Folding lambda-repressor at its speed limit

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.

Probing the folding transition state of ubiquitin mutants by temperature-jump-induced downhill unfolding

Crucial to revealing mechanistic details of protein folding is a characterization of the transition state ensemble and its structural dynamics. To probe the transition state of ubiquitin thermal unfolding, we examine unfolding dynamics and kinetics of wild-type and mutant ubiquitin using time-resolved nonlinear infrared spectroscopy after a nanosecond temperature jump. We observe spectral changes on two different time scales. A fast nonexponential microsecond phase is attributed to downhill unfolding from the transition state region, which is induced by a shift of the barrier due to the rapid temperature change. Slow millisecond changes arise from thermally activated folding and unfolding kinetics. Mutants that stabilize or destabilize beta strands III-V lead to a decreased or increased amplitude of the microsecond phase, indicating that the disruption or weakening of these strands occurs in the transition state. Unfolding features from microseconds to milliseconds can be explained by temperature-dependent changes of a two-dimensional free energy surface constructed by the native contacts between beta strands of the protein. In addition, the results support the possibility of an intermediate state in thermal unfolding.

Dynamics of one-state downhill protein folding

The small helical protein BBL has been shown to fold and unfold in the absence of a free energy barrier according to a battery of quantitative criteria in equilibrium experiments, including probe-dependent equilibrium unfolding, complex coupling between denaturing agents, characteristic DSC thermogram, gradual melting of secondary structure, and heterogeneous atom-by-atom unfolding behaviors spanning the entire unfolding process. Here, we present the results of nanosecond T-jump experiments probing backbone structure by IR and end-to-end distance by FRET. The folding dynamics observed with these two probes are both exponential with common relaxation times but have large differences in amplitude following their probe-dependent equilibrium unfolding. The quantitative analysis of amplitude and relaxation time data for both probes shows that BBL folding dynamics are fully consistent with the one-state folding scenario and incompatible with alternative models involving one or several barrier crossing events. At 333 K, the relaxation time for BBL is 1.3 micros, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 micros), indicating a relatively rough underlying energy landscape. Our results in BBL expose the dynamic features of one-state folding and chart the intrinsic time-scales for conformational motions along the folding process. Interestingly, the simple self-averaging folding dynamics of BBL are the exact dynamic properties required in molecular rheostats, thus supporting a biological role for one-state folding.

Exploiting the downhill folding regime via experiment

Traditionally, folding experiments have been directed at determining equilibrium and relaxation rate constants of proteins that fold with two-state-like kinetics. More recently, the combination of free energy surface approaches inspired by theory with the discovery of proteins that fold in the downhill regime has greatly widened the battlefield for experimentalists. Downhill folding proteins cross very small or no free energy barrier at all so that all relevant partially folded conformations become experimentally accessible. From these combined efforts we now have tools to estimate the height of thermodynamic and kinetic folding barriers. Procedures to measure with atomic resolution the structural heterogeneity of conformational ensembles at varying unfolding degrees are also available. Moreover, determining the dynamic modes driving folding and how they change as folding proceeds is finally at our fingertips. These developments allow us to address via experiment fundamental questions such as the origin of folding cooperativity, the relationship between structure and stability, or how to engineer folding barriers. Moreover, the level of detail attained in this new breed of experiments should provide powerful benchmarks for computer simulations of folding and force-field refinement.

Temperature-dependent downhill unfolding of ubiquitin. I. Nanosecond-to-millisecond resolved nonlinear infrared spectroscopy

Transient thermal unfolding of ubiquitin is investigated using nonlinear infrared spectroscopy after a nanosecond laser temperature jump (T-jump). The abrupt change in the unfolding free energy surface and the ns time resolution allow us to observe a fast response on ns to micros time-scales, which we attribute to downhill unfolding, before a cross-over to ms kinetics. The downhill unfolding by a sub-population of folded proteins is induced through a shift of the barrier toward the native state. By adjusting the T-jump width, the effect of the initial (T(i)) and final (T(f)) temperature on the unfolding dynamics can be separated. From the amplitude of the fast downhill unfolding, the fractional population prepared at the unfolding transition state is obtained. This population increases with both T(i) and with T(f). A two-state kinetic analysis of the ms refolding provides thermodynamic information about the barrier height. By a combination of the fast and slow unfolding and folding parameters, a quasi-two-state kinetic analysis is performed to calculate the time-dependent population changes of the folded state. This calculation coincides with the experimentally obtained population changes at low temperature but deviations are found in the T-jump from 67 to 78 degrees C. Using temperature-dependent barrier height changes, a temperature Phi value analysis is performed. The result shows a decreasing trend of Phi(T) with temperature, which indicates an increase of the heterogeneity of the transition state. We conclude that ubiquitin unfolds along a well-defined pathway at low temperature which expands with increasing temperature to include multiple routes.

Determining denaturation midpoints in multiprobe equilibrium protein folding experiments

Multiprobe equilibrium unfolding experiments in the downhill regime (i.e., maximal barrier < 3 RT) can resolve the folding process with atomic resolution [ Munoz ( 2002) Int. J. Quantum Chem. 90, 1522 -1528] . Such information is extracted from hundreds of heterogeneous atomic equilibrium unfolding curves, which are characterized according to their denaturation midpoint (e.g., T m for thermal denaturation). Using statistical methods, we analyze T m accuracy when determined from the extremum of the derivative of the unfolding curve and from two-state fits under different sets of simulated experimental conditions. We develop simple procedures to discriminate between real unfolding heterogeneity at the atomic level and experimental uncertainty in the single T m of conventional two-state folding. We apply these procedures to the recently published multiprobe NMR experiments of BBL [ Sadqi et al. ( 2006) Nature 442, 317 -321 ] and conclude that for the 122 single transition atomic unfolding curves reported for this protein the mean T m accuracy is better than 1.8 K for both methods, compared to the 60 K spread in T m determined experimentally. Importantly, we also find that when the pre- or posttransition baseline is incomplete, the two-state fits systematically drift the estimated T m value toward the center of the experimental range. Therefore, the reported 60 K T m spread in BBL is in fact a lower limit. The derivative method is significantly less sensitive to this problem and thus is a better choice for multiprobe experiments with a broad T m distribution. The results we obtain in this work lay the foundations for the quantitative analysis of future multiprobe unfolding experiments in fast-folding proteins.

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.

Origins of barriers and barrierless folding in BBL

In contrast to classical chemical phenomenology, theory suggests that proteins may undergo downhill folding without an activation barrier under certain thermodynamic conditions. Recently, the BBL protein was proposed to fold by such a downhill scenario, but discrepancies between experimental results found in different groups argue against this. After briefly reviewing the major experimental studies of the BBL folding mechanism, we show that simulations of both coarse-grained and atomistic models can reconcile the seemingly conflicting observations.

Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece

We have performed molecular dynamics simulations on a set of nine unfolded conformations of the fastest-folding protein yet discovered, a variant of the villin headpiece subdomain (HP-35 NleNle). The simulations were generated using a new distributed computing method, yielding hundreds of trajectories each on a time scale comparable to the experimental folding time, despite the large (10,000 atom) size of the simulation system. This strategy eliminates the need to assume a two-state kinetic model or to build a Markov state model. The relaxation to the folded state at 300 K from the unfolded configurations (generated by simulation at 373 K) was monitored by a method intended to reflect the experimental observable (quenching of tryptophan by histidine). We also monitored the relaxation to the native state by directly comparing structural snapshots with the native state. The rate of relaxation to the native state and the number of resolvable kinetic time scales both depend upon starting structure. Moreover, starting structures with folding rates most similar to experiment show some native-like structure in the N-terminal helix (helix 1) and the phenylalanine residues constituting the hydrophobic core, suggesting that these elements may exist in the experimentally relevant unfolded state. Our large-scale simulation data reveal kinetic complexity not resolved in the experimental data. Based on these findings, we propose additional experiments to further probe the kinetics of villin folding.

Single molecule analysis of bacterial polymerase chain reaction products in submicrometer fluidic channels

Laser induced fluorescence in submicrometer fluidic channels was used to characterize the synthesis of polymerase chain reaction (PCR) products from a model bacterial system in order to explore the advantages and limitations of on chip real time single molecule PCR analysis. Single oligonucleotide universal bacterial primers and PCR amplicons from the 16S rDNA of Thermobifida fusca (325 bp) were directly detected at all phases of the reaction with low sample consumption and without post-amplification purification or size screening. Primers were fluorescently labeled with single Alexa Fluor 488 or Alexa Fluor 594 fluorophores, resulting in double labeled, two color amplicons. PCR products were driven electrokinetically through a fused silica channel with a 250 nm by 500 nm rectangular cross section. Lasers with 488 nm and 568 nm wavelengths were focused and overlapped on the channel for fluorescence excitation. All molecules entering the channel were rapidly and uniformly analyzed. Photon burst analysis was used to detect and identify individual primers and amplicons, and fluorescence correlation and cross-correlation spectroscopy were used to account for analyte flow speed. Conventional gel and capillary electrophoresis were also used to characterize the PCR amplification, and the results of differences in detection sensitivity and analyte discrimination were examined. Limits were imposed by the purity and labeling efficiency of the PCR reagents, which must be improved in parallel with increases in detection sensitivity.

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.

Engineering a beta-sheet protein toward the folding speed limit

Recent experimental studies have shown that alpha-helical proteins can approach the folding "speed limit", where folding switches from an activated to a downhill process in free energy. beta-sheet proteins are generally thought to fold more slowly than helix bundles. However, based on studies of hairpins, folding should still be able to approach the microsecond time scale. Here we demonstrate how the hPin1 WW domain, a triple-stranded beta-sheet protein with a sharp thermodynamic melting transition, can be engineered toward the folding "speed limit" without a significant loss in thermal denaturation cooperativity.

Free energy landscape of a biomolecule in dihedral principal component space: sampling convergence and correspondence between structures and minima

Dihedral principal component analysis (dPCA) has recently been developed and shown to display complex features of the free energy landscape of a biomolecule that may be absent in the free energy landscape plotted in principal component space due to mixing of internal and overall rotational motion that can occur in principal component analysis (PCA) [Mu et al., Proteins: Struct Funct Bioinfo 2005;58:45-52]. Another difficulty in the implementation of PCA is sampling convergence, which we address here for both dPCA and PCA using a tetrapeptide as an example. We find that for both methods the sampling convergence can be reached over a similar time. Minima in the free energy landscape in the space of the two largest dihedral principal components often correspond to unique structures, though we also find some distinct minima to correspond to the same structure.

Conformational Dynamics and Ensembles in Protein Folding

Recent experimental developments are changing the ways we interpret experimental data in protein folding, leading to a closer connection with theory and an improved understanding of some long-standing questions in the field. We now have a basic roadmap of the types of polypeptide motions and timescales that are relevant to the various folding stages. The folding barriers estimated with a variety of independent methods are consistently small, indicating that several fast-folding proteins are near or within the downhill folding regime. Finally, the structural and statistical analysis of global downhill folding is promising to open a new avenue of research in which folding mechanisms and the networks of noncovalent interactions that stabilize native structures are directly resolved in equilibrium experiments of nonmutated proteins.

Soybean disease resistance protein RHG1-LRR domain expressed, purified and refolded from Escherichia coli inclusion bodies: preparation for a functional analysis

Introduction and expression of foreign genes in bacteria often results accumulation of the foreign protein(s) in inclusion bodies (IBs). The subsequent processes of refolding are slow, difficult and often fail to yield significant amounts of folded protein. RHG1 encoded by rhg1 was a soybean (Glycine max L. Merr.) transmembrane receptor-like kinase (EC 2.7.11.1) with an extracellular leucine-rich repeat domain. The LRR of RHG1 was believed to be involved in elicitor recognition and interaction with other plant proteins. The aim, here, was to express the LRR domain in Escherichia coli (RHG1-LRR) and produce refolded protein. Urea titration experiments showed that the IBs formed in E. coli by the extracellular domain of the RHG1 protein could be solubilized at different urea concentrations. The RHG1 proteins were eluted with 1.0-7.0M urea in 0.5M increments. Purified RHG1 protein obtained from the 1.5 and 7.0M elutions was analyzed for secondary structure through circular dichroism (CD) spectroscopy. Considerable secondary structure could be seen in the former, whereas the latter yielded CD curves characteristic of denatured proteins. Both elutions were subjected to refolding by slowly removing urea in the presence of arginine and reduced/oxidized glutathione. Detectable amounts of refolded protein could not be recovered from the 7.0M urea sample, whereas refolding from the 1.5M urea sample yielded 0.2mg/ml protein. The 7.0M treatment resulted in the formation of a homogenous denatured state with no apparent secondary structure. Refolding from this fully denatured state may confer kinetic and/or thermodynamic constraints on the refolding process, whereas the kinetic and/or thermodynamic barriers to attain the folded conformation appeared to be lesser, when refolding from a partially folded state.

Probing the folding intermediate of Rd-apocyt b562 by protein engineering and infrared T-jump

Small proteins often fold in an apparent two-state manner with the absence of detectable early-folding intermediates. Recently, using native-state hydrogen exchange, intermediates that exist after the rate-limiting transition state have been identified for several proteins. However, little is known about the folding kinetics from these post-transition intermediates to their corresponding native states. Herein, we have used protein engineering and a laser-induced temperature-jump (T-jump) technique to investigate this issue and have applied it to Rd-apocyt b(562) , a four-helix bundle protein. Previously, it has been shown that Rd-apocyt b(562) folds via an on-pathway hidden intermediate, which has only the N-terminal helix unfolded. In the present study, a double mutation (V16G/I17A) in the N-terminal helix of Rd-apocyt b(562) was made to further increase the relative population of this intermediate state at high temperature by selectively destabilizing the native state. In the circular dichroism thermal melting experiment, this mutant showed apparent two-state folding behavior. However, in the T-jump experiment, two kinetic phases were observed. Therefore, these results are in agreement with the idea that a folding intermediate is populated on the folding pathway of Rd-apocyt b(562) . Moreover, it was found that the exponential growth rate of the native state from this intermediate state is roughly (25 microsec)(-1) at 65 degrees C.

Tuning lambda6-85 towards downhill folding at its melting temperature

The five-helix bundle lambda6-85* is a fast two-state folder. Several stabilized mutants have been reported to fold kinetically near-downhill or downhill. These mutants undergo a transition to two-state folding kinetics when heated. It has been suggested that this transition is caused by increased hydrophobicity at higher temperature. Here we investigate two histidine-containing mutants of lambda6-85* to see if a weaker hydrophobic core can extend the temperature range of downhill folding. The very stable lambdaHA is the fastest-folding lambda repressor to date (k(f)(-1) approximately k(obs)(-1)=2.3 micros at 44 degrees C). It folds downhill at low temperature, but transits back to two-state folding at its unfolding midpoint. lambdaHG has a weakened hydrophobic core. It is less stable than some slower folding mutants of lambda6-85*, and it has more exposed hydrophobic surface area in the folded state. This mutant nonetheless folds very rapidly, and has the non-exponential folding kinetics of an incipient downhill folder even at the unfolding midpoint (k(m)(-1) approximately 2 micros, k(a)(-1)=15 micros at 56 degrees C). We also compare the thermodynamic melting transition of lambdaHG with the nominal two-state folding mutant lambdaQG, which has a similar melting temperature. Unlike lambdaQG, lambdaHG yields fluorescence wavelength-dependent cooperativities and probe-dependent melting temperatures. This result combined with previous work shows that the energy landscapes of lambda repressor mutants support all standard folding mechanisms.

Ultrafast dynamics of protein collapse from single-molecule photon statistics

We use the statistics of photon emission from single molecules to probe the ultrafast dynamics of an unfolded protein via Förster resonance energy transfer. Global reconfiguration of the chain occurs on a time scale of approximately equal to 50 ns and slows down concomitant with chain collapse under folding conditions. These diffusive dynamics provide a missing link between the phenomenological chemical kinetics commonly used in protein folding and a physical description in terms of quantitative free energy surfaces. The experiments demonstrate the potential of single-molecule methods in accessing the biologically important nanosecond time scales even in heterogeneous populations.

Solvent-tuning the collapse and helix formation time scales of lambda(6-85)*

The lambda(6-85)(*) pseudo-wild type of lambda repressor fragment is a fast two-state folder (k(f) approximately 35 microsec(-1) at 58 degrees C). Previously, highly stable lambda(6-85)(*) mutants with k(f) > 30 microsec(-1) have been engineered to fold nearly or fully downhill. Stabilization of the native state by solvent tuning might also tune lambda(6-85)(*) away from two-state folding. We test this prediction by examining the folding thermodynamics and kinetics of lambda(6-85)(*) in a stabilizing solvent, 45% by weight aqueous ethylene glycol at -28 degrees C. Detection of kinetics by circular dichroism at 222 nm (sensitive to helix content) and small angle X-ray scattering (measuring the radius of gyration) shows that refolding from guanidine hydrochloride denatured conditions exhibits very different time scales for collapse and secondary structure formation: the two processes become decoupled. Collapse remains a low-barrier activated process, while the fastest of several secondary structure formation time scales approaches the downhill folding limit. Two-state folding of lambda(6-85)(*) is not a robust process.

Ultrafast and downhill protein folding

Ultrafast folding proteins have served an important role in benchmarking molecular dynamics simulations and testing protein folding theories. These proteins are simple enough and fold fast enough that realistic simulations are possible, which facilitates the direct comparison of absolute folding rates and folding mechanisms with those observed experimentally. Such comparisons have achieved remarkable success, but have also revealed the shortcomings that remain in experiment, theory and simulation alike. Some ultrafast folding proteins may fold without encountering an activation barrier (downhill folding), allowing the exploration of the molecular timescale of folding and the roughness of the energy landscape. The biological significance of ultrafast folding remains uncertain, but its practical significance is crucial to progress in understanding how proteins fold.

Computational design of proteins stereochemically optimized in size, stability, and folding speed

Artificial proteins potentially barrier-free in the folding kinetics are approached computationally under the guidance of protein-folding theories. The smallest and fastest folding globular protein triple-helix-bundle (THB) is so modified as to minimize or eliminate its presumed barriers in folding speed. As the barriers may reside in the ordering of either secondary or tertiary structure, the elements of both secondary and tertiary structure in the protein are targeted for prenucleation with suitable stereochemically constrained amino acid residues. The required elements of topology and sequence for the THB are optimized independently; first the topology is optimized with simulated annealing in polypeptides of highly simplified alphabet; next, the sequence in side chains is optimized using the standard inverse design methods. The resultant three best-adapted THBs, variable in topology and distinctive in sequences, are assessed by comparing them with a few benchmark proteins. The results of mainly molecular dynamics (MD) comparisons, undertaken in explicit water at different temperatures, show that the designed sequences are favorably placed against the chosen benchmarks as THB proteins potentially thermostable in the native folds. Folding simulation experiments with MD establish that the designed sequences are rapid in the folding of individual helices, but not in the evolution of tertiary structure; energetic cum topological frustrations remain but could be the artifacts of the starting conformations that were chosen in the THBs in the folding simulations. Overall, a practical high-throughput approach for de novo protein design has been developed that may have fruitful application for any type of tertiary structure.

Dynamics, energetics, and structure in protein folding

For many decades, protein folding experimentalists have worked with no information about the time scales of relevant protein folding motions and without methods for estimating the height of folding barriers. Protein folding experiments have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiments was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (approximately 14RT for the very slow folder AcP) to nonexistent. While slow-folding (i.e., > or = 1 ms) single-domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with a marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic factors from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single-molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.

Criteria for downhill protein folding: Calorimetry, chevron plot, kinetic relaxation, and single-molecule radius of gyration in chain models with subdued degrees of cooperativity

Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.

Natural selection for kinetic stability is a likely origin of correlations between mutational effects on protein energetics and frequencies of amino acid occurrences in sequence alignments

It appears plausible that natural selection constrains, to some extent at least, the stability in many natural proteins. If, during protein evolution, stability fluctuates within a comparatively narrow range, then mutations are expected to be fixed with frequencies that reflect mutational effects on stability. Indeed, we recently reported a robust correlation between the effect of 27 conservative mutations on the thermodynamic stability (unfolding free energy) of Escherichia coli thioredoxin and the frequencies of residues occurrences in sequence alignments. We show here that this correlation likely implies a lower limit to thermodynamic stability of only a few kJ/mol below the unfolding free energy of the wild-type (WT) protein. We suggest, therefore, that the correlation does not reflect natural selection of thermodynamic stability by itself, but of some other factor which is linked to thermodynamic stability for the mutations under study. We propose that this other factor is the kinetic stability of thioredoxin in vivo, since( i) kinetic stability relates to irreversible denaturation, (ii) the rate of irreversible denaturation in a crowded cellular environment (or in a harsh extracellular environment) is probably determined by the rate of unfolding, and (iii) the half-life for unfolding changes in an exponential manner with activation free energy and, consequently, comparatively small free energy effects can have deleterious consequences for kinetic stability. This proposal is supported by the results of a kinetic study of the WT form and the 27 single-mutant variants of E. coli thioredoxin based on the global analyses of chevron plots and equilibrium unfolding profiles determined from double-jump unfolding assays. This kinetic study suggests, furthermore, one of the factors that may contribute to the high activation free energy for unfolding in thioredoxin (required for kinetic stability), namely the energetic optimization of native-state residue environments in regions, which become disrupted in the transition state for unfolding.

Low barrier kinetics: dependence on observables and free energy surface

Dynamics on free energy surfaces with high activation barriers are usually treated by few-state kinetics models, yielding characteristic rate coefficients and amplitudes depending on the connectivity of the states. When the barriers are low (< 3 kT), the assumption of instantaneous equilibration of the transition state, and hence, the few-state kinetics treatment, break down. Langevin dynamics is used here to explore the characteristic trends that occur in such cases, as a function of barrier height, number of barriers, dimensionality of the free energy surface, and switching functions that describe how spectroscopic probes vary from reactant to product. The result is a systematic phenomenological description of low barrier kinetics and dynamics.

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.

T-jump infrared study of the folding mechanism of coiled-coil GCN4-p1

Partially folded intermediates have been frequently observed in equilibrium and kinetic protein folding studies. However, folding intermediates that exist at the native side of the rate-limiting step are rather difficult to study because they often evade detection by conventional folding kinetic methods. Here, we demonstrated that a laser-induced temperature-jump method can potentially be used to identify the existence of such post-transition or hidden intermediates. Specifically, we studied two cross-linked variants of GCN4-p1 coiled-coil. The GCN4 leucine zipper has been studied extensively and most of these studies have regarded it as a two-state folder. Our static circular dichroism and infrared data also indicate that the thermal unfolding of these two monomeric coiled-coils can be adequately described by an apparent two-state model. However, their temperature-jump-induced relaxation kinetics exhibit non-monoexponential behavior, dependent upon sequence and temperature. Taken together, our results support a folding mechanism wherein at least one folding intermediate populates behind the main rate-limiting step.

Downhill protein folding: evolution meets physics

Proteins can be redesigned to fold downhill on a free energy surface characterized by only a few coordinates, confirming a principal prediction of the 'energy-landscape' model. Nonetheless, natural proteins have small but significant barriers. Spectroscopy and kinetics reveal potential biological causes for activation barriers during protein folding: evolution against protein aggregation and for protein function.

Kinetic equivalence of the heat and cold structural transitions of lambda6-85

Heat- and cold-denatured proteins are considered separate thermodynamic states because temperature tuning requires the protein to pass through two 'soft' first-order phase transitions. When both pressure and temperature changes are allowed, the heat- and cold-denatured states of proteins can be interconverted without going through the native state. This raises the question of whether these states are distinguished from one another by their folding kinetics. For the Tyr22Trp/Ala37Gly/Ala49Gly mutant of the 80 residue five-helix bundle protein lambda(6-85), we show that viscosity-corrected folding rates do not distinguish the cold- and heat-denatured states. We attribute this to a folding mechanism dominated by hydrophobic collapse. Our 'temperature-symmetric' approach offers an alternative to viscosity tuning with solvent additives in such cases.

Alpha-helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time-resolved IR spectroscopy

Photo-triggered alpha-helix formation of a 16-residue peptide featuring a built-in conformational photoswitch is monitored by time-resolved IR spectroscopy. An experimental approach with 2-ps time resolution and a scanning range up to 30 micros is used to cover all time scales of the peptide dynamics. Experiments are carried out at different temperatures between 281 and 322 K. We observe single-exponential kinetics of the amide I' band at 322 K on a time scale comparable to a recent temperature-jump folding experiment. When lowering the temperature, the kinetics become slower and nonexponential. The transition is strongly activated. Spectrally dispersed IR measurements provide multiple spectroscopic probes simultaneously in one experiment by resolving the amide I' band, isotope-labeled amino acid residues, and side chains. We find differing relaxation dynamics at different spectral positions.

Kinetics are probe-dependent during downhill folding of an engineered lambda6-85 protein

The Y22W/Q33Y/G46,48A mutant of the protein lambda6-85 folds in a few microseconds at room temperature. We find that its folding kinetics are probe-dependent under a strong bias toward the native state, a new signature for downhill folding. The IR- and fluorescence-detected relaxation time scales converge when the native bias is removed by raising the temperature, recovering activated two-state folding. Langevin dynamics simulations on one- and 2D free energy surfaces tunable from two-state to downhill folding reproduce the difference between the IR and fluorescence experiments, as well as the temperature and viscosity trends. In addition, the 2D surface reproduces the stretched exponential dynamics that we fit to the glucose solution experimental data at short times. Nonexponential dynamics at <10 micros is a signature either for local free energy minima along the reaction coordinate ("longitudinal roughness"), or for folding on a higher-dimensional free energy surface ("transverse roughness").

Variations in the fast folding rates of the lambda-repressor: a hybrid molecular dynamics study

The ability to predict the effects of mutations on protein folding rates and mechanisms would greatly facilitate folding studies. Using a realistic full atom potential coupled with a Gō-like potential biased to the native state structure, we have investigated the effects of point mutations on the folding rates of a small single domain protein. The hybrid potential provides a detailed level of description of the folding mechanism that we correlate to features of the folding energy landscapes of fast and slow mutants of an 80-residue-long fragment of the lambda-repressor. Our computational reconstruction of the folding events is compared to the recent experimental results of W. Y. Yang and M. Gruebele (see companion article) and T. G. Oas and co-workers on the lambda-repressor, and helps to clarify the differences observed in the folding mechanisms of the various mutants.

Conformational changes during the nanosecond-to-millisecond unfolding of ubiquitin

Steady-state and transient conformational changes upon the thermal unfolding of ubiquitin were investigated with nonlinear IR spectroscopy of the amide I vibrations. Equilibrium temperature-dependent 2D IR spectroscopy reveals the unfolding of the beta-sheet of ubiquitin through the loss of cross peaks formed between transitions arising from delocalized vibrations of the beta-sheet. Transient unfolding after a nanosecond temperature jump is monitored with dispersed vibrational echo spectroscopy, a projection of the 2D IR spectrum. Whereas the equilibrium study follows a simple two-state unfolding, the transient experiments observe complex relaxation behavior that differs for various spectral components and spans 6 decades in time. The transient behavior can be separated into fast and slow time scales. From 100 ns to 0.5 ms, the spectral features associated with beta-sheet unfolding relax in a sequential, nonexponential manner, with time constants of 3 micros and 80 micros. By modeling the amide I vibrations of ubiquitin, this observation is explained as unfolding of the less stable strands III-V of the beta-sheet before unfolding of the hairpin that forms part of the hydrophobic core. This downhill unfolding is followed by exponential barrier-crossing kinetics on a 3-ms time scale.

Exploring protein-folding ensembles: a variable-barrier model for the analysis of equilibrium unfolding experiments

Recent theoretical and experimental results point to the existence of small barriers to protein folding. These barriers can even be absent altogether, resulting in a continuous folding transition (i.e., downhill folding). With small barriers, the detailed properties of folding ensembles may become accessible to equilibrium experiments. However, further progress is hampered because folding experiments are interpreted with chemical models (e.g., the two-state model), which assume the existence of well defined macrostates separated by arbitrarily high barriers. Here we introduce a phenomenological model based on the classical Landau theory for critical transitions. In this physical model the height of the thermodynamic free energy barrier and the general properties of the folding ensemble are directly obtained from the experimental data. From the analysis of differential scanning calorimetry data alone, our model identifies the presence of a significant (>35 kJ/mol) barrier for the two-state protein thioredoxin and the absence of a barrier for BBL, a previously characterized downhill folding protein. These results illustrate the potential of our approach for extracting the general features of protein ensembles from equilibrium folding experiments.