Folding Transition Research Articles

Improved Estimates of Folding Stabilities and Kinetics with Multiensemble Markov Models.

Markov State Models (MSMs) have been widely applied to understand protein folding mechanisms by predicting long time scale dynamics from ensembles of short molecular simulations. Most MSM estimators enforce detailed balance, assuming that trajectory data are sampled at an equilibrium. This is rarely the case for ab initio folding studies, however, and as a result, MSMs can severely underestimate protein folding stabilities from such data. To remedy this problem, we have developed an enhanced-sampling protocol in which (1) unbiased folding simulations are performed and sparse tICA is used to obtain features that best capture the slowest events in folding, (2) umbrella sampling along this reaction coordinate is performed to observe folding and unfolding transitions, and (3) the thermodynamics and kinetics of folding are estimated using multiensemble Markov models (MEMMs). Using this protocol, folding pathways, rates, and stabilities of a designed α-helical hairpin, Z34C, can be predicted in good agreement with experimental measurements. These results indicate that accurate simulation-based estimates of absolute folding stabilities are within reach, with implications for the computational design of folded miniproteins and peptidomimetics.

Folding behaviors of two-dimensional flexible polymers.

Unlike one-dimensional polymers, the theoretical framework on the behaviors of two-dimensional (2D) polymers is far from completeness. In this study, we model single-layer flexible 2D polymers of different sizes and examine their scaling behaviors in solution, represented by Rg ∼ Lν, where Rg is the radius of gyration and L is the side length of a 2D polymer. We find that the scaling exponent ν is 0.96 for a good solvent and 0.64 for under poor solvent condition. Interestingly, we observe a previously unnoticed phenomenon: under intermediate solvent conditions, the 2D polymer folds to maintain a flat structure, and as L becomes larger, multiple folded structures emerge. We introduce a shape parameter Q to diagram the relationship of folded structures with the polymer size and solvent condition. Theoretically, we explain the folding transitions by the competition between bending and solvophobic free energies.

Magnesium Regulates RNA Ring Dynamics and Folding in Subgenomic Flaviviral RNA.

Mosquito-borne flaviviruses including dengue, Zika, yellow fever, and regional encephalitis produce a large amount of short subgenomic flaviviral RNAs during infection. A segment of these RNAs named as xrRNA1 features a multi-pseudoknot (PK)-associated structure, which resists the host cell enzyme (XRN1) from degrading the viral RNA. We investigate how this long-range RNA PK folds in the presence of counterions, specifically in a mix of monovalent (K+) and divalent (Mg2+) salts at physiological concentrations. In this study, we use extensive explicit solvent molecular dynamics (MD) simulations to characterize the RNA ion environment of the folded RNA conformation, as determined by the crystal structure. This allowed us to identify the precise locations of various coordinated RNA-Mg2+ interactions, including inner-sphere/chelated and outer-sphere coordinated Mg2+. Given that RNA folding involves large-scale conformational changes, making it challenging to explore through classical MD simulations, we investigate the folding mechanism of xrRNA1 using an all-atom structure-based RNA model with a hybrid implicit-explicit treatment of the ion environment via the dynamic counterion condensation model, both with and without physiological Mg2+ concentration. The study reveals potential folding pathways for this xrRNA1, which is consistent with the results obtained from optical tweezer experiments. The equilibrium and free energy simulations both capture a dynamic equilibrium between the ring-open and ring-close states of the RNA, driven by a long-range PK interaction. Free energy calculations reveal that with the addition of Mg2+ ions, the equilibrium shifts more toward the ring-close state. A detailed analysis of the free energy pathways and ion-mediated contact probability map highlights the critical role of Mg2+ in bridging G50 and A33. This Mg2+-mediated connection helps form the long-range PK which in turn controls the transition between the ring-open and ring-close states. The study underscores the critical role of Mg2+ in the RNA folding transition, highlighting specific locations of Mg2+ contributing to the stabilization of long-range PK connections likely to enhance the robustness of Xrn1 resistance of flaviviral xrRNAs.

Scaling Laws for Protein Folding under Confinement.

Spatial confinement significantly affects protein folding. Without the confinement provided by chaperones, many proteins cannot fold correctly. However, the quantitative effect of confinement on protein folding remains elusive. In this study, we observed scaling laws between the variation in folding transition temperature and the size of confinement, (Tf - Tfbulk)/Tfbulk ∼ L-ν. The scaling exponent v is significantly influenced by both the protein's topology and folding cooperativity. Specifically, for a given protein, v can decrease as the folding cooperativity of the model increases, primarily due to the heightened sensitivity of the unfolded state energy to changes in cage size. For proteins with diverse topologies, variations in topological complexity influence scaling exponents in multiple ways. Notably, v exhibits a clear positive correlation with contact order and the proportion of nonlocal contacts, as this complexity significantly enhances the sensitivity of entropy loss in the unfolded state. Furthermore, we developed a novel scaling argument yielding 5/3 ≤ ν ≤ 10/3, consistent with the simulation results.

Cross-Effects in Folding and Phase Transitions of hnRNP A1 and C9Orf72 RNA G4 In Vitro.

Abnormal intracellular phase transitions in mutant hnRNP A1 may underlie the development of several neurodegenerative diseases. The risk of these diseases increases upon C9Orf72 repeat expansion and the accumulation of the corresponding G-quadruplex (G4)-forming RNA, but the link between this RNA and the disruption of hnRNP A1 homeostasis has not been fully explored so far. Our aim was to clarify the mutual effects of hnRNP A1 and C9Orf72 G4 in vitro. Using various optical methods and atomic force microscopy, we investigated the influence of the G4 on the formation of cross-beta fibrils by the mutant prion-like domain (PLD) of hnRNP A1 and on the co-separation of the non-mutant protein with a typical SR-rich fragment of a splicing factor (SRSF), which normally drives the assembly of nuclear speckles. The G4 was shown to act in a holdase-like manner, i.e., to restrict the fibrillation of the hnRNP A1 PLD, presumably through interactions with the PLD-flanking RGG motif. These interactions resulted in partial unwinding of the G4, suggesting a helicase-like activity of hnRNP A1 RGG. At the same time, the G4 was shown to disrupt hnRNP A1 co-separation with SRSF, suggesting its possible contribution to pathology through interference with splicing regulation.

The significance of fuzzy boundaries of the barrier regions in single-molecule measurements of failed barrier crossing attempts.

A recent ground-breaking experimental study [Lyons et al., Phys. Rev. X 14(1), 011017 (2024)] reports on measuring the temporal duration and the spatial extent of failed attempts to cross an activation barrier (i.e., "loops") for a folding transition in a single molecule and for a Brownian particle trapped within a bistable potential. Within the model of diffusive dynamics, however, both of these quantities are, on average, exactly zero because of the recrossings of the barrier region boundary. That is, an observer endowed with infinite spatial and temporal resolution would find that finite loops do not exist (or, more precisely, form a set of measure zero). Here we develop a description of the experiment that takes the "fuzziness" of the boundaries caused by finite experimental resolution into account and show how the experimental uncertainty of localizing the point, in time and space, where the barrier is crossed leads to observable distributions of loop times and sizes. Although these distributions generally depend on the experimental resolution, this dependence, in certain cases, may amount to a simple resolution-dependent factor and, therefore, the experiments do probe inherent properties of barrier crossing dynamics.

Learning Collective Variables with Synthetic Data Augmentation through Physics-Inspired Geodesic Interpolation.

In molecular dynamics simulations, rare events, such as protein folding, are typically studied using enhanced sampling techniques, most of which are based on the definition of a collective variable (CV) along which acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. This new data can be used to improve the accuracy of classifier-based methods. Alternatively, a regression-based learning scheme for CV models can be adopted by leveraging the interpolation progress parameter.

Advanced sampling simulations of coupled folding and binding of phage P22 N-peptide to boxB RNA

Protein-RNA interactions are crucially important for numerous cellular processes and often involve coupled folding and binding of peptide segments upon association. The Nut-utilization site (N)-protein of bacteriophages contains an N-terminal arginine-rich motif that undergoes such a folding transition upon binding to the boxB RNA hairpin loop target structure. Molecular dynamics free energy simulations were used to calculate the absolute binding free energy of the N-peptide of bacteriophage P22 in complex with the boxB RNA hairpin motif at different salt concentrations and using two different water force field models. We obtained good agreement with experiment also at different salt concentrations for the TIP4P-D water model that has a stabilizing effect on unfolded protein structures. It allowed us to estimate the free energy contribution resulting from restricting the molecules’ spatial and conformational freedom upon binding, which makes a large opposing contribution to binding. In a second set of umbrella sampling simulations to dissociate/associate the complex along a separation coordinate, we analyzed the onset of preorientation of the N-peptide and onset of structure formation relative to the RNA and its dependence on the salt concentration. Peptide orientation and conformational transitions are significantly coupled to the first contact formation between peptide and RNA. The initial contacts are mostly formed between peptide residues and the boxB hairpin loop nucleotides. A complete transition to an α-helical bound peptide conformation occurs only at a late stage of the binding process a few angstroms before the complexed state has been reached. However, the N-peptide orients also at distances beyond the contact distance such that the sizable positive charge points toward the RNA’s center-of-mass. Our result may have important implications for understanding protein- and peptide-RNA complex formation frequently involving coupled folding and association processes.

Targeting the protein folding transition state by mutation: Large scale (un)folding rate accelerations without altering native stability.

Proteins are constantly undergoing folding and unfolding transitions, with rates that determine their homeostasis in vivo and modulate their biological function. The ability to optimize these rates without affecting overall native stability is hence highly desirable for protein engineering and design. The great challenge is, however, that mutations generally affect folding and unfolding rates with inversely complementary fractions of the net free energy change they inflict on the native state. Here we address this challenge by targeting the folding transition state (FTS) of chymotrypsin inhibitor 2 (CI2), a very slow and stable two-state folding protein with an FTS known to be refractory to change by mutation. We first discovered that the CI2's FTS is energetically taxed by the desolvation of several, highly conserved, charges that form a buried salt bridge network in the native structure. Based on these findings, we designed a CI2 variant that bears just four mutations and aims to selectively stabilize the FTS. This variant has >250-fold faster rates in both directions and hence identical native stability, demonstrating the success of our FTS-centric design strategy. With an optimized FTS, CI2 also becomes 250-fold more sensitive to proteolytic degradation by its natural substrate chymotrypsin, and completely loses its activity as inhibitor. These results indicate that CI2 has been selected through evolution to have a very unstable FTS in order to attain the kinetic stability needed to effectively function as protease inhibitor. Moreover, the CI2 case showcases that protein (un)folding rates can critically pivot around a few key residues-interactions, which can strongly modify the general effects of known structural factors such as domain size and fold topology. From a practical standpoint, our results suggest that future efforts should perhaps focus on identifying such critical residues-interactions in proteins as best strategy to significantly improve our ability to predict and engineer protein (un)folding rates.

Hydrogen bonding heterogeneity correlates with protein folding transition state passage time as revealed by data sonification

Protein-protein and protein-water hydrogen bonding interactions play essential roles in the way a protein passes through the transition state during folding or unfolding, but the large number of these interactions in molecular dynamics (MD) simulations makes them difficult to analyze. Here, we introduce a state space representation and associated "rarity" measure to identify and quantify transition state passage (transit) events. Applying this representation to a long MD simulation trajectory that captured multiple folding and unfolding events of the GTT WW domain, a small protein often used as a model for the folding process, we identified three transition categories: Highway (faster), Meander (slower), and Ambiguous (intermediate). We developed data sonification and visualization tools to analyze hydrogen bond dynamics before, during, and after these transition events. By means of these tools, we were able to identify characteristic hydrogen bonding patterns associated with "Highway" versus "Meander" versus "Ambiguous" transitions and to design algorithms that can identify these same folding pathways and critical protein-water interactions directly from the data. Highly cooperative hydrogen bonding can either slow down or speed up transit. Furthermore, an analysis of protein-water hydrogen bond dynamics at the surface of WW domain shows an increase in hydrogen bond lifetime from folded to unfolded conformations with Ambiguous transitions as an outlier. In summary, hydrogen bond dynamics provide a direct window into the heterogeneity of transits, which can vary widely in duration (by a factor of 10) due to a complex energy landscape.

Folding Kinetics and Volume Variation of the β-Hairpin Peptide Chignolin upon Ultrafast pH-Jumps.

In-depth characterization of fundamental folding steps of small model peptides is crucial for a better understanding of the folding mechanisms of more complex biomacromolecules. We have previously reported on the folding/unfolding kinetics of a model α-helix. Here, we study folding transitions in chignolin (GYDPETGTWG), a short β-hairpin peptide previously used as a model to study conformational changes in β-sheet proteins. Although previously suggested, until now, the role of the Tyr2-Trp9 interaction in the folding mechanism of chignolin was not clear. In the present work, pH-dependent conformational changes of chignolin were characterized by circular dichroism (CD), nuclear magnetic resonance (NMR), ultrafast pH-jump coupled with time-resolved photoacoustic calorimetry (TR-PAC), and molecular dynamics (MD) simulations. Taken together, our results present a comprehensive view of chignolin's folding kinetics upon local pH changes and the role of the Tyr2-Trp9 interaction in the folding process. CD data show that chignolin's β-hairpin formation displays a pH-dependent skew bell-shaped curve, with a maximum close to pH 6, and a large decrease in β-sheet content at alkaline pH. The β-hairpin structure is mainly stabilized by aromatic interactions between Tyr2 and Trp9 and CH-π interactions between Tyr2 and Pro4. Unfolding of chignolin at high pH demonstrates that protonation of Tyr2 is essential for the stability of the β-hairpin. Refolding studies were triggered by laser-induced pH-jumps and detected by TR-PAC. The refolding of chignolin from high pH, mainly due to the protonation of Tyr2, is characterized by a volume expansion (10.4 mL mol-1), independent of peptide concentration, in the microsecond time range (lifetime of 1.15 μs). At high pH, the presence of the deprotonated hydroxyl (tyrosinate) hinders the formation of the aromatic interaction between Tyr2 and Trp9 resulting in a more disorganized and dynamic tridimensional structure of the peptide. This was also confirmed by comparing MD simulations of chignolin under conditions mimicking neutral and high pH.

Quantum Defect Sensitization via Phase-Changing Supercharged Antibody Fragments.

Quantum defects in single-walled carbon nanotubes promote exciton localization, which enables potential applications in biodevices and quantum light sources. However, the effects of local electric fields on the emissive energy states of quantum defects and how they can be controlled are unexplored. Here, we investigate quantum defect sensitization by engineering an intrinsically disordered protein to undergo a phase change at a quantum defect site. We designed a supercharged single-chain antibody fragment (scFv) to enable a full ligand-induced folding transition from an intrinsically disordered state to a compact folded state in the presence of a cytokine. The supercharged scFv was conjugated to a quantum defect to induce a substantial local electric change upon ligand binding. Employing the detection of a proinflammatory biomarker, interleukin-6, as a representative model system, supercharged scFv-coupled quantum defects exhibited robust fluorescence wavelength shifts concomitant with the protein folding transition. Quantum chemical simulations suggest that the quantum defects amplify the optical response to the localization of charges produced upon the antigen-induced folding of the proteins, which is difficult to achieve in unmodified nanotubes. These findings portend new approaches to modulate quantum defect emission for biomarker sensing and protein biophysics and to engineer proteins to modulate binding signal transduction.

The Mechanism of Folding of Human Frataxin in Comparison to the Yeast Homologue – Broad Energy Barriers and the General Properties of the Transition State

The funneled energy landscape theory suggests that the folding pathway of homologous proteins should converge at the late stages of folding. In this respect, proteins displaying a broad energy landscape for folding are particularly instructive, allowing inferring both the early, intermediate and late stages of folding. In this paper we explore the folding mechanisms of human frataxin, an essential mitochondrial protein linked to the neurodegenerative disorder Friedreich's ataxia. Building upon previous studies on the yeast homologue, the folding pathway of human frataxin is thoroughly examined, revealing a mechanism implying the presence of a broad energy barrier, reminiscent of the yeast counterpart. Through an extensive site-directed mutagenesis, we employed a Φ -value analysis to map native-like contacts in the folding transition state. The presence of a broad energy barrier facilitated the exploration of such contacts in both early and late folding events. We compared results from yeast and human frataxin providing insights into the impact of native topology on the folding mechanism and elucidating the properties of the underlying free energy landscape. The findings are discussed in the context of the funneled energy landscape theory of protein folding.

Determination of the Eutectic to Peritectic Fold Transition in the Cu(Ni)–Fe–S System by Directional Crystallization of Melts

Determination of the Eutectic to Peritectic Fold Transition in the Cu(Ni)–Fe–S System by Directional Crystallization of Melts

Identical sequences, different behaviors: Protein diversity captured at the single-molecule level

The classical “one sequence, one structure, one function” paradigm has shaped much of our intuition of how proteins work inside the cell. Partially due to the insight provided by bulk biochemical assays, individual biomolecules are often assumed to behave as identical entities, and their characterization relies on ensemble averages that flatten any conformational diversity into a unique phenotype. While the emergence of single-molecule techniques opened the gates to interrogating individual molecules, technical shortcomings typically limit the duration of these measurements, which precludes a complete characterization of an individual protein and, hence, capturing the heterogeneity among molecular populations. Here, we introduce an ultrastable magnetic tweezers design, which enables us to measure the folding dynamics of a single protein during several uninterrupted days with high temporal and spatial resolution. Thanks to this instrumental development, we fully characterize the nanomechanics of two proteins with a very distinct force response, the talin R3IVVI domain and protein L. Days-long recordings on the same protein individual accumulate thousands of folding transitions with submicrosecond resolution, allowing us to reconstruct their free energy landscapes and describe how they evolve with force. By mapping the nanomechanical identity of many different protein individuals, we directly capture their molecular diversity as a quantifiable dispersion on their force response and folding kinetics. By significantly expanding the measurable timescales, our instrumental development offers a tool for profiling individual molecules, opening the gates to directly characterizing biomolecular heterogeneity.

Chirality effects in molecular chainmail.

Motivated by the observation of positive Gaussian curvature in kinetoplast DNA networks, we consider the effect of linking chirality in square lattice molecular chainmail networks using Langevin dynamics simulations and constrained gradient optimization. Linking chirality here refers to ordering of over-under versus under-over linkages between a loop and its neighbors. We consider fully alternating linking, maximally non-alternating, and partially non-alternating linking chiralities. We find that in simulations of polymer chainmail networks, the linking chirality dictates the sign of the Gaussian curvature of the final state of the chainmail membranes. Alternating networks have positive Gaussian curvature, similar to what is observed in kinetoplast DNA networks. Maximally non-alternating networks form isotropic membranes with negative Gaussian curvature. Partially non-alternating networks form flat diamond-shaped sheets which undergo a thermal folding transition when sufficiently large, similar to the crumpling transition in tethered membranes. We further investigate this topology-curvature relationship on geometric grounds by considering the tightest possible configurations and the constraints that must be satisfied to achieve them.

Topological Reaction Coordinate Captures the Folding Transition State Ensemble in a Pierced Lasso Protein.

Proteins with a pierced lasso topology (PLT) have a covalent loop created by a disulfide bond, and the backbone circles back to thread the loop. This threaded topology has unique features compared to knotted topologies; notably, the topology is controlled by the chemical environment and the covalent loop remains intact even when denatured. In this work, we use the hormone leptin as our model PLT system and study its folding using molecular dynamics simulations that employ a structure-based (Go̅-like) model. We find that the reduced protein has a two-state folding mechanism with a transition state ensemble (TSE) that can be characterized by the reaction coordinate Q, the fraction of native contacts formed. In contrast, the oxidized protein, which must thread part of the polypeptide chain through a covalent loop, has a folding process that is poorly characterized by Q. Instead, we find that a topological coordinate that monitors the residue crossing the loop can identify the TSE of oxidized leptin. By precisely identifying the predicted TSE, one may now reliably calculate theoretical phi-values for the PLT protein, thereby enabling a comparison with experimental measurements. We find the loop-threading constraint leads to noncanonical phi-values that are uniformly small because this PLT protein has a flat energy landscape through the TSE.

IraM remodels the RssB segmented helical linker to stabilize σs against degradation by ClpXP

Upon Mg2+ starvation, a condition often associated with virulence, enterobacteria inhibit the ClpXP-dependent proteolysis of the master transcriptional regulator, σs, via IraM, a poorly understood antiadaptor that prevents RssB-dependent loading of σs onto ClpXP. This inhibition results in σs accumulation and expression of stress resistance genes. Here, we report on the structural analysis of RssB bound to IraM, which reveals that IraM induces two folding transitions within RssB, amplified via a segmented helical linker. These conformational changes result in an open, yet inhibited RssB structure in which IraM associates with both the C-terminal and N-terminal domains of RssB and prevents binding of σs to the 4-5-5 face of the N-terminal receiver domain. This work highlights the remarkable structural plasticity of RssB and reveals how a stress-specific RssB antagonist modulates a core stress response pathway that could be leveraged to control biofilm formation, virulence, and the development of antibiotic resistance.

Comprehensive comparisons of crystal structure, Hirshfeld surface and thermochemical properties of two succinic acid metal complexes [LiC2H2O2]2(s) and [NaC2H2O2·3H2O]2(s)

In this work, two aqueous and nonaqueous metal complexes of succinic acid were synthesized, namely Li-succinate (CCDC: 2284044) and hexahydrate Na-succinate (CCDC: 2296979). Their crystal structures were determined by single crystal X-ray crystallography. The Li-succinate crystallizes in trigonal space group R3¯ and the hexahydrate Na-succinate in triclinic P1¯. The Hirshfeld surfaces and the corresponding 2D fingerprints of the two complexes were recorded, showing that the nature of the intermolecular interactions between Li-succinate are mainly coordination bonds and that the intermolecular interactions between hexahydrate Na-succinate are mainly intermolecular hydrogen formation. The experimental heat capacities of the two complexes in the low-temperature interval were determined using a precise automatic adiabatic calorimeter, and the polynomial equations for the variation of the heat capacities with the folding transition temperature were obtained by fitting the measured experimental heat capacities using the least squares method, on the basis of which the values of their Sulpine heat capacities at intervals of 5 K in the low temperature interval and the values of their thermodynamic functions with respect to 298.15 K were calculated. The TG/DSC curves also reveal the molecular structure of the title complexes.

Structural and dynamic mechanisms for coupled folding and tRNA recognition of a translational T-box riboswitch

T-box riboswitches are unique riboregulators where gene regulation is mediated through interactions between two highly structured RNAs. Despite extensive structural insights, how RNA-RNA interactions drive the folding and structural transitions of T-box to achieve functional conformations remains unclear. Here, by combining SAXS, single-molecule FRET and computational modeling, we elaborate the folding energy landscape of a translational T-box aptamer consisting of stems I, II and IIA/B, which Mg2+-induced global folding and tRNA binding are cooperatively coupled. smFRET measurements reveal that high Mg2+ stabilizes IIA/B and its stacking on II, which drives the pre-docking of I and II into a competent conformation, subsequent tRNA binding promotes docking of I and II to form a high-affinity tRNA binding groove, of which the essentiality of IIA/B and S-turn in II is substantiated with mutational analysis. We highlight a delicate balance among Mg2+, the intra- and intermolecular RNA-RNA interactions in modulating RNA folding and function.