Folding Transition Research Articles

A Tale of Two Desolvation Potentials: An Investigation of Protein Behavior under High Hydrostatic Pressure.

Hydrostatic pressure is a common perturbation to probe the conformations of proteins. There are two common forms of pressure-dependent potentials of mean force (PMFs) derived from hydrophobic molecules available for coarse-grained molecular simulations of protein folding and unfolding under hydrostatic pressure. Although both PMFs include a desolvation barrier separating the direct contact well and the solvent-mediated contact well, how these features vary with hydrostatic pressure is still debated. There is a need for a systematic comparison of these two PMFs on a protein. We investigated the two different pressure-dependencies on the desolvation potential in a structure-based protein model using coarse-grained molecular simulations. We compared the simulation results to the known behavior of proteins based on experimental evidence. We showed that the protein's folding transition curve on the pressure-temperature phase diagram depends on the relationship between the potential well minima and pressure. For a protein that reduces its total volume under pressure, the PMF needs to carry the feature that the direct contact well is less stable than the water-mediated contact well at high pressure. We also comment on the practicality and importance of structure-based minimalist models for understanding the phenomenological behavior of proteins under a wide range of phase space.

Planar Hall effect and anisotropic magnetoresistance in polar-polar interface of LaVO3-KTaO3 with strong spin-orbit coupling

Among the perovskite oxide family, KTaO3 (KTO) has recently attracted considerable interest as a possible system for the realization of the Rashba effect. In this work, we report a novel conducting interface by placing KTO with another insulator, LaVO3 (LVO) and report planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) measurements. This interface exhibits a signature of strong spin-orbit coupling. Our experimental observations of two fold AMR and PHE at low magnetic fields (B) is similar to those obtained for topological systems and can be intuitively understood using a phenomenological theory for a Rashba spin-split system. Our experimental data show a B2 dependence of AMR and PHE at low magnetic fields that could also be explained based on our model. At high fields (~8 T), we see a two fold to four fold transition in the AMR that could not be explained using only Rashba spin-split energy spectra.

Learning Dynamical Information from Static Protein and Sequencing Data

Many complex processes, from protein folding and virus evolution to brain activity and neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. While efficient algorithms for cluster detection and data completion in high-dimensional spaces have been developed and applied over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here, we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. Our approach combines Gaussian mixture approximations and self-consistent dimensionality reduction with minimal-energy path estimation and multi-dimensional transition-state theory. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein folding transitions, gene regulatory network motifs and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations and phylogenetic trees, respectively. The underlying numerical protocol thus allows the recovery of relevant dynamical information from instantaneous ensemble measurements, effectively alleviating the need for time-dependent data in many situations. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein sequencing datasets and future cryo-electron-microscopy data, and can guide the design of new experimental approaches towards studying complex multiphase phenomena.

Microcanonical thermostatistics of aggregation transition in a system with anisotropically interacting molecules

Microcanonical thermostatistics analysis has been introduced as an important method in the study of phase transitions observed in intrinsically small systems, such as folding transitions in proteins and surface adsorption transitions of polymeric chains. Here we consider a lattice model and apply microcanonical analysis to investigate the aggregation transition of a system with anisotropically interacting molecules. By performing multicanonical Monte Carlo simulations we are able to obtain free-energy profiles from where we extract physical quantities related to the aggregation transition such as its transition temperature, latent heat, and free-energy barriers. Our results confirms that the aggregation transition is a first-order type of transition and that it is related to the nucleation of molecules into elongated aggregates. Also, our analysis revealed an unexpected non-monotonic behavior for the free-energy barrier as a function of the anisotropic ratio ξ between strong and weak interactions of the molecules, indicating that the nucleation kinetics might be also influenced by ξ.

Improved Estimates of Folding Stabilities and Kinetics from Multiensemble Markov Models

In the last few years, Markov State Model (MSM) approaches have been widely applied to understand folding mechanisms and predict long timescale dynamics from ensembles of short molecular simulations. Most MSM estimators enforce detailed balance, assuming that trajectory data is sampled at equilibrium. This is rarely the case for ab initio folding studies, however, and as a result, protein folding stabilities can be severely underestimated. To remedy this problem, we propose an enhanced-sampling protocol in which we (1) perform unbiased folding simulations and use sparse tICA to obtain features that best capture the slowest events in folding, (2) perform umbrella sampling along this reaction coordinate to observe folding and unfolding transitions, and (3) estimate the thermodynamics and kinetics of folding using multiensemble Markov models (MEMMs).

Using Dihedral Stabilities to Characterize Protein Folding Transitions

Using Dihedral Stabilities to Characterize Protein Folding Transitions

Catching Fast Protein Folding in the Act: Resolving (Un)Folding Transition Paths using Advanced Single-molecule Spectroscopy

Catching Fast Protein Folding in the Act: Resolving (Un)Folding Transition Paths using Advanced Single-molecule Spectroscopy

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or “width” of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.

Extension-Dependent Drift Velocity and Diffusion (DrDiff) Directly Reconstructs the Folding Free Energy Landscape of Atomic Force Microscopy Experiments.

Two equilibrium force microscopy trajectories [q(t)] of high-precision single-molecule spectroscopy assays were analyzed: the pulling of an HIV RNA hairpin and of a 3-aa sequence of the bacteriorhodopsin membrane protein. Both present hundreds of two-state folding transitions, and their free-energy [F(q)] landscapes were previously obtained by deconvolving time signals with the inverse Boltzmann and pfold methods. In this letter, the two F profiles were reconstructed directly from the measured time-series by the drift-diffusion (DrDiff) framework that characterized the effective conformational drift-velocity [v(q)] and diffusion [D(q)] coefficients. The two thermodynamic F profiles reconstructed with DrDiff directly from q(t) were in good agreement with those previously obtained from the deconvolved time signals. q(t) trajectories simulated with a two-dimensional framework in which the diffusion coefficient of the pulling setup (q coordinate) differed from the molecule (x coordinate) were also analyzed by DrDiff. The performance in reconstructing F was investigated in different conditions of diffusion anisotropy in the simulated time-series using Brownian dynamics. In addition, recently developed theories were used in order to evaluate the quality of the analysis performed in the experimental time series: the memory effects and the intrinsic biomolecular dynamic properties after connecting the probe to the molecule. With the 2-dimensional diffusive models and the additional analyses, it is proposed that the different physical regimes imposed by the stiffer probes of the two biomolecules will have an impact in the measured extension-dependent D and, thus, in the reconstruction of F by DrDiff. Stiffer AFM probes may reflect the molecular behavior more faithfully and reconstruction of F might be more successful. The reported quantities extracted directly from q(t) highlights the current state of the biomolecule characterization by force spectroscopy experiments: it is still challenging despite the recent advances, yet it is very promising.

Potential energy landscape and thermodynamic transitions of coarse-grained protein models revealed by the multicanonical generalized hybrid Monte Carlo method.

In the present study, thermodynamic properties of coarse-grained protein models have been studied by an extended ensemble method. Two types of protein model were analyzed; one is categorized into a fast folder and the other into a slow folder. Both models exhibit the following thermodynamic transitions: the collapse transition between random coil states and spatially compact, but non-native states and the folding transition between the collapsed states and the folded native states. Caloric curve for the fast folder shows strong statistical ensemble dependence, while almost no ensemble dependence is found for the slow folder. Microcanonical caloric curve for the fast folder exhibits S-shaped temperature dependence on the internal energy around the collapse transition which is reminiscent of the van der Waals loop observed for the first order transition; at the transition temperature, the collapsed and random coil states coexist dynamically. The corresponding microcanonical heat capacity is found to have negative region around the transition. This kind of exotic behaviors could be utilized to distinguish fast folding proteins.

NMR Chemical Exchange Measurements Reveal That N6-Methyladenosine Slows RNA Annealing.

N6-Methyladenosine (m6A) is an abundant epitranscriptomic modification that plays important roles in many aspects of RNA metabolism. While m6A is thought to mainly function by recruiting reader proteins to specific RNA sites, the modification can also reshape RNA-protein and RNA-RNA interactions by altering RNA structure mainly by destabilizing base pairing. Little is known about how m6A and other epitranscriptomic modifications might affect the kinetic rates of RNA folding and other conformational transitions that are also important for cellular activity. Here, we used NMR R1ρ relaxation dispersion and chemical exchange saturation transfer to noninvasively and site-specifically measure nucleic acid hybridization kinetics. The methodology was validated on two DNA duplexes and then applied to examine how a single m6A alters the hybridization kinetics in two RNA duplexes. The results show that m6A minimally impacts the rate constant for duplex dissociation, changing koff by ∼1-fold but significantly slows the rate of duplex annealing, decreasing kon by ∼7-fold. A reduction in the annealing rate was observed robustly for two different sequence contexts at different temperatures, both in the presence and absence of Mg2+. We propose that rotation of the N6-methyl group from the preferred syn conformation in the unpaired nucleotide to the energetically disfavored anti conformation required for Watson-Crick pairing is responsible for the reduced annealing rate. The results help explain why in mRNA m6A slows down tRNA selection and more generally suggest that m6A may exert cellular functions by reshaping the kinetics of RNA conformational transitions.

Explicit Characterization of the Free-Energy Landscape of a Protein in the Space of All Its Cα Carbons.

By using an approach that allows computing the free energy in high-dimensional spaces together with a clustering technique capable of identifying kinetic attractors stabilized by conformational disorder, we analyze a molecular dynamics trajectory of the Villin headpiece from Lindorff-Larsen, K.; et al. How fast-folding proteins fold. Science 2011, 334, 517-520. We compute its free-energy landscape in the space of all its Cα carbons. This landscape has the shape of a 12-dimensional funnel with the free energy decreasing monotonically as a function of the native contacts. There are no significant folding barriers. The funnel can be partitioned in five regions, three mainly folded and two unfolded, which behave as Markov states. The slowest relaxation time among these states corresponds to the folding transition. The second slowest time is only twice smaller and corresponds to a transition within the unfolded state. This indicates that the unfolded part of the funnel has a nontrivial shape, which induces a sizable kinetic barrier between disordered states.

Learning dynamical information from static protein and sequencing data

Many complex processes, from protein folding to neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. Although efficient algorithms for cluster detection in high-dimensional spaces have been developed over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein-folding transitions, gene-regulatory network motifs, and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations, and phylogenetic trees, respectively. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein-sequencing datasets, and future cryo-electron microscopy (cryo-EM) data.

The Anti-Aggregation Holdase Hsp33 Promotes the Formation of Folded Protein Structures

Holdase chaperones are known to be central to suppressing aggregation, but how they affect substrate conformations remains poorly understood. Here, we use optical tweezers to study how the holdase Hsp33 alters folding transitions within single maltose binding proteins and aggregation transitions between maltose binding protein substrates. Surprisingly, we find that Hsp33 not only suppresses aggregation but also guides the folding process. Two modes of action underlie these effects. First, Hsp33 binds unfolded chains, which suppresses aggregation between substrates and folding transitions within substrates. Second, Hsp33 binding promotes substrate states in which most of the chain is folded and modifies their structure, possibly by intercalating its intrinsically disordered regions. A statistical ensemble model shows how Hsp33 function results from the competition between these two contrasting effects. Our findings reveal an unexpectedly comprehensive functional repertoire for Hsp33 that may be more prevalent among holdases and dispels the notion of a strict chaperone hierarchy.

Single-nucleotide control of tRNA folding cooperativity under near-cellular conditions

RNA folding is often studied by renaturing full-length RNA in vitro and tracking folding transitions. However, the intracellular transcript folds as it emerges from the RNA polymerase. Here, we investigate the folding pathways and stability of numerous late-transcriptional intermediates of yeast and Escherichia coli transfer RNAs (tRNAs). Transfer RNA is a highly regulated functional RNA that undergoes multiple steps of posttranscriptional processing and is found in very different lengths during its lifetime in the cell. The precursor transcript is extended on both the 5' and 3' ends of the cloverleaf core, and these extensions get trimmed before addition of the 3'-CCA and aminoacylation. We studied the thermodynamics and structures of the precursor tRNA and of late-transcriptional intermediates of the cloverleaf structure. We examined RNA folding at both the secondary and tertiary structural levels using multiple biochemical and biophysical approaches. Our findings suggest that perhaps nature has selected for a single-base addition to control folding to the functional 3D structure. In near-cellular conditions, yeast tRNAPhe and E. coli tRNAAla transcripts fold in a single, cooperative transition only when nearly all of the nucleotides in the cloverleaf are transcribed by indirectly enhancing folding cooperativity. Furthermore, native extensions on the 5' and 3' ends do not interfere with cooperative core folding. This highly controlled cooperative folding has implications for recognition of tRNA by processing and modification enzymes and quality control of tRNA in cells.

Folding of the Ig-Like Domain of the Dengue Virus Envelope Protein Analyzed by High-Hydrostatic-Pressure NMR at a Residue-Level Resolution.

Dengue fever is a mosquito-borne endemic disease in tropical and subtropical regions, causing a significant public health problem in Southeast Asia. Domain III (ED3) of the viral envelope protein contains the two dominant putative epitopes and part of the heparin sulfate receptor binding region that drives the dengue virus (DENV)’s fusion with the host cell. Here, we used high-hydrostatic-pressure nuclear magnetic resonance (HHP-NMR) to obtain residue-specific information on the folding process of domain III from serotype 4 dengue virus (DEN4-ED3), which adopts the classical three-dimensional (3D) ß-sandwich structure known as the Ig-like fold. Interestingly, the folding pathway of DEN4-ED3 shares similarities with that of the Titin I27 module, which also adopts an Ig-like fold, but is functionally unrelated to ED3. For both proteins, the unfolding process starts by the disruption of the N- and C-terminal strands on one edge of the ß-sandwich, yielding a folding intermediate stable over a substantial pressure range (from 600 to 1000 bar). In contrast to this similarity, pressure-jump kinetics indicated that the folding transition state is considerably more hydrated in DEN4-ED3 than in Titin I27.

Cross-linker mediated compaction and local morphologies in a model chromosome

Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.

Sampling the Folding Transition State Ensemble in a Tube-like Model of Protein

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformationalroot mean square deviation (rmsd) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

Substance P in the Gas Phase: Conformational Changes and Dissociations Induced by Collisional Activation in a Drift Tube.

The work presented below is related to our companion paper in this issue, entitled: Substance P in solution: trans-to-cis configurational changes of penultimate prolines initiate non-enzymatic peptide bond cleavages. Two-dimensional ion mobility spectrometry (IMS-IMS) and mass spectrometry techniques are used to investigate structural transitions for [M+3H]3+ ions of substance P (subP) upon collisional activation (CA) in the gas phase. In this approach, different conformations of ions having a specified mobility are selected after an initial IMS separation, collisionally activated to produce new conformers, and these product structures are separated again using a second IMS region. In this way, it is possible to follow folding and unfolding transitions of different conformations. The analysis shows evidence for five conformations. Unlike other systems, every transition is irreversible. Studies as a function of activation voltage are used to discern pathways of structural changes prior to reaching the energy required for dissociation. Thresholds associated with the onsets of transitions are calibrated to obtain estimates of the energetic barriers between different structures and semi-quantitative potential energy diagrams are presented. Overall, barriers associated with structural transitions of [subP+3H]3+ in the absence of solvent are on the order of ~ 40kJmol-1, substantially lower than the ~ 90kJmol-1 required for some similar structural transitions in solutions of ethanol. Comparisons of the transition energies in the gas phase with thermochemistry for similar transitions in solution provide clues about why reverse transitions are prohibited. Graphical Abstract.

Nature's Shortcut to Protein Folding.

This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.