New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Probing the transition state ensemble of a protein folding reaction by pressure-dependent NMR relaxation dispersion

The F61A/A90G mutant of a redesigned form of apocytochrome b562 folds by an apparent two-state mechanism. We have used the pressure dependence of 15N NMR relaxation dispersion rate profiles to study the changes in volumetric parameters that accompany the folding reaction of this protein at 45 degrees C. The experiments were performed under conditions where the folding/unfolding equilibrium could be studied at each pressure without addition of denaturants. The exquisite sensitivity of the methodology to small changes in folding/unfolding rates facilitated the use of relatively low-pressure values (between 1 and 270 bar) so that pressure-induced changes to the unfolded state ensemble could be minimized. A volume change for unfolding of -81 mL/mol is measured (at 1 bar), a factor of 1.4 larger (in absolute value) than the volume difference between the transition state ensemble (TSE) and the unfolded state. Notably, the changes in the free energy difference between folded and unfolded states and in the activation free energy for folding were not linear with pressure. Thus, the difference in the isothermal compressibility upon unfolding (-0.11 mL mol(-1) bar(-1)) and, for the first time, the compressibility of the TSE relative to the unfolded state (0.15 mL mol(-1) bar(-1)) could be calculated. The results argue for a TSE that is collapsed but loosely packed relative to the folded state and significantly hydrated, suggesting that the release of water occurs after the rate-limiting step in protein folding. The notion of a collapsed and hydrated TSE is consistent with expectations based on earlier temperature-dependent folding studies, showing that the barrier to folding at 45 degrees C is entropic (Choy, W. Y.; Zhou, Z.; Bai, Y.; Kay, L. E. J. Am. Chem. Soc. 2005, 127, 5066-5072).     

Charge density of divalent metal cations determines RNA stability

RNA molecules are exquisitely sensitive to the properties of counterions. The folding equilibrium of the Tetrahymena ribozyme is measured by nondenaturing gel electrophoresis in the presence of divalent group IIA metal cations. The stability of the folded ribozyme increases with the charge density (zeta) of the cation. Similar scaling is found when the free energy of the RNA folded in small and large metal cations is measured by urea denaturation. Brownian dynamics simulations of a polyelectrolyte show that the experimental observations can be explained by nonspecific ion-RNA interactions in the absence of site-specific metal chelation. The experimental and simulation results establish that RNA stability is largely determined by a combination of counterion charge and the packing efficiency of condensed cations that depends on the excluded volume of the cations.     

Electrostatics of nucleic acid folding under conformational constraint

RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.     

Folding transition-state and denatured-state ensembles of FSD-1 from folding and unfolding simulations

Characterization of the folding transition-state ensemble and the denatured-state ensemble is an important step toward a full elucidation of protein folding mechanisms. We report herein an investigation of the free-energy landscape of FSD-1 protein by a total of four sets of folding and unfolding molecular dynamics simulations with explicit solvent. The transition-state ensemble was initially identified from unfolding simulations at 500 K and was verified by simulations at 300 K starting from the ensemble structures. The denatured-state ensemble and the early-stage folding were studied by a combination of unfolding simulations at 500 K and folding simulations at 300 K starting from the extended conformation. A common feature of the transition-state ensemble was the substantial formation of the native secondary structures, including both the alpha-helix and beta-sheet, with partial exposure of the hydrophobic core in the solvent. Both the native and non-native secondary structures were observed in the denatured-state ensemble and early-stage folding, consistent with the smooth experimental melting curve. Interestingly, the contact orders of the transition-state ensemble structures were similar to that of the native structure and were notably lower than those of the compact structures found in early-stage folding, implying that chain and topological entropy might play significant roles in protein folding. Implications for FSD-1 folding mechanisms and the rate-limiting step are discussed. Analyses further revealed interesting non-native interactions in the denatured-state ensemble and early-stage folding and the possibility that destabilization of these interactions could help to enhance the stability and folding rate of the protein.     

Evidence of an intermediate and parallel pathways in protein unfolding from single-molecule fluorescence

Determining how proteins fold into their native structures is a subject of great importance, since ultimately it will allow protein structure and function to be predicted from primary sequence data. In addition, there is now a clear link between protein unfolding and misfolding events and many disease states. However, since proteins fold over rugged, multidimensional energy landscapes, this is a challenging experimental and theoretical problem. Single-molecule fluorescence methods developed over the past decade have the potential to follow the unfolding/folding of individual molecules. Mapping out the landscape without ensemble averaging will enable the identification of intermediate states which may not be significantly populated, in addition to the presence of multiple pathways. To date, there have been only a limited number of single-molecule folding/unfolding studies under nonequilibrium conditions and no intermediates have been observed. Here, for the first time, we present a single-molecule study of the unfolding of a large autofluorescent protein, Citrine, a variant of green fluorescent protein. Single-molecule fluorescence techniques are used to directly detect an intermediate on the unfolding/folding pathway and the existence of parallel unfolding pathways. This work, and the novel methods used, shows that single-molecule fluorescence can now provide new, hitherto experimentally inaccessible, insights into the folding/unfolding of proteins.     

Transition network based on equilibrium sampling: a new method for extracting kinetic information from Monte Carlo simulations of protein folding

We propose a new type of transition network for modeling of protein dynamics. The nodes of the network correspond to the conformations taken from random sampling of equilibrium ensemble available, e.g., by Monte Carlo simulations. Although this approach does not provide absolute values of folding/unfolding rates, it allows identification of reaction pathways, transition state ensemble, and, eventually, intermediates. The new method is verified by a comparison with direct molecular dynamic simulations performed for a coarse-grained Gō-like model of proteins. As an illustrative example, we analyze kinetics of formation of a small β-hairpin (Trp zipper 1) in the all-atom representation.     

The study of protein folding and dynamics by determination of intramolecular distance distributions and their fluctuations using ensemble and single-molecule FRET measurements.

The folding and dynamics of globular proteins is a multidimensional problem. The structures of the heterogeneous population of refolding protein molecules are characterized by multiple distances and time constants. Deciphering the mechanism of folding depends on studies of the processes rather than the folded structures alone. Spectroscopy is indispensable for these sorts of studies. Herein, it is shown that the determination of intramolecular distance distributions by ensemble and single-molecule FRET experiments enable the exploration of partially folded states of refolding protein molecules.     

Direct observation of the folding and unfolding of a beta-hairpin in explicit water through computer simulation

The cooperative folding and unfolding of a beta-hairpin structure are observed in explicit water at native folding conditions through self-guided molecular dynamics simulation. The folded structure agrees excellently with the NMR NOE data. After going through a fully hydrated state, the peptide folds into a beta-hairpin structure in a highly cooperative process. During the folding process it is observed that side chain interaction occurs first, while intrapeptide hydrogen bonds only form at the final stage. On the contrary, the unfolding process starts with the breaking of interstrand hydrogen bonds. Energetic analysis indicates that the driving force of the folding is the intrapeptide interaction, while the solvent interaction opposes the folding.     

Probing the complete folding trajectory of a DNA hairpin using dual beam fluorescence fluctuation spectroscopy

The conformational fluctuations of dye-quencher labeled DNA hairpin molecules in aqueous solution were investigated using dual probe beam fluorescence fluctuation spectroscopy. The measurements revealed the flow and diffusion times of the DNA molecules through two spatially offset optical probe regions, the absolute and relative concentrations of each conformational substate of the DNA, and the kinetics of the DNA hairpin folding and unfolding reactions in the 1 micros to 10 ms time range. A DNA hairpin containing a 21-nucleotide polythymine loop and a 4-base pair stem exhibited double exponential relaxation kinetics, with time constants of 84 and 393 micros. This confirms that folding and melting of the DNA hairpin structure is not a two state process but proceeds by way of metastable intermediate states. The fast time constant corresponds to formation and unfolding of an intermediate, and the slow time constant is due to formation and disruption of the fully base-paired stem. This is consistent with a previous study of a similar DNA hairpin with a 5-base pair stem, in which the fast reaction was attributed to the fluctuations of an intermediate DNA conformation [J. Am. Chem. Soc. 2006, 128, 1240-1249]. In that case, reactions involving the native conformation could not be observed directly due to the limited observation time range of the fluorescence correlation spectroscopy experiment. The intermediate states of the DNA hairpins are suggested to be due to a collapsed ensemble of folded hairpins containing various partially folded or misfolded conformations.     

Two-state folding observed in individual protein molecules

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.     

Length dependent folding kinetics of phenylacetylene oligomers: structural characterization of a kinetic trap

Using simulation to study the folding kinetics of 20-mer poly-phenylacetylene (pPA) oligomers, we find a long time scale trapped kinetic phase in the cumulative folding time distribution. This is demonstrated using molecular dynamics to simulate an ensemble of over 100 folding trajectories. The simulation data are fit to a four-state kinetic model which includes the typical folded and unfolded states, along with an intermediate state, and most surprisingly, a kinetically trapped state. Topologically diverse conformations reminiscent of alpha helices, beta turns, and sheets in proteins are observed, along with unique structures in the form of knots. The nonhelical conformations are implicated, on the basis of structural correlations to kinetic parameters, to contribute to the trapped kinetic behavior. The strong solvophobic forces which mediate the folding process and produce a stable helical folded state also serve to overstabilize the nonhelical conformations, ultimately trapping them. From our simulations, the folding time is predicted to be on the order of 2.5-12.5 mus in the presence of the trapped kinetic phase. The folding mechanism for these 20-mer chains is compared with the previously reported folding mechanism for the pPA 12-mer chains. A linear scaling relationship between the chain length and the mean first passage time is predicted in the absence of the trapped kinetic phase. We discuss the major implications of this discovery in the design of self-assembling nanostructures.     

Direct measurement of tertiary contact cooperativity in RNA folding

All structured biological macromolecules must overcome the thermodynamic folding problem to populate a unique functional state among a vast ensemble of unfolded and alternate conformations. The exploration of cooperativity in protein folding has helped reveal and distinguish the underlying mechanistic solutions to this folding problem. Analogous dissections of RNA tertiary stability remain elusive, however, despite the central biological importance of folded RNA molecules and the potential to reveal fundamental properties of structured macromolecules via comparisons of protein and RNA folding. We report a direct quantitative measure of tertiary contact cooperativity in a folded RNA. We precisely measured the stability of an independently folding P4-P6 domain from the Tetrahymena thermophila group I intron by single molecule fluorescence resonance energy transfer (smFRET). Using wild-type and mutant RNAs, we found that cooperativity between the two tertiary contacts enhances P4-P6 stability by 3.2 +/- 0.2 kcal/mol.     

Millisecond time-scale folding and unfolding of DNA hairpins using rapid-mixing stopped-flow kinetics

We report stopped-flow kinetics experiments to study the folding and unfolding of 5 base-pair stem and 21 nucleotide polythymidine loop DNA hairpins over various concentrations of NaCl. The reactions occurred on a time scale of milliseconds, considerably longer than the microsecond time scale suggested by previous kinetics studies of similar-sized hairpins. In comparison to a recent fluorescence correlation spectroscopy study (J. Am. Chem. Soc. 2006, 128, 1240-1249), we suggest the microsecond time-scale reactions are due to intermediate states and the millisecond time-scale reactions reported here are due to the formation of the fully folded DNA hairpin. These results support our view that DNA hairpin folding occurs via a minimum three-state mechanism.     

Absence of reptation in the high-temperature folding of the trpzip2 beta-hairpin peptide

We have carried out extensive all atom explicit solvent simulations of the high-temperature folding and unfolding of the trpzip2 beta-hairpin peptide and examined the resulting trajectories for evidence of folding via a reptation mechanism. Over 300 microcanonical simulations of 10 ns each were initiated from a Boltzmann ensemble of conformations at 425 K. Though we observed numerous folding and unfolding events, no evidence of reptation was found. The diffusional dynamics of the peptide are orders of magnitude faster than any observed reptation-like motion. Our data suggest that the dominant mechanisms for beta-hairpin folding under these conditions are hydrophobic collapse and turn formation, and that rearrangements occur via significant expansion of the polypeptide chain.     

Cold denaturation of the hammerhead ribozyme

Cold denaturation is a thermodynamic phenomenon resulting from a difference in the heat capacities, DeltaCp, of the folded and unfolded states of a macromolecule. Whereas this phenomenon has been extensively studied in proteins, it has been thought not to occur in nucleic acids due to a negligible DeltaCp of folding. Questioning the validity of this assumption, the low-temperature structure of the hammerhead ribozyme, a small catalytic RNA, was investigated by circular dichroism spectroscopy. In the presence of 10 mM Mg2+ at pH 5.0 and 40% methanol, a cold unfolding event likely corresponding to tertiary structure loss was observed with a Tm of -20 degrees C. In 500 mM NaCl at pH 6.6, and 40% methanol, large-scale unfolding of the ribozyme at both hot (Tm = 53 degrees C) and cold (Tm = -1 degrees C) temperatures occurred. Fitting of these data to a two-state model allowed determination of DeltaCp = 3.4 kJ mol-1 K-1, corresponding to >/=0.18 kJ K-1 (mol base pair)-1, in good agreement with recently published calorimetric values for DNA duplexes. These results constitute the first direct observation of cold denaturation of a nucleic acid, and point to the importance of DeltaCp terms in the thermodynamics of nucleic acid folding.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.