USA 102 2368-2372.
[7] Horn, R. A. and Johnson, C. R. (1985). Matrix Analysis . Cambridge Univ. Press, Cambridge. · Zbl 0576.15001
[8] Jacobson, R. H., Zhang, X. J., DuBose, R. F. and Matthews, B. W. (1994). Three-dimensional structure of \(\beta\)-galactosidase from E. coli. Nature 369 761-766.
[9] Kou, S. C. (2008a). Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins. Ann. Appl. Stat. 2 501-535. · Zbl 1400.62272
[10] Kou, S. C. (2008b). Stochastic networks in nanoscale biophysics: Modeling enzymatic reaction of a single protein. J. Amer. Statist. Assoc. 103 961-975. · Zbl 1205.62172
[11] Kou, S. C. (2009). A selective view of stochastic inference and modeling problems in nanoscale biophysics. Sci. China Ser. A 52 1181-1211. · Zbl 1211.62185
[12] Kou, S. C. and Xie, X. S. (2004). Generalized Langevin equation with fractional Gaussian noise: Subdiffusion within a single protein molecule. Phys. Rev. Lett. 93 180603(1)-180603(4).
[13] Kou, S. C., Xie, X. S. and Liu, J. S. (2005). Bayesian analysis of single-molecule experimental data. J. Roy. Statist. Soc. Ser. C 54 469-506. · Zbl 05188696
[14] Kou, S. C., Cherayil, B., Min, W., English, B. and Xie, X. S. (2005). Single-molecule Michaelis-Menten equations. J. Phys. Chem. B 109 19068-19081.
[15] Lu, H. P., Xun, L. and Xie, X. S. (1998). Single-molecule enzymatic dynamics. Science 282 1877-1882.
[16] Min, W., English, B., Luo, G., Cherayil, B., Kou, S. C. and Xie, X. S. (2005a). Fluctuating enzymes: Lessons from single-molecule studies. Acc. Chem. Res. 38 923-931.
[17] Min, W., Luo, G., Cherayil, B., Kou, S. C. and Xie, X. S. (2005b). Observation of a power law memory kernel for fluctuations within a single protein molecule. Phys. Rev. Lett. 94 198302(1)-198302(4).
[18] Min, W., Gopich, I. V., English, B., Kou, S. C., Xie, X. S. and Szabo, A. (2006). When does the Michaelis-Menten equation hold for fluctuating enzymes? J. Phys. Chem. B 110 20093-20097.
[19] Moerner, W. (2002). A dozen years of single-molecule spectroscopy in physics, chemistry, and biophysics. J. Phys. Chem. B 106 910-927.
[20] Nie, S. and Zare, R. (1997). Optical detection of single molecules. Ann. Rev. Biophys. Biomol. Struct. 26 567-596.
[21] Pushkarev, D., Neff, N. and Quake, S. (2009). Single-molecule sequencing of an individual human genome. Nature Biotechnology 27 847-852.
[22] Segel, I. H. (1975). Enzyme Kinetics : Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems . Wiley, New York. · Zbl 0653.92006
[23] Tamarat, P., Maali, A., Lounis, B. and Orrit, M. (2000). Ten years of single-molecule spectroscopy. J. Phys. Chem. A 104 1-16.
[24] Weiss, S. (2000). Measuring conformational dynamics of biomolecules by single molecule fluorescence spectroscopy. Nature Struct. Biol. 7 724-729.
[25] Wilkinson, J. H. (1988). The Algebraic Eigenvalue Problem . Clarendon Press, Oxford. · Zbl 0626.65029
[26] Xie, X. S. and Lu, H. P. (1999). Single-molecule enzymology. J. Bio. Chem. 274 15967-15970.
[27] Xie, X. S. and Trautman, J. K. (1998). Optical studies of single molecules at room temperature. Ann. Rev. Phys. Chem. 49 441-480.
[28] Yang, H., Luo, G., Karnchanaphanurach, P., Louise, T. M., Rech, I., Cova, S., Xun, L. and Xie, X. S. (2003). Protein conformational dynamics probed by single-molecule electron transfer. Science 302 262-266.
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