Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Perspective
  • Published:

Dissipative adaptation in driven self-assembly

Abstract

In a collection of assembling particles that is allowed to reach thermal equilibrium, the energy of a given microscopic arrangement and the probability of observing the system in that arrangement obey a simple exponential relationship known as the Boltzmann distribution. Once the same thermally fluctuating particles are driven away from equilibrium by forces that do work on the system over time, however, it becomes significantly more challenging to relate the likelihood of a given outcome to familiar thermodynamic quantities. Nonetheless, it has long been appreciated that developing a sound and general understanding of the thermodynamics of such non-equilibrium scenarios could ultimately enable us to control and imitate the marvellous successes that living things achieve in driven self-assembly. Here, I suggest that such a theoretical understanding may at last be emerging, and trace its development from historic first steps to more recent discoveries. Focusing on these newer results, I propose that they imply a general thermodynamic mechanism for self-organization via dissipation of absorbed work that may be applicable in a broad class of driven many-body systems.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Assembly probability in the presence of thermal fluctuations.
Figure 2: Dynamical irreversibility and heat production.
Figure 3: Driven barrier hopping.

Similar content being viewed by others

References

  1. Boyer, P. D. The ATP synthase — a splendid molecular machine. Annu. Rev. Biochem. 66, 717–749 (1997).

    Article  CAS  Google Scholar 

  2. Bushnell, D. A., Westover, K. D., Davis, R. E. & Kornberg, R. D. Structural basis of transcription: an RNA polymerase II-TFIIB cocrystal at 4.5 angstroms. Science 303, 983–988 (2004).

    Article  CAS  Google Scholar 

  3. Xiang, Y. et al. Crystallographic insights into the autocatalytic assembly mechanism of a bacteriophage tail spike. Mol. Cell 34, 375–386 (2009).

    Article  Google Scholar 

  4. Tompa, P. Intrinsically unstructured proteins. Trends Biochem. Sci. 27, 527–533 (2002).

    Article  CAS  Google Scholar 

  5. Jarzynski, C. & Langer, J. Equalities and inequalities: irreversibility and the second law of thermodynamics at the nanoscale. Annu. Rev. Condens. Matter Phys. 2, 329–351 (2011).

    Article  CAS  Google Scholar 

  6. Pathria, R. K. Statistical Mechanics (Butterworth Heinemann, 2001).

    Google Scholar 

  7. Prigogine, I. & Nicolis, G. Biological order, structure and instabilities. Q. Rev. Biophys. 4, 107–148 (1971).

    Article  CAS  Google Scholar 

  8. Spanner, D. Biological systems and the principle of minimum entropy production. Nature 172, 1094–1095 (1953).

    Article  Google Scholar 

  9. Crooks, G. E. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 60, 2721–2726 (1999).

    Article  CAS  Google Scholar 

  10. Jarzynski, C. Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997).

    Article  CAS  Google Scholar 

  11. Crooks, G. E. Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361–2366 (2000).

    Article  CAS  Google Scholar 

  12. Hatano, T. & Sasa, S.-i. Steady-state thermodynamics of Langevin systems. Phys. Rev. Lett. 86, 3463–3466 (2001).

    Article  CAS  Google Scholar 

  13. Liphardt, J., Dumont, S., Smith, S. B., Tinoco, I. & Bustamante, C. Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality. Science 296, 1832–1835 (2002).

    Article  CAS  Google Scholar 

  14. Trepagnier, E. H. et al. Experimental test of Hatano and Sasa's nonequilibrium steady-state equality. Proc. Natl Acad. Sci. USA 101, 15038–15041 (2004).

    Article  CAS  Google Scholar 

  15. Collin, D. et al. Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies. Nature 437, 231–234 (2005).

    Article  CAS  Google Scholar 

  16. Esposito, M. & Van den Broeck, C. Three detailed fluctuation theorems. Phys. Rev. Lett. 104, 090601 (2010).

    Article  Google Scholar 

  17. Sivak, D. & Crooks, G. Near-equilibrium measurements of nonequilibrium free energy. Phys. Rev. Lett. 108, 150601 (2012).

    Article  Google Scholar 

  18. Barato, A. C. & Seifert, U. Thermodynamic uncertainty relation for biomolecular processes. Phys. Rev. Lett. 114, 158101 (2015).

    Article  Google Scholar 

  19. England, J. Statistical physics of self-replication. J. Chem. Phys. 139, 121923 (2013).

    Article  Google Scholar 

  20. Landauer, R. Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961).

    Article  Google Scholar 

  21. Ito, S. et al. Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams. Sci. Rep. 3, 3047 (2013).

    Article  Google Scholar 

  22. Carnall, J. M. A. et al. Mechanosensitive self-replication driven by self-organization. Science 327, 1502–1506 (2010).

    Article  CAS  Google Scholar 

  23. Yokobayashi, Y., Weiss, R. & Arnold, F. H. Directed evolution of a genetic circuit. Proc. Natl Acad. Sci. USA 99, 16587–16591 (2002).

    Article  CAS  Google Scholar 

  24. Joyce, G. F. Directed evolution of nucleic acid enzymes. Annu. Rev. Biochem. 73, 791–836 (2004).

    Article  CAS  Google Scholar 

  25. Jackel, C., Kast, P. & Hilvert, D. Protein design by directed evolution. Annu. Rev. Biophys. 37, 153–173 (2008).

    Article  CAS  Google Scholar 

  26. Kondepudi, D., Kay, B. & Dixon, J. End-directed evolution and the emergence of energy-seeking behavior in a complex system. Phys. Rev. E 91, 050902 (2015).

    Article  Google Scholar 

  27. Jun, J. K. & Hübler, A. H. Formation and structure of ramified charge transportation networks in an electromechanical system. Proc. Natl Acad. Sci. USA 102, 536–540 (2005).

    Article  CAS  Google Scholar 

  28. Schaller, V., Weber, C., Semmrich, C., Frey, E. & Bausch, A. R. Polar patterns of driven filaments. Nature 467, 73–77 (2010).

    Article  CAS  Google Scholar 

  29. Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The author thanks the Cabot family for its generous support, and A. Bausch and Z. Dogic for helpful discussion.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeremy L. England.

Ethics declarations

Competing interests

The author declares no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

England, J. Dissipative adaptation in driven self-assembly. Nature Nanotech 10, 919–923 (2015). https://doi.org/10.1038/nnano.2015.250

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2015.250

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing