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Current issue   Ukr. J. Phys. 2015, Vol. 60, N 11, p.1163-1176
https://doi.org/10.15407/ujpe60.11.1163    Paper

Teslenko V.I., Kapitanchuk O.L.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: vtes@bitp.kiev.ua)

Fractional Cooperativity of a Few-State System in the Environment

Section: General problems of theoretical physics
Original Author's Text: English

Abstract: Cooperativity represents a type of the not well-defined quantities implemented in different fields ranging from physics to chemistry, biology, informatics, etc. In the present work, we define the cooperativity from the physical point of view by relating it to the stability of a few-state system with respect to the irreversibility. First, we reduce this system evolving in time to the pair of fluctuating energy levels of different dimensionalities with the initial population of one level, different probabilities of microscopically reversible transitions between the levels, and some probability of irreversible decay of another level. Then we make an average of the reduced system over the energy level fluctuations to provide between-level transition rates with the explicit impacts of external controls on levels’ positions and dimensionalities. Finally, we demonstrate the emergence of the cooperativity of a fractional degree ranging between 2/e and unity when normalized in this system and observe that, at the lower bound of such degree, the system becomes unstable, so that, to restore the stability, one needs either to decrease the irreversible decay rate or to make the reversible backward transitions faster.

Key words: irreversible kinetic processes, energy fluctuations, dissipating environment, cooperativity, Hill’s coefficient, ligand-receptor assembly.

References:

  1. J. Gates, The Ownership Solution (Penguin, London, 1998).
  2. J. Rothschild and J. Allen-Whitt, The Cooperative Workplace (Cambridge Univ. Press, Cambridge, 1986).
  3. H. Hotelling, Economic J. 39, 41 (1929). https://doi.org/10.2307/2224214
  4. C. Bohr, Zentralblatt Physiol. 23, 688 (1904).
  5. A.J. Clark, The Mode of Action of Drugs on Cells (Edward Arnold, London, 1933)
  6. J.B.S. Haldane, Enzymes (MIT Press, Cambridge, MA, 1965).
  7. F.C. Frank, Proc. Roy. Soc. A 215, 43 (1952). https://doi.org/10.1098/rspa.1952.0194
  8. A.W. Adamson, J. Am. Chem. Soc. 76, 1578 (1954). https://doi.org/10.1021/ja01635a030
  9. F.H. Stillinger and T.A. Weber, Phys. Rev. A 28, 2408 (1983). https://doi.org/10.1103/PhysRevA.28.2408
  10. K.A. Connors, Binding Constants: The Measurements of Molecular Complex Stability (Wiley, New York, 1987).
  11. P. Hobza and R. Zahradnik, Intermolecular Complexes (Elsevier, Amsterdam, 1988).
  12. J.-M. Lehn, Supramolecular Chemistry: Concepts and Perspectives (Wiley-VCH, Weinheim, 1995). https://doi.org/10.1002/3527607439
  13. J.C. Dyre, Rev. Mod. Phys. 78, 953 (2006). https://doi.org/10.1103/RevModPhys.78.953
  14. A.V. Hill, J. Physiol. 40, 389 (1910). https://doi.org/10.1113/jphysiol.1910.sp001377
  15. R. Heinrich and T.A. Rapoport, Acta Biol. Med. Ger. 31, 479 (1973).
  16. J. H. Hofmeyr and A. Cornish-Bowden, Eur. J. Biochem. 200, 223 (1991). https://doi.org/10.1111/j.1432-1033.1991.tb21071.x
  17. R. Heinrich and S. Schuster, The Regulation of Cellular Systems (Chapman and Hall, New York, 1996).
  18. G.S. Adair, J. Biol. Chem. 63, 529 (1925).
  19. L. Pauling, Proc. Nat. Acad. Sci. USA 21, 186 (1935). https://doi.org/10.1073/pnas.21.4.186
  20. J. Monod, J. Wyman and J.-P. Changeux, J. Mol. Biol. 12, 88 (1965). https://doi.org/10.1016/S0022-2836(65)80285-6
  21. D.E. Koshland, Jr., G. Nemethy, and D. Filmer, Biochemistry 5, 365 (1966). https://doi.org/10.1021/bi00865a047
  22. W.G. Bardsley and R.E. Childs, Biochem. J. 149, 313 (1975). https://doi.org/10.1042/bj1490313
  23. J. Ricard and A. Cornish-Bowden, Eur. J. Biochem. 166, 255 (1987). https://doi.org/10.1111/j.1432-1033.1987.tb13510.x
  24. A.L. Horovitz and A.R. Fersht, J. Mol. Biol. 214, 613 (1990). https://doi.org/10.1016/0022-2836(90)90275-Q
  25. T. Shem-Ad and O. Yifrach, J. Gen. Physiol. 141, 507 (2013). https://doi.org/10.1085/jgp.201310976
  26. A. Cornish-Bowden, FEBS J. 281, 621 (2014). https://doi.org/10.1111/febs.12469
  27. Q. Cui and M. Karplus, Protein Sci. 17, 1295 (2008). https://doi.org/10.1110/ps.03259908
  28. G.R. Fleming and M. Ratner, Phys. Today July, 28 (2008). https://doi.org/10.1063/1.2963009
  29. H.E. Stanley, Rev. Mod. Phys. 71, S358 (1999). https://doi.org/10.1103/RevModPhys.71.S358
  30. K. Lindenberg and B.J. West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems (Wiley-VCH, New York, 1990).
  31. A. Rivas and S.F. Huelga, Open Quantum Systems: An Introduction (Springer, Heidelberg, 2012). https://doi.org/10.1007/978-3-642-23354-8
  32. C.H. Fleming and B.L. Hu, Ann. Phys. 327, 1238 (2012). https://doi.org/10.1016/j.aop.2011.12.006
  33. M.A. Miller, J.P.K. Doe, and D.J. Wales, Phys. Rev. E 60, 3701 (1999). https://doi.org/10.1103/PhysRevE.60.3701
  34. Y. Levy, J. Jortner, and R.S. Berry, Phys. Chem. Chem. Phys. 4, 5052 (2002). https://doi.org/10.1039/b203534k
  35. J. Cao and R.J. Silbey, J. Phys. Chem. A 113, 13825 (2009). https://doi.org/10.1021/jp9032589
  36. Y.R. Chemla, J.R. Moffitt, and C. Bustamante, J. Phys. Chem. B 112, 6025 (2008). https://doi.org/10.1021/jp076153r
  37. A.I. Burshtein, Adv. Phys. Chem. 2009, 214219 (2009). https://doi.org/10.1155/2009/214219
  38. G. Lindblad, Nonequilibrium Entropy and Irreversibility (Reidel, Dordrecht, 1983). https://doi.org/10.1007/978-94-009-7206-3
  39. E.C.G. Sudarshan, Phys. Rev. A 46, 37 (1992). https://doi.org/10.1103/PhysRevA.46.37
  40. N.N. Bogoliubov, Lectures on Quantum Statistics (Gordon and Breach, New York, 1967), Vol. 1.
  41. N.N. Bogoliubov, Lectures on Quantum Statistics (Gordon and Breach, New York, 1970), Vol. 2.
  42. S. Nakajima, Progr. Theor. Phys. 20, 948 (1958). https://doi.org/10.1143/PTP.20.948
  43. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960). https://doi.org/10.1063/1.1731409
  44. E.G. Petrov, Eur. Phys. J. Special Topics 216, 205 (2013). https://doi.org/10.1140/epjst/e2013-01744-0
  45. I. Goychuk and P. Hanggi, Adv. Phys. 54, 525 (2005). https://doi.org/10.1080/00018730500429701
  46. E.G. Petrov and V.I. Teslenko, Theor. Math. Phys. 84, 986 (1991). https://doi.org/10.1007/BF01017358
  47. E.G. Petrov, V.I. Teslenko, and I.A. Goychuk, Phys. Rev. E 49, 3894 (1994). https://doi.org/10.1103/PhysRevE.49.3894
  48. E.G. Petrov, I.A. Goychuk, and V. May, Physica A 233, 560 (1996). https://doi.org/10.1016/S0378-4371(96)00252-X
  49. V.I. Teslenko, E.G. Petrov, A. Verkhatsky, and O.A. Krishtal, Phys. Rev. Lett. 104, 178105 (2010). https://doi.org/10.1103/PhysRevLett.104.178105
  50. E.G. Petrov and V.I. Teslenko, Chem. Phys. 375, 243 (2010). https://doi.org/10.1016/j.chemphys.2010.05.029
  51. V.I. Teslenko and O.L. Kapitanchuk, Int. J. Mod. Phys. B 27, 1350169 (2013). https://doi.org/10.1142/S0217979213501695
  52. E. Langmann and G. Lindblad, J. Stat. Phys. 134, 749 (2009). https://doi.org/10.1007/s10955-009-9700-x
  53. A. Nitzan, Chemical Dynamics in Condensed Phases (Oxford Univ. Press, Oxford, 2006).
  54. R.D. Coalson, D.G. Evans, and A. Nitzan, J. Chem. Phys. 101, 436 (1994). https://doi.org/10.1063/1.468153
  55. J. Jortner, J. Chem. Phys. 64, 4860 (1976). https://doi.org/10.1063/1.432142
  56. J. Gunawardena, Mol. Biol. Cell 23, 517 (2012). https://doi.org/10.1091/mbc.E11-07-0643
  57. B. Efron and R. Tibshirani, Science 253, 390 (1991). https://doi.org/10.1126/science.253.5018.390
  58. K. Banerjee, B. Das, and G. Gangopadhyay, J. Chem. Phys. 136, 154502 (2012). https://doi.org/10.1063/1.3703505
  59. S.S. Plotkin, J. Wang, and P.G. Wolynes, J. Phys. I 7, 395 (1997). https://doi.org/10.1051/jp1:1997168
  60. V.N. Smelyanskiy, M.I. Dykman, H. Rabitz, and B.E. Vugmeister, Phys. Rev. Lett. 79, 3113 (1997). https://doi.org/10.1103/PhysRevLett.79.3113
  61. A. Fiasconaro, B. Spagnolo, and S. Boccaletti, Phys. Rev E 72, 061110 (2005). https://doi.org/10.1103/PhysRevE.72.061110
  62. G.G. Hammes, Proc. Natl. Acad. Sci. USA 79, 6881 (1982). https://doi.org/10.1073/pnas.79.22.6881
  63. D. Alvarado, D.E. Klein, and M.A. Lemmon, Cell 142, 568 (2010). https://doi.org/10.1016/j.cell.2010.07.015
  64. C. Czaplewski, A. Liwo, D.R. Ripoll, and H.A. Scheraga, J. Phys. Chem. B 109, 8108 (2005). https://doi.org/10.1021/jp040691b
  65. L. Wang, R.A. Freisner, and B.J. Berne, Faraday Discuss. 146, 247 (2010). https://doi.org/10.1039/b925521b
  66. A. Cornish-Bowden, Fundamentals of Enzyme Kinetics (Wiley-VCH, Weinheim, 2012).
  67. H. Hooyberghs, B. Van Schaeybroeck, and J.O. Indekeu, Physica A 389, 2920 (2010). https://doi.org/10.1016/j.physa.2009.12.068
  68. D. Wren and A.G. Bedeian, The Evolution of the Management Thought (Wiley, New York, 2009).