Abstract
Single molecule spectroscopy provides us with a new means to look deeply into the question of how an individual molecule behaves when performing biological functions in a thermally fluctuating environment. However, what information one can extract from the observed data is still an open question. We overview our new method which extracts the underlying reaction scheme, a state-space network (SSN), from the time series data of an experimental measurement. We demand that a time series analysis should provide not only an interpretation of the dynamical behavior but also provide new insights into biological functions buried in ensemble-based measurements. Our method is based on the combination of information theory and Wavelet multiresolution decomposition analysis. The resultant reaction scheme does not rely on an a priori ansatz like local equilibrium and detailed balance. It is mathematically assured as unique, minimally complex and stochastic, but best predictive. We demonstrate the potential of this method by applying it to the analysis of an anomalous conformation in Flavin oxidoreductase dependent on the timescale of observation. We also discuss future perspectives concerning its use as a new means for the exploration of single molecule biophysics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97
Baba A, Komatsuzaki T (2007) Construction of effective free energy landscape from single-molecule time series. Proc Natl Acad Sci USA 104(49):19,297–19,302
Baba A, Komatsuzaki T (2010) Multidimensional energy landscapes in single molecule biophysics. Adv Chem Phys 145: in press
Ball KD, Berry RS, Kunz RE, Li FY, Proykova A, Wales DJ (1996) From Topographies to dynamics on multidimensional potential energy surfaces of atomic clusters. Science 271:963
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Barkai E, Jung Y, Silbey R (2004) Protein conformational dynamics probed by single-molecule electron transfer. Annu Rev Phys Chem 55:457–507
Crutchfield JP, Young K (1989) Inferring statistical complexity. Phys Rev Lett 63:105
Daubechies I (1992) Ten lectures on wavelets. (Soc Indust Appl Math, New York)
Debnath P, Min W, Xie XS, Cherayil BJ (2005) Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: a one-dimensional generalized langevin equation treatment. J Chem Phys 123:204,903
Evans DA, Wales DJ (2003) Free energy landscapes of model peptides and proteins. J Chem Phys 118(8):3891–3897
Frauenfelder H, Sligar SG, Wolynes PG (1991) The energy landscapes and motions of proteins. Science 254:1598–1603
Gallos LK, Song C, Havlin S, Makse HA (2007) Scaling theory of transport in complex biological networks. Proc Natl Acad Sci USA 104:7746–7751
Gfeller D, Rios PDL, Caflisch A, Rao F (2007) Complex network analysis of free-energy landscapes. Proc Natl Acad Sci USA 104:1817–1822
Gopich IV, Szabo A (2003) Single-macromolecule fluorescence resonance energy transfer and free-energy profiles. J Phys Chem B 107:5058–5063
Grote RF, Hynes JT (1980) The stable states picture of chemical reactions. II. rate constants for condensed and gas phase reaction models. J Chem Phys 73:2715–2732
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond A 454:908
Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106:620
Jaynes ET (1957) Information theory and statistical mechanics II. Phys Rev 108:171
Kalafut B, Visscher K (2008) An objective, model-independent method for detection of non-uniform steps in noisy signals. Comp Phys Commun 179:716
Kinoshita M, Kamagata K, Maeda M, Goto Y, Komatsuzaki T, Takahashi S (2007) Development of a technique for the investigation of folding dynamics of single proteins for extended time periods. Proc Natl Acad Sci USA 104:10,453
Klimov DK, Thirumalai D (1997) Viscosity dependence of the folding rates of proteins. Phys Rev Lett 79:317–320
Komatsuzaki T, Baba A, Kawai S, Toda M, Straub JE, Berry RS (2010) Ergodic problems for real complex systems in chemical physics. Adv Chem Phys 145: in press
Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–304
Krivov SV, Karplus M (2004) Hidden complexity of free energy surfaces for peptide (protein) folding. Proc Natl Acad Sci USA 101:14,766–14,770
Krzanowski WJ (2003) Non-parametric estimation of distance between groups. J App Stat 30(7):743–750
Li CB, Yang H, Komatsuzaki T (2008) Complex network of protein conformational fluctuation buried in single molecule time series. Proc Natl Acad Sci USA 105:536–541
Li CB, Yang H, Komatsuzaki T (2009) New quantification of local transition heterogeneity of multiscale complex networks constructed from single-molecule time series. J Phys Chem B 113:14,732–14,741
Lippitz M, Kulzer F, Orrit M (2005) Statistical evaluation of single nano-object fluorescence. ChemPhysChem 6:770–789
Luo G, Andricioaei I, Xie XS, Karplus M (2006) Dynamic distance disorder in proteins is caused by trapping. J Phys Chem B 110:9363–9367
Michalet X, Weiss S, Jager M (2006) Single-molecule fluorescence studies of protein folding and conformational dynamics. Chem Rev 106(5):1785–1813
Min W, Luo G, Cherayil BJ, Kou SC, Xie XS (2005) Observation of a power-law memory Kernel for fluctuations within a single protein molecule. Phys Rev Lett 94: 198,302
Moerner WE, Fromm DP (2003) Methods of single-molecule fluorescence spectroscopy and microscopy. Rev Sci Inst 74(8):3597–3619
Moser CC, Keske JM, Warncke K, Farid RS, Dutton PL (1992) Nature of biological electron-transfer. Nature 355(6363):796–802
Rao F, Caflisch A (2004) The protein folding network. J Mol Biol 342:299–306
Rhoades E, Gussakovsky E, Haran G (2003) Watching proteins fold one molecule at a time. Proc Natl Acad Sci USA 100(6):3197–3202
Schuler B, Lipman EA, Eaton EA (2002) Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopy. Nature 419:743–747
Shalizi CR, Crutchfield JP (2001) Computational mechanics: pattern and prediction, structure and simplicity. J Stat Phys 104:819–881
Shannon C, Weaver W (1948) A mathematical theory of communication. University of Illinois Press, Urbana, IL
Socci ND, Onuchic JN, Wolynes PG (1996) Diffusive dynamics of the reaction coordinate for protein folding funnels. J Chem Phys 104:5860–5868
Still S, Cutchfield JP, Ellison CJ (2007) Optimal causal inference. http://lanl.arxiv.org/abs/0708.1580
Stillinger FH (1995) A topographic view of supercooled liquids and glass formation. Science 267:1935–1939
Talaga DS, Lau WL, Roder H, Tang JY, Jia YW, DeGrado WF, Hochstrasser RM (2000) Dynamics and folding of single two-stranded coiled-coil peptides studied by fluorescent energy transfer confocal microscopy. Proc Natl Acad Sci USA 97(24):13,021–13,026
Tang J, Marcus RA (2006) Chain dynamics and Power-law distance fluctuations of single-molecule systems. Phys Rev E 73:022,102
Wales DJ (2003) Energy landscapes. Cambridge University Press, Cambridge
Watkins LP, Yang H (2005) Detection of intensity change points in time-resolved single-molecule measurements. J Phys Chem B 109(1):617–628
Xie XS, Trautman JK (1998) Optical studies of single molecules at room temperature. Annu Rev Phys Chem 49:441–480
Yanagida T, Ishii Y (2009) Single molecule dynamics in life science. Wiley, Weinheim
Yang H, Luo G, Karnchanaphanurach P, Louie TM, Rech I, Cova S, Xun L, Xie XS (2003) Protein conformational dynamics probed by single-molecule electron transfer. Science 302:262–266
Zhang K, Chang H, Fu A, Alivisatos AP, Yang H (2006) Continuous distribution of emission intensity and its non-linear correlation to luminescence decay rates from single cdse/zns quantum dots. Nano Lett 6:843–847
Acknowledgements
We thank Prof. Haw Yang for his continuous valuable contributions to our project from his experimentalist’s viewpoint. We also thank Profs. Satoshi Takahashi and Mikito Toda for their valuable discussions. We acknowledge financial support from JSPS, JST/CREST, Grant-in-Aid for Research on Priority Areas ‘Systems Genomics,’ ‘Real Molecular Theory’, and ‘Innovative nano-science,’ MEXT.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Netherlands
About this chapter
Cite this chapter
Li, C.B., Komatsuzaki, T. (2011). Extracting the Underlying Unique Reaction Scheme from a Single-Molecule Time Series. In: Sako, Y., Ueda, M. (eds) Cell Signaling Reactions. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9864-1_11
Download citation
DOI: https://doi.org/10.1007/978-90-481-9864-1_11
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9863-4
Online ISBN: 978-90-481-9864-1
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)