A Limiting Speed for Protein Folding at Low Solvent Viscosity

Qiu, Linlin; Hagen, Stephen J.

doi:10.1021/ja049966r

Cited by 80 publications

(101 citation statements)

References 17 publications

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“…For simple barrier-crossing processes, D ‡ ϭ RT/ , where the friction coefficient, , is proportional to the solvent viscosity, , so a plot of vs. should be linear with zero intercept. The crucial assumption in determining the viscosity dependence is, of course, that the viscogen does not alter the free energy surface, but only changes the observed relaxation rate through its effect on the dynamics of motion on the surface, namely D ‡ .In all but one of the previous protein folding studies a chemical denaturant was used to counter the increase in stability caused by the viscogen and thereby maintain a constant equilibrium population of folded to unfolded molecules (equal to u / f ) (11)(12)(13)(15)(16)(17). The use of denaturant to maintain a constant equilibrium population ratio does not guarantee that the free energy surface, defined by the 5 parameters of Eq.…”

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confidence: 99%

“…In all but one of the previous protein folding studies a chemical denaturant was used to counter the increase in stability caused by the viscogen and thereby maintain a constant equilibrium population of folded to unfolded molecules (equal to u / f ) (11)(12)(13)(15)(16)(17). The use of denaturant to maintain a constant equilibrium population ratio does not guarantee that the free energy surface, defined by the 5 parameters of Eq.…”

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confidence: 99%

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Measuring internal friction of an ultrafast-folding protein

Cellmer

Henry²,

Hofrichter³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

154

193

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Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.funneled energy landscape ͉ Ising-like model ͉ Kramers ͉ polypeptide ͉ viscosity D espite the complexity of the protein folding process, the kinetics and mechanisms of folding can be usefully and accurately described by diffusion over barriers on a lowdimensional free-energy surface (1-5). For ultrafast-folding proteins, the barriers are small and the rates may be affected by the variation of the diffusion coefficient along the reaction coordinate. In addition to solvent friction, the diffusion coefficient is determined by internal friction, which reflects the ''roughness'' of the energy landscape that arises from drag because of intrachain interactions and escape from local minima on the energy surface (1, 4, 6, 7). Both theoretical studies (1,8) and simulations (4, 9, 10) indicate that the internal friction depends on position along the reaction coordinate, but there have been no experiments that address this important issue in the physics of protein folding. In this work, we obtain a quantitative measure of the contribution of internal friction to the dynamics of folding from experiments on the viscosity dependence of the kinetics for the ultrafast-folding villin subdomain. Fitting the data with an Ising-like theoretical model, moreover, yields information on the position dependence of the diffusion coefficient. Unlike all previous studies of the viscosity dependence of protein-folding kinetics (11-17), we carried out experiments under conditions where there is no effect of the viscogen on the equilibrium thermal unfolding, as was done in a previous study of ␣-helix and ␤-hairpin formation (18).For barriers Ͼϳ 3RT separating folded and unfolded states, Kramers theory (19) predicts that the relaxation rate, 1/ , is given by:where is the relaxation time, f and u are the folding and unfolding times, ⌬G f ‡ is the free energy barrier to folding, ⌬G u ‡ is the free energy barrier to unfolding, R is the gas constant, T is the absolute temperature, ( u ) 2 is the curvature in the unfolded free energy well, ( f ) 2 is the curvature in the folded free energy well, ( ‡ ) 2 is the curvature a...

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confidence: 99%

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confidence: 99%

Measuring internal friction of an ultrafast-folding protein

Cellmer

Henry²,

Hofrichter³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

154

193

View full text Add to dashboard Cite

show abstract

“…Nevertheless, results from recent experiments on small peptides under different solvent conditions indicate that intrachain interactions (which can be interpreted kinetically as a kind of internal friction) induce local activation barriers that renormalize the effective monomer diffusion coefficient (48,49). Although controversial, internal friction may explain why the speed limit of protein folding is fixed at ϳO(0.1-1.0 s) (50).…”

Section: Resultsmentioning

confidence: 99%

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates

Portman

2007

Proc. Natl. Acad. Sci. U.S.A.

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A coarse-grained variational model is used to investigate the polymer dynamics of barrier crossing for a diverse set of two-state folding proteins. The model gives reliable folding rate predictions provided excluded volume terms that induce minor structural cooperativity are included in the interaction potential. In general, the cooperative folding routes have sharper interfaces between folded and unfolded regions of the folding nucleus and higher free energy barriers. The calculated free energy barriers are strongly correlated with native topology as characterized by contact order. Increasing the rigidity of the folding nucleus changes the local structure of the transition state ensemble nonuniformly across the set of proteins studied. Nevertheless, the calculated prefactors k0 are found to be relatively uniform across the protein set, with variation in 1/k0 less than a factor of 5. This direct calculation justifies the common assumption that the prefactor is roughly the same for all small two-state folding proteins. Using the barrier heights obtained from the model and the best-fit monomer relaxation time 30 ns, we find that 1/k0 ϳ 1-5 s (with average 1/k0 ϳ 4 s). This model can be extended to study subtle aspects of folding such as the variation of the folding rate with stability or solvent viscosity and the onset of downhill folding.nucleation ͉ prefactor ͉ topology F olding in small proteins is often well characterized as a cooperative transition between two well defined structural populations: an unstructured globule ensemble and a structured folded ensemble. The transition rate between free energy minima is controlled by the dynamics of passing through an unstable transition region determined by saddlepoints in the free energy surface. Accordingly, the rate is expected to follow Arrhenius formwhere ␤ ϭ 1/k B T is the inverse temperature and ⌬F † is the free energy difference between the unfolded and transition-state ensembles. The exponential factor in Eq. 1 reflects the equilibrium population of the transition-state ensemble relative to unfolded ensemble and the prefactor, k 0 , is the time scale associated with the dynamics of crossing the free energy barrier. Successful identification of specific residues structured in the transition-state ensemble by several different theoretical models (1-8) and numerous simulation studies (see, e.g., refs. 9-11 and references therein) has established that the topology of the native structure determines the folding mechanism of these proteins. In addition, two-state folding rates are well correlated with very simple measures of the native state topology such as contact order (12-15). While additive potentials often produce reasonable structural characterization of the transition state ensemble, the range of simulated folding rates and their relationship with contact order does not agree with experiment (10). In this paper we present direct folding rate calculations that capture the trends noted earlier in lattice models (16, 17) and very recently in continuum models ...

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“…Recently it was shown that internal friction varies substantially along the folding pathway of a peptide chain which suggests a connection between friction and formation of hydrogen bonds upon folding [66]. While such studies on proteins are ubiquitous [68][69][70], there is obviously a lack of experimental data on roughness of DNA and RNA conformational transition. …”

Section: Internal Frictionmentioning

confidence: 99%

Correlation Force Spectroscopy for Single Molecule Measurements

Radiom

2015

Springer Theses

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This thesis addresses development of a new force spectroscopy tool, correlation force spectroscopy (CFS), for the measurement of the mechanical properties of very small volumes of material (molecular to µm 3 ) at kHz-MHz time-scales. CFS is based on atomic force microscopy (AFM) and the principles of CFS resemble those of dual-trap optical tweezers. CFS consists of was validated by comparison between experimental data and finite element modeling of the deterministic vibrations of the cantilevers using the known viscosity and density of fluids. Work in this thesis shows that the data can also be accurately fitted using a simple harmonic oscillator model, which can be used for rapid rheometric measurements, after calibration. The mechanical properties of biomolecules such as dextran and single stranded DNA (ssDNA) are also described. Working with this prominent scientist and researcher, and learning from him, were not only highlights of an academic life, but advent of a new lifestyle. This is due to his special character and charismatic behavior. His insights, ideas, perseverance and encouragements were great source of success in this project.

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A Limiting Speed for Protein Folding at Low Solvent Viscosity

Cited by 80 publications

References 17 publications

Measuring internal friction of an ultrafast-folding protein

Measuring internal friction of an ultrafast-folding protein

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates

Correlation Force Spectroscopy for Single Molecule Measurements

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