Fast protein folding kinetics

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico. All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats.

Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

We propose to combine a mean-field approach with all-atom molecular dynamics (MD) into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic-level precision. As an example, we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast, and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins that pose a serious challenge to existing modeling techniques. We argue that a room-temperature monomeric Myc is in a dynamical state, it oscillates between different conformations that we identify. For this we adopt the Cα backbone of Myc in a crystallographic heteromer as an initial ansatz for the monomeric structure. We construct a multisoliton of the pertinent Landau free energy to describe the Cα profile with ultrahigh precision. We use Glauber dynamics to resolve how the multisoliton responds to repeated increases and decreases in ambient temperature. We confirm that the initial structure is unstable in isolation. We reveal a highly degenerate ground-state landscape, an attractive set towards which Glauber dynamics converges in the limit of vanishing ambient temperature. We analyze the thermal stability of this Glauber attractor using room-temperature molecular dynamics. We identify and scrutinize a particularly stable subset in which the two helical segments of the original multisoliton align in parallel next to each other. During the MD time evolution of a representative structure from this subset, we observe intermittent quasiparticle oscillations along the C-terminal α helix, some of which resemble a translating Davydov's Amide-I soliton. We propose that the presence of oscillatory motion is in line with the expected intrinsically disordered character of Myc.

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.

Folding of Protein Ions in the Gas Phase after Cation-to-Anion Proton-Transfer Reactions

The structure and folding of a protein in solution depends on noncovalent interactions within the protein and those with surrounding ions and molecules. Decoupling these interactions in solution is challenging, which has hindered the development of accurate physics-based models for structure prediction. Investigations of proteins in the gas phase can be used to selectively decouple factors affecting the structures of proteins. Here, we use cation-to-anion proton-transfer reactions (CAPTR) to reduce the charge states of denatured ubiquitin ions in the gas phase, and ion mobility to probe their structures. In CAPTR, a precursor charge state is selected (P) and reacted with monoanions to generate charge-reduced product ions (C). Following each CAPTR event, denatured ubiquitin ions (13+ to 6+) yield products that rapidly isomerize to structures that have smaller collision cross sections (Ω). The Ω values of CAPTR product ions depend strongly on C and very weakly on P. Pre- and post-CAPTR activation was then used to probe the potential-energy surfaces of the precursor and product ions, respectively. Post-CAPTR activation showed that ions of different P fold differently and populate different regions of the potential-energy surface of that ion. Finally, pre-CAPTR activation showed that the structures of protein ions can be indirectly investigated using ion mobility of their CAPTR product ions, even for subtle structural differences that are not apparent from ion mobility characterization of the activated precursor ions. More generally, these results show that CAPTR strongly complements existing techniques for characterizing the structures and dynamics of biological molecules in the gas phase.

Kinetics of peptide folding in lipid membranes

Despite our extensive understanding of water-soluble protein folding kinetics, much less is known about the folding dynamics and mechanisms of membrane proteins. However, recent studies have shown that for relatively simple systems, such as peptides that form a transmembrane α-helix, helical dimer, or helix-turn-helix, it is possible to assess the kinetics of several important steps, including peptide binding to the membrane from aqueous solution, peptide folding on the membrane surface, helix insertion into the membrane, and helix-helix association inside the membrane. Herein, we provide a brief review of these studies and also suggest new initiation and probing methods that could lead to improved temporal and structural resolution in future experiments.

Selenomethionine, p-cyanophenylalanine pairs provide a convenient, sensitive, non-perturbing fluorescent probe of local helical structure

The use of selenomethionine (MSe)-p-cyanophenylalanine (FCN) pairs to probe protein structure is demonstrated. MSe quenches FCN fluorescence via electron transfer. Both residues can be incorporated recombinantly or by peptide synthesis. Time-resolved and steady-state fluorescence measurements demonstrate that MSe-FCN pairs provide specific local probes of helical structure.

Cooperative folding near the downhill limit determined with amino acid resolution by hydrogen exchange

The relationship between folding cooperativity and downhill, or barrier-free, folding of proteins under highly stabilizing conditions remains an unresolved topic, especially for proteins such as λ-repressor that fold on the microsecond timescale. Under aqueous conditions where downhill folding is most likely to occur, we measure the stability of multiple H bonds, using hydrogen exchange (HX) in a λYA variant that is suggested to be an incipient downhill folder having an extrapolated folding rate constant of 2 × 10(5) s(-1) and a stability of 7.4 kcal·mol(-1) at 298 K. At least one H bond on each of the three largest helices (α1, α3, and α4) breaks during a common unfolding event that reflects global denaturation. The use of HX enables us to both examine folding under highly stabilizing, native-like conditions and probe the pretransition state region for stable species without the need to initiate the folding reaction. The equivalence of the stability determined at zero and high denaturant indicates that any residual denatured state structure minimally affects the stability even under native conditions. Using our ψ analysis method along with mutational ϕ analysis, we find that the three aforementioned helices are all present in the folding transition state. Hence, the free energy surface has a sufficiently high barrier separating the denatured and native states that folding appears cooperative even under extremely stable and fast folding conditions.

Conformational transitions in the glycine-bound GluN1 NMDA receptor LBD via single-molecule FRET

The N-methyl-D-aspartate receptor (NMDAR) is a member of the glutamate receptor family of proteins and is responsible for excitatory transmission. Activation of the receptor is thought to be controlled by conformational changes in the ligand binding domain (LBD); however, glutamate receptor LBDs can occupy multiple conformations even in the activated form. This work probes equilibrium transitions among NMDAR LBD conformations by monitoring the distance across the glycine-bound LBD cleft using single-molecule Förster resonance energy transfer (smFRET). Recent improvements in photoprotection solutions allowed us to monitor transitions among the multiple conformations. Also, we applied a recently developed model-free algorithm called "step transition and state identification" to identify the number of states, their smFRET efficiencies, and their interstate kinetics. Reversible interstate conversions, corresponding to transitions among a wide range of cleft widths, were identified in the glycine-bound LBD, on much longer timescales compared to channel opening. These transitions were confirmed to be equilibrium in nature by shifting the distribution reversibly via denaturant. We found that the NMDAR LBD proceeds primarily from one adjacent smFRET state to the next under equilibrium conditions, consistent with a cleft-opening/closing mechanism. Overall, by analyzing the state-to-state transition dynamics and distributions, we achieve insight into specifics of long-lived LBD equilibrium structural dynamics, as well as obtain a more general description of equilibrium folding/unfolding in a conformationally dynamic protein. The relationship between such long-lived LBD dynamics and channel function in the full receptor remains an open and interesting question.

Testing Landscape Theory for Biomolecular Processes with Single Molecule Fluorescence Spectroscopy

Although Kramers' theory for diffusive barrier crossing on a 1D free energy profile plays a central role in landscape theory for complex biomolecular processes, it has not yet been rigorously tested by experiment. Here we test this 1D diffusion scenario with single molecule fluorescence measurements of DNA hairpin folding. We find an upper bound of 2.5  μs for the average transition path time, consistent with the predictions by theory with parameters determined from optical tweezer measurements.

A Method for Extracting the Free Energy Surface and Conformational Dynamics of Fast-Folding Proteins from Single Molecule Photon Trajectories

Single molecule fluorescence spectroscopy holds the promise of providing direct measurements of protein folding free energy landscapes and conformational motions. However, fulfilling this promise has been prevented by technical limitations, most notably, the difficulty in analyzing the small packets of photons per millisecond that are typically recorded from individual biomolecules. Such limitation impairs the ability to accurately determine conformational distributions and resolve sub-millisecond processes. Here we develop an analytical procedure for extracting the conformational distribution and dynamics of fast-folding proteins directly from time-stamped photon arrival trajectories produced by single molecule FRET experiments. Our procedure combines the maximum likelihood analysis originally developed by Gopich and Szabo with a statistical mechanical model that describes protein folding as diffusion on a one-dimensional free energy surface. Using stochastic kinetic simulations, we thoroughly tested the performance of the method in identifying diverse fast-folding scenarios, ranging from two-state to one-state downhill folding, as a function of relevant experimental variables such as photon count rate, amount of input data, and background noise. The tests demonstrate that the analysis can accurately retrieve the original one-dimensional free energy surface and microsecond folding dynamics in spite of the sub-megahertz photon count rates and significant background noise levels of current single molecule fluorescence experiments. Therefore, our approach provides a powerful tool for the quantitative analysis of single molecule FRET experiments of fast protein folding that is also potentially extensible to the analysis of any other biomolecular process governed by sub-millisecond conformational dynamics.

Comparing Fast Pressure Jump and Temperature Jump Protein Folding Experiments and Simulations

The unimolecular folding reaction of small proteins is now amenable to a very direct mechanistic comparison between experiment and simulation. We present such a comparison of microsecond pressure and temperature jump refolding kinetics of the engineered WW domain FiP35, a model system for β-sheet folding. Both perturbations produce experimentally a faster and a slower kinetic phase, and the "slow" microsecond phase is activated. The fast phase shows differences between perturbation methods and is closer to the downhill limit by temperature jump, but closer to the transiently populated intermediate limit by pressure jump. These observations make more demands on simulations of the folding process than just a rough comparison of time scales. To complement experiments, we carried out several pressure jump and temperature jump all-atom molecular dynamics trajectories in explicit solvent, where FiP35 folded in five of the six simulations. We analyzed our pressure jump simulations by kinetic modeling and found that the pressure jump experiments and MD simulations are most consistent with a 4-state kinetic mechanism. Together, our experimental and computational data highlight FiP35's position at the boundary where activated intermediates and downhill folding meet, and we show that this model protein is an excellent candidate for further pressure jump molecular dynamics studies to compare experiment and modeling at the folding mechanism level.

pH-jump induced leucine zipper folding beyond the diffusion limit

The folding of a pH-sensitive leucine zipper, that is, a GCN4 mutant containing eight glutamic acid residues, has been investigated. A pH-jump induced by a caged proton (o-nitrobenzaldehyde, oNBA) is employed to initiate the process, and time-resolved IR spectroscopy of the amide I band is used to probe it. The experiment has been carefully designed to minimize the buffer capacity of the sample solution so that a large pH jump can be achieved, leading to a transition from a completely unfolded to a completely folded state with a single laser shot. In order to eliminate the otherwise rate-limiting diffusion-controlled step of the association of two peptides, they have been covalently linked. The results for the folding kinetics of the cross-linked peptide are compared with those of an unlinked peptide, which reveals a detailed picture of the folding mechanism. That is, folding occurs in two steps, one on an ∼1-2 μs time scale leading to a partially folded α-helix even in the monomeric case and a second one leading to the final coiled-coil structure on distinctively different time scales of ∼30 μs for the cross-linked peptide and ∼200 μs for the unlinked peptide. By varying the initial pH, it is found that the folding mechanism is consistent with a thermodynamic two-state model, despite the fact that a transient intermediate is observed in the kinetic experiment.

Folding dynamics and pathways of the trp-cage miniproteins

Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.