Unfolding thermodynamics of Trp-cage, a 20 residue miniprotein, studied by differential scanning calorimetry and circular dichroism spectroscopy

Buckets Instead of Umbrellas for Enhanced Sampling and Free Energy Calculations

Umbrella sampling has been a workhorse for free energy calculations in molecular simulations for several decades. In conventional umbrella sampling, restraining bias potentials are strategically applied along one or several collective variables. Major drawbacks associated with this method are the requirement of a large number of bias windows and the poor sampling of the transverse coordinates. In this work, we propose an alternate formalism that departs from the traditional umbrella sampling to mitigate these issues, where we replace umbrella-type restraining bias potentials with bucket-type wall potentials. This modification permits one to formulate an efficient computational strategy leveraging wall potentials and metadynamics sampling. This new method, called "bucket sampling", can significantly reduce the computational cost of obtaining converged high-dimensional free energy surfaces. Extensions of the proposed method with temperature acceleration and replica exchange solute tempering are also demonstrated.

Influence of Trp-Cage on the Function and Stability of GLP-1R Agonist Exenatide Derivatives

Exenatide (Ex4), a GLP-1 incretin mimetic polypeptide, is an effective therapeutic agent against diabetes and obesity. We highlight the indirect role of Ex4's structure-stabilizing Trp-cage (Tc) motif in governing GLP-1 receptor (GLP-1R) signal transduction. We use various Ex4 derivatives to explore how Tc compactness influences thermal stability, aggregation, enhancement of insulin secretion, and GLP-1R binding. We found that Ex4 variants decorated with fortified Tc motifs exhibit increased resistance to unfolding and aggregation but show an inverse relationship between the bioactivity and stability. Molecular dynamics simulations coupled with a rigid-body segmentation protocol to analyze dynamic interconnectedness revealed that the constrained Tc motifs remain intact within the receptor-ligand complexes but interfere with one of the major stabilizing contacts and recognition loci on the extracellular side of GLP-1R, dislodging the N-terminal activating region of the hormone mimetics, and restrict the free movement of TM6, the main signal transduction device of GLP-1R.

NPEX: Never give up protein exploration with deep reinforcement learning

Elucidating unknown structures of proteins, such as metastable states, is critical in designing therapeutic agents. Protein structure exploration has been performed using advanced computational methods, especially molecular dynamics and Markov chain Monte Carlo simulations, which require untenably long calculation times and prior structural knowledge. Here, we developed an innovative method for protein structure determination called never give up protein exploration (NPEX) with deep reinforcement learning. The NPEX method leverages the soft actor-critic algorithm and the intrinsic reward system, effectively adding a bias potential without the need for prior knowledge. To demonstrate the method's effectiveness, we applied it to four models: a double well, a triple well, the alanine dipeptide, and the tryptophan cage. Compared with Markov chain Monte Carlo simulations, NPEX had markedly greater sampling efficiency. The significantly enhanced computational efficiency and lack of prior domain knowledge requirements of the NPEX method will revolutionize protein structure exploration.

Opposing roles of organic salts on mini-protein structure

We investigated the effects of 1-ethyl-3-methylimidazolium chloride ([EMIM][Cl]) and choline chloride ([Chol][Cl]) on the local environment and conformational landscapes of Trp-cage and Trpzip4 mini-proteins using experimental and computational approaches. Fluorescence experiments and computational simulations revealed distinct behaviors of the mini-proteins in the presence of these organic salts. [EMIM][Cl] showed a strong interaction with Trp-cage, leading to fluorescence quenching and destabilization of its native structural interactions. Conversely, [Chol][Cl] had a negligible impact on Trp-cage fluorescence at low concentrations but increased it at high concentrations, indicating a stabilizing role. Computational simulations elucidated that [EMIM][Cl] disrupted the hydrophobic core packing and decreased proline-aromatic residue contacts in Trp-cage, resulting in a more exposed environment for Trp residues. In contrast, [Chol][Cl] subtly influenced the hydrophobic core packing, creating a hydrophobic environment near the tryptophan residues. Circular dichroism experiments revealed that [Chol][Cl] stabilized the secondary structure of both mini-proteins, although computational simulations did not show significant changes in secondary content at the explored concentrations. The simulations also demonstrated a more rugged free energy landscape for Trp-cage and Trpzip4 in [EMIM][Cl], suggesting destabilization of the tertiary structure for Trp-cage and secondary structure for Trpzip4. Similar fluorescence trends were observed for Trpzip4, with [EMIM][Cl] quenching fluorescence and exhibiting stronger interaction, while [Chol][Cl] increased the fluorescence at high concentrations. These findings highlight the interplay between [EMIM][Cl] and [Chol][Cl] with the mini-proteins and provide a detailed molecular-level understanding of how these organic salts impact the nearby surroundings and structural variations. Understanding such interactions is valuable for diverse applications, from biochemistry to materials science.

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.

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.

Influence of TMAO and Pressure on the Folding Equilibrium of TrpCage

Trimethylamine-N-oxide (TMAO) is an osmolyte known for its ability to counteract the pressure denaturation of proteins. Computational studies addressing the molecular mechanisms of TMAO's osmolyte action have however focused exclusively on its protein-stabilizing properties at ambient pressure, neglecting the changes that may occur under high-pressure conditions where TMAO's hydration structure changes to that of increased water binding. Here, we present the first study on the combined effect of pressure and TMAO on a mini-protein, TrpCage. The results showed that at high pressures, nonpolar residues packed less tightly and the salt bridge of TrpCage was destabilized. This effect was mitigated by TMAO which was found to be strongly depleted from the protein/water interface at 1 kbar than at 1 bar ambient pressure, thus counterbalancing the thermodynamically unfavorable effect of elevated pressure in the free energy of folding. TMAO was depleted from charged groups, like the salt bridge-forming ones, and accumulated around hydrophobic groups. Still, it stabilized both kinds of interactions. Furthermore, enthalpically favorable TrpCage-water hydrogen bonds were reduced in the presence of TMAO, causing a stronger destabilization of the unfolded state than the folded state. This shifted the protein-folding equilibrium toward the folded state. Therefore, TMAO showed stabilizing effects on different kinds of groups, which were partially enhanced at high pressures.

Computational Modeling of the Thermodynamics of the Mesophilic and Thermophilic Mutants of Trp-Cage Miniprotein

We characterize the folding-unfolding thermodynamics of two mutants of the miniprotein Trp-cage by combining extended molecular dynamics simulations and an advanced statistical-mechanical-based approach. From a set of molecular dynamics simulations in an explicit solvent performed along a reference isobar, we evaluated the structural and thermodynamic behaviors of a mesophilic and a thermophilic mutant of the Trp-cage and their temperature dependence. In the case of the thermophilic mutant, computational data confirm that our theoretical-computational approach is able to reproduce the available experimental estimate with rather good accuracy. On the other hand, the mesophilic mutant does not show a clear two-state (folded and unfolded) behavior, preventing us from reconstructing its thermodynamics; thus, an analysis of its structural behavior along a reference isobar is presented. Our results show that an extended sampling of these kinds of systems coupled to an advanced statistical-mechanical-based treatment of the data can provide an accurate description of the folding-unfolding thermodynamics along a reference isobar, rationalizing the discrepancies between the simulated and experimental systems.

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.

Residue Folding Degree-Relationship to Secondary Structure Categories and Use as Collective Variable

Recently, we have shown that the residue folding degree, a network-based measure of folded content in proteins, is able to capture backbone conformational transitions related to the formation of secondary structures in molecular dynamics (MD) simulations. In this work, we focus primarily on developing a collective variable (CV) for MD based on this residue-bound parameter to be able to trace the evolution of secondary structure in segments of the protein. We show that this CV can do just that and that the related energy profiles (potentials of mean force, PMF) and transition barriers are comparable to those found by others for particular events in the folding process of the model mini protein Trp-cage. Hence, we conclude that the relative segment folding degree (the newly proposed CV) is a computationally viable option to gain insight into the formation of secondary structures in protein dynamics. We also show that this CV can be directly used as a measure of the amount of α-helical content in a selected segment.

A Conserved Hydrophobic Moiety and Helix-Helix Interactions Drive the Self-Assembly of the Incretin Analog Exendin-4

Exendin-4 is a pharmaceutical peptide used in the control of insulin secretion. Structural information on exendin-4 and related peptides especially on the level of quaternary structure is scarce. We present the first published association equilibria of exendin-4 directly measured by static and dynamic light scattering. We show that exendin-4 oligomerization is pH dependent and that these oligomers are of low compactness. We relate our experimental results to a structural hypothesis to describe molecular details of exendin-4 oligomers. Discussion of the validity of this hypothesis is based on NMR, circular dichroism and fluorescence spectroscopy, and light scattering data on exendin-4 and a set of exendin-4 derived peptides. The essential forces driving oligomerization of exendin-4 are helix–helix interactions and interactions of a conserved hydrophobic moiety. Our structural hypothesis suggests that key interactions of exendin-4 monomers in the experimentally supported trimer take place between a defined helical segment and a hydrophobic triangle constituted by the Phe22 residues of the three monomeric subunits. Our data rationalize that Val19 might function as an anchor in the N-terminus of the interacting helix-region and that Trp25 is partially shielded in the oligomer by C-terminal amino acids of the same monomer. Our structural hypothesis suggests that the Trp25 residues do not interact with each other, but with C-terminal Pro residues of their own monomers.

Pressure Unfolding of Proteins: New Insights into the Role of Bound Water

High pressures can be detrimental for protein stability, resulting in unfolding and loss of function. This phenomenon occurs because the unfolding transition is accompanied by a decrease in volume, which is typically attributed to the elimination of cavities that are present within the native state as a result of packing defects. We present a novel computational approach that enables the study of pressure unfolding in atomistically detailed protein models in implicit solvent. We include the effect of pressure using a transfer free energy term that allows us to decouple the effect of protein residues and bound water molecules on the volume change upon unfolding. We discuss molecular dynamics simulations results using this protocol for two model proteins, Trp-cage and staphylococcal nuclease (SNase). We find that the volume reduction of bound water is the key energetic term that drives protein denaturation under the effect of pressure, for both Trp-cage and SNase. However, we note differences in unfolding mechanisms between the smaller Trp-cage and the larger SNase protein. Indeed, the unfolding of SNase, but not Trp-cage, is seen to be further accompanied by a reduction in the volume of internal cavities. Our results indicate that, for small peptides, like Trp-cage, pressure denaturation is driven by the increase in solvent accessibility upon unfolding, and the subsequent increase in the number of bound water molecules. For larger proteins, like SNase, the cavities within the native fold act as weak spots, determining the overall resistance to pressure denaturation. Our simulations display a striking agreement with the pressure-unfolding profile experimentally obtained for SNase and represent a promising approach for a computationally efficient and accurate exploration of pressure-induced denaturation of proteins.

Cold-Active β-Galactosidases: Insight into Cold Adaption Mechanisms and Biotechnological Exploitation

β-galactosidases (EC 3.2.1.23) catalyze the hydrolysis of β-galactosidic bonds in oligosaccharides and, under certain conditions, transfer a sugar moiety from a glycosyl donor to an acceptor. Cold-active β-galactosidases are identified in microorganisms endemic to permanently low-temperature environments. While mesophilic β-galactosidases are broadly studied and employed for biotechnological purposes, the cold-active enzymes are still scarcely explored, although they may prove very useful in biotechnological processes at low temperature. This review covers several issues related to cold-active β-galactosidases, including their classification, structure and molecular mechanisms of cold adaptation. Moreover, their applications are discussed, focusing on the production of lactose-free dairy products as well as on the valorization of cheese whey and the synthesis of glycosyl building blocks for the food, cosmetic and pharmaceutical industries.

Sampling of the conformational landscape of small proteins with Monte Carlo methods

Computer simulation provides an increasingly realistic picture of large-scale conformational change of proteins, but investigations remain fundamentally constrained by the femtosecond timestep of molecular dynamics simulations. For this reason, many biologically interesting questions cannot be addressed using accessible state-of-the-art computational resources. Here, we report the development of an all-atom Monte Carlo approach that permits the modelling of the large-scale conformational change of proteins using standard off-the-shelf computational hardware and standard all-atom force fields. We demonstrate extensive thermodynamic characterization of the folding process of the α-helical Trp-cage, the Villin headpiece and the β-sheet WW-domain. We fully characterize the free energy landscape, transition states, energy barriers between different states, and the per-residue stability of individual amino acids over a wide temperature range. We demonstrate that a state-of-the-art intramolecular force field can be combined with an implicit solvent model to obtain a high quality of the folded structures and also discuss limitations that still remain.

Visible-light-driven photocontrol of the Trp-cage protein fold by a diazocine cross-linker

Diazocines are characterized by extraordinary photochemical properties rendering them of particular interest for switching the conformation of biomolecules with visible light. Current developments afford synthetic access to unprecedented diazocine derivatives promising particular opportunities in photocontrol of proteins and biological systems. In this work, the well-established approach of photocontrolling the secondary structure of α-helices was exploited using a diazocine to reversibly fold and unfold the tertiary structure of a small protein. The protein of choice was the globulary folded Trp-cage, a widely used model system for the elucidation of protein folding pathways. A specifically designed, short and rigid dicarboxy-functionalized diazocine-based cross-linker was attached to two solvent-exposed side chains at the α-helix of the miniprotein through the use of a primary amine-selective active ester. This cross-linking strategy is orthogonal to the common cysteine-based chemistry. The cross-linked Trp-cage was successfully photoisomerized and exhibited a strong correlation between protein fold and diazocine isomeric state. As determined by NMR spectroscopy, the cis-isomer stabilized the fold, while the trans-isomer led to complete protein unfolding. The successful switching of the protein fold in principle demonstrates the ability to control protein function, as the activity depends on their structural integrity.

Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes

The accuracy of atomistic physics-based force fields for the simulation of biological macromolecules has typically been benchmarked experimentally using biophysical data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters associated with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromolecules, such as proteins and nucleic acids, and these interactions are often essential for proper biological function. Here, we show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. Our objective involved refitting not only the parameters associated with torsion-angle potentials but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which we call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calculated protein-protein association free energies still appear to deviate substantially from experiment, a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.

Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy

The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.

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.

Theoretical-computational modelling of the temperature dependence of the folding-unfolding thermodynamics and kinetics: the case of a Trp-cage

Here we present a theoretical-computational study of the thermodynamics and kinetics of an aqueous Trp-cage, a 20-residue long miniprotein. The combined use of accurate molecular dynamics simulations rigorously reconstructing the proper isobar of the system and a sound statistical-mechanical model provides a quantitative description of the temperature dependence of the relevant physical-chemical properties and insights into the detailed mechanisms regulating the folding-unfolding properties.

Computational investigation of retro-isomer equilibrium structures: Intrinsically disordered, foldable, and cyclic peptides

We use all-atom modeling and advanced-sampling molecular dynamics simulations to investigate quantitatively the effect of peptide bond directionality on the equilibrium structures of four linear (two foldable, two disordered) and two cyclic peptides. We find that the retro forms of cyclic and foldable linear peptides adopt distinctively different conformations compared to their parents. While the retro form of a linear intrinsically disordered peptide with transient secondary structure fails to reproduce a secondary structure content similar to that of its parent, the retro form of a shorter disordered linear peptide shows only minor differences compared to its parent.

Energetic, Structural and Dynamic Properties of Nucleobase-Urea Interactions that Aid in Urea Assisted RNA Unfolding

Understanding the structure-function relationships of RNA has become increasingly important given the realization of its functional role in various cellular processes. Chemical denaturation of RNA by urea has been shown to be beneficial in investigating RNA stability and folding. Elucidation of the mechanism of unfolding of RNA by urea is important for understanding the folding pathways. In addition to studying denaturation of RNA in aqueous urea, it is important to understand the nature and strength of interactions of the building blocks of RNA. In this study, a systematic examination of the structural features and energetic factors involving interactions between nucleobases and urea is presented. Results from molecular dynamics (MD) simulations on each of the five DNA/RNA bases in water and eight different concentrations of aqueous urea, and free energy calculations using the thermodynamic integration method are presented. The interaction energies between all the nucleobases with the solvent environment and the transfer free energies become more favorable with respect to increase in the concentration of urea. Preferential interactions of urea versus water molecules with all model systems determined using Kirkwood-Buff integrals and two-domain models indicate preference of urea by nucleobases in comparison to water. The modes of interaction between urea and the nucleobases were analyzed in detail. In addition to the previously identified hydrogen bonding and stacking interactions between urea and nucleobases that stabilize the unfolded states of RNA in aqueous solution, NH-π interactions are proposed to be important. Dynamic properties of each of these three modes of interactions have been presented. The study provides fundamental insights into the nature of interaction of urea molecules with nucleobases and how it disrupts nucleic acids.

Computational Investigation of the Effect of Pressure on Protein Stability

Previous studies show parabolic or elliptical regions of protein stability in the pressure-temperature ( P, T) plane. The construction of stability diagrams requires accessing a sufficiently broad ( P, T) range, which is often frustrated by ice formation in experiments and sampling challenges in simulations. We perform a fully atomistic computational study of the miniprotein Trp-cage over the range of temperatures 210 ≤ T ≤ 420 K and pressures P ≤ 5 kbar and construct the corresponding stability diagram. At ambient temperature, pressure shifts the conformational states toward unfolding. Below 250 K, the native fold's stability depends nonmonotonically on pressure. While cold unfolding and thermal denaturation differ significantly at ambient pressure, they exhibit progressive similarity at elevated pressures. At ambient pressure, cold denaturation is an enthalpically driven process that preserves significant elements of Trp-cage's secondary structure. In contrast, cold unfolding at elevated pressures involves a more substantial loss of secondary and tertiary structure, similar to thermal denaturation.

Examination of Trifluoroethanol Interactions with Trp-Cage in Trifluoroethanol-Water at 298 K through Molecular Dynamics Simulations and Intermolecular Nuclear Overhauser Effects

Molecular dynamics simulations of the protein model Trp-cage in 42% trifluoroethanol (TFE)-water at 298 K have been carried out with the goal of exploring peptide hydrogen-solvent fluorine nuclear spin cross-relaxation. The TFE5 model of TFE developed in a previous work was used with the TIP5P-Ew model of water. System densities and component translational diffusion coefficients predicted by the simulations were within 20% of the experimental values. Consideration of the calculated relative amounts of TFE and water surrounding the hydrogens of Trp-cage indicated that the composition of the solvent mixture beyond ∼1.5 nm from the van der Waals surface of the peptide is close to the composition of the bulk solvent, but as observed by others, TFE accumulates preferentially near the peptide surface. In the simulations, both TFE and water molecules make contacts with the peptide surface; water molecules predominate in contacts with the peptide backbone atoms and TFE molecules generally preferentially interact with side chains. Translational diffusion of solvent molecules appears to be slowed near the surface of the peptide. Depending on the location in the structure, TFE molecules form complexes with the peptide that may persist for up to ∼7 ns. Many of the peptide spin-solvent fluorine cross-relaxation parameters (Σ_HF) for which experimental values are available are reasonably well-predicted from the simulations. However, the calculated Σ_HF values were too small for some hydrogens of the 6Trp indole ring and the amino acid hydrogens near this residue in the native structure, whereas Σ_HF values for hydrogens on the side chains of 1Asn, 4Ile, and 7Leu are too large. In 42% TFE-water, persistent conformations of Trp-cage are found, which differ from the conformation found in water by the orientation of the 3Tyr ring.

Hydration shell differentiates folded and disordered states of a Trp-cage miniprotein, allowing characterization of structural heterogeneity by wide-line NMR measurements

Hydration properties of folded and unfolded/disordered miniproteins were monitored in frozen solutions by wide-line 1H-NMR. The amount of mobile water as function of T (-80 °C < T < 0 °C) was found characteristically different for folded (TC5b), semi-folded (pH < 3, TCb5(H+)) and disordered (TC5b_N1R) variants. Comparing results of wide-line 1H-NMR and molecular dynamics simulations we found that both the amount of mobile water surrounding proteins in ice, as well as their thaw profiles differs significantly as function of the compactness and conformational heterogeneity of their structure. We found that (i) at around -50 °C ~50 H2Os/protein melt (ii) if the protein is well-folded then this amount of mobile water remains quasi-constant up to -20 °C, (iii) if disordered then the quantity of the lubricating mobile water increases with T in a constant manner up to ~200 H2Os/protein by reaching -20 °C. Especially in the -55 °C ↔ -15 °C temperature range, wide-line 1H-NMR detects the heterogeneity of protein fold, providing the size of the hydration shell surrounding the accessible conformers at a given temperature. Results indicate that freezing of protein solutions proceeds by the gradual selection of the enthalpically most favored states that also minimize the number of bridging waters.

Effect of osmolytes on the thermal stability of proteins: replica exchange simulations of Trp-cage in urea and betaine solutions

Although osmolytes are known to modulate the folding equilibrium, the molecular mechanism of their effect on thermal denaturation of proteins is still poorly understood. Here, we simulated the thermal denaturation of a small model protein (Trp-cage) in the presence of denaturing (urea) and stabilizing (betaine) osmolytes, using the all-atom replica exchange molecular dynamics simulations. We found that urea destabilizes Trp-cage by enthalpically-driven association with the protein, acting synergistically with temperature to induce unfolding. In contrast, betaine is sterically excluded from the protein surface thereby exerting entropic depletion forces that contribute to the stabilization of the native state. In fact, we find that while at low temperatures betaine slightly increases the folding free energy of Trp-cage by promoting another near-native conformation, it protects the protein against temperature-induced denaturation. This, in turn, can be attributed to enhanced exclusion of betaine at higher temperatures that arises from less attractive interactions with the protein surface.

Peptide-surfactant interactions: A combined spectroscopic and molecular dynamics simulation approach

In the present contribution, we report a combined spectroscopic and computational approach aiming to unravel at atomic resolution the effect of the anionic SDS detergent on the structure of two model peptides, the α-helix TrpCage and the β-stranded TrpZip. A detailed characterization of the specific amino acids involved is performed. Monomeric (single molecules) and micellar SDS species differently interact with the α-helix and β-stranded peptides, emphasizing the different mechanisms occurring below and above the critical aggregation concentration (CAC). Below the CAC, the α-helix peptide is fully unfolded, losing its hydrophobic core and its Asp-Arg salt bridge, while the β-stranded peptide keeps its native structure with its four Trp well oriented. Above the CAC, the SDS micelles have the same effect on both peptides, that is, destabilizing the tertiary structure while keeping their secondary structure. Our studies will be helpful to deepen our understanding of the action of the denaturant SDS on peptides and proteins.

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.

Ion-induced alterations of the local hydration environment elucidate Hofmeister effect in a simple classical model of Trp-cage miniprotein

Protein stability is known to be influenced by the presence of Hofmeister active ions in the solution. In addition to direct ion-protein interactions, this influence manifests through the local alterations of the interfacial water structure induced by the anions and cations present in this region. In our earlier works it was pointed out that the effects of Hofmeister active salts on the stability of Trp-cage miniprotein can be modeled qualitatively using non-polarizable force fields. These simulations reproduced the structure-stabilization and structure-destabilization effects of selected kosmotropic and chaotropic salts, respectively. In the present study we use the same model system to elucidate atomic processes behind the chaotropic destabilization and kosmotropic stabilization of the miniprotein. We focus on changes of the local hydration environment of the miniprotein upon addition of NaClO₄ and NaF salts to the solution. The process is separated into two parts. In the first, 'promotion' phase, the protein structure is fixed, and the local hydration properties induced by the simultaneous presence of protein and ions are investigated, with a special focus on the interaction of Hofmeister active anions with the charged and polar sites. In the second, 'rearrangement' phase we follow changes of the hydration of ions and the protein, accompanying the conformational relaxation of the protein. We identify significant factors of an enthalpic and entropic nature behind the ion-induced free energy changes of the protein-water system, and also propose a possible atomic mechanism consistent with the Collins's rule, for the chaotropic destabilization and kosmotropic stabilization of protein conformation.

Effects of Trimethylamine-N-oxide on the Conformation of Peptides and its Implications for Proteins

To provide insights into the stabilizing mechanisms of trimethylamine-N-oxide (TMAO) on protein structures, we perform all-atom molecular dynamics simulations of peptides and the Trp-cage miniprotein. The effects of TMAO on the backbone and charged residues of peptides are found to stabilize compact conformations, whereas effects of TMAO on nonpolar residues lead to peptide swelling. This suggests competing mechanisms of TMAO on proteins, which accounts for hydrophobic swelling, backbone collapse, and stabilization of charge-charge interactions. These mechanisms are observed in Trp cage.

Protein Stability and Unfolding Following Glycine Radical Formation

Glycine (Gly) residues are particularly susceptible to hydrogen abstraction; which results in the formation of the capto-dative stabilized C_α-centered Gly radical (GLR) on the protein backbone. We examined the effect of GLR formation on the structure of the Trp cage; tryptophan zipper; and the villin headpiece; three fast-folding and stable miniproteins; using all-atom (OPLS-AA) molecular dynamics simulations. Radicalization changes the conformation of the GLR residue and affects both neighboring residues but did not affect the stability of the Trp zipper. The stability of helices away from the radical center in villin were also affected by radicalization; and GLR in place of Gly15 caused the Trp cage to unfold within 1 µs. These results provide new evidence on the destabilizing effects of protein oxidation by reactive oxygen species.

Computational investigation of cold denaturation in the Trp-cage miniprotein

The functional native states of globular proteins become unstable at low temperatures, resulting in cold unfolding and impairment of normal biological function. Fundamental understanding of this phenomenon is essential to rationalizing the evolution of freeze-tolerant organisms and developing improved strategies for long-term preservation of biological materials. We present fully atomistic simulations of cold denaturation of an α-helical protein, the widely studied Trp-cage miniprotein. In contrast to the significant destabilization of the folded structure at high temperatures, Trp-cage cold denatures at 210 K into a compact, partially folded state; major elements of the secondary structure, including the α-helix, are conserved, but the salt bridge between aspartic acid and arginine is lost. The stability of Trp-cage's α-helix at low temperatures suggests a possible evolutionary explanation for the prevalence of such structures in antifreeze peptides produced by cold-weather species, such as Arctic char. Although the 310-helix is observed at cold conditions, its position is shifted toward Trp-cage's C-terminus. This shift is accompanied by intrusion of water into Trp-cage's interior and the hydration of buried hydrophobic residues. However, our calculations also show that the dominant contribution to the favorable energetics of low-temperature unfolding of Trp-cage comes from the hydration of hydrophilic residues.

Empirical estimation of local dielectric constants: Toward atomistic design of collagen mimetic peptides

One of the key challenges in modeling protein energetics is the treatment of solvent interactions. This is particularly important in the case of peptides, where much of the molecule is highly exposed to solvent due to its small size. In this study, we develop an empirical method for estimating the local dielectric constant based on an additive model of atomic polarizabilities. Calculated values match reported apparent dielectric constants for a series of Staphylococcus aureus nuclease mutants. Calculated constants are used to determine screening effects on Coulombic interactions and to determine solvation contributions based on a modified Generalized Born model. These terms are incorporated into the protein modeling platform protCAD, and benchmarked on a data set of collagen mimetic peptides for which experimentally determined stabilities are available. Computing local dielectric constants using atomistic protein models and the assumption of additive atomic polarizabilities is a rapid and potentially useful method for improving electrostatics and solvation calculations that can be applied in the computational design of peptides.

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.