Temperature and urea induced denaturation of the TRP-cage mini protein TC5b: A simulation study consistent with experimental observations

Developing a User-Friendly Code for the Fast Estimation of Well-Behaved Real-Space Partial Charges

The Quantum Theory of Atoms in Molecules (QTAIM) provides an intuitive, yet physically sound, strategy to determine the partial charges of any chemical system relying on the topology induced by the electron density ρ(r) . In a previous work [J. Chem. Phys. 2022, 156, 014112], we introduced a machine learning (ML) model for the computation of QTAIM charges of C, H, O, and N atoms at a fraction of the conventional computational cost. Unfortunately, the independent nature of the atomistic predictions implies that the raw atomic charges may not necessarily reconstruct the exact molecular charge, limiting the applicability of the latter in the chemistry realm. Trying to solve such an inconvenience, we introduce NNAIMGUI, a user-friendly code which combines the inferring abilities of ML with an equilibration strategy to afford adequately behaved partial charges. The performance of this approach is put to the test in a variety of scenarios including interpolation and extrapolation regimes (e.g chemical reactions) as well as large systems. The results of this work prove that the equilibrated charges retain the chemically accurate behavior reproduced by the ML models. Furthermore, NNAIMGUI is a fully flexible architecture allowing users to train and use tailor-made models targeted at any atomic property of choice. In this way, the GUI-interfaced code, equipped with visualization utilities, makes the computation of real-space atomic properties much more appealing and intuitive, paving the way toward the extension of QTAIM related descriptors beyond the theoretical chemistry community.

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.

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.

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.

Multiscale Simulation of Protein Hydration Using the SWINGER Dynamical Clustering Algorithm

To perform computationally efficient concurrent multiscale simulations of biological macromolecules in solution, where the all-atom (AT) models are coupled to supramolecular coarse-grained (SCG) solvent models, previous studies resorted to modified AT water models, such as the bundled-simple point charge (SPC) models, that use semiharmonic springs to restrict the relative movement of water molecules within a cluster. Those models can have a significant impact on the simulated biomolecules and can lead, for example, to a partial unfolding of a protein. In this work, we employ the recently developed alternative approach with a dynamical clustering algorithm, SWINGER, which enables a direct coupling of original unmodified AT and SCG water models. We perform an adaptive resolution molecular dynamics simulation of a Trp-Cage miniprotein in multiscale water, where the standard SPC water model is interfaced with the widely used MARTINI SCG model, and demonstrate that, compared to the corresponding full-blown AT simulations, the structural and dynamic properties of the solvated protein and surrounding solvent are well reproduced by our approach.

The effect of chirality and steric hindrance on intrinsic backbone conformational propensities: tools for protein design

The conformational propensities of amino acids are an amalgamation of sequence effects, environmental effects and underlying intrinsic behavior. Many have attempted to investigate neighboring residue effects to aid in our understanding of protein folding and improve structure prediction efforts, especially with respect to difficult to characterize states, such as disordered or unfolded states. Host-guest peptide series are a useful tool in examining the propensities of the amino acids free from the surrounding protein structure. Here, we compare the distributions of the backbone dihedral angles (φ/ψ) of the 20 proteogenic amino acids in two different sequence contexts using the AAXAA and GGXGG host-guest pentapeptide series. We further examine their intrinsic behaviors across three environmental contexts: water at 298 K, water at 498 K, and 8 M urea at 298 K. The GGXGG systems provide the intrinsic amino acid propensities devoid of any conformational context. The alanine residues in the AAXAA series enforce backbone chirality, thereby providing a model of the intrinsic behavior of amino acids in a protein chain. Our results show modest differences in φ/ψ distributions due to the steric constraints of the Ala side chains, the magnitudes of which are dependent on the denaturing conditions. One of the strongest factors modulating φ/ψ distributions was the protonation of titratable side chains, and the largest differences observed were in the amino acid propensities for the rarely sampled αL region.

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.

Structural insights into the Trp-cage folding intermediate formation

The 20 residue long Trp-cage is the smallest protein known, and thus has been the subject of several in vitro and in silico folding studies. Here, we report the multistate folding scenario of the miniprotein in atomic detail. We detected and characterized different intermediate states by temperature dependent NMR measurements of the (15)N and (13)C/(15)N labeled protein, both at neutral and acidic pH values. We developed a deconvolution technique to characterize the invisible--fully folded, unfolded and intermediate--fast exchanging states. Using nonlinear fitting methods we can obtain both the thermodynamic parameters (ΔH(F-I), T(m)(F-I), ΔC(p)(F-I) and ΔH(I-U), T(m)(I-U), ΔC(p)(I-U)) and the NMR chemical shifts of the conformers of the multistate unfolding process. During the unfolding of Trp-cage distinct intermediates evolve: a fast-exchanging intermediate is present under neutral conditions, whereas a slow-exchanging intermediate-pair emerges at acidic pH. The fast-exchanging intermediate has a native-like structure with a short α-helix in the G(11)-G(15) segment, whereas the slow-exchanging intermediate-pair presents elevated dynamics, with no detectable native-like residue contacts in which the G(11)-P(12) peptide bond has either cis or trans conformation. Heteronuclear relaxation studies combined with MD simulations revealed the source of backbone mobility and the nature of structural rearrangements during these transitions. The ability to detect structural and dynamic information about folding intermediates in vitro provides an excellent opportunity to gain new insights into the energetic aspects of the energy landscape of protein folding. Our new experimental data offer exceptional testing ground for further computational simulations.

Effect of surfactant hydrophobicity on the pathway for unfolding of ubiquitin

This paper describes the interaction between ubiquitin (UBI) and three sodium n-alkyl sulfates (SC(n)S) that have the same charge (Z = -1) but different hydrophobicity (n = 10, 12, or 14). Increasing the hydrophobicity of the n-alkyl sulfate resulted in (i) an increase in the number of distinct intermediates (that is, complexes of UBI and surfactant) that form along the pathway of unfolding, (ii) a decrease in the minimum concentrations of surfactant at which intermediates begin to form (i.e., a more negative ΔG(binding) of surfactant for UBI), and (iii) an increase in the number of surfactant molecules bound to UBI in each intermediate or complex. These results demonstrate that small changes in the hydrophobicity of a surfactant can significantly alter the binding interactions with a folded or unfolded cytosolic protein.

Structure and stability of a thermostable carboxylesterase from the thermoacidophilic archaeon Sulfolobus tokodaii

The hormone-sensitive lipase (HSL) family is comprised of carboxylesterases and lipases with similarity to mammalian HSL. Thermophilic enzymes of this family have a high potential for use in biocatalysis. We prepared and crystallized a carboxylesterase of the HSL family from Sulfolobus tokodaii (Sto-Est), and determined its structures in the presence and absence of an inhibitor. Sto-Est forms a dimer in solution and the crystal structure suggests the presence of a stable biological dimer. We identified a residue close to the dimer interface, R267, which is conserved in archaeal enzymes of HSL family and is in close proximity to the same residue from the other monomer. Mutations of R267 to Glu, Gly and Lys were conducted and the resultant R267 mutants were characterized and crystallized. The structures of R267E, R267G and R267K are highly similar to that of Sto-Est with only slight differences in atomic coordinates. The dimerized states of R267E and R267G are unstable under denaturing conditions or at high temperature, as shown by a urea-induced dimer dissociation experiment and molecular dynamics simulation. R267E is the most unstable mutant protein, followed by R267G and R267K, as shown by the thermal denaturation curve and optimum temperature for activity. From the data, we discuss the importance of R267 in maintaining the dimer integrity of Sto-Est.

Comparison of chemical and thermal protein denaturation by combination of computational and experimental approaches. II

Chemical and thermal denaturation methods have been widely used to investigate folding processes of proteins in vitro. However, a molecular understanding of the relationship between these two perturbation methods is lacking. Here, we combined computational and experimental approaches to investigate denaturing effects on three structurally different proteins. We derived a linear relationship between thermal denaturation at temperature T(b) and chemical denaturation at another temperature T(u) using the stability change of a protein (ΔG). For this, we related the dependence of ΔG on temperature, in the Gibbs-Helmholtz equation, to that of ΔG on urea concentration in the linear extrapolation method, assuming that there is a temperature pair from the urea (T(u)) and the aqueous (T(b)) ensembles that produces the same protein structures. We tested this relationship on apoazurin, cytochrome c, and apoflavodoxin using coarse-grained molecular simulations. We found a linear correlation between the temperature for a particular structural ensemble in the absence of urea, T(b), and the temperature of the same structural ensemble at a specific urea concentration, T(u). The in silico results agreed with in vitro far-UV circular dichroism data on apoazurin and cytochrome c. We conclude that chemical and thermal unfolding processes correlate in terms of thermodynamics and structural ensembles at most conditions; however, deviations were found at high concentrations of denaturant.

Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I

Proteins fold and function in the crowded environment of the cell's interior. In the recent years it has been well established that the so-called "macromolecular crowding" effect enhances the folding stability of proteins by destabilizing their unfolded states for selected proteins. On the other hand, chemical and thermal denaturation is often used in experiments as a tool to destabilize a protein by populating the unfolded states when probing its folding landscape and thermodynamic properties. However, little is known about the complicated effects of these synergistic perturbations acting on the kinetic properties of proteins, particularly when large structural fluctuations, such as protein folding, have been involved. In this study, we have first investigated the folding mechanism of Trp-cage dependent on urea concentration by coarse-grained molecular simulations where the impact of urea is implemented into an energy function of the side chain and/or backbone interactions derived from the all-atomistic molecular dynamics simulations with urea through a Boltzmann inversion method. In urea solution, the folding rates of a model miniprotein Trp-cage decrease and the folded state slightly swells due to a lack of contact formation between side chains at the terminal regions. In addition, the equilibrium m-values of Trp-cage from the computer simulations are in agreement with experimental measurements. We have further investigated the combined effects of urea denaturation and macromolecular crowding on Trp-cage's folding mechanism where crowding agents are modeled as hard-spheres. The enhancement of folding rates of Trp-cage is most pronounced by macromolecular crowding effect when the extended conformations of Trp-cast dominate at high urea concentration. Our study makes quantitatively testable predictions on protein folding dynamics in a complex environment involving both chemical denaturation and macromolecular crowding effects.

The CLN025 decapeptide retains a β-hairpin conformation in urea and guanidinium chloride

The conformational stability of the β-hairpin miniprotein, CLN025, a variant of chignolin in which the N- and C-terminal glycines are replaced by tyrosines, in various concentrations of guanidinium chloride (GdmCl) and urea was examined by molecular dynamics simulations and electronic circular dichroism (ECD) spectropolarimetry. The peptide maintains its β-hairpin conformation in GdmCl and urea solutions. In GdmCl, Gly7 influences the turn to reduce the number of Asp3-Gly7 H-bonds and the Tyr1-Trp9 H-bond is lost. The structure of the peptide is less stable in 3 M GdmCl than in water or 6 M GdmCl, because the number of Asp3-Thr8 and Tyr1-Tyr10 H-bonds are reduced and the Tyr2 side chain moves away from the Pro4 and Trp9 side chains and toward the Tyr10 side chain. This reduces the number of Tyr2-Pro4 CH-π interactions and Tyr2-Trp9 and Tyr1-Tyr10 aromatic-aromatic (Ar-Ar) interactions and increases the number of Tyr2-Tyr10 Ar-Ar interactions. In 6 M GdmCl at 300 and 333 K, the number of Tyr1-Tyr10 and Asp3-Thr8 H-bonds increases, but fewer structures have Tyr2-Pro4 CH-π and Tyr1-Tyr10 and Tyr2-Trp9 Ar-Ar interactions. In urea, Gly7 is in a mixture of β-turn and random meander structures and the number of Asp3-Thr6 and Tyr1-Tyr10 H-bonds are reduced as are the number of Tyr2-Pro4 CH-π interactions and Tyr1-Tyr10 and Tyr2-Trp9 Ar-Ar interactions. In 4 M urea, a shorter turn places Gly7 into the β-sheet region and Tyr10 is pushed out into the solvent. In 8 M urea, the number of Asp3-Glu5 H-bonds is increased and the β-sheet is lost, but the electrostatic interaction between the charged termini is restored and a cation-π interaction between the indolyl ring of Trp9 and the positively charged N-terminus is formed. In 8 M urea at 333 K, the β-hairpin conformation is almost lost. The structure of CLN025 is stable, because the weakly polar interactions and H-bonds maintain the β-hairpin conformation in the various environments. CLN025 should not be considered a miniprotein, because it lacks a well-defined tertiary structure, it is resistant to denaturation, it does not have an increased heat capacity near its melting temperature, and the structures near and above the melting temperature retain a β-hairpin conformation.

Multiscale investigation of chemical interference in proteins

We developed a multiscale approach (MultiSCAAL) that integrates the potential of mean force obtained from all-atomistic molecular dynamics simulations with a knowledge-based energy function for coarse-grained molecular simulations in better exploring the energy landscape of a small protein under chemical interference such as chemical denaturation. An excessive amount of water molecules in all-atomistic molecular dynamics simulations often negatively impacts the sampling efficiency of some advanced sampling techniques such as the replica exchange method and it makes the investigation of chemical interferences on protein dynamics difficult. Thus, there is a need to develop an effective strategy that focuses on sampling structural changes in protein conformations rather than solvent molecule fluctuations. In this work, we address this issue by devising a multiscale simulation scheme (MultiSCAAL) that bridges the gap between all-atomistic molecular dynamics simulation and coarse-grained molecular simulation. The two key features of this scheme are the Boltzmann inversion and a protein atomistic reconstruction method we previously developed (SCAAL). Using MultiSCAAL, we were able to enhance the sampling efficiency of proteins solvated by explicit water molecules. Our method has been tested on the folding energy landscape of a small protein Trp-cage with explicit solvent under 8M urea using both the all-atomistic replica exchange molecular dynamics and MultiSCAAL. We compared computational analyses on ensemble conformations of Trp-cage with its available experimental NOE distances. The analysis demonstrated that conformations explored by MultiSCAAL better agree with the ones probed in the experiments because it can effectively capture the changes in side-chain orientations that can flip out of the hydrophobic pocket in the presence of urea and water molecules. In this regard, MultiSCAAL is a promising and effective sampling scheme for investigating chemical interference which presents a great challenge when modeling protein interactions in vivo.

Thermodynamics of the Trp-cage miniprotein unfolding in urea

The thermodynamic properties of unfolding of the Trp-cage mini protein in the presence of various concentrations of urea have been characterized using temperature-induced unfolding monitored by far-UV circular dichroism spectroscopy. Analysis of the data using a two-state model allowed the calculation of the Gibbs energy of unfolding at 25 degrees C as a function of urea concentration. This in turn was analyzed by the linear extrapolation model that yielded the dependence of Gibbs energy on urea concentration, i.e. the m-value for Trp-cage unfolding. The m-value obtained from the experimental data, as well as the experimental heat capacity change upon unfolding, were correlated with the structural parameters derived from the three dimensional structure of Trp-cage. It is shown that the m-value can be predicted well using a transfer model, while the heat capacity changes are in very good agreement with the empirical models based on model compounds studies. These results provide direct evidence that Trp-cage, despite its small size, is an excellent model for studies of protein unfolding and provide thermodynamic data that can be used to compare with atomistic computer simulations.

Equilibrium study of protein denaturation by urea

Though urea is commonly used to denature proteins, the molecular mechanism of its denaturing ability is still a subject of considerable debate. Previous molecular dynamics simulation studies have sought to elucidate the mechanism of urea denaturation by focusing on the pathway of denaturation rather than examining the effect of urea on the folding/unfolding equilibrium, which is commonly measured in experiment. Here we report the reversible folding/unfolding equilibrium of Trp-cage miniprotein in the presence of urea, over a broad range of urea concentrations, using all-atom Replica exchange MD simulations. The simulations capture the experimentally observed linear dependence of unfolding free energy on urea concentration. We find that the denaturation is driven by favorable direct interaction of urea with the protein through both electrostatic and van der Waals forces and quantify their contribution. Though the magnitude of direct electrostatic interaction of urea is larger than van der Waals, the difference between unfolded and folded ensembles is dominated by the van der Waals interaction. We also find that hydrogen bonding of urea to the peptide backbone does not play a dominant role in denaturation. The unfolded ensemble sampled depends on urea concentration, with greater urea concentration favoring conformations with greater solvent exposure. The m-value is predicted to increase with temperature and more strongly so with pressure.