Diffusional Barrier in the Unfolding of a Small Protein

Pradeep, Lovy; Udgaonkar, Jayant B.

doi:10.1016/j.jmb.2006.11.064

Cited by 40 publications

(55 citation statements)

References 57 publications

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“…Due to this stabilization these experiments are performed using the stronger denaturant, GdmCl. The stability of the transition state, ΔG TS , cannot be determined and the isostability approach is widely applied to overcome this (8)(9)(10)(11)(12)(13)28). Such an approach has been criticized (29), but the strength of our experiments is the comparative nature of our study.…”

Section: Resultsmentioning

confidence: 99%

“…R16 and R17 have two sequential transition states, and for both domains the first of these (TS1) shows significant landscape roughness (or "internal friction") (7). This has not been seen for any other domain of comparable size and folding kinetics, although theory has long predicted the possibility of such landscape roughness (8)(9)(10)(11)(12)(13)(14)(15). R15 has a broad transition state (characterized by "rollover" in the unfolding limb for some mutants and for wild type under some conditions), but due to the speed of folding and unfolding it is not known whether it has two sequential transition states (16).…”

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confidence: 99%

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Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

Wensley

Kwa

Shammas

et al. 2012

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

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The elongated three-helix bundle domains spectrin R16 and R17 fold some two to three orders of magnitude more slowly than their homologue R15. We have shown that this slow folding is due, at least in part, to roughness in the free-energy landscape of R16 and R17. We have proposed that this roughness is due to a frustrated search for the correct docking of partly preformed helices. However, this accounts for only a small part of the slowing of folding and unfolding. Five residues on the A helix of R15, when inserted together into R16 or R17, increase the folding rate constants, reduce landscape roughness, and alter the folding mechanism to one resembling R15. The effect of each of these mutations individually is investigated here. No one mutation causes the behavior seen for the five in combination. However, two mutations, E18F and K25V, significantly increase the folding and unfolding rates of both R16 and R17 but without a concomitant loss in landscape roughness. E18F has the greatest effect on the kinetics, and a Φ-value analysis of the C helix reveals that the folding mechanism is unchanged. For both E18F and K25V the removal of the charge and resultant transition state stabilization is the main origin of the faster folding. Consequently, the major cause of the unusually slow folding of R16 and R17 is the non-native burial of the two charged residues in the transition state. The slowing due to landscape roughness is only about fivefold.free energy landscape | frustration | phi value | protein folding T he 15th, 16th, and 17th domains of chicken brain α-spectrin (R15, R16, and R17) have very similar structures, stabilities, and β-Tanford (β T ) values (which reflect the compactness of the transition state for folding and unfolding) (1-6). However, the folding of R15 differs from that of R16 and R17 in a number of respects. R15 folds and unfolds two orders of magnitude faster than R16 and three orders of magnitude faster than R17. R16 and R17 have two sequential transition states, and for both domains the first of these (TS1) shows significant landscape roughness (or "internal friction") (7). This has not been seen for any other domain of comparable size and folding kinetics, although theory has long predicted the possibility of such landscape roughness (8-15). R15 has a broad transition state (characterized by "rollover" in the unfolding limb for some mutants and for wild type under some conditions), but due to the speed of folding and unfolding it is not known whether it has two sequential transition states (16). However, the early transition state of R15 (which corresponds to TS1 of R16 and R17 and will be referred to as such) has a smoother, less frustrated landscape (7).Φ-value analysis shows that for all three domains the A and C helices are partially structured at TS1, whereas the B helix is relatively unstructured (16-18). R16 and R17 fold via a framework-like mechanism, with some tertiary contacts formed but more extensive secondary structure that extends throughout the A and C helices. In contrast, R1...

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

Wensley

Kwa

Shammas

et al. 2012

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

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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.…”

mentioning

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.…”

mentioning

confidence: 99%

“…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)(12)(13)(14)(15)(16)(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).…”

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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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How cooperative are protein folding and unfolding transitions?

2016

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A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.

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Diffusional Barrier in the Unfolding of a Small Protein

Cited by 40 publications

References 57 publications

Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

Measuring internal friction of an ultrafast-folding protein

How cooperative are protein folding and unfolding transitions?

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