Folding Transition Temperature Research Articles

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.

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.

Folding and escape of nascent proteins at ribosomal exit tunnel.

We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein.

Relaxation mode analysis and Markov state relaxation mode analysis for chignolin in aqueous solution near a transition temperature.

It is important to extract reaction coordinates or order parameters from protein simulations in order to investigate the local minimum-energy states and the transitions between them. The most popular method to obtain such data is principal component analysis, which extracts modes of large conformational fluctuations around an average structure. We recently applied relaxation mode analysis for protein systems, which approximately estimates the slow relaxation modes and times from a simulation and enables investigations of the dynamic properties underlying the structural fluctuations of proteins. In this study, we apply this relaxation mode analysis to extract reaction coordinates for a system in which there are large conformational changes such as those commonly observed in protein folding/unfolding. We performed a 750-ns simulation of chignolin protein near its folding transition temperature and observed many transitions between the most stable, misfolded, intermediate, and unfolded states. We then applied principal component analysis and relaxation mode analysis to the system. In the relaxation mode analysis, we could automatically extract good reaction coordinates. The free-energy surfaces provide a clearer understanding of the transitions not only between local minimum-energy states but also between the folded and unfolded states, even though the simulation involved large conformational changes. Moreover, we propose a new analysis method called Markov state relaxation mode analysis. We applied the new method to states with slow relaxation, which are defined by the free-energy surface obtained in the relaxation mode analysis. Finally, the relaxation times of the states obtained with a simple Markov state model and the proposed Markov state relaxation mode analysis are compared and discussed.

Effects of macromolecular crowding on protein folding

Folding of proteins in vivo is influenced by the presence of a high concentration of macromolecules in the cytosol. In this study we investigate the effects of macromolecular crowding on folding of proteins by using molecular dynamics simulation method with Langevin equations. The protein is considered in a Go-like model whereas crowders are modeled as soft spheres. In our simulations, protein and crowders are enclosed in a spherical container. It is shown that the crowders enhance the folding transition temperature as well as folding stability of protein. The effect of crowders on the folding free energy is found to agree with Minton's scaled particle theory.

Transition Path Times in Protein Folding Studied by Structure-Based Simulation

In trajectories of protein folding and unfolding processes, the transition path that connects denatured and native states is the most interesting part. Recently, single-molecule FRET experiments together with a statistical inference theory successfully identified the transition path times for folding of some small proteins. Yet, its underlying physics is poorly understood. Here we conducted a comprehensive survey of transition path times for 29 small-to-medium two-state-folding proteins using structure-based coarse-grained molecular dynamics simulations. Using the multi-canonical ensemble method, we first identified folding transition temperature accurately. At the transition temperature, we then performed relatively long simulations observing reversible folding and unfolding events, from which we identified and analyzed the transition path times. The distribution of transition path time for each protein can be explained as free diffusion of particle in a reaction coordinate. We sought what reaction coordinates correlate with the transition path time. Among tested coordinates, we found that the average transition path time is most strongly correlated to the difference in the numbers of native contacts, i.e., contact energies, between native and denatured states. These results imply that the transition path time series can be approximated as the nearly free diffusion in the reaction coordinate of native contacts.

Improvement of the Treatment of Loop Structures in the UNRES Force Field by Inclusion of Coupling between Backbone- and Side-Chain-Local Conformational States

The UNited RESidue (UNRES) coarse-grained model of polypeptide chains, developed in our laboratory, enables us to carry out millisecond-scale molecular-dynamics simulations of large proteins effectively. It performs well in ab initio predictions of protein structure, as demonstrated in the last Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP10). However, the resolution of the simulated structure is too coarse, especially in loop regions, which results from insufficient specificity of the model of local interactions. To improve the representation of local interactions, in this work we introduced new side-chain-backbone correlation potentials, derived from a statistical analysis of loop regions of 4585 proteins. To obtain sufficient statistics, we reduced the set of amino-acid-residue types to five groups, derived in our earlier work on structurally optimized reduced alphabets, based on a statistical analysis of the properties of amino-acid structures. The new correlation potentials are expressed as one-dimensional Fourier series in the virtual-bond-dihedral angles involving side-chain centroids. The weight of these new terms was determined by a trial-and-error method, in which Multiplexed Replica Exchange Molecular Dynamics (MREMD) simulations were run on selected test proteins. The best average root-mean-square deviations (RMSDs) of the calculated structures from the experimental structures below the folding-transition temperatures were obtained with the weight of the new side-chain-backbone correlation potentials equal to 0.57. The resulting conformational ensembles were analyzed in detail by using the Weighted Histogram Analysis Method (WHAM) and Ward's minimum-variance clustering. This analysis showed that the RMSDs from the experimental structures dropped by 0.5 Å on average, compared to simulations without the new terms, and the deviation of individual residues in the loop region of the computed structures from their counterparts in the experimental structures (after optimum superposition of the calculated and experimental structure) decreased by up to 8 Å. Consequently, the new terms improve the representation of local structure.

Configuration-Dependent Diffusion Dynamics of Downhill and Two-State Protein Folding

Configuration-dependent diffusion (CDD) is important for protein folding kinetics with small thermodynamic barriers. CDD can be even more crucial in downhill folding without thermodynamic barriers. We explored the CDD of a downhill protein (BBL), and a two-state protein (CI2). The hidden kinetic barriers due to CDD were revealed. The increased ~1 k(B)T kinetic barrier is in line with experimental value based on other fast folding proteins. Compared to that of CI2, the effective free-energy profile of BBL is found to be significantly influenced by CDD, and the kinetics are totally determined by diffusion. These findings are consistent with both earlier bulk and single-molecule fluorescence measurements. In addition, we found the temperature dependence of CDD. We also found that the ratio of folding transition temperature against optimal kinetic folding temperature can provide both a quantitative measure for the underlying landscape topography and an indicator for the possible appearance of downhill folding. Our study can help for a better understanding of the role of diffusion in protein folding dynamics.

Enhanced Wang Landau sampling of adsorbed protein conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical "temperature" that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.

Hidden Protein Folding Pathways in Free-Energy Landscapes Uncovered by Network Analysis

A network analysis is used to uncover hidden folding pathways in free-energy landscapes usually defined in terms of such arbitrary order parameters as root-mean-square deviation from the native structure, radius of gyration, etc. The analysis has been applied to molecular dynamics (MD) trajectories of the B-domain of staphylococcal protein A, generated with the coarse-grained united-residue (UNRES) force field in a broad range of temperatures (270K ≤ T ≤ 325K). Thousands of folding pathways have been identified at each temperature. Out of these many folding pathways, several most probable ones were selected for investigation of the conformational transitions during protein folding. Unlike other conformational space network (CSN) methods, a node in the CSN variant implemented in this work is defined according to the nativelikeness class of the structure, which defines the similarity of segments of the compared structures in terms of secondary-structure, contact-pattern, and local geometry, as well as the overall geometric similarity of the conformation under consideration to that of the reference (experimental) structure. Our previous findings, regarding the folding model and conformations found at the folding-transition temperature for protein A (Maisuradze et al., J. Am. Chem. Soc. 132, 9444, 2010), were confirmed by the conformational space network analysis. In the methodology and in the analysis of the results, the shortest path identified by using the shortest-path algorithm corresponds to the most probable folding pathway in the conformational space network.

Molecular dynamics characterisations of the Trp-cage folding mechanisms: in the absence and presence of water solvents

Protein folding is an important and yet challenging topic in current molecular biology. In this work, the folding dynamics and mechanisms of the Trp-cage mini-protein were studied with molecular dynamics simulations, in the absence and presence of water solvents. The important intermediates during the Trp-cage folding were determined by gradually decreasing the simulation temperature. The folding transition temperature was identified to be approximately 400 K, and the folding pathway was decomposed into six steps: U ↔ I 1 ↔ I 2 ↔ I 3 ↔ I 4 ↔ F 1 ↔ F 2, where U, I and F represent the unfolded, intermediate and folded states, respectively. The finding that the two helical subunits are successively formed is consistent with the experimental observations, and the Asp9/Arg16 salt bridge forms at the final stage and does not play a significant role during folding kinetics. The presence of water solvents induces hydrophobic collapse as the whole cage comparatively closes. Within aqueous solutions, the Trp-cage folding begins to contract into the meta-stable state, and by traversing the transition state it arrives at the native-like structure, which resembles the experimental structure closely.

Enrichment and proteome analysis of a hyperthermostable protein set of archaeon Thermococcus onnurineus NA1

Thermococcus onnurineus NA1 is a hyperthermophilic archaeon that can be used for the screening of thermophilic enzymes. Previously, we characterized the metabolic enzymes of the cytosolic proteome by two-dimensional electrophoresis/tandem mass spectrometry (2-DE/MS-MS). In this study, we identified a subset of hyperthermostable proteins in the cytosolic proteome using enrichment by in vitro heat treatment and protein identification. After heat treatment at 100°C for 2 h, 13 and 149 proteins were identified from the soluble proteome subset by 2-DE/MS-MS and 1-DE/MS-MS analysis, respectively. Representative proteins included intracellular protease I, thioredoxin reductase, triosephosphate isomerase, putative hydroperoxide reductase, proteasome, and translation initiation factors. Intracellular protease, deblocking aminopeptidases, and fructose-1,6-bisphosphatase were overexpressed in Escherichia coli and biological activity above 85°C was confirmed. The folding transition temperature (Tm) of identified proteins was analyzed using the in silico prediction program TargetStar. The proteins enriched with the heat treatment have higher Tm than the homologous proteins from mesophilic strains. These results suggested that the heat-stable protein set of hyperthermophilic T. onnurineus NA1 can be effectively fractionated and enriched by in vitro heat treatment.

Expression and characterization of an antifreeze protein from the perennial rye grass, Lolium perenne

Antifreeze proteins (AFP) are an evolutionarily diverse class of stress response products best known in certain metazoans that adopt a freeze-avoidance survival strategy. The perennial ryegrass, Lolium perenne ( Lp), cannot avoid winter temperatures below the crystallization point and is thought to use its LpAFP in a freeze-tolerant strategy. In order to examine properties of LpAFP in relation to L. perenne’s life history, cDNA cloning, recombinant protein characterization, ice-binding activities, gene copy number, and expression responses to low temperature were examined. Transcripts, encoded by only a few gene copies, appeared to increase in abundance after diploid plants were transferred to 4 °C for 1–2 days, and in parallel with the ice recrystallization inhibition activities. Circular dichroism spectra of recombinant LpAFP showed three clear folding transition temperatures including one between 10 and 15 °C, suggesting to us that folding modifications of the secreted AFP could allow the targeted degradation of the protein in planta when temperatures increase. Although LpAFP showed low thermal hysteresis activity and partitioning into ice, it was similar to AFPs from freeze-avoiding organisms in other respects. Therefore, the type of low temperature resistance strategy adopted by a particular species may not depend on the type of AFP. The independence of AFP sequence and life-history has practical implications for the development of genetically-modified crops with enhanced freeze tolerance.

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.

Evidence, from Simulations, of a Single State with Residual Native Structure at the Thermal Denaturation Midpoint of a Small Globular Protein

The folding of the B-domain of staphylococcal protein A has been studied by coarse-grained canonical and multiplexed replica-exchange molecular dynamics simulations with the UNRES force field in a broad range of temperatures (270 K < or = T < or = 350 K). In canonical simulations, the folding was found to occur either directly to the native state or through kinetic traps, mainly the topological mirror image of the native three-helix bundle. The latter folding scenario was observed more frequently at low temperatures. With increase of temperature, the frequency of the transitions between the folded and misfolded/unfolded states increased and the folded state became more diffuse with conformations exhibiting increased root-mean-square deviations from the experimental structure (from about 4 A at T = 300 K to 8.7 A at T = 325 K). An analysis of the equilibrium conformational ensemble determined from multiplexed replica exchange simulations at the folding-transition temperature (T(f) = 325 K) showed that the conformational ensemble at this temperature is a collection of conformations with residual secondary structures, which possess native or near-native clusters of nonpolar residues in place, and not a 50-50% mixture of fully folded and fully unfolded conformations. These findings contradict the quasi-chemical picture of two- or multistate protein folding, which assumes an equilibrium between the folded, unfolded, and intermediate states, with equilibrium shifting with temperature but with the native conformations remaining essentially unchanged. Our results also suggest that long-range hydrophobic contacts are the essential factor to keep the structure of a protein thermally stable.

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp-cage miniprotein using detailed molecular dynamics simulations of an all-atom model of the protein in explicit solvent using the Amberff99SB force field. Replica-exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 mus/replica timescale. The total simulation time used in the calculations exceeds 100 mus. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, DeltaG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The DeltaG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure-induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T(f) = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins.

Effect of solvation-related interaction on the low-temperature dynamics of proteins

The effect of solvation-related interaction on the low-temperature dynamics of proteins is studied by taking into account the desolvation barriers in the interactions of native contacts. It is found out that about the folding transition temperature, the protein folds in a cooperative manner, and the water molecules are expelled from the hydrophobic core at the final stage in the folding process. At low temperature, however, the protein would generally be trapped in many metastable conformations with some water molecules frozen inside the protein. The desolvation takes an important role in these processes. The number of frozen water molecules and that of frozen states of proteins are further analyzed with the methods based on principal component analysis (PCA) and the clustering of conformations. It is found out that both the numbers of frozen water molecules and the frozen states of the protein increase quickly below a certain temperature. Especially, the number of frozen states of the protein increases exponentially following the decrease in the temperature, which resembles the basic features of glassy dynamics. Interestingly, it is observed that the freezing of water molecules and that of protein conformations happen at almost the same temperature. This suggests that the solvation-related interaction performs an important role for the low-temperature dynamics of the model protein.

Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field.

Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .

The folding of knotted proteins: insights from lattice simulations

We carry out systematic Monte Carlo simulations of Gō lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.

Calculation of Protein Heat Capacity from Replica-Exchange Molecular Dynamics Simulations with Different Implicit Solvent Models

The heat capacity has played a major role in relating microscopic and macroscopic properties of proteins and their disorder-order phase transition of folding. Its calculation by atomistic simulation methods remains a significant challenge due to the complex and dynamic nature of protein structures, their solvent environment, and configurational averaging. To better understand these factors on calculating a protein heat capacity, we provide a comparative analysis of simulation models that differ in their implicit solvent description and force-field resolution. Our model protein system is the src Homology 3 (SH3) domain of alpha-spectrin, and we report a series of 10 ns replica-exchange molecular dynamics simulations performed at temperatures ranging from 298 to 550 K, starting from the SH3 native structure. We apply the all-atom CHARMM22 force field with different modified analytical generalized Born solvent models (GBSW and GBMV2) and compare these simulation models with the distance-dependent dielectric screening of charge-charge interactions. A further comparison is provided with the united-atom CHARMM19 plus a pairwise GB model. Unfolding-folding transition temperatures of SH3 were estimated from the temperature-dependent profiles of the heat capacity, root-mean-square distance from the native structure, and the fraction of native contacts, each calculated from the density of states by using the weighted histogram analysis method. We observed that, for CHARMM22, the unfolding transition and energy probability density were quite sensitive to the implicit solvent description, in particular, the treatment of the protein-solvent dielectric boundary in GB models and their surface-area-based hydrophobic term. Among the solvent models tested, the calculated melting temperature varied in the range 353-438 K and was higher than the experimental value near 340 K. A reformulated GBMV2 model of employing a smoother molecular-volume dielectric interface was the most accurate in reproducing the native conformation and a two-state folding landscape, although the melting transition temperature did not show the smallest deviation from experiment. For the lower-resolution CHARMM19/GB model, the simulations failed to yield a bimodal energy distribution, yet the melting temperature was observed to be a good estimate of higher-resolution simulation models. We also demonstrate that a careful analysis of a relatively long simulation is necessary to avoid trapping in local minima and to find a true thermodynamic transition temperature.