Folding Transition Temperature Research Articles

Coarse-grained lattice model simulations of sequence-structure fitness of a ribosome-inactivating protein

Many realistic protein-engineering design problems extend beyond the computational limits of what is considered practical when applying all-atom molecular-dynamics simulation methods. Lattice models provide computationally robust alternatives, yet most are regarded as too simplistic to accurately capture the details of complex designs. We revisit a coarse-grained lattice simulation model and demonstrate that a multiresolution modeling approach of reconstructing all-atom structures from lattice chains is of sufficient accuracy to resolve the comparability of sequence-structure modifications of the ricin A-chain (RTA) protein fold. For a modeled structure, the unfolding-folding transition temperature was calculated from the heat capacity using either the potential energy from the lattice model or the all-atom CHARMM19 force-field plus a generalized Born solvent approximation. We found, that despite the low-resolution modeling of conformational states, the potential energy functions were capable of detecting the relative change in the thermodynamic transition temperature that distinguishes between a protein design and the native RTA fold in excellent accord with reported experimental studies of thermal denaturation. A discussion is provided of different sequences fitted to the RTA fold and a possible unfolding model.

Reversible Stiffening Transition in β-Hairpin Hydrogels Induced by Ion Complexation

We have previously shown that properly designed lysine and valine-rich peptides undergo a random coil to beta-hairpin transition followed by intermolecular self-assembly into a fibrillar hydrogel network only after the peptide solutions are heated above the intramolecular folding transition temperature. Here we report that these hydrogels also undergo a stiffening transition as they are cooled below a critical temperature only when boric acid is used to buffer the peptide solution. This stiffening transition is characterized by rheology, dynamic light scattering, and small angle neutron scattering. Rheological measurements show that the stiffening transition causes an increase in the hydrogel storage modulus (G') by as much as 1 order of magnitude and is completely reversible on subsequently raising the temperature. Although this reversible transition exhibits rheological properties that are similar to polyol/borax solutions, the underlying mechanism does not involve hydroxyl-borate complexation. The stiffening transition is mainly caused by the interactions between lysine and boric acid/borate anion and is not driven by the changes in the secondary structure of the beta-hairpin peptide. Addition of glucose to boric acid and peptide solution disrupts the stiffening transition due to competitive glucose-borate complexation.

NEW METHOD OF EVALUATING RELATIVE THERMAL STABILITIES OF PROTEINS BASED ON THEIR AMINO ACID SEQUENCES: TARGETSTAR

Several computational methods have been developed to solve the problem of protein thermostabilization. One common drawback of them is that they must have the information of a backbone structure of a protein for the generation of a proper amino acid sequence. In this paper, we propose a new method called TargetStar by incorporating computational biology and statistical physics, in which an approximate partition function and a specific heat are used to calculate the folding transition temperature of a protein and then to predict the relative thermal stabilities for given proteins based only on their amino acid sequences. To evaluate the prediction accuracy of TargetStar, we calculated folding transition temperatures of 289 orthologous protein pairs using the proposed method, where each protein pair contains one hyperthermophilic protein and one mesophilic protein. According to our evaluation, hyperthermophilic and mesophilic proteins are distinguished from each other in terms of relative thermal stabilities with 77% prediction accuracy. Thus, TargetStar may serve as an efficient method to design an amino acid sequence of a target protein with the desired thermal stability prior to the expensive and time-consuming mutagenesis experiment.

Temperature-Dependent Folding Pathways of Pin1 WW Domain: An All-Atom Molecular Dynamics Simulation of a Gō Model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded β-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small β-protein at its folding transition temperature has a well-established hairpin 1 made of β1 and β2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of β2 and β3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.

The Length Dependence of the PolyQ-mediated Protein Aggregation

Polyglutamine (polyQ) repeat disorders are caused by the expansion of CAG tracts in certain genes, resulting in transcription of proteins with abnormally long polyQ inserts. When these inserts expand beyond 35-45 glutamines, affected proteins form toxic aggregates, leading to neuron death. Chymotrypsin inhibitor 2 (CI2) with an inserted glutamine repeat has previously been used to model polyQ-mediated aggregation in vitro. However, polyQ insertion lengths in these studies have been kept below the pathogenic threshold. We perform molecular dynamics simulations to study monomer folding dynamics and dimer formation in CI2-polyQ chimeras with insertion lengths of up to 80 glutamines. Our model recapitulates the experimental results of previous studies of chimeric CI2 proteins, showing high folding cooperativity of monomers as well as protein association via domain swapping. Surprisingly, for chimeras with insertion lengths above the pathogenic threshold, monomer folding cooperativity decreases and the dominant mode for dimer formation becomes interglutamine hydrogen bonding. These results support a mechanism for pathogenic polyQ-mediated aggregation, in which expanded polyQ tracts destabilize affected proteins and promote the formation of partially unfolded intermediates. These unfolded intermediates form aggregates through associations by interglutamine interactions.

Protein folding with the adaptive tempering Monte Carlo method

Characterization of the folding transition in a model protein was achieved with the recent multicanonical tempering method implemented with Monte Carlo the adaptive tempering Monte Carlo (ATMC) (X. Dong and E. Blaisten-Barojas. Adaptive tempering Monte Carlo method. J. Comput. Theor. Nanosci., 3, p. 118 2006). The folding transition temperature was successfully determined and a spread of states was observed around the interface between native and folded regions. Energy states collected from all tempering events in a series of parallel runs were used in the calculation of the free energy, internal energy, order parameter and radius of gyration as a function of temperature through the weighted histogram method. Not only the calculated thermodynamic properties are in good agreement with results from Langevin dynamics simulations (D. K. Klimov and D. Thirumalai. Native topology determines forced-induced pathways in global proteins. Proc. Natl. Acad. Sci. USA. 97, p. 7254 2000), but also this multicanonical approach is noticeably more efficient because of the adaptive manner in which the system visits states near a transition in the interface between two phases. Additionally, the ATMC is advantageous for protein simulation over regular single canonical ensemble methods because it accelerates the hopping between local energy minima on the potential energy surface.

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins.

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta

Insights into Allosteric Control of Vinculin Function from Its Large Scale Conformational Dynamics

Vinculin is an important constituent of both cell-cell and cell-matrix junctions, where it plays crucial roles in the regulation of cell adhesion and migration. When activated, it mediates the linkage between cadherins (cell-cell) or integrins (cell-matrix) and the actin cytoskeleton through interactions with various proteins. The activation of vinculin requires structural conversions from an autoinhibited conformation to the "open" conformations in which the occluded binding sites of its different ligands become exposed, while the structural dynamics underlying the vinculin activation remains largely unknown. Here we report the first computational study of large scale conformational dynamics of full-length vinculin. We find that the "holding" and "releasing" motions between vinculin tail and pincer-like structure formed by first three domains of vinculin are the dominant motions near the native state of vinculin, indicating that an inherent flexibility of vinculin has a large influence on its allostery. We also find a cooperative dissociation between the head and tail domains of vinculin with increasing temperature in both thermodynamic and kinetic simulations, implying that vinculin may function as an allosteric switch in response to external signals. We show that the kinetics of vinculin unfolding exhibits specific sequential patterns, suggesting that a sophisticated interplay between domains may synergistically contribute to vinculin activation. We further find that the interaction between vinculin-binding site peptide from talin and vinculin significantly destabilizes the intramolecular head-tail interactions, suggesting a direct role of talin binding in vinculin activation.

Elucidating Quantitative Stability/Flexibility Relationships Within Thioredoxin and its Fragments Using a Distance Constraint Model

Numerous quantitative stability/flexibility relationships, within Escherichia coli thioredoxin (Trx) and its fragments are determined using a minimal distance constraint model (DCM). A one-dimensional free energy landscape as a function of global flexibility reveals Trx to fold in a low-barrier two-state process, with a voluminous transition state. Near the folding transition temperature, the native free energy basin is markedly skewed to allow partial unfolded forms. Under native conditions the skewed shape is lost, and the protein forms a compact structure with some flexibility. Predictions on ten Trx fragments are generally consistent with experimental observations that they are disordered, and that complementary fragments reconstitute. A hierarchical unfolding pathway is uncovered using an exhaustive computational procedure of breaking interfacial cross-linking hydrogen bonds that span over a series of fragment dissociations. The unfolding pathway leads to a stable core structure (residues 22-90), predicted to act as a kinetic trap. Direct connection between degree of rigidity within molecular structure and non-additivity of free energy is demonstrated using a thermodynamic cycle involving fragments and their hierarchical unfolding pathway. Additionally, the model provides insight about molecular cooperativity within Trx in its native state, and about intermediate states populating the folding/unfolding pathways. Native state cooperativity correlation plots highlight several flexibly correlated regions, giving insight into the catalytic mechanism that facilitates access to the active site disulfide bond. Residual native cooperativity correlations are present in the core substructure, suggesting that Trx can function when it is partly unfolded. This natively disordered kinetic trap, interpreted as a molten globule, has a wide temperature range of metastability, and it is identified as the "slow intermediate state" observed in kinetic experiments. These computational results are found to be in overall agreement with a large array of experimental data.

An RNA foldability metric; implications for the design of rapidly foldable RNA sequences

Evidence is presented suggesting, for the first time, that the protein foldability metric σ = ( T θ − T f ) / T θ , where T θ and T f are, respectively, the collapse and folding transition temperatures, could be used also to measure the foldability of RNA sequences. These results provide further evidence of similarities between the folding energy landscapes of proteins and RNA. The importance of σ is discussed in the context of the in silico design of rapidly foldable RNA sequences.

Free energy landscape and folding mechanism of a β‐hairpin in explicit water: A replica exchange molecular dynamics study

The free energy landscape and the folding mechanism of the C-terminal beta-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a beta-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the beta-hairpin occurs as the sequence: collapse of hydrophobic core --> formation of H-bond --> formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart.

LENGTH SCALE EFFECTS OF SMALL MODEL PROTEIN FOLDING

The purpose of this paper is to investigate the length scale effects of small protein folding by lattice modeling. Heat capacity is computed to analyze folding transition temperature of the model proteins of different lengths. The results show that there is an evident phase transition when the lengths of the model proteins are similar to those of foldons. Furthermore, it is found that the folding transition temperature is proportional to the sequence length.

Multiple folding mechanisms of protein ubiquitin

Based on the C(alpha) Go-type model, the folding kinetics and mechanisms of protein ubiquitin with mixed alpha/beta topology are studied by molecular dynamics simulations. The relaxation kinetics shows that there are three phases, namely the major phase, the intermediate phase and the slowest minor phase. The existence of these three phases are relevant to the phenomenon found in experiments. According to our simulations, the folding at high temperatures around the folding transition temperature T(f) is of a two-state process, and the folding nucleus is consisted of contacts between the front end of alpha-helix and the turn(4). The folding at low temperature (approximately T = 0.8) is also studied, where an A-state like structure is found lying on the major folding pathway. The appearance of this structure is related to the stability of the first part (residue 1-51) of protein ubiquitin. As the temperature decreases, the formation of secondary structures, tertiary structures and collapse of the protein are found to be decoupled gradually and the folding mechanism changes from the nucleation-condensation to the diffusion-collision. This feature indicates a unifying common folding mechanism for proteins. The intermediate phase is also studied and is found to represent a folding process via a long-lived intermediate state which is stabilized by strong interactions between the beta(1) and the beta(5) strand. These strong interactions are important for the function of protein ubiquitin as a molecular chaperone. Thus the intermediate phase is assumed as a byproduct of the requirement of protein function. In addition, the validity of the current Go-model is also investigated, and a lower limited temperature for protein ubiquitin T(limit) = 0.8 is proposed. At temperatures higher than this value, the kinetic traps due to glass dynamics cannot be significantly populated and the intermediate states can be reliably identified although there is slight chevron rollover in the folding rates. At temperature lower than T(limit), however, the traps due to glass dynamics become dominant and may be mistaken for real intermediate states. This limitation of valid temperature range prevents us to reveal the burst phase intermediate in the major folding phase since it might only be stabilized at temperatures lower than T(limit), according to experiments. Our works show that caution must be taken when studying low-temperature intermediate states by using the C(alpha) Go-models.

Finite Size Effects on Thermal Denaturation of Globular Proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omegac, scales as Nzeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta=1+gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires TF approximately Ttheta, where Ttheta and TF are the collapse and folding transition temperatures, respectively.

The Complex Kinetics of Protein Folding in Wide Temperature Ranges

The complex protein folding kinetics in wide temperature ranges is studied through diffusive dynamics on the underlying energy landscape. The well-known kinetic chevron rollover behavior is recovered from the mean first passage time, with the U-shape dependence on temperature. The fastest folding temperature T 0 is found to be smaller than the folding transition temperature T f. We found that the fluctuations of the kinetics through the distribution of first passage time show rather universal behavior, from high-temperature exponential Poissonian kinetics to the relatively low-temperature highly non-exponential kinetics. The transition temperature is at T k and T 0 < T k < T f. In certain low-temperature regimes, a power law behavior at long time emerges. At very low temperatures (lower than trapping transition temperature T < T 0/(4∼6)), the kinetics is an exponential Poissonian process again.

Temperature dependence of the free energy landscape of the src-SH3 protein domain.

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.

Thermal denaturation and folding rates of single domain proteins: size matters

We analyze the dependence of thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N. Using lattice Go models we show that Δ T/ T F∼ N −1, where T F is the folding transition temperature and Δ T is the transition width computed using the temperature dependence of the order parameter that distinguishes between the unfolded state and the native basin of attraction. This finding is consistent with finite size effects expected for the systems undergoing a phase transition from a disordered to an ordered phase. The dependence of the folding rates on N for lattice models and the dataset of 57 proteins and peptides shows that k F≃k F 0 exp(−CN β) with 0< β≤2/3 provides a good fit, where C is a β-dependent constant. We find that k F ≃k F 0 exp(−1.1N 1/2) with an average (over the dataset of proteins) k F 0≈(0.4 μs) −1, can estimate optimal protein folding rates, to within an order of magnitude in most cases. By using this fit for a set of proteins with β-sheet topology we find that k F 0≈ k U 0, the prefactor for unfolding. The maximum ratio of k U 0/ k F 0≈10 for this class of proteins.

Temperature dependence of the distribution of the first passage time: results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G.

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Gō-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T(opt). The optimal folding temperature T(opt) is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T(opt) and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T(opt) and start to diverge when the temperature is lower than T(opt). The distribution of FPT is close to a log-normal-like distribution at T > or = T(opt). At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Investigation of the folding profiles of evolutionarily selected model proteins

Minimalist models of proteins, in which amino acid chains are represented by a necklace of beads that reconfigure the native fold on the sites of a cubic lattice, have been an important tool to infer early events in folding and to typify the energy landscapes of small globular proteins. In this paper, we try to determine in what sense these models are viable to describe protein evolution. An important first step toward this goal is to establish whether there are any limitations on the lattice model, such as on heterogeneity of the interactions and the size and topology of the native folds, that are necessary before cooperative (2-statelike) folding behavior typical of small proteins evolves robustly from the sequence selection process. The model we construct to test this feature selects sequences that fold reliably to a fixed topology on relevant timescales near their folding transition temperatures. The cross-chain (nonbonded) interactions are defined by empirical amino acid contact potentials, and the sequences evolve by random drift subject to the selection criteria. We investigate the folding profiles of these evolutionarily selected sequences in terms of the free energy, F(Q), and the participation of native contacts, Qj(Q), along a folding reaction coordinate Q (the percentage of native contacts formed). Both size and topology effects are evident in the results, and weakly heterogeneous, 2-statelike folding behavior emerges most consistently from larger folds that are specially selected to suppress the effect of heterogeneity in native interactions.

Structural and energetic heterogeneity in protein folding. I. Theory

A general theoretical framework is developed using free-energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from nonuniformity in native stabilizing interactions, as well as entropic heterogeneity intrinsic to the topology of the native structure, are both investigated as to their impact on the folding free-energy landscape and resulting folding mechanism. Given a minimally frustrated protein, both structural and energetic heterogeneity lower the thermodynamic barrier to folding. When energy functions consist of pair interactions, designing in sufficient heterogeneity can eliminate the barrier at the folding transition temperature. Sequences with different distributions of native stabilizing interactions and correspondingly different folding mechanisms may still be good folders to the same structure. This theoretical framework allows for a systematic study of the coupled effects of energetics and topology in protein folding, and provides interpretations and predictions for future experiments which may investigate these effects.