Fast protein folding kinetics

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.

From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

The Role of Force Fields and Water Models in Protein Folding and Unfolding Dynamics

Protein folding is a fascinating, not fully understood phenomenon in biology. Molecular dynamics (MD) simulations are an invaluable tool to study conformational changes in atomistic detail, including folding and unfolding processes of proteins. However, the accuracy of the conformational ensembles derived from MD simulations inevitably relies on the quality of the underlying force field in combination with the respective water model. Here, we investigate protein folding, unfolding, and misfolding of fast-folding proteins by examining different force fields with their recommended water models, i.e., ff14SB with the TIP3P model and ff19SB with the OPC model. To this end, we generated long conventional MD simulations highlighting the perks and pitfalls of these setups. Using Markov state models, we defined kinetically independent conformational substates and emphasized their distinct characteristics, as well as their corresponding state probabilities. Surprisingly, we found substantial differences in thermodynamics and kinetics of protein folding, depending on the combination of the protein force field and water model, originating primarily from the different water models. These results emphasize the importance of carefully choosing the force field and the respective water model as they determine the accuracy of the observed dynamics of folding events. Thus, the findings support the hypothesis that the water model is at least equally important as the force field and hence needs to be considered in future studies investigating protein dynamics and folding in all areas of biophysics.

Experimental Evidence for Millisecond-Timescale Structural Evolution Following the Microsecond-Timescale Folding of a Small Protein

Prior work has shown that small proteins can fold (i.e., convert from unstructured to structured states) within 10  μs. Here we use time-resolved solid state nuclear magnetic resonance (ssNMR) methods to show that full folding of the 35-residue villin headpiece subdomain (HP35) requires a slow annealing process that has not been previously detected. ^{13}C ssNMR spectra of frozen HP35 solutions, acquired with a variable time τ_{e} at 30 °C after rapid cooling from 95 °C and before rapid freezing, show changes on the 3-10 ms timescale, attributable to slow rearrangements of protein sidechains during τ_{e}.

The Role of Transient Intermediate Structures in the Unfolding of the Trp-Cage Fast-Folding Protein: Generating Ensembles from Time-Resolved X-ray Solution Scattering with Genetic Algorithms

The Trp-cage miniprotein is one of the smallest systems to exhibit a stable secondary structure and fast-folding dynamics, serving as an apt model system to study transient intermediates with both experimental and computational analyses. Previous spectroscopic characterizations that have been done on Trp-cage have inferred a single stable intermediate on a pathway from folded to unfolded basins. We aim to bridge the understanding of Trp-cage structural folding dynamics on microsecond-time scales, by utilizing time-resolved X-ray solution scattering to probe the temperature-induced unfolding pathway. Our results indicate the formation of a conformationally extended intermediate on the time scale of 1 μs, which undergoes complete unfolding within 5 μs. We further investigated the atomistic structural details of the unfolding pathway using a genetic algorithm to generate ensemble model fits to the scattering profiles. This analysis paves the way for direct benchmarking of theoretical models of protein folding ensembles produced with molecular dynamics simulations.

Transient On- and Off-Pathway Protein Folding Intermediate States Characterized with NMR Relaxation Dispersion

The earliest events in the folding of a protein are in general poorly understood. We used NMR R2 relaxation dispersion experiments to study transient local collapse events in the unfolded-state (U) conformational ensemble of apomyoglobin (apoMb). Local residual secondary structure (seen in regions corresponding to the A, D, E, and H helices of the folded protein) is largely unchanged over the pH range of 2.3-2.75, yet a significant pH-dependent increase in the conformational exchange contribution to the R2 relaxation rate (Rex) indicates that transient intramolecular contacts occur on a microsecond to millisecond time scale at pH 2.75. A comparison of 15N and 13CO relaxation dispersion data at pH 2.75 for residues in the A, B, G, and H regions, which participate in the earliest folding intermediates, indicates that chain collapse and secondary structure formation are rapid and concomitant. Increasingly stabilizing conditions (lower temperature, higher pH) result in the observation of a relaxation dispersion in the C, CD, and E regions of the protein, which are known to fold at later stages. Mutation of Trp14 in the A-helix region to Ala eliminates conformational exchange throughout the protein, and the mutation of hydrophobic residues in other regions results in the selective inhibition of conformational exchange in the B, G, or H regions. The R2 dispersion data for WT apoMb at pH 2.75 and 10 °C are best fit to a four-state model ABGH ⇆ AGH ⇆ U ⇆ ABCD that includes on-pathway (AGH and ABGH) and off-pathway (ABCD) transiently folded states, both of which are required to explain the behavior of the mutant proteins. The off-pathway intermediate is destabilized at higher temperatures. Our analysis provides insights into the earliest stages of apoMb folding where the collapsing polypeptide chain samples both productive and nonproductive states with stabilized secondary structure.

Protein Design: From the Aspect of Water Solubility and Stability

Water solubility and structural stability are key merits for proteins defined by the primary sequence and 3D-conformation. Their manipulation represents important aspects of the protein design field that relies on the accurate placement of amino acids and molecular interactions, guided by underlying physiochemical principles. Emulated designer proteins with well-defined properties both fuel the knowledge-base for more precise computational design models and are used in various biomedical and nanotechnological applications. The continuous developments in protein science, increasing computing power, new algorithms, and characterization techniques provide sophisticated toolkits for solubility design beyond guess work. In this review, we summarize recent advances in the protein design field with respect to water solubility and structural stability. After introducing fundamental design rules, we discuss the transmembrane protein solubilization and de novo transmembrane protein design. Traditional strategies to enhance protein solubility and structural stability are introduced. The designs of stable protein complexes and high-order assemblies are covered. Computational methodologies behind these endeavors, including structure prediction programs, machine learning algorithms, and specialty software dedicated to the evaluation of protein solubility and aggregation, are discussed. The findings and opportunities for Cryo-EM are presented. This review provides an overview of significant progress and prospects in accurate protein design for solubility and stability.

Time-resolved solid state NMR of biomolecular processes with millisecond time resolution

We review recent efforts to develop and apply an experimental approach to the structural characterization of transient intermediate states in biomolecular processes that involve large changes in molecular conformation or assembly state. This approach depends on solid state nuclear magnetic resonance (ssNMR) measurements that are performed at very low temperatures, typically 25-30 K, with signal enhancements from dynamic nuclear polarization (DNP). This approach also involves novel technology for initiating the process of interest, either by rapid mixing of two solutions or by a rapid inverse temperature jump, and for rapid freezing to trap intermediate states. Initiation by rapid mixing or an inverse temperature jump can be accomplished in approximately-one millisecond. Freezing can be accomplished in approximately 100 microseconds. Thus, millisecond time resolution can be achieved. Recent applications to the process by which the biologically essential calcium sensor protein calmodulin forms a complex with one of its target proteins and the process by which the bee venom peptide melittin converts from an unstructured monomeric state to a helical, tetrameric state after a rapid change in pH or temperature are described briefly. Future applications of millisecond time-resolved ssNMR are also discussed briefly.

Direct Observation of Single-Protein Transition State Passage by Nanopore Ionic Current Jumps

Conformational transitions of proteins are governed by chemical kinetics, often toggled by passage through an activated state separating two conformational ensembles. The passage time of a protein through the activated state can be too fast to be detected by single-molecule experiments without the aid of viscogenic agents. Here, we use high-bandwidth nanopore measurements to resolve microsecond-duration transitions that occur between conformational states of individual protein molecules partly blocking pore current. We measure the transition state passage time between folded and unfolded states of a two-state λ_6-85 mutant and between metastable intermediates and the unfolded state of the multistate folder cytochrome c. Consistent with the principle of microscopic reversibility, the transition state passage time is the same for the forward and backward reactions. A passage time distribution whose tail is broader than a single exponential observed in cytochrome c suggests a multidimensional energy landscape for this protein.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Folding Intermediates, Heterogeneous Native Ensembles and Protein Function

Single domain proteins fold via diverse mechanisms emphasizing the intricate relationship between energetics and structure, which is a direct consequence of functional constraints and demands imposed at the level of sequence. On the other hand, elucidating the interplay between folding mechanisms and function is challenging in large proteins, given the inherent shortcomings in identifying metastable states experimentally and the sampling limitations associated with computational methods. Here, we show that free energy profiles and surfaces of large systems (>150 residues), as predicted by a statistical mechanical model, display a wide array of folding mechanisms with ubiquitous folding intermediates and heterogeneous native ensembles. Importantly, residues around the ligand binding or enzyme active site display a larger tendency to partially unfold and this manifests as intermediates or excited states along the folding coordinate in ligand binding domains, transcription repressors, and representative enzymes from all the six classes, including the SARS-CoV-2 receptor binding domain (RBD) of the spike protein and the protease M^pro. It thus appears that it is relatively easier to distill the imprints of function on the folding landscape of larger proteins as opposed to smaller systems. We discuss how an understanding of energetic-entropic features in ordered proteins can pinpoint specific avenues through which folding mechanisms, populations of partially structured states and function can be engineered.

The A39G FF domain folds on a volcano-shaped free energy surface via separate pathways

Conformational dynamics play critical roles in protein folding, misfolding, function, misfunction, and aggregation. While detecting and studying the different conformational states populated by protein molecules on their free energy surfaces (FESs) remain a challenge, NMR spectroscopy has emerged as an invaluable experimental tool to explore the FES of a protein, as conformational dynamics can be probed at atomic resolution over a wide range of timescales. Here, we use chemical exchange saturation transfer (CEST) to detect "invisible" minor states on the energy landscape of the A39G mutant FF domain that exhibited "two-state" folding kinetics in traditional experiments. Although CEST has mostly been limited to studies of processes with rates between ∼5 to 300 s^-1 involving sparse states with populations as low as ∼1%, we show that the line broadening that is often associated with minor state dips in CEST profiles can be exploited to inform on additional conformers, with lifetimes an order of magnitude shorter and populations close to 10-fold smaller than what typically is characterized. Our analysis of CEST profiles that exploits the minor state linewidths of the 71-residue A39G FF domain establishes a folding mechanism that can be described in terms of a four-state exchange process between interconverting states spanning over two orders of magnitude in timescale from ∼100 to ∼15,000 μs. A similar folding scheme is established for the wild-type domain as well. The study shows that the folding of this small domain proceeds through a pair of sparse, partially structured intermediates via two discrete pathways on a volcano-shaped FES.

Stabilization and Kinetics of an Adsorbed Protein Depends on the Poly(N-isopropylacrylamide) Grafting Density

The solubility transition at the lower critical solution temperature (LCST, 32 °C) of poly(N-isopropylacrylamide) (PNIPAM) is widely used as a thermal switch to rapidly and reversibly capture and release proteins and cells. It is generally assumed that proteins adsorbed to PNIPAM above the LCST are unaffected by polymer interactions. Here we show that the folding stability of the enzyme phosphoglycerate kinase (PGK) is increased by interactions with end-grafted PNIPAM films above the LCST. We systematically compare two protein mutants with different stabilities. The stabilization mirrors the degree of protein adsorption under grafting conditions studied previously. Maximum stabilization occurs when proteins adsorb to low density, collapsed polymer "mushrooms". In the denser polymer "brush" regime, protein stabilization decreases back to a value indistinguishable from the bulk solution, consistent with low protein adsorption on dense, collapsed brushes. The temperature-dependent kinetics measured by Fast Relaxation Imaging reveals that PNIPAM does not affect the overall folding/unfolding mechanism. Based on the different stabilizations of two mutants and the relaxation kinetics, we hypothesize that the polymer acts mainly by increasing the conformational entropy of the folded protein by interacting with the protein surface and less by crowding the unfolded state of PGK.

First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

Using a model β-hairpin protein as a representative example of simple two-state folders whose kinetics are uncomplicated by the presence of on- and off-pathway intermediates, it is studied how the search for the protein's native state among native-like states affects the folding kinetics. It is revealed that the first-passage time (FPT) distributions are essentially single-exponential not only for the times to overcome the free energy barrier between the unfolded and native-like states but also for the times to find the native state among the native-like ones. The FPT distributions of this type are observed through all studied two-state-like regimes of protein folding, varying from a regime close to two-state folding to a regime close to downhill folding. If the protein explores native-like states for a time much longer than the time to overcome the free energy barrier, which is characteristic of high temperatures, the resulting FPT distribution to reach the native state remains close to exponential but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like states. In particular, the mean time to overcome the free energy barrier is in reasonable agreement with the Kramers rate formula and generally far shorter than the overall MFPT to reach the native state. The observed increase of the overall MFPT, as a result of longer exploration of native-like states, may lead to an overestimate of the height of the free energy barrier between the unfolded and folded states when it is calculated from the overall MFPT.

Potential of Raman spectroscopic techniques to study proteins

Proteins are large, complex molecules responsible for various biological processes. However, protein misfolding may lead to various life-threatening diseases. Therefore, it is vital to understand the shape and structure of proteins. Despite numerous techniques, a mechanistic understanding of the protein folding process is still unclear. Therefore, new techniques are continually being explored. In the present article, we have discussed the importance of Raman spectroscopy, Raman Optical Activity (ROA) and various other advancements in Raman spectroscopy to understand protein structure and conformational changes based on the review of our earlier work and recent literature. A Raman spectrum of a protein provides unique signatures for various secondary structures like helices, beta-sheets, turns, random structures, etc., and various amino acid residues such as tyrosine, tryptophan, and phenylalanine. We have shown how Raman spectra can differentiate between bovine serum albumin (BSA) and lysozyme protein based on their difference in sequence and structure (primary, secondary and tertiary). Although it is challenging to elucidate the structure of a protein using a Raman spectrum alone, Raman spectra can be used to differentiate small changes in conformations of proteins such as BSA during melting. Various new advancements in technique and data analyses in Raman spectroscopic studies of proteins have been discussed. The last part of the review focuses on the importance of the ROA spectrum to understand additional features about proteins. The ROA spectrum is rich in information about the protein backbone due to its rigidity compared to its side chains. Furthermore, the ROA spectra of lysozyme and BSA have been presented to show how ROA provides extra information about the solvent properties of proteins.

Review of bio-optical imaging systems with a high space-bandwidth product

Optical imaging has served as a primary method to collect information about biosystems across scales-from functionalities of tissues to morphological structures of cells and even at biomolecular levels. However, to adequately characterize a complex biosystem, an imaging system with a number of resolvable points, referred to as a space-bandwidth product (SBP), in excess of one billion is typically needed. Since a gigapixel-scale far exceeds the capacity of current optical imagers, compromises must be made to obtain either a low spatial resolution or a narrow field-of-view (FOV). The problem originates from constituent refractive optics-the larger the aperture, the more challenging the correction of lens aberrations. Therefore, it is impractical for a conventional optical imaging system to achieve an SBP over hundreds of millions. To address this unmet need, a variety of high-SBP imagers have emerged over the past decade, enabling an unprecedented resolution and FOV beyond the limit of conventional optics. We provide a comprehensive survey of high-SBP imaging techniques, exploring their underlying principles and applications in bioimaging.

Polarizable and non-polarizable force fields: Protein folding, unfolding, and misfolding

Molecular dynamics simulations are an invaluable tool to characterize the dynamic motions of proteins in atomistic detail. However, the accuracy of models derived from simulations inevitably relies on the quality of the underlying force field. Here, we present an evaluation of current non-polarizable and polarizable force fields (AMBER ff14SB, CHARMM 36m, GROMOS 54A7, and Drude 2013) based on the long-standing biophysical challenge of protein folding. We quantify the thermodynamics and kinetics of the β-hairpin formation using Markov state models of the fast-folding mini-protein CLN025. Furthermore, we study the (partial) folding dynamics of two more complex systems, a villin headpiece variant and a WW domain. Surprisingly, the polarizable force field in our set, Drude 2013, consistently leads to destabilization of the native state, regardless of the secondary structure element present. All non-polarizable force fields, on the other hand, stably characterize the native state ensembles in most cases even when starting from a partially unfolded conformation. Focusing on CLN025, we find that the conformational space captured with AMBER ff14SB and CHARMM 36m is comparable, but the ensembles from CHARMM 36m simulations are clearly shifted toward disordered conformations. While the AMBER ff14SB ensemble overstabilizes the native fold, CHARMM 36m and GROMOS 54A7 ensembles both agree remarkably well with experimental state populations. In addition, GROMOS 54A7 also reproduces experimental folding times most accurately. Our results further indicate an over-stabilization of helical structures with AMBER ff14SB. Nevertheless, the presented investigations strongly imply that reliable (un)folding dynamics of small proteins can be captured in feasible computational time with current additive force fields.

Protein folding and surface interaction phase diagrams in vitro and in cells

Protein stability is subject to environmental perturbations such as pressure and crowding, as well as sticking to other macromolecules and quinary structure. Thus, the environment inside and outside the cell plays a key role in how proteins fold, interact, and function on the scale from a few molecules to macroscopic ensembles. This review discusses three aspects of protein phase diagrams: first, the relevance of phase diagrams to protein folding and function in vitro and in cells; next, how the evolution of protein surfaces impacts on interaction phase diagrams; and finally, how phase separation plays a role on much larger length-scales than individual proteins or oligomers, when liquid phase-separated regions form to assist protein function and cell homeostasis.

Unfolding bovine α-lactalbumin with T-jump: Characterizing disordered intermediates via time-resolved x-ray solution scattering and molecular dynamics simulations

The protein folding process often proceeds through partially folded transient states. Therefore, a structural understanding of these disordered states is crucial for developing mechanistic models of the folding process. Characterization of unfolded states remains challenging due to their disordered nature, and incorporating multiple methods is necessary. Combining the time-resolved x-ray solution scattering (TRXSS) signal with molecular dynamics (MD), we are able to characterize transient partially folded states of bovine α-lactalbumin, a model system widely used for investigation of molten globule states, during its unfolding triggered by a temperature jump. We track the unfolding process between 20 µs and 70 ms and demonstrate that it passes through three distinct kinetic states. The scattering signals associated with these transient species are then analyzed with TRXSS constrained MD simulations to produce protein structures that are compatible with the input signals. Without utilizing any experimentally extracted kinetic information, the constrained MD simulation successfully drove the protein to an intermediate molten globule state; signals for two later disordered states are refined to terminal unfolded states. From our examination of the structural characteristics of these disordered states, we discuss the implications disordered states have on the folding process, especially on the folding pathway. Finally, we discuss the potential applications and limitations of this method.

Downhill, Ultrafast and Fast Folding Proteins Revised

Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form.

Effect of Structure on Polypeptide Blobs: A Model Study Using Poly(l-lysine)

The conformation of a series of pyrene-labeled poly(l-lysine)s (Py-PLLs) in 60:40 and 90:10 (v/v) acetonitrile:water mixtures was determined by comparing the results obtained from the fluorescence blob model (FBM) analysis of their fluorescence decays with those obtained from molecular mechanics optimizations (MMOs). PLL aggregates formed in both solutions as demonstrated by FRET experiments between naphthalene- and pyrene-labeled PLLs. Addition of an excess of unlabeled PLL allowed the conformational study of isolated Py-PLL embedded in a matrix of unlabeled PLLs. By varying the acetonitrile (ACN) content of the solution from 60 to 90 vol % ACN, Py-PLL was found to undergo a conformational change from a random coil to an α-helix. The conformational change induced an increase in the maximum number of lysines (N_blob) separating two pyrene-labeled lysines that could still form an excimer between an excited- and a ground-state pyrene. N_blob obtained from the FBM analysis increased from 15.2 ± 2.1 to 25.2 ± 1.2 lysines as PLL changed its conformation from a random coil to an α-helix. AFM revealed that the α-helical PLLs organized themselves into structured bundles ∼22 nm in diameter. The FBM analysis of the decays acquired with a solution of aggregated Py-PLLs in a 90:10 ACN:water mixture yielded a larger N_blob value of 36.6 ± 3.4. The increase in N_blob indicated that the Py-PLL constructs could now interact with one another in the helical bundles. This increase in N_blob was then used in conjunction with MMOs to determine an interhelical spacing of 2.9 ± 0.1 nm for Py-PLLs in a bundle. This interhelical spacing resulted in a local density of 0.25 ± 0.01 g·cm^-3 for the bundles of PLL α-helices, which was a reasonable density for a protein in solution. This study describes an experimental means to probe the number of amino acids that interact with each other as the conformation of a polypeptide evolves from that of a random coil to that of an α-helix to finally that of a bundle of α-helices.

Folding and Unfolding of the Short Light-Triggered β-Hairpin Peptide AzoChignolin Occurs within 100 ns

To map the underlying molecular mechanisms of folding dynamics in proteins, light-operated peptides have emerged as promising tools. In this study, we reveal the complete sequence of light-induced structural changes of AzoChignolin, a short β-hairpin peptide containing an azobenzene photoswitch in its loop region. Light-triggered structural changes were monitored by time-resolved IR spectroscopy. Formation and destruction of the hairpin structure is very fast and occurs within 100 ns for AzoChignolin in methanol. Atomistic molecular dynamics simulations using two explicit solvents, methanol and water, revealed the underlying molecular processes and allowed us to gain further insight into the reaction mechanism. Despite its rapid reaction time, hairpin formation in these solvents is not force-driven by the molecular switch but proceeded via formation of interstrand hydrogen bonds and contacts between aromatic residues. Moreover, the combined experimental and theoretical study demonstrates that the solvent (methanol vs water) does not dictate the velocity of β-hairpin formation in the AzoChignolin peptide comprising only a few hydrophobic residues in the strands.

Proteins: "Boil 'Em, Mash 'Em, Stick 'Em in a Stew"

Cells of the vast majority of organisms are subject to temperature, pressure, pH, ionic strength, and other stresses. We discuss these effects in the light of protein folding and protein interactions in vitro, in complex environments, in cells, and in vivo. Protein phase diagrams provide a way of organizing different structural ensembles that occur under stress and how one can move among ensembles. Experiments that perturb biomolecules in vitro or in cells by stressing them have revealed much about the underlying forces that are competing to control protein stability, folding, and function. Two phenomena that emerge and serve to broadly classify effects of the cellular environment are crowding (mainly due to repulsive forces) and sticking (mainly due to attractive forces). The interior of cells is closely balanced between these emergent effects, and stress can tip the balance one way or the other. The free energy scale involved is small but significant on the scale of the "on/off switches" that control signaling in cells or of protein-protein association with a favorable function such as increased enzyme processivity. Quantitative tools from biophysical chemistry will play an important role in elucidating the world of crowding and sticking under stress.

How the dyes affect folding of small proteins in single-molecule FRET experiments: A simulation study

A key question in the application of the single-molecule Förster resonance energy transfer (smFRET) technique to study protein folding is how the dyes affect the protein behavior. Understanding of these effects is particularly important for small proteins, for which the dyes, along with their linkers, can be comparable in size (mass) with the protein. Using a coarse-grained model, we simulated folding of BBL protein and two of its FRET constructs. The obtained results suggest that even for small proteins, such as the 45-residue BBL, the appearance of the excluded volume in the protein conformation space due to the presence of dyes does not change the overall picture of folding. At the same time, some deviations from folding of the original protein are observed, in particular, the FRET constructs fold considerably slower than the original protein because the protein collapse in the initial state of folding is slowed down due to the protein loading with relatively massive dyes.

CalFitter: a web server for analysis of protein thermal denaturation data

Despite significant advances in the understanding of protein structure-function relationships, revealing protein folding pathways still poses a challenge due to a limited number of relevant experimental tools. Widely-used experimental techniques, such as calorimetry or spectroscopy, critically depend on a proper data analysis. Currently, there are only separate data analysis tools available for each type of experiment with a limited model selection. To address this problem, we have developed the CalFitter web server to be a unified platform for comprehensive data fitting and analysis of protein thermal denaturation data. The server allows simultaneous global data fitting using any combination of input data types and offers 12 protein unfolding pathway models for selection, including irreversible transitions often missing from other tools. The data fitting produces optimal parameter values, their confidence intervals, and statistical information to define unfolding pathways. The server provides an interactive and easy-to-use interface that allows users to directly analyse input datasets and simulate modelled output based on the model parameters. CalFitter web server is available free at https://loschmidt.chemi.muni.cz/calfitter/.

Application of millisecond time-resolved solid state NMR to the kinetics and mechanism of melittin self-assembly

Common experimental approaches for characterizing structural conversion processes such as protein folding and self-assembly do not report on all aspects of the evolution from an initial state to the final state. Here, we demonstrate an approach that is based on rapid mixing, freeze-trapping, and low-temperature solid-state NMR (ssNMR) with signal enhancements from dynamic nuclear polarization (DNP). Experiments on the folding and tetramerization of the 26-residue peptide melittin following a rapid pH jump show that multiple aspects of molecular structure can be followed with millisecond time resolution, including secondary structure at specific isotopically labeled sites, intramolecular and intermolecular contacts between specific pairs of labeled residues, and overall structural order. DNP-enhanced ssNMR data reveal that conversion of conformationally disordered melittin monomers at low pH to α-helical conformations at neutral pH occurs on nearly the same timescale as formation of antiparallel melittin dimers, about 6 to 9 ms for 0.3 mM melittin at 24 °C in aqueous solution containing 20% (vol/vol) glycerol and 75 mM sodium phosphate. Although stopped-flow fluorescence data suggest that melittin tetramers form quickly after dimerization, ssNMR spectra show that full structural order within melittin tetramers develops more slowly, in ∼60 ms. Time-resolved ssNMR is likely to find many applications to biomolecular structural conversion processes, including early stages of amyloid formation, viral capsid formation, and protein-protein recognition.

Stabilizing and Understanding a Miniprotein by Rational Redesign

Miniproteins reduce the complexity of the protein-folding problem allowing systematic studies of contributions to protein folding and stabilization. Here, we describe the rational redesign of a miniprotein, PPα, comprising a polyproline II helix, a loop, and an α helix. The redesign provides a de novo framework for interrogating noncovalent interactions. Optimized PPα has significantly improved thermal stability with a midpoint unfolding temperature (T_M) of 51 °C. Its nuclear magnetic resonance structure indicates a density of stabilizing noncovalent interactions that is higher than that of the parent peptide, specifically an increased number of CH-π interactions. In part, we attribute this to improved long-range electrostatic interactions between the two helical elements. We probe further sequence-stability relationships in the miniprotein through a series of rational mutations.

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.

Modeling of Multicolor Single-Molecule Förster Resonance Energy-Transfer Experiments on Protein Folding

Using a coarse-grained, C_α-model of BBL protein, a multicolor single-molecule Förster resonance energy transfer (FRET) experiment is modeled. Three fluorophores are introduced, which, for simplicity, are associated with C_α beads. Two fluorophores are placed at the ends of protein chain and the third one at the middle of the chain. The free-energy surfaces (FESs) depending on the interfluorophore distances and on the FRET efficiencies corresponding to these distances have been constructed and compared with the FESs depending on the conventional collective variables, such as the fraction of native contacts and radius of gyration. It has been found that multicolor experiments can successfully resolve all essential BBL states that are revealed by the conventional FESs. The resolution of these states with the FRET-efficiency histogram is found to be successful if the energy transfer is measured between the fluorophores at the BBL ends. We also show that, although the present model construct of BBL is very simple, it captures some characteristic features of the single-molecule FRET experiments, such as the pattern of the FRET-efficiency histograms and their evolution with the denaturant concentration.

Transition-path properties for folding reactions in the limit of small barriers

Transition paths are of great interest because they encapsulate information about the mechanisms of barrier-crossing reactions. Analysis of experiments measuring biomolecular folding reactions has relied on expressions for properties of transition paths such as transition-path times and velocities that hold in the limit of large harmonic barriers, but real molecules often have relatively small barriers. Recent theoretical work presented more general expressions for transition-path properties. Here we extend this work, deriving expressions from the general case that can be applied to small harmonic barriers. We first compared the performance of small-barrier, large-barrier, and general solutions when applied to simulated transitions, focusing on improvements in estimates of the diffusion coefficient determined from transition times and velocities. We then applied these expressions to experimental data from force spectroscopy measurements of DNA hairpins. We found that the low-barrier approximation and exact solution reduced or resolved the small but systematic inconsistencies that had arisen from assuming large harmonic barriers, demonstrating the practical utility of the new equations for analyzing experimental data.

Protein Folding Cooperativity and Thermodynamic Barriers of the Simplest β-Sheet Fold: A Survey of WW Domains

Theory and experiments have shown that microsecond folding proteins exhibit characteristic thermodynamic properties that reflect the limited cooperativity of folding over marginal barriers (downhill folding). Those studies have mostly focused on proteins with large α-helical contents and small size, which tend to be the fastest folders. A key open question is whether such properties are also present in the fastest all-β proteins. We address this issue by investigating the unfolding thermodynamics of a collection of WW domains as representatives of the simplest β-sheet fold. WW domains are small microsecond folders, although they do not fold as fast as their α-helical counterparts. In previous work on the NEDD4-WW4 domain, we reported deviations from two-state thermodynamics that were less apparent and thus suggestive of an incipient downhill scenario. Here we investigate the unfolding thermodynamics of four other WW domains (NEDD4-WW3, YAP65-WW1(L30K), FBP11-WW1, and FBP11-WW2) by performing all of the thermodynamic tests for downhill folding that have been previously developed on α-helical proteins. This set of five WW domains shares low sequence identity and include examples from two specificity classes, thus providing a comprehensive survey. Thermodynamic analysis of the four new WW domains consistently reveals all of the properties of downhill folding equilibria, which are in all cases more marked than what we found before in NEDD4-WW4. Our results show that fast-folding all-β proteins do share limited cooperativity and gradual unfolding thermodynamics with fast α-helical proteins and suggest that the free energy barrier to folding of natural proteins is mostly determined by size and fold topology and much less by the specific amino acid sequence.

Probabilistic analysis for identifying the driving force of protein folding

Toward identifying the driving force of protein folding, energetics was analyzed in water for Trp-cage (20 residues), protein G (56 residues), and ubiquitin (76 residues) at their native (folded) and heat-denatured (unfolded) states. All-atom molecular dynamics simulation was conducted, and the hydration effect was quantified by the solvation free energy. The free-energy calculation was done by employing the solution theory in the energy representation, and it was seen that the sum of the protein intramolecular (structural) energy and the solvation free energy is more favorable for a folded structure than for an unfolded one generated by heat. Probabilistic arguments were then developed to determine which of the electrostatic, van der Waals, and excluded-volume components of the interactions in the protein-water system governs the relative stabilities between the folded and unfolded structures. It was found that the electrostatic interaction does not correspond to the preference order of the two structures. The van der Waals and excluded-volume components were shown, on the other hand, to provide the right order of preference at probabilities of almost unity, and it is argued that a useful modeling of protein folding is possible on the basis of the excluded-volume effect.

Roles of conformational disorder and downhill folding in modulating protein-DNA recognition

Transcription factors are thought to efficiently search for their target DNA site via a combination of conventional 3D diffusion and 1D diffusion along the DNA molecule mediated by non-specific electrostatic interactions. This process requires the DNA-binding protein to quickly exchange between a search competent and a target recognition mode, but little is known as to how these two binding modes are encoded in the conformational properties of the protein. Here, we investigate this issue on the engrailed homeodomain (EngHD), a DNA-binding domain that folds ultrafast and exhibits a complex conformational behavior consistent with the downhill folding scenario. We explore the interplay between folding and DNA recognition using a coarse-grained computational model that allows us to manipulate the folding properties of the protein and monitor its non-specific and specific binding to DNA. We find that conformational disorder increases the search efficiency of EngHD by promoting a fast gliding search mode in addition to sliding. When gliding, EngHD remains loosely bound to DNA moving linearly along its length. A partially disordered EngHD also binds more dynamically to the target site, reducing the half-life of the specific complex via a spring-loaded mechanism. These findings apply to all conditions leading to partial disorder. However, we also find that at physiologically relevant temperatures EngHD is well folded and can only obtain the conformational flexibility required to accelerate 1D diffusion when it folds/unfolds within the downhill scenario (crossing a marginal free energy barrier). In addition, the conformational flexibility of native downhill EngHD enables its fast reconfiguration to lock into the specific binding site upon arrival, thereby affording finer control of the on- and off-rates of the specific complex. Our results provide key mechanistic insights into how DNA-binding domains optimize specific DNA recognition through the control of their conformational dynamics and folding mechanism.

Global analysis of protein folding using massively parallel design, synthesis, and testing

Proteins fold into unique native structures stabilized by thousands of weak interactions that collectively overcome the entropic cost of folding. Although these forces are "encoded" in the thousands of known protein structures, "decoding" them is challenging because of the complexity of natural proteins that have evolved for function, not stability. We combined computational protein design, next-generation gene synthesis, and a high-throughput protease susceptibility assay to measure folding and stability for more than 15,000 de novo designed miniproteins, 1000 natural proteins, 10,000 point mutants, and 30,000 negative control sequences. This analysis identified more than 2500 stable designed proteins in four basic folds-a number sufficient to enable us to systematically examine how sequence determines folding and stability in uncharted protein space. Iteration between design and experiment increased the design success rate from 6% to 47%, produced stable proteins unlike those found in nature for topologies where design was initially unsuccessful, and revealed subtle contributions to stability as designs became increasingly optimized. Our approach achieves the long-standing goal of a tight feedback cycle between computation and experiment and has the potential to transform computational protein design into a data-driven science.

Disulfide driven folding for a conditionally disordered protein

Conditionally disordered proteins are either ordered or disordered depending on the environmental context. The substrates of the mitochondrial intermembrane space (IMS) oxidoreductase Mia40 are synthesized on cytosolic ribosomes and diffuse as intrinsically disordered proteins to the IMS, where they fold into their functional conformations; behaving thus as conditionally disordered proteins. It is not clear how the sequences of these polypeptides encode at the same time for their ability to adopt a folded structure and to remain unfolded. Here we characterize the disorder-to-order transition of a Mia40 substrate, the human small copper chaperone Cox17. Using an integrated real-time approach, including chromatography, fluorescence, CD, FTIR, SAXS, NMR, and MS analysis, we demonstrate that in this mitochondrial protein, the conformational switch between disordered and folded states is controlled by the formation of a single disulfide bond, both in the presence and in the absence of Mia40. We provide molecular details on how the folding of a conditionally disordered protein is tightly regulated in time and space, in such a way that the same sequence is competent for protein translocation and activity.

Disulfide driven folding for a conditionally disordered protein

Conditionally disordered proteins are either ordered or disordered depending on the environmental context. The substrates of the mitochondrial intermembrane space (IMS) oxidoreductase Mia40 are synthesized on cytosolic ribosomes and diffuse as intrinsically disordered proteins to the IMS, where they fold into their functional conformations; behaving thus as conditionally disordered proteins. It is not clear how the sequences of these polypeptides encode at the same time for their ability to adopt a folded structure and to remain unfolded. Here we characterize the disorder-to-order transition of a Mia40 substrate, the human small copper chaperone Cox17. Using an integrated real-time approach, including chromatography, fluorescence, CD, FTIR, SAXS, NMR, and MS analysis, we demonstrate that in this mitochondrial protein, the conformational switch between disordered and folded states is controlled by the formation of a single disulfide bond, both in the presence and in the absence of Mia40. We provide molecular details on how the folding of a conditionally disordered protein is tightly regulated in time and space, in such a way that the same sequence is competent for protein translocation and activity.

Conservation of folding and association within a family of spidroin N-terminal domains

Web spiders synthesize silk fibres, nature’s toughest biomaterial, through the controlled assembly of fibroin proteins, so-called spidroins. The highly conserved spidroin N-terminal domain (NTD) is a pH-driven self-assembly device that connects spidroins to super-molecules in fibres. The degree to which forces of self-assembly is conserved across spider glands and species is currently unknown because quantitative measures are missing. Here, we report the comparative investigation of spidroin NTDs originating from the major ampullate glands of the spider species Euprosthenops australis, Nephila clavipes, Latrodectus hesperus, and Latrodectus geometricus. We characterized equilibrium thermodynamics and kinetics of folding and self-association using dynamic light scattering, stopped-flow fluorescence and circular dichroism spectroscopy in combination with thermal and chemical denaturation experiments. We found cooperative two-state folding on a sub-millisecond time scale through a late transition state of all four domains. Stability was compromised by repulsive electrostatic forces originating from clustering of point charges on the NTD surface required for function. pH-driven dimerization proceeded with characteristic fast kinetics yielding high affinities. Results showed that energetics and kinetics of NTD self-assembly are highly conserved across spider species despite the different silk mechanical properties and web geometries they produce.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈R_g〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈R_g〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈R_g〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈R_g〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R_g² distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.

How fast fast-folding proteins fold in silico

In reported microcanonical molecular dynamics simulations, fast-folding proteins CLN025 and Trp-cage autonomously folded to experimentally determined native conformations. However, the folding times of these proteins derived from the simulations were more than 4-10 times longer than their experimental values. This article reports autonomous folding of CLN025 and Trp-cage in isobaric-isothermal molecular dynamics simulations with agreements within factors of 0.69-1.75 between simulated and experimental folding times at different temperatures. These results show that CLN025 and Trp-cage can now autonomously fold in silico as fast as in experiments, and suggest that the accuracy of folding simulations for fast-folding proteins begins to overlap with the accuracy of folding experiments. This opens new prospects of developing computer algorithms that can predict both ensembles of conformations and their interconversion rates for a protein from its sequence for artificial intelligence on how and when a protein acts as a receiver, switch, and relay to facilitate various subcellular-to-tissue communications. Then the genetic information that encodes proteins can be better read in the context of intricate biological functions.