Granular Matter

, Volume 16, Issue 2, pp 259–268 | Cite as

Empirically modeling polymer collapse in a poor solvent via a non-equilibrium, granular chain experiment

  • Benjamin Bammes
  • Jeffrey S. Olafsen
Original Paper


We present a new empirical method for investigating the collapse of a semi-flexible, homogeneous polymer-like structure in a poor solvent. A stainless steel chain in a thin film of water that is vertically oscillated plays the role of the polymer in our model system. As the system is shaken, the chain collapses into a steady-state compact configuration. Collapse is largely dominated by the surface tension of the water; however other factors also contribute in a one-to-one correspondence with real homopolymers. This system may be tailored to investigate the physics of polymer folding in a fundamental manner. We use the normalized radius of gyration to compare collapse dynamics between experiments of different chain lengths. Free energy minimizing behavior is observed as the polymer passes through both “on-pathway” and “off-pathway” intermediate states. At all chain lengths, nucleation (formation of pearls) dominates the early stage of collapse dynamics. If the ends of the chain remain within the radius of gyration, collapse occurs quickly. However, when the ends of the chain stray far outside the radius of gyration, nucleation is impeded and collapse progresses more slowly.


Granular Non-equilibrium Polymer Folding 


  1. 1.
    Huang, K.: Lectures on Statistical Physics and Protein Folding. World Scientific Publishing Co., Hackensack, NJ (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Montesi, A., Pasquali, M., Macintosh, F.C.: Collapse of a semiflexible polymer in poor solvent. Phys. Rev. E 69, 021916 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    Schnurr, B., Gittes, F., Macintosh, F.C.: Metastable intermediates in the condensation of semiflexible polymers. Phys. Rev. E 65, 061904 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Sakaue, T., Yoshikawa, K.: Folding/unfolding kinetics on a semiflexible polymer chain. J. Chem. Phys. 117, 6323 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Noguchi, H., Yoshikawa, K.: Folding path in a semiflexible homopolymer chain: A Brownian dynamics simulation. J. Chem. Phys. 113, 854 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    Noguchi, H.: Folding dynamics in a semiflexible polymer as a model of DNA. Int. J. Bifurcat. Chaos 12, 2003 (2002)CrossRefGoogle Scholar
  7. 7.
    Kuznetsov, S.V., Shen, Y., Benight, A.S., Ansari, A.: A semiflexible polymer model applied to loop formation in DNA hairpins. Biophys. J. 81, 2864 (2001)CrossRefGoogle Scholar
  8. 8.
    Chang, R., Yethiraj, A.: Solvent effects on collapse dynamics of polymers. J. Chem. Phys. 114, 7688 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Abrams, C.F., Lee, N., Obukhov, S.: Collapse dynamics of a polymer chain: Theory and simulation. Europhys. Lett. 59, 391 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    Pande, V.S., Grosberg, A.Y., Tanaka, T.: Thermodynamics of the coil to frozen globule transition in heteropolymers. J. Chem. Phys. 107, 5118 (1997)ADSCrossRefGoogle Scholar
  11. 11.
    Dill, K.A., Bromberg, A., Yue, K., Fiebig, K.M., Yee, D.P., Thomas, P.D., Chan, H.S.: Principles of protein folding: a perspective from simple exact models. Protein Sci. 4, 561 (1995)CrossRefGoogle Scholar
  12. 12.
    Zhou, H.-X.: Polymer models of protein stability, folding and interactions. Biochemistry 43, 2141 (2004)CrossRefGoogle Scholar
  13. 13.
    Pretti, M.: Semi-flexible polymer in the cactus approximation. Phys. Rev. E 66, 061802 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    Doniach, S., Garel, T., Orland, H.: Phase diagram of a semiflexible polymer chain in a \(\theta \) solvent: application to protein folding. J. Chem. Phys. 105, 1601 (1996)Google Scholar
  15. 15.
    Halperin, A., Goldbart, P.M.: Early stages of homopolymer collapse. Phys. Rev. E 61, 565 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    Brinker, A., Pfeifer, G., Kerner, M.J., Naylor, D.J., Harti, F.U., Hayer-Harti, M.: Dual function of protein confinement in chaperonin-assisted protein folding. Cell 107, 223 (2001)CrossRefGoogle Scholar
  17. 17.
    Jewett, A.I., Baumketner, A., Shea, J.-E.: Accelerated folding in the weak hydrophobic environment of a chaperonin-cavity: creation of an alternate fast folding pathway. Proc. Natl. Acad. Sci. 101, 13192 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    Pasquali, M., Morse, D.C.: An efficient algorithm for metric correction forces in simulations of linear polymers with constrained bond lengths. J. Chem. Phys. 116, 1834 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Rapaport, D.C.: Dynamics of polymer chain collapse into compact states. Phys. Rev. E 68, 041801 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Hastings, M.B., Daya, Z.A., Ben-Naim, E., Ecke, R.E.: Entropic tightening of vibrated chains. Phys. Rev. E 66, 025102 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    Bammes, B., Olafsen, J.S.: Polymerlike folding of a two-dimensional granular chain in water. Chaos 14, S9 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    Safford, K., Kantor, Y., Kardar, M., Kudrolli, A.: Structure and dynamics of vibrated granular chains: comparison to equilibrium polymers. Phys. Rev. E 79, 061304 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Jeng, P.-R., Chen, K.H., Hwang, G., Lien, C., To, K., Chou, Y.C.: Collapse kinetics of vibrated granular chains. J. Chem. Phys. 135, 244903 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    Cross, M.C., Hohenberg, P.C.: Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851 (1993)ADSCrossRefGoogle Scholar
  25. 25.
    Rouse, P.E. Jr.: A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21, 1272 (1953)Google Scholar
  26. 26.
    Zimm, B.H.: Dynamics of polymer molecules in dilute solution: visoelasticity, flow birefringence and dielectric loss. J. Chem. Phys. 24, 269 (1956)ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    Benichou, O., Desbois, J.: Statistical properties of the 2D attached Rouse chain. J. Stat. Phys. 101, 921 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Benichou, O., Desbois, J.: Windings of the 2D free Rouse chain. J. Phys. A Gen. Math. 33, 6655 (2000) Google Scholar
  29. 29.
    Xue, B., Wang, W.: Influence of external vibration on tether chain in ligand-receptor binding. J. Chem. Phys. 122, 194912 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Dill, K.: Polymer principles and protein folding. Protein Sci. 8, 1166 (1999)CrossRefGoogle Scholar
  31. 31.
    Kikuchi, N., Ryder, J.F., Pooley, C.M., Yeomans, J.M.: Kinetics of the polymer collapse transition: the role of hydrodynamics. Phys. Rev. E 71, 061804 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    Aranson, I.S., Tsimring, L.S.: Dynamics of the constrained polymer collapse. Eur. Lett. 62, 848 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    Dill, K.A., Stigter, D.: Modeling protein stability as heteropolymer collapse. Adv. Protein Chem. 46, 59 (1995)CrossRefGoogle Scholar
  34. 34.
    Fawzi, N.L., Okabe, Y., Yap, E.-H., Head-Gordon, T.: Determining the critical nucleus and mechanism of fibril elongation of the alzheimer’s A \(\upbeta _{1-40}\) peptide. J. Mol. Biol. 365, 535 (2007)CrossRefGoogle Scholar
  35. 35.
    Lisy, V., Tothova, J., Zatovsky, A.V.: Long-time dynamics of Rouse–Zimm polymers in dilute solutions with hydrodynamic memory. J. Chem. Phys. 121, 10699 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    Xue, B., Wang, J., Wang, W.: Collapse of homopolymer chains with two fixed terminals. J. Chem. Phys. 119, 7534 (2003)ADSCrossRefGoogle Scholar
  37. 37.
    Boue, L., Katzav, E.: Folding of flexible rods confined in 2D space. Eur. Lett. 80, 54002 (2007)ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Baylor College of MedicineHoustonUSA
  2. 2.Direct ElectronLPSan DiegoUSA
  3. 3.Department of PhysicsBaylor UniversityWacoUSA

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