|
In biophysics and related fields, reduced dimension forms (RDFs) are unique on-off mechanisms for random walks that generate two-state trajectories (see Fig. 1 for an example of a RDF and Fig. 2 for an example of a two-state trajectory). It has been shown that RDFs solve two-state trajectories, since only one RDF can be constructed from the data,〔O. Flomenbom, and R. J. Silbey, Utilizing the information content in two-state trajectories, Proc. Natl. Acad. Sci. USA 103, 10907-10910 (2006).〕 where this property does not hold for on-off kinetic schemes, where many kinetic schemes can be constructed from a particular two-state trajectory (even from an ideal on-off trajectory). Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules 〔)>Moerner, W. E. & Orrit, M. (1999) Science 283, 1670–1676.〕〔)>Weiss, S. (1999) Science 283, 1676–1683.〕 (e.g. measurements of protein dynamics and DNA and RNA dynamics,〔)>Schuler, B., Lipman, E. A. & Eaton, W. A. (2002) Nature 419, 743–747.〕〔)>Yang, H., Luo, G., Karnchanaphanurach, P., Louie, T., Rech, I., Cova, S., Xun, L., Xie, X. S. (2003) Science 302, 262–266.〕〔)>Min, W., Lou, G., Cherayil, B. J., Kou, S. C., & Xie, X. S. (2005) Phys. Rev. Lett. 94, 198302.〕〔)>Rhoades, E., Gussakovsky, E. & Haran, G. (2003) Proc. Natl. Acad. Sci. USA 100, 3197–3202.〕〔)>Zhuang, X., Kim, H., Pereira, M. J. B., Babcock, H. P., Walter, N. G., & Chu, S. (2002) Science 296, 1473–1476.〕〔)>Barsegov, V. & Thirumalai, D. (2005) Phys. Rev. Lett. 95, 168302-1-4.〕〔)>Kolomeisky, A. B. & Fisher, M. E. (2000) J. Chem. Phys. 113, 10867-10877.〕 activity of ion channels,〔)>Neher, E. & Sakmanm, B. (1976) Nature 260, 799–802.〕〔)>Kasianowicz, J. J., Brandin, E., Branton, D., & Deamer, D. W. (1996) Proc. Natl. Acad. Sci. USA 93, 13770–13773.〕〔)>Kullman, L., Gurnev, P. A., Winterhalter, M., & Bezrukov, S. M. (2006) Phys. Rev. Lett. 96, 038101-038104.〕 enzyme activity,〔)>Lu, H., Xun, L. & Xie, X. S. (1998) Science 282, 1877–1882.〕〔)>. Edman, L., Földes-Papp, Z., Wennmalm, S. & Rigler, R. (1999) Chem. Phys. 247, 11–22.〕〔)>Velonia, K., Flomenbom, O., Loos, D., Masuo, S., Cotlet, M., Engelborghs, Y., Hofkens, J., Rowan, A. E., Klafter, J., Nolte, R. J. M., et al. (2005) Angew. Chem. Int. Ed. 44, 560–564.〕〔)>Flomenbom, O., Velonia, K., Loos, D., Masuo, S., Cotlet, M., Engelborghs, Y., Hofkens, J., Rowan, A. E., Nolte, R. J. M., Van der Auweraer, M., et al. (2005) Proc. Natl. Acad. Sci. USA. 102, 2368–2372.〕〔)>English, B. P., Min, W., van Oijen, A. M., Lee, K. T., Luo, G., Sun, H., Cherayil, B. J., Kou, S. C., & Xie., X. S. (2006) Nat. chem. Biol. 2, 87–94.〕〔)>Agmon, N. (2000) J. Phys. Chem. B 104, 7830–7834.〕〔)>Qian, H. & Elson, E. L. (2002) Biophys. Chem. 101, 565–576.〕〔)>Kou, S. C., Cherayil, B. J., Min, W., English, B. P., & Xie, X. S. (2005) J. Phys. Chem. B 109, 19068–19081.〕〔)>Sung, J. Y. & Silbey, R. J. (2005) Chem. Phys. Lett. 415, 10–14.〕〔)>Shaevitz, J. W., Block, S. M., & Schnitzer, M. J. (2005) Biophys. J. 89, 2277–2285.〕〔)>Goychuk, I. & Hänggi, P. (2004) Phys. Rev. E 70, 051915-1-9.〕 quantum dots 〔)>Nie, S., Chiu, D. T. & Zare R. N. (1994) Science 266, 1018–1021.〕〔)>Shusterman, R., Alon, S., Gavrinyov, T., & Krichevsky, O. (2004) Phys. Rev. Lett. 92, 048303-1-4.〕〔)>Zumofen, G., Hohlbein, J. & Hübner, C. G. (2004) Phys. Rev. Lett. 93, 260601-1-4.〕〔)>Cohen, A. E. & Moerner, W. E. (2006) Proc. Natl. Acad. Sci. USA. 103, 4362–4365.〕〔)>Dickson, R. M., Cubitt, A. B., Tsien, R. Y., & Moerner, W. E. (1997) Nature 388, 355-358.〕〔)>Chung, I. & Bawendi M. G. (2004) Phys. Rev. B. 70, 165304-1-5.〕〔)>Barkai, E., Jung, Y. & Silbey, R. (2004) Annu. Rev. Phys. Chem. 55, 457-507.〕〔)>Tang, J. & Marcus, R. A. (2005) J. Chem. Phys. 123, 204511-1-6.〕) thus making RDFs an important tool in the analysis of data in these fields. Since RDFs are uniquely obtained from the data,〔)>O. Flomenbom, and R. J. Silbey, Toolbox for analyzing finite two-state trajectories, (Phys. Rev. E 78, 066105 (2008) ).〕〔)>O Flomenbom, Adv. Chem. Phys., in press (2011).〕 they have many advantages over other mathematical and statistical methods that were developed for solving two-state trajectories.〔)>Horn, R. & Lange, K. (1983) Biophys. J. 43, 207–223.〕〔)>Qin. F., Auerbach, A. & Sachs, F. (2000) Biophys. J. 79, 1915–1927.〕〔)>Bruno, W. J., Yang, J. & Pearson, J. (2005) Proc. Natl. Acad. Sci. USA. 102, 6326–6331.〕〔)>Bauer, R. J., Bowman, B. F. & Kenyon, J. L. (1987) Biophys. J. 52, 961 – 978.〕〔)>Kienker, P. (1989) Proc. R. Soc. London B. 236, 269–309.〕〔)>Fredkin, D. R. & Rice, J. A. (1986) J. Appl. Prob. 23, 208–214.〕〔)>Colquhoun, D. & Hawkes A. G. (1982) Philos. Trans. R. Soc. Lond. B Biol. Sci. 300, 1–59.〕〔)>Song, L. & Magdeby, K. L. (1994) Biophys. J. 67, 91–104.〕〔)>Cao, J. (2000) Chem. Phys. Lett. 327, 38–44.〕〔)>Vlad, M. O., Moran, F., Schneider, F. W., & Ross, J. (2002) Proc. Natl. Acad. Sci. USA. 99, 12548–12555.〕〔)>Yang, S. & Cao, J. (2002) J. Chem. Phys. 117, 10996–11009.〕〔)>Šanda, F., & Mukamel, S. (2006) J. Chem. Phys. 108, 124103-1-15.〕〔)>Allegrini, P., Aquino, G., Grigolini, P., Palatella, L., & Rosa, A. (2003) Phys. Rev. E 68, 056123-1-11.〕 ==Description of RDF== A RDF is a lattice of substates, each substate represents either the on state or the off state, and has a particular number (see Figure 1). The connections are only among substates of different states. A simulation of an on-off trajectory from a RDF is made with a generalized Gillespie algorithm, where here a random jumping time is first taken from density functions that are (usually) not exponential using the rejection method, and then the specific next substate is chosen according to the jumping probabilities that are determined from the jumping time probability density functions. A RDF can have irreversible connections, yet, it generates an on-off trajectory that has the property of microscopic reversibility, meaning that the physical system fluctuates around equilibrium. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reduced dimensions form」の詳細全文を読む スポンサード リンク
|