Squeezed Exponential Kinetics to Describe a Nonglassy Downhill Folding as Observed in a Lattice Protein Model

Hironori K. Nakamura, Masaki Sasai, Mitsunori Takano*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We previously studied the so-called strange kinetics in the two-dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27-mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two-state-like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or "shrunken") exponential function, exp [-(t/τ)β] with > 1, temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the non-glassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single-domain proteins may follow the squeezed exponential kinetics at about the room temperature.

Original languageEnglish
Pages (from-to)99-106
Number of pages8
JournalProteins: Structure, Function and Genetics
Issue number1
Publication statusPublished - 2004 Apr 1
Externally publishedYes


  • First passage time
  • Free energy profile
  • Kinetic partitioning
  • Monte Carlo simulation
  • Population analysis
  • Stretched exponential
  • Subdiffusion
  • Temperature dependence
  • Two-state folder

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • Molecular Biology


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