Comment on Probe-dependent and nonexponential relaxation kinetics: unreliable signatures of downhill protein folding

How cooperative are protein folding and unfolding transitions?

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.

Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage

The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.

Fast protein folding kinetics

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Isomerization- and temperature-jump-induced dynamics of a photoswitchable β-hairpin

Conformational changes in proteins and peptides can be initiated by diverse processes. This raises the question how the variation of initiation mechanisms is connected to differences in folding or unfolding processes. In this work structural dynamics of a photoswitchable β-hairpin model peptide were initiated by two different mechanisms: temperature jump (T-jump) and isomerization of a backbone element. In both experiments the structural changes were followed by time-resolved IR spectroscopy in the nanosecond to microsecond range. When the photoisomerization of the azobenzene backbone switch initiated the folding reaction, pronounced absorption changes related to folding into the hairpin structure were found with a time constant of about 16 μs. In the T-jump experiment kinetics with the same time constant were observed. For both initiation processes the reaction dynamics revealed the same strong dependence of the reaction time on temperature. The highly similar transients in the microsecond range show that the peptide dynamics induced by T-jump and isomerization are both determined by the same mechanism and exclude a downhill-folding process. Furthermore, the combination of the two techniques allows a detailed model for folding and unfolding to be presented: The isomerization-induced folding process ends in a transition-state reaction scheme, in which a high energetic barrier of 48 kJ mol(-1) separates unfolded and folded structures.

Navigating the downhill protein folding regime via structural homologues

Proteins that fold over free-energy barriers <or= 3RT are classified as downhill folders. This regime is characterized by equilibrium unfolding that is proportionally broader and more complex the lower the folding barrier. Downhill proteins are also expected to fold up in a few microseconds. However, the relationship between rate and equilibrium signatures is affected by other factors such as protein size and folding topology. Here we perform a direct comparison of the kinetics and equilibrium unfolding of two structural homologues: BBL and PDD. BBL folds-unfolds in just approximately 1 micros at 335 K and displays the equilibrium signatures expected for a protein at the bottom of the downhill folding regime. PDD, which has the same 3D structure and size, folds-unfolds approximately 8 times more slowly and, concomitantly, exhibits all the downhill equilibrium signatures to a lesser degree. Our results demonstrate that the equilibrium signatures of downhill folding are proportional to the changes in folding rate once structural and size-scaling effects are factored out. This conclusion has two important implications: (1) it confirms that the quantitative analysis of equilibrium experiments in ultrafast folding proteins does provide direct information about free-energy barriers, a result that is incompatible with the conventional view of protein folding as a highly activated process, and (2) it advocates for equilibrium-kinetic studies of homologous proteins as a powerful tool to navigate the downhill folding regime via comparative analysis. The latter should prove extremely useful for the investigation of sequence, functional, and evolutionary determinants of protein folding barriers.

Analyzing protein folding cooperativity by differential scanning calorimetry and NMR spectroscopy

Some marginally stable proteins undergo microsecond time scale folding reactions that involve significant populations of partly ordered forms, making it difficult to discern individual steps in their folding pathways. It has been suggested that many of these proteins fold non-cooperatively, with no significant barriers to separate the energy landscape into distinct thermodynamic states. Here we present an approach for studying the cooperativity of rapid protein folding with a combination of differential scanning calorimetry (DSC), nuclear magnetic resonance (NMR) relaxation dispersion experiments, and an analysis of the temperature dependence of amide (1)H and (15)N chemical shifts. We applied this method to the PBX homeodomain (PBX-HD), which folds on the microsecond time scale and produces a broad DSC thermogram with an elevated and steeply sloping native-state heat capacity baseline, making it a candidate for barrierless folding. However, by globally fitting the NMR thermal melt and DSC data, and by comparing these results to those obtained from the NMR relaxation dispersion experiments, we show that the native form of the protein undergoes two-state exchange with a small population of the thermally denatured form, well below the melting temperature. This result directly demonstrates the coexistence of distinct folded and unfolded forms and firmly establishes that folding of PBX-HD is cooperative. Further, we see evidence of large-scale structural and dynamical changes within the native state by NMR, which helps to explain the broad and shallow DSC profile. This study illustrates the potential of combining calorimetry with NMR dynamics experiments to dissect mechanisms of protein folding.

A survey of lambda repressor fragments from two-state to downhill folding

We survey the two-state to downhill folding transition by examining 20 lambda(6-85)* mutants that cover a wide range of stabilities and folding rates. We investigated four new lambda(6-85)* mutants designed to fold especially rapidly. Two were engineered using the core remodeling of Lim and Sauer, and two were engineered using Ferreiro et al.'s frustratometer. These proteins have probe-dependent melting temperatures as high as 80 degrees C and exhibit a fast molecular phase with the characteristic temperature dependence of the amplitude expected for downhill folding. The survey reveals a correlation between melting temperature and downhill folding previously observed for the beta-sheet protein WW domain. A simple model explains this correlation and predicts the melting temperature at which downhill folding becomes possible. An X-ray crystal structure with a 1.64-A resolution of a fast-folding mutant fragment shows regions of enhanced rigidity compared to the full wild-type protein.

Direct observation of downhill folding of lambda-repressor in a microfluidic mixer

The protein lambda(6-85) has been implicated in barrierless folding by observations of kinetic relaxation after nanosecond T-jump. In this work we observed folding of this protein after dilution of a high denaturant in an ultrarapid microfluidic mixer at temperatures far below the thermal midpoint. The observations of total intensity and spectral shift of tryptophan fluorescence yielded distinctly different kinetics and activation energies. These results may be explained as diffusion on a low-barrier, one-dimensional, free-energy surface, with different probes having different sensitivities along the reaction coordinate. Additionally, we observed an extremely fast phase within the mixing time that was not observed by T-jump, suggesting that the ensemble of unfolded states populated at high denaturant is distinct from those accessible at high temperature.

Slowing down downhill folding: a three-probe study

The mutant Tyr22Trp/Glu33Tyr/Gly46Ala/Gly48Ala of lambda repressor fragment lambda(6-85) was previously assigned as an incipient downhill folder. We slow down its folding in a cryogenic water-ethylene-glycol solvent (-18 to -28 degrees C). The refolding kinetics are probed by small-angle x-ray scattering, circular dichroism, and fluorescence to measure the radius of gyration, the average secondary structure content, and the native packing around the single tryptophan residue. The main resolved kinetic phase of the mutant is probe independent and faster than the main phase observed for the pseudo-wild-type. Excess helical structure formed early on by the mutant may reduce the formation of turns and prevent the formation of compact misfolded states, speeding up the overall folding process. Extrapolation of our main cryogenic folding phase and previous T-jump measurements to 37 degrees C yields nearly the same refolding rate as extrapolated by Oas and co-workers from NMR line-shape data. Taken together, all the data consistently indicate a folding speed limit of approximately 4.5 micros for this fast folder.

A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D

We present fluorescence-detected measurements of the temperature-jump relaxation kinetics of the designed three-helix bundle protein alpha(3)D taken under solvent conditions identical to previous infrared-detected kinetics. The fluorescence-detected rate is similar to the IR-detected rate only at the lowest temperature where we could measure it (326 K). The fluorescence-detected rate decreases by a factor of 3 over the 326-344 K temperature range, whereas the IR-detected rate remains nearly constant over the same range. To investigate this probe dependence, we tested an extensive set of physically reasonable one-dimensional (1D) free energy surfaces by Langevin dynamics simulation. The simulations included coordinate- and temperature-dependent roughness, diffusion coefficients, and IR/fluorescence spectroscopic signatures. None of these can reproduce the IR and fluorescence data simultaneously, forcing us to the conclusion that a 1D free energy surface cannot accurately describe the folding of alpha(3)D. This supports the hypothesis that alpha(3)D has a multidimensional free energy surface conducive to downhill folding at 326 K, and that it is already an incipient downhill folder with probe-dependent kinetics near its melting point.

Probing the nanosecond dynamics of a designed three-stranded beta-sheet with a massively parallel molecular dynamics simulation

Recently a temperature-jump FTIR study of a designed three-stranded sheet showing a fast relaxation time of approximately 140 +/- 20 ns was published. We performed massively parallel molecular dynamics simulations in explicit solvent to probe the structural events involved in this relaxation. While our simulations produce similar relaxation rates, the structural ensemble is broad. We observe the formation of turn structure, but only very weak interaction in the strand regions, which is consistent with the lack of strong backbone-backbone NOEs in previous structural NMR studies. These results suggest that either (D)P(D)P-II folds at time scales longer than 240 ns, or that (D)P(D)P-II is not a well-defined three-stranded beta-sheet. This work also provides an opportunity to compare the performance of several popular forcefield models against one another.

Barrierless evolution of structure during the submillisecond refolding reaction of a small protein

To determine whether a protein folding reaction can occur in the absence of a dominant barrier is crucial for understanding its complexity. Here direct ultrafast kinetic measurements have been used to study the initial submillisecond (sub-ms) folding reaction of the small protein barstar. The cooperativity of the initial folding reaction has been explored by using two probes: fluorescence resonance energy transfer, through which the contraction of two intramolecular distances is measured, and the binding of 8-anilino-1-naphthalene sulfonic acid, through which the formation of hydrophobic clusters is monitored. A fast chain contraction is shown to precede the formation of hydrophobic clusters, indicating that the sub-ms folding reaction is not cooperative. The observed rate constant of the sub-ms folding reaction monitored by 8-anilino-1-naphthalene sulfonic acid fluorescence has been found to be the same in stabilizing conditions (low urea concentrations), in which specific structure is formed, and in marginally stabilizing conditions (higher urea concentrations), where virtually no structure is formed in the product of the sub-ms folding reaction. The observation that the folding rate is independent of the folding conditions suggests that the initial folding reaction occurs in the absence of a dominant free energy barrier. These results provide kinetic evidence that the formation of specific structure need not be slowed down by any significant free energy barrier during the course of a very fast protein folding reaction.

An experimental survey of the transition between two-state and downhill protein folding scenarios

A kinetic and thermodynamic survey of 35 WW domain sequences is used in combination with a model to discern the energetic requirements for the transition from two-state folding to downhill folding. The sequences used exhibit a 600-fold range of folding rates at the temperature of maximum folding rate. Very stable proteins can achieve complete downhill folding when the temperature is lowered sufficiently below the melting temperature, and then at even lower temperatures they become two-state folders again because of cold denaturation. Less stable proteins never achieve a sufficient bias to fold downhill because of the onset of cold denaturation. The model, considering both heat and cold denaturation, reveals that to achieve incipient downhill folding (barrier <3 RT) or downhill folding (no barrier), the WW domain average melting temperatures have to be >/=50 degrees C for incipient downhill folding and >/=90 degrees C for downhill folding.