Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2009 Jan 7;11(1):83-93.
doi: 10.1039/b813961j. Epub 2008 Nov 14.

Collapse transition in proteins

Guy Ziv  1 , D Thirumalai, Gilad Haran
Affiliations

Collapse transition in proteins

Guy Ziv et al. Phys Chem Chem Phys. .

Abstract

The coil-globule transition, a tenet of the physics of polymers, has been identified in recent years as an important unresolved aspect of the initial stages of the folding of proteins. We describe the basics of the collapse transition, starting with homopolymers and continuing with proteins. Studies of denatured-state collapse under equilibrium are then presented. An emphasis is placed on single-molecule fluorescence experiments, which are particularly useful for measuring properties of the denatured state even under conditions of coexistence with the folded state. Attempts to understand the dynamics of collapse, both theoretically and experimentally, are then described. Only an upper limit for the rate of collapse has been obtained so far. Improvements in experimental and theoretical methodology are likely to continue to push our understanding of the importance of the denatured-state thermodynamics and dynamics for protein folding in the coming years.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
Temperature dependence of the radius of gyration (here labeled S), and the hydrodynamic radius, RH, of a homopolymer (polystyrene, Mw = 2.6 × 107). Reused with permission from ref. .Copyright 1980, American Institute of Physics.
Fig. 2
Fig. 2
The end-to-end distribution P (Ree) for different values of the interaction energy ε, calculated as described in text following eqn (6) for a protein of 64 amino acids. Arrow indicates direction of growth of ε. As ε increases, the average distance shortens and the distribution becomes narrower. Sample chain configurations at low ε and high ε are shown as insets. P (Ree) can be used to calculate average FRET efficiency as a function of ε using eqn (5).
Fig. 3
Fig. 3
Analysis of the CG transition in 3 different proteins using the modified Sanchez theory described in the text. FRET efficiency values measured in single-molecule experiments were matched to calculated values obtained from eqn (5) by varying the interaction energy ε. These values were subsequently used (with eqn (6) and eqn (7)) to calculate other average quantities. (A) The expansion factor, α2 = Rg 2/Rg,02, as a function of denaturant concentration. (B) The interaction energy ε as a function of denaturant concentration. Symbols are calculated from experimental points (see references to original papers in Table 1). A linear fit of ε, shown in (B), is used to calculate the solid lines in (A), indicating that a linear model captures the essential features of the collapse process.
Fig. 4
Fig. 4
Lattice simulation of the collapse kinetics for two sequences with two different values of σ = (Tθ − Tf)/Tθ, that of sequence A being smaller than that of sequence B. Folding is initiated by quenching the temperature from Tθ to TQ<Tf. The values of TQ are adjusted so that the native states of A and B have the same stability. (A) Dependence of the radius of gyration, Rg(t), as a function of time for sequence A (green line) that undergoes specific collapse prior to reaching the native state. Time is measured in terms of Monte Carlo Steps (MCS). Red line shows Rg(t) for fast track molecules for sequence B, and the black line is a multi-exponential fit. The structures sampled by the denatured-state ensemble prior to reaching the native state for sequences A and B are similar. (B) Rg(t) as a function of t for the slow track molecules that pause in an ensemble of compact metastable structures. This curve is for sequence B. The transition to the metastable minima from the unfolded state occurs rapidly (inset). Note that the timescales in (A) and (B) are different.
Fig. 5
Fig. 5
Time-dependent acquisition of the native state. (A) The fraction of native contacts, fN(t), for sequences A and B. Just as for Rg(t) the changes in fN(t) for sequence A (green) and the fast track molecules in sequence B (red) are identical. The blue line shows fN(t) for the slow track molecules of sequence B. (B) Fraction of non-native contacts fNN(t) for sequence A (green), fast track molecules of sequence B (red), and slow track molecules of sequence B (blue). On a rapid time scale (~5 × 106 MCS) fNN(t) in the red and green curves reach the equilibrium values while fNN(t) in blue curve has not decayed to the equilibrium value. Note that time scales in (A) and (B) are different.
Fig. 6
Fig. 6
A unified view of two-state folding with denatured-state collapse/expansion. (A) under native conditions, the denatured state is fully collapsed (and potentially contains some residual secondary structure) and its free energy is higher than that of the folded state. (B) As denaturant concentration is increased, the denatured state expands and its Rg becomes larger, while its free energy becomes lower relative to the folded state. (C) In high [C], the denatured state has a much larger Rg than the folded state. Under each set of conditions, though, only two states co-exist, folded (labeled F) and unfolded (labeled D).
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

See all "Cited by" articles

References

    1. Anfinsen CB, Haber E. J. Biol. Chem. 1961;236:1361–1363. - PubMed
    1. Thirumalai D, Hyeon C. Biochemistry. 2005;44:4957–4970. - PubMed
    1. Shakhnovich E. Chem. Rev. 2006;106:1559–1588. - PMC - PubMed
    1. Oliveberg M, Wolynes PG. Q. Rev. Biophys. 2005;38:245–288. - PubMed
    1. Munoz V. Annu. Rev. Biophys. Biomol. Struct. 2007;36:395–412. - PubMed

Publication types