UV−Resonance Raman Thermal Unfolding Study of Trp-Cage Shows That It Is Not a Simple Two-State Miniprotein

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

Amyloidogenic and non-amyloidogenic molten globule conformation of β-lactoglobulin in self-crowded regime

Molecular insights on the β-lactoglobulin thermal unfolding and aggregation are derived from FTIR and UV Resonance Raman (UVRR) investigations. We propose an in situ and in real-time approach that thanks to the identification of specific spectroscopic markers can distinguish the two different unfolding pathways pursued by β-lactoglobulin during the conformational transition from the folded to the molten globule state, as triggered by the pH conditions. For both the investigated pH values (1.4 and 7.5) the greatest conformational variation of β-lactoglobulin occurs at 80 °C and a high degree of structural reversibility after cooling is observed. In acidic condition β-lactoglobulin exposes to the solvent its hydrophobic moieties in a much higher extent than in neutral solution, resulting on a highly open conformation. Moving from the diluted to the self-crowded regime, the solution pH and consequently the different molten globule conformation select the amyloid or non-amyloid aggregation pathway. At acidic condition the amyloid aggregates form during the heating cycle leading to the formation of transparent hydrogel. On the contrary, in neutral condition the amyloid aggregates never form. Information on the secondary structure conformational change of β-lactoglobulin and the formation of amyloid aggregates are obtained by FTIR spectroscopy and are related to the information of the structural changes localized around the aromatic amino acid sites by UVRR technique. Our results highlight a strong involvement of the chain portions where tryptophan is located on the formation of amyloid aggregates.

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.

Label-Free Surface-Enhanced Raman Spectroscopic Analysis of Proteins: Advances and Applications

Surface-enhanced Raman spectroscopy (SERS) is powerful for structural characterization of biomolecules under physiological condition. Owing to its high sensitivity and selectivity, SERS is useful for probing intrinsic structural information of proteins and is attracting increasing attention in biophysics, bioanalytical chemistry, and biomedicine. This review starts with a brief introduction of SERS theories and SERS methodology of protein structural characterization. SERS-active materials, related synthetic approaches, and strategies for protein-material assemblies are outlined and discussed, followed by detailed discussion of SERS spectroscopy of proteins with and without cofactors. Recent applications and advances of protein SERS in biomarker detection, cell analysis, and pathogen discrimination are then highlighted, and the spectral reproducibility and limitations are critically discussed. The review ends with a conclusion and a discussion of current challenges and perspectives of promising directions.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Distinct and Nonadditive Effects of Urea and Guanidinium Chloride on Peptide Solvation

Using enhanced-sampling replica exchange fully atomistic molecular dynamics simulations, we show that, individually, urea and guanidinium chloride (GdmCl) denature the Trpcage protein, but remarkably, the helical segment ¹NLYIQWL⁷ of the protein is stabilized in mixed denaturant solutions. GdmCl induces protein denaturation via a combination of direct and indirect effects involving dehydration of the protein and destabilization of stabilizing salt bridges. In contrast, urea denatures the protein through favorable protein-urea preferential interactions, with peptide-specific indirect effects of urea on the water structure around the protein. In the case of the helical segment of Trpcage, urea "oversolvates" the peptide backbone by reorganizing water molecules from the peptide side chains to the peptide backbone. An intricate nonadditive thermodynamic balance between GdmCl-induced dehydration of the peptide and the urea-induced changes in solvation structure triggers partial counteraction to urea denaturation and stabilization of the helix.

Effects of number of parallel runs and frequency of bias-strength replacement in generalized ensemble molecular dynamics simulations

Background

The generalized ensemble approach with the molecular dynamics (MD) method has been widely utilized. This approach usually has two features. (i) A bias potential, whose strength is replaced during a simulation, is applied. (ii) Sampling can be performed by many parallel runs of simulations. Although the frequency of the bias-strength replacement and the number of parallel runs can be adjusted, the effects of these settings on the resultant ensemble remain unclear.

Method

In this study, we performed multicanonical MD simulations for a foldable mini-protein (Trp-cage) and two unstructured peptides (8- and 20-residue poly-glutamic acids) with various settings.

Results

As a result, running many short simulations yielded robust results for the Trp-cage model. Regarding the frequency of the bias-potential replacement, although using a high frequency enhanced the traversals in the potential energy space, it did not promote conformational changes in all the systems.

Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps

The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.

Nitration of hIAPP promotes its toxic oligomer formation and exacerbates its toxicity towards INS-1 cells

Amyloid formation of human islet amyloid polypeptide (hIAPP) is one of the most common pathological features of type 2 diabetes (T2D). Increasing evidences have shown that the overproduction of reactive oxygen species (ROS) and reactive nitrogen species (RNS) play an important role in the development of the T2D. Interestingly, our previous studies indicated that heme could bind to hIAPP, and the complex might induce the nitration of tyrosine residue (Y37) of hIAPP in the presence of hydrogen peroxide and nitrite. However, it remains unclear about effect of the nitration on the implicated function of hIAPP in the development of T2D. In this study, fluorescent assays, transmission electron microscopy (TEM), atomic force microscope (AFM) were used to demonstrate that nitration of hIAPP significantly decreased its fibril formation. But the decreased fibril formation was not through the diminished aggregation of hIAPP monomer as suggested by the results of circular dichroism spectroscopy (CD) and gel electrophoresis assay. Surface-enhanced raman spectroscopy (SERS) indicated that nitration of hIAPP impaired the intermolecular hydrogen bonding. On the basis of these results, we hypothesize that nitration of hIAPP may block the intermolecular hydrogen bonding, leading to the inhibition of its fibril formation. In addition, cytotoxicity study of native and modified hIAPP was also performed on INS-1 cells, which revealed exacerbated toxicity of hIAPP by its nitration. The findings in this study that nitration of hIAPP promotes its oligomer formation and thus exacerbates its cytotoxicity suggests a possible link between the nitrite (or the sum of nitrite and nitrate) levels and T2D, and ameliorated nitration of hIAPP by diminishing nitrative stress might be a promising therapeutic strategy for T2D.

Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration

Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto-associative artificial neural networks ("autoencoders") to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data-driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp-cage, and have developed an open-source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.

Statistical Model To Decipher Protein Folding/Unfolding at a Local Scale

Protein folding/unfolding can be analyzed experimentally at a local scale by monitoring the physical properties of local probes as a function of the temperature, for example, the distance between fluorophores or the values of chemical shifts of backbone atoms. Here, the analytical Lifson-Roig model for the helix-coil transition is modified to analyze local thermal unfolding of the fast-folder W protein of bacteriophage lambda (gpW) simulated by all-atom molecular dynamics (MD) simulations in explicit solvent at 15 different temperatures. The protein structure is described by the coarse-grained dihedral angles (γ) and bond angles (θ) built between successive C^α-C^α virtual bonds. Each (γ,θ) pair serves as a local probe of protein unfolding. Local native/non-native states are defined for each pair of (γ,θ) angles by analyzing the free-energy landscapes Δ G(γ,θ) computed from MD trajectories. The three local elementary equilibrium constants of the model are extracted for each (γ,θ) pair along the sequence from MD simulations, and the model predictions are compared to the MD data. Using only the local equilibrium constants as an input, we show that the local denaturation curves computed from the model partition function fit their MD simulated counterparts in a satisfying manner without any adjustment. In the model and MD simulations, gpW unfolds gradually between 320 and 340 K, with an average native percentage decreasing from 0.8 (320 K) to 0.2 (340 K). In the prism of the model, there is no stable structure at the local scale in this 20 K unfolding temperature range. The enthalpy change upon local unfolding computed from the model and from MD trajectories suggests that the unfolded state between 320 and 340 K corresponds to a dynamical equilibrium between a large ensemble of constantly changing structures. The present results confirm the downhill unfolding of gpW, which does not obey a two-state global folding/unfolding model, and shed light on the interpretation of local denaturation curves.

Temperature evolution of Trp-cage folding pathways: An analysis by dividing the probability flux field into stream tubes

Owing to its small size and very fast folding rate, the Trp-cage miniprotein has become a benchmark system to study protein folding. Two folding pathways were found to be characteristic of this protein: pathway I, in which the hydrophobic collapse precedes the formation of α-helix, and pathway II, in which the events occur in the reverse order. At the same time, the relative contribution of these pathways at different temperatures as well as the nature of transition from one pathway to the other remain unclear. To gain insight into this issue, we employ a recently proposed hydrodynamic description of protein folding, in which the process of folding is considered as a motion of a "folding fluid" (Chekmarev et al., Phys. Rev. Lett. 100(1), 018107 2008). Using molecular dynamics simulations, we determine the field of probability fluxes of transitions in a space of collective variables and divide it into stream tubes. Each tube contains a definite fraction of the total folding flow and can be associated with a certain pathway. Specifically, three temperatures were considered, T = 285K, T = 315K, and T = 325K. We have found that as the temperature increases, the contribution of pathway I, which is approximately 90% of the total folding flow at T = 285K, decreases to approximately 10% at T = 325K, i.e., pathway II becomes dominant. At T = 315K, both pathways contribute approximately equally. All these temperatures are found below the calculated melting point, which suggests that the Trp-cage folding mechanism is determined by kinetic factors rather than thermodynamics.

Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts

Spontaneous transitions between the native and non-native protein conformations are normally rare events that hardly take place in typical unbiased molecular dynamics simulations. It was recently demonstrated that such transitions can be well described by a reaction coordinate, Q, that represents the collective fraction of the native contacts between the protein atoms. Here we attempt to use this reaction coordinate to enhance the conformational sampling. We perform umbrella sampling simulations with biasing potentials on Q for two model proteins, Trp-Cage and BBA, using the CHARMM force field. Hamiltonian replica exchange is implemented in these simulations to further facilitate the sampling. The simulations appear to have reached satisfactory convergence, resulting in unbiased free energies as a function of Q. In addition to the native structure, multiple folded conformations are identified in the reconstructed equilibrium ensemble. Some conformations without any native contacts nonetheless have rather compact geometries and are stabilized by hydrogen bonds not present in the native structure. Whereas the enhanced sampling along Q reasonably reproduces the equilibrium conformational space, we also find that the folding of an α-helix in Trp-Cage is a slow degree of freedom orthogonal to Q and therefore cannot be accelerated by biasing the reaction coordinate. Overall, we conclude that whereas Q is an excellent parameter to analyze the simulations, it is not necessarily a perfect reaction coordinate for enhanced sampling, and better incorporation of other slow degrees of freedom may further improve this reaction coordinate.

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.

Copper Ion Binding Site in β-Amyloid Peptide

β-Amyloid aggregates in the brain play critical roles in Alzheimer's disease, a chronic neurodegenerative condition. Amyloid-associated metal ions, particularly zinc and copper ions, have been implicated in disease pathogenesis. Despite the importance of such ions, the binding sites on the β-amyloid peptide remain poorly understood. In this study, we use scanning tunneling microscopy, circular dichroism, and surface-enhanced Raman spectroscopy to probe the interactions between Cu²⁺ ions and a key β-amyloid peptide fragment, consisting of the first 16 amino acids, and define the copper-peptide binding site. We observe that in the presence of Cu²⁺, this peptide fragment forms β-sheets, not seen without the metal ion. By imaging with scanning tunneling microscopy, we are able to identify the binding site, which involves two histidine residues, His13 and His14. We conclude that the binding of copper to these residues creates an interstrand histidine brace, which enables the formation of β-sheets.

Can Local Probes Go Global? A Joint Experiment-Simulation Analysis of λ(6-85) Folding

The process of protein folding is known to involve global motions in a cooperative affair; the structure of most of the protein sequences is gained or lost over a narrow range of temperature, denaturant, or pressure perturbations. At the same time, recent simulations and experiments reveal a complex structural landscape with a rich set of local motions and conformational changes. We couple experimental kinetic and thermodynamic measurements with specifically tailored analysis of simulation data to isolate local versus global folding probes. We find that local probes exhibit lower melting temperatures, smaller surface area changes, and faster kinetics compared to global ones. We also see that certain local probes of folding match the global behavior more closely than others. Our work highlights the importance of using multiple probes to fully characterize protein folding dynamics by theory and experiment.

Exploring the structure and formation mechanism of amyloid fibrils by Raman spectroscopy: a review

Amyloid fibrils are β-sheet rich protein aggregates that are strongly associated with various neurodegenerative diseases. Raman spectroscopy has been broadly utilized to investigate protein aggregation and amyloid fibril formation and has been shown to be capable of revealing changes in secondary and tertiary structures at all stages of fibrillation. When coupled with atomic force (AFM) and scanning electron (SEM) microscopies, Raman spectroscopy becomes a powerful spectroscopic approach that can investigate the structural organization of amyloid fibril polymorphs. In this review, we discuss the applications of Raman spectroscopy, a unique, label-free and non-destructive technique for the structural characterization of amyloidogenic proteins, prefibrilar oligomers, and mature fibrils.

Comparison of hydration behavior and conformational preferences of the Trp-cage mini-protein in different rigid-body water models

Trp-cage unfolds at different temperatures in different water models revealing the sensitivity of conformational order metrics to the choice of water models.

A hydrodynamic view of the first-passage folding of Trp-cage miniprotein

We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential.

Folding Thermodynamics and Mechanism of Five Trp-Cage Variants from Replica-Exchange MD Simulations with RSFF2 Force Field

To test whether our recently developed residue-specific force field RSFF2 can reproduce the mutational effect on the thermal stability of Trp-cage mini-protein and decipher its detailed folding mechanism, we carried out long-time replica-exchange molecular dynamics (REMD) simulations on five Trp-cage variants, including TC5b and TC10b. Initiated from their unfolded structures, the simulations not only well-reproduce their experimental structures but also their melting temperatures and folding enthalpies reasonably well. For each Trp-cage variant, the overall folding free energy landscape is apparently two-state, but some intermediate states can be observed when projected on more detailed coordinates. We also found different variants have the same major folding pathway, including the well formed PII-helix in the unfolded state, the formation of W6-P12/P18/P19 contacts and the α-helix before the transition state, the following formation of most native contacts, and the final native loop formation. The folding mechanism derived here is consistent with many previous simulations and experiments.

Correlation analysis for heat denaturation of Trp-cage miniprotein with explicit solvent

Energetics was analyzed for Trp-cage miniprotein in water to elucidate the solvation effect in heat denaturation. The solvation free energy was computed for a set of protein structures at room and high temperatures with all-atom molecular dynamics simulation combined with the solution theory in the energy representation, and its correlations were investigated against the intramolecular (structural) energy of the protein and the average interaction energy of the protein with the solvent water. It was observed both at room and high temperatures that the solvation free energy is anticorrelated to the structural energy and varies in parallel to the electrostatic component of the protein-water interaction energy without correlations to the van der Waals and excluded-volume components. When the set of folded structures sampled at room temperature was compared with the set of unfolded ones at high temperature, it was found that the preference order of the two sets is in correspondence to the van der Waals and excluded-volume components in the sum of the protein intramolecular and protein-water intermolecular interactions and is not distinguished by the electrostatic component.

Accelerated molecular dynamics simulations of protein folding

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.

Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage

The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.

Tackling sampling challenges in biomolecular simulations

Molecular dynamics (MD) simulations are a powerful tool to give an atomistic insight into the structure and dynamics of proteins. However, the time scales accessible in standard simulations, which often do not match those in which interesting biological processes occur, limit their predictive capabilities. Many advanced sampling techniques have been proposed over the years to overcome this limitation. This chapter focuses on metadynamics, a method based on the introduction of a time-dependent bias potential to accelerate sampling and recover equilibrium properties of a few descriptors that are able to capture the complexity of a process at a coarse-grained level. The theory of metadynamics and its combination with other popular sampling techniques such as the replica exchange method is briefly presented. Practical applications of these techniques to the study of the Trp-Cage miniprotein folding are also illustrated. The examples contain a guide for performing these calculations with PLUMED, a plugin to perform enhanced sampling simulations in combination with many popular MD codes.

Sampling the equilibrium kinetic network of Trp-cage in explicit solvent

We employed the single replica multiple state transition interface sampling (MSTIS) approach to sample the kinetic (un)folding network of Trp-cage mini-protein in explicit water. Cluster analysis yielded 14 important metastable states in the network. The MSTIS simulation thus resulted in a full 14 × 14 rate matrix. Analysis of the kinetic rate matrix indicates the presence of a near native intermediate state characterized by a fully formed alpha helix, a slightly disordered proline tail, a broken salt-bridge, and a rotated arginine residue. This intermediate was also found in recent IR experiments. Moreover, the predicted rate constants and timescales are in agreement with previous experiments and simulations.

Folding dynamics and pathways of the trp-cage miniproteins

Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.

Folding simulation of Trp-cage utilizing a new AMBER compatible force field with coupled main chain torsions

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity Cvis only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032Dis an accurate force field that can be used for protein folding simulations.

Allosteric transition induced by Mg²⁺ ion in a transactivator monitored by SERS

We demonstrate the utility of the surface-enhanced Raman spectroscopy (SERS) to monitor conformational transitions in protein upon ligand binding. The changes in protein's secondary and tertiary structures were monitored using amide and aliphatic/aromatic side chain vibrations. Changes in these bands are suggestive of the stabilization of the secondary and tertiary structure of transcription activator protein C in the presence of Mg(2+) ion, whereas the spectral fingerprint remained unaltered in the case of a mutant protein, defective in Mg(2+) binding. The importance of the acidic residues in Mg(2+) binding, which triggers an overall allosteric transition in the protein, is visualized in the molecular model. The present study thus opens up avenues toward the application of SERS as a potential tool for gaining structural insights into the changes occurring during conformational transitions in proteins.

Following easy slope paths on a free energy landscape: the case study of the Trp-cage folding mechanism

In this work a new method for the automatic exploration and calculation of multidimensional free energy landscapes is proposed. Inspired by metadynamics, it uses several collective variables that are relevant for the investigated process and a bias potential that discourages the sampling of already visited configurations. The latter potential allows escaping a local free energy minimum following the direction of slow motions. This is different from metadynamics in which there is no specific direction of the biasing force and the computational effort increases significantly with the number of collective variables. The method is tested on the Ace-Ala3-Nme peptide, and then it is applied to investigate the Trp-cage folding mechanism. For this protein, within a few hundreds of nanoseconds, a broad range of conformations is explored, including nearly native ones, initiating the simulation from a completely unfolded conformation. Finally, several folding/unfolding trajectories give a systematic description of the Trp-cage folding pathways, leading to a unified view for the folding mechanisms of this protein. The proposed mechanism is consistent with NMR chemical shift data at increasing temperature and recent experimental observations pointing to a pivotal role of secondary structure elements in directing the folding process toward the native state.