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User:Flomenbom/Two state trajectories

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Figure 1 Two-state trajectories

Two state trajectories (also termed, two-state trajectories, two state time trajectories, trajectories with two states). A two-state trajectory is a dynamical signal that fluctuates among two distinct values (ON-OFF, opened-closed, plus-minus, etc). In most applications, the signal is stochastic; nevertheless, it can have deterministic ON-OFF components. A completly deterministic two-state trajectory is a square wave.

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Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules [1][2] (e.g. measurements of protein dynamics and DNA and RNA dynamics, [3][4][5][6][7] activity of ion channels, [8] [9][10] enzyme activity, [11][12][13][14][15] quantum dots [16][17][18][19][20][21]) From these experiments, one aims at finding the correct model. [22][23][24][25][26] [27][28] [29][30][31][32][33] Examples for such experiments are listed in what follows.

Ion channels

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Since the ion channel is either opened or closed, when recording the number of ions that go through the channel when time elapses, one sees a two-state trajectory of the current versus time.

Enzymes

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Here, there are several possible experiments on the activity of individual enzymes with a two-state signal. For example, one can create substrate that only upon the enzymatic activity shines light when activated (with a laser pulse). So, each time the enzyme acts, we see bursts of photons that last for the time period the product molecule is in the laser area.

Dynamics of biological molecules

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Structural changes of molecules are viewed in various experiments' type. Förster resonance energy transfer is an example. In many cases one sees a time trajectory that fluctuates among several cleared define

Quantum dots

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Another system that fluctuates among an on state and an off state is a quantum dot. Here, the fluctuations tell the story of a special state of the molecule that is influenced also from its interactions with the surroundings.

See also

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References

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  1. ^ Moerner, W. E. & Orrit, M. (1999) Science 283, 1670-1676.
  2. ^ Weiss, S. (1999) Science 283, 1676-1683.
  3. ^ Schuler, B., Lipman, E. A. & Eaton, W. A. (2002) Nature 419, 743-747.
  4. ^ Yang, H., Luo, G., Karnchanaphanurach, P., Louie, T., Rech, I., Cova, S., Xun, L., Xie, X. S. (2003) Science 302, 262-266.
  5. ^ Min, W., Lou, G., Cherayil, B. J., Kou, S. C., & Xie, X. S. (2005) Phys. Rev. Lett. 94, 198302.
  6. ^ Rhoades, E., Gussakovsky, E. & Haran, G. (2003) Proc. Natl. Acad. Sci. USA 100, 3197-3202.
  7. ^ Zhuang, X., Kim, H., Pereira, M. J. B., Babcock, H. P., Walter, N. G., & Chu, S. (2002) Science 296, 1473-1476.
  8. ^ Neher, E. & Sakmanm, B. (1976) Nature 260, 799-802.
  9. ^ Kasianowicz, J. J., Brandin, E., Branton, D., & Deamer, D. W. (1996) Proc. Natl. Acad. Sci. USA 93, 13770–13773.
  10. ^ Kullman, L., Gurnev, P. A., Winterhalter, M., & Bezrukov, S. M. (2006) Phys. Rev. Lett. 96, 038101-038104.
  11. ^ Lu, H., Xun, L. & Xie, X. S. (1998) Science 282, 1877-1882.
  12. ^ . Edman, L., Földes-Papp, Z., Wennmalm, S. & Rigler, R. (1999) Chem. Phys. 247, 11-22.
  13. ^ 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.
  14. ^ 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.
  15. ^ 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.
  16. ^ Nie, S., Chiu, D. T. & Zare R. N. (1994) Science 266, 1018-1021.
  17. ^ Shusterman, R., Alon, S., Gavrinyov, T., & Krichevsky, O. (2004) Phys. Rev. Lett. 92, 048303-1-4.
  18. ^ Zumofen, G., Hohlbein, J. & Hübner, C. G. (2004) Phys. Rev. Lett. 93, 260601-1-4.
  19. ^ Cohen, A. E. & Moerner, W. E. (2006) Proc. Natl. Acad. Sci. USA. 103, 4362-4365.
  20. ^ Dickson, R. M., Cubitt, A. B., Tsien, R. Y., & Moerner, W. E. (1997) Nature 388, 355-358.
  21. ^ Chung, I. & Bawendi M. G. (2004) Phys. Rev. B. 70, 165304-1-5.
  22. ^ Horn, R. & Lange, K. (1983) Biophys. J. 43, 207-223.
  23. ^ Bauer, R. J., Bowman, B. F. & Kenyon, J. L. (1987) Biophys. J. 52, 961 – 978.
  24. ^ Kienker, P. (1989) Proc. R. Soc. London B. 236, 269-309.
  25. ^ Fredkin, D. R. & Rice, J. A. (1986) J. Appl. Prob. 23, 208-214.
  26. ^ Colquhoun, D. & Hawkes A. G. (1982) Philos. Trans. R. Soc. Lond. B Biol. Sci. 300, 1–59.
  27. ^ Song, L. & Magdeby, K. L. (1994) Biophys. J. 67, 91-104.
  28. ^ Qin. F., Auerbach, A. & Sachs, F. (2000) Biophys. J. 79, 1915-1927.
  29. ^ Bruno, W. J., Yang, J. & Pearson, J. (2005) Proc. Natl. Acad. Sci. USA. 102, 6326-6331.
  30. ^ O. Flomenbom, and R. J. Silbey, Utilizing the information content in two-state trajectories, Proc. Natl. Acad. Sci. USA 103, 10907-10910 (2006).
  31. ^ Flomenbom, O., Klafter, J. & Szabo, A. (2005) Biophys. J. 88, 3780-3783.
  32. ^ O. Flomenbom, and R. J. Silbey, Toolbox for analyzing finite two-state trajectories, Phys. Rev. E 78, 066105 (2008).
  33. ^ O. Flomenbom, Making it possible: constructing a reliable mechanism from a finite trajectory, Adv. Chem. Phys., in press (2011)
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