Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.

Current experimental data show a 9-orders-of-magnitude span in the folding times of proteins. Such a wide range is typically considered a direct consequence of the complexity in structural and sequence patterns of natural proteins. By using a database of 69 proteins and peptides analyzed experimentally, we observe that the folding time scales with the number of residues in the protein. The correlation coefficient is 0.74 or higher, and indicates that it is possible to predict the folding time of a protein with a precision of approximately 1.1 times decades from just its size. A simple thermodynamic analysis of this correlation suggests that the smallest proteins are expected to have very marginal free energy barriers to folding.

Previously, we identified the protein BBL as a downhill folder. This conclusion was based on the statistical mechanical analysis of equilibrium experiments performed in two variants of BBL, one with a fluorescent label at the N-terminus, and another one labeled at both ends. A recent report has claimed that our results are an artifact of label-induced aggregation and that BBL with no fluorescent labels and a longer N-terminal tail folds in a two-state fashion. Here, we show that singly and doubly labeled BBL do not aggregate, unfold reversibly, and have the same thermodynamic properties when studied under appropriate experimental conditions (e.g., our original conditions (1)). With an elementary analysis of the available data on the nonlabeled BBL (2), we also show that this slightly more stable BBL variant is not a two-state folder. We discuss the problems that led to its previous misclassification and how they can be avoided. Finally, we investigate the equilibrium unfolding of the singly labeled BBL with both ends protected by acetylation and amidation. This variant has the same thermodynamic stability of the nonlabeled BBL and displays all the equilibrium signatures of downhill folding. From all these observations, we conclude that fluorescent labels do not perturb the thermodynamic properties of BBL, which consistently folds downhill regardless of its stability and specific protein tails. The work on BBL illustrates the shortcomings of applying conventional procedures intended to distinguish between two-state and three-state folding models to small fast-folding proteins.

Protein folding mechanisms are probed experimentally using single-point mutant perturbations. The relative effects on the folding (ϕ-values) and unfolding (1 − ϕ) rates are used to infer the detailed structure of the transition-state ensemble (TSE). Here we analyze kinetic data on >800 mutations carried out for 24 proteins with simple kinetic behavior. We find two surprising results: (i) all mutant effects are described by the equation: ΔΔG ‡ unfold ¼ 0.76ΔΔG eq AE 1.8 kJ∕mol. Therefore all data are consistent with a single ϕ-value (0.24) with accuracy comparable to experimental precision, suggesting that the structural information in conventional ϕ-values is low. (ii) ϕ-values change with stability, increasing in mean value and spread from native to unfolding conditions, and thus cannot be interpreted without proper normalization. We eliminate stability effects calculating the ϕ-values at the mutant denaturation midpoints; i.e., conditions of zero stability (ϕ 0 ). We then show that the intrinsic variability is ϕ 0 ¼ 0.36 AE 0.11, being somewhat larger for β-sheet-rich proteins than for α-helical proteins. Importantly, we discover that ϕ 0 -values are proportional to how many of the residues surrounding the mutated site are local in sequence. High ϕ 0 -values correspond to protein surface sites, which have few nonlocal neighbors, whereas core residues with many tertiary interactions produce the lowest ϕ 0 -values. These results suggest a general mechanism in which the TSE at zero stability is a broad conformational ensemble stabilized by local interactions and without specific tertiary interactions, reconciling ϕ-values with many other empirical observations. kinetics | mutations | phi-values | perturbation analysis | free energy relationships P rotein engineering has dominated the experimental study of folding mechanisms for nearly two decades(1-3). In this method, single-point mutations are studied kinetically to determine the relative effects in folding and unfolding rates. The basic approach is based on the common observation that the logarithm of the folding relaxation rate changes with chemical denaturant in a V-shaped fashion (i.e., the chevron plot) (4). For a two-state folding protein the low and high denaturant limbs report on the folding and unfolding rate constants, respectively. Linear chevron limbs are taken to imply that there is a thermodynamically well-defined transition-state ensemble (TSE) with intermediate sensitivity to chemical denaturant (4). Accordingly, the perturbation free energy produced by mutation (ΔΔG eq ) partitions between the folding (ϕ) and unfolding limbs (1 − ϕ) depending on how it affects the TSE. High ϕ-values (>0.7) indicate a TSE as perturbed as the native state, and low ϕ-values (<0.3) little effects on the TSE. ϕ-values are viewed as probes of the degree of native structure present in the TSE at the residue level (1) with high values defining the folding nucleus (5).The large number of proteins studied experimentally with this approach has turned ϕ-values into critical...

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 probedependent 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 s, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 s), 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.downhill folding ͉ folding landscape ͉ landscape topography ͉ protein dynamics T heory asserts that protein folding kinetics can be described as diffusion on a low dimensional free energy surface obtained by projecting the hyperdimensional energy landscapes of proteins into one or a few suitable order parameters (1, 2). The overall topography of such free energy surface and the conformational motions guiding folding are not resolvable by classical folding kinetics, but could be probed by time-resolved experiments of downhill folding (3). The difficulty resides in identifying examples of downhill folding relaxations. Stretched exponential decays and kinetic memory effects are not reliable signatures because they require the downhill free energy landscape to be rugged (4), and can also originate from other sources (5). Recently, downhill folding has been pursued by reengineering the fast-folding -repressor to accelerate folding with either mutations (6, 7) or stabilizing cosolvents (8). Approach to the barrierless regime was correlated with the emergence of an additional faster kinetic relaxation interpreted as the downhill decay from a vanishing barrier top (7). From these experiments, a folding speed limit of Ϸ2.5 s at 340 K was proposed for -repressor. This time-scale is close to the recent upper limit estimate of N/100 s (9) for -repressor [N ϭ 80] residues.A powerful alternative would be to measure conformational dynamics ...

Charged residues on the surface of a protein are known hot-spots for post-translational modification, protein/ligand-binding, and tuning conformational stabilities. Recent experimental evidence points to the fact that surface electrostatics can also modulate thermodynamic barriers and hence folding mechanisms. To probe for this behavior across different proteins, we develop a novel version of the Wako-Saitô-Muñoz-Eaton (WSME) model in which we include an electrostatic potential term in the energy function while simplifying the treatment of solvation free energy. Both of the energy terms are obtained by quantitatively fitting the model to differential scanning calorimetry (DSC) experiments that carry critical information on the protein partition function. We characterize four sets of structural/functional homologues (HEWL/BLA, CspB, engrailed, α-spectrin) either by fitting the experimental data of a single domain in the homologous set and predicting the conformational behavior of the rest with the same set of parameters or by performing semiblind predictions. The model with the added electrostatic term is able to successfully reproduce the order of thermodynamic stabilities and relaxation rates of most of the homologues. In parallel, we predict diverse conformational features including a wide range of thermodynamic barriers (∼9-40 kJ/mol), broad native ensembles in helical proteins, structured unfolded states and intermediates, rugged folding landscapes, and further provide an independent protein-specific estimate of the folding speed limit at 298 K (1/(7-300 μs)). Our results are evidence that protein surface electrostatics can be tailored to not only engineer stabilities but also folding mechanisms and the ruggedness of the underlying landscape.

For many decades, protein folding experimentalists have worked with no information about the timescales of relevant protein folding motions and without methods for estimating the height of folding barriers. Experiments in protein folding 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 experiment 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 (~14 RT for the very slow folder AcP) to nonexisting. While slow-folding (i.e. 1 millisecond or longer) 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 marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic 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.In folding to their biologically active 3D structures, proteins must coordinate the vast number of degrees of freedom of their polypeptide chains by forming complex networks of noncovalent interactions. Therefore, understanding protein folding involves determining the relations between the energetics of weak interactions and protein conformation, and the collective chain dynamics that govern the search in conformational space. In modern rate theory, these issues are resolved by mapping the potential energy of the molecule as a function of the relevant coordinates. The dynamics are then represented as diffusion on such an energy surface(1,2). For folding reactions, however, even the solvent-averaged free energy surface is hyper-dimensional due to the large number of relevant coordinates (i.e. thousands of atomic coordinates for a small protein)(3). Folding hypersurfaces should also be topographically complex due to frustration between the myriads of possible interactions (3,4). Moreover, molecular simulations(5-8) and NMR dynamics experiments(9) indicate that protein conformational motions span a wide range of timescales (i.e. from picoseconds to milliseconds). The implication is that measuri...

A large body of work has gone into understanding the effect of mutations on protein structure and function. Conventional treatments have involved quantifying the change in stability, activity and relaxation rates of the mutants with respect to the wild-type protein. However, it is now becoming increasingly apparent that mutational perturbations consistently modulate the packing and dynamics of a significant fraction of protein residues, even those that are located >10–15 Å from the mutated site. Such long-range modulation of protein features can distinctly tune protein stability and the native conformational ensemble contributing to allosteric modulation of function. In this review, I summarize a series of experimental and computational observations that highlight the incredibly pliable nature of proteins and their response to mutational perturbations manifested via the intra-protein interaction network. I highlight how an intimate understanding of mutational effects could pave the way for integrating stability, folding, cooperativity and even allostery within a single physical framework.