Journal of Biological Physics

, Volume 38, Issue 2, pp 201–207

Hill’s small systems nanothermodynamics: a simple macromolecular partition problem with a statistical perspective

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Abstract

Using a simple example of biological macromolecules which are partitioned between bulk solution and membrane, we investigate T.L. Hill’s phenomenological nanothermodynamics for small systems. By introducing a system size-dependent equilibrium constant for the bulk-membrane partition, we obtain Hill’s results on differential and integral chemical potentials μ and \(\hat{\mu}\) from computations based on standard Gibbsian equilibrium statistical mechanics. It is shown that their difference can be understood from an equilibrium re-partitioning between bulk and membrane fractions upon a change in the system’s size; it is closely related to the system’s fluctuations and inhomogeneity. These results provide a better understanding of nanothermodynamics and clarify its logical relation with the theory of statistical mechanics.

Keywords

Nanothermodynamics Ensemble Fluctuation Small systems  Statistical mechanics 

References

  1. 1.
    Bustamante, C., Liphardt, J., Ritort, F.: The nonequilibrium thermodynamics of small systems. Phys. Today 58, 43–48 (2005)CrossRefGoogle Scholar
  2. 2.
    Rajagopal, A.K., Pande, C.S., Abe, S.: Nanothermodynamics—a generic approach to material properties at nanoscale. arxiv.org/abs/cond-mat/0403738 (2004)
  3. 3.
    Hill, T.L.: A different approach to nanothermodynamics. Nano Lett. 1, 273–275 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Hill, T.L.: Thermodynamics of Small Systems. Dover, New York (1994)Google Scholar
  5. 5.
    Chamberlin, R.V.: Mean-field cluster model for the critical behaviour of ferromagnets. Nature 408, 337–339 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    Schnell, S.K., Vlugt, T.J.H., Simon, J.-M., Bedeaux, D., Kjelstrup, S.: Thermodynamics of a small system in a μT reservoir. Chem. Phys. Lett. 504, 199–201 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Timasheff, S.N.: Thermodynamic binding and site occupancy in the light of the Schellman exchange concept. Biophys. Chem. 101-102, 99–111 (2002)CrossRefGoogle Scholar
  8. 8.
    Schellman, J.A.: A simple model for salvation in mixed solvents: applications to the stabilization and destabilization of macromolecular structures. Biophys. Chem. 37, 121–140 (1990)CrossRefGoogle Scholar
  9. 9.
    Schellman, J.A.: The relation between the free energy of interaction and binding. Biophy. Chem. 45, 273–279 (1993)CrossRefGoogle Scholar
  10. 10.
    Qian H., Hopfield, J.J.: Entropy-enthalpy compensation: perturbation and relaxation in thermodynamic systems. J. Chem. Phys. 105, 9292–9298 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    Qian, H.: Entropy-enthalpy compensation: conformational fluctuation and induced-fit. J. Chem. Phys. 109, 10015–10017 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    Ben-Naim, A.: Statistical Thermodynamics for Chemists and Biochemists. Plenum, New York (1992)Google Scholar
  13. 13.
    Ben-Naim, A.: Hydrophobic interaction and structural changes in the solvent. Biopolymers 14, 1337–1355 (1975)CrossRefGoogle Scholar
  14. 14.
    Zwanzig, R.W.: High-temperature equation of state by a perturbation method. I. Nonpolar gases. J. Chem. Phys. 22, 1420–1426 (1954)ADSCrossRefGoogle Scholar
  15. 15.
    Widom, B.: Some topics in the theory of fluids. J. Chem. Phys. 39, 2808–2812 (1963)ADSCrossRefGoogle Scholar
  16. 16.
    Qian, H.: Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems: an analytical theory. Nonlinearity 24, R19–R49 (2011)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Qian, H.: Cellular biology in terms of stochastic nonlinear biochemical dynamics: emergent properties, isogenetic variations and chemical system inheritability. J. Stat. Phys. 141, 990–1013 (2010)MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Qian, H.: An asymptotic comparative analysis of the thermodynamics of non-covalent association. J. Math. Biol. 52, 277–289 (2006)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Murray, J.D.: Asymptotic Analysis. Springer, Berlin (1984)MATHCrossRefGoogle Scholar
  20. 20.
    Kjelstrup, S., Bedeaux, D.: Non-equilibrium Thermodynamics of Heterogeneous Systems. World Scientific, Singapore (2008)MATHCrossRefGoogle Scholar
  21. 21.
    Reguera, D., Rubí, J.M., Vilar, J.M.G.: The mesoscopic dynamics of thermodynamic systems. J. Phys. Chem. B 109, 21502–21515 (2005)CrossRefGoogle Scholar
  22. 22.
    Ge, H., Qian, H.: The physical origins of entropy production, free energy dissipation and their mathematical representations. Phys. Rev. E 81, 051133 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Hill, T.L., Chamberlin, R.V.: Extension of the thermodynamics of small systems to open metastable states: an example. Proc. Natl. Acad. Sci. U.S.A. 95, 12779–12782 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    Rubí, J.M., Bedeaux, D., Kjelstrup, S.: Thermodynamics for single-molecule stretching experiments. J. Phys. Chem. B 110, 12733–12737 (2006)CrossRefGoogle Scholar
  25. 25.
    Rubí, J.M., Bedeaux, D., Kjelstrup, S.: Unifying thermodynamic and kinetic descriptions of single-molecule processes: RNA unfolding under tension. J. Phys. Chem. B 111, 9598–9602 (2007)CrossRefGoogle Scholar
  26. 26.
    Qian, H.: A simple theory of motor protein kinetics and energetics. Biophys. Chem. 67, 263–267 (1997)CrossRefGoogle Scholar
  27. 27.
    Qian, H.: Cycle kinetics, steady-state thermodynamics and motors—a paradigm for living matter physics. J. Phys. Condens. Matter 17, S3783–S3794 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    Qian, H.: Open-system nonequilibrium steady-state: statistical thermodynamics, fluctuations and chemical oscillations. J. Phys. Chem. B 110, 15063–15074 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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