Theoretical studies of protein folding and unfolding

A Stochastic Landscape Approach for Protein Folding State Classification

Protein folding is a critical process that determines the functional state of proteins. Proper folding is essential for proteins to acquire their functional three-dimensional structures and execute their biological role, whereas misfolded proteins can lead to various diseases, including neurodegenerative disorders like Alzheimer's and Parkinson's. Therefore, a deeper understanding of protein folding is vital for understanding disease mechanisms and developing therapeutic strategies. This study introduces the Stochastic Landscape Classification (SLC), an innovative, automated, nonlearning algorithm that quantitatively analyzes protein folding dynamics. Focusing on collective variables (CVs) - low-dimensional representations of complex dynamical systems like molecular dynamics (MD) of macromolecules - the SLC approach segments the CVs into distinct macrostates, revealing the protein folding pathway explored by MD simulations. The segmentation is achieved by analyzing changes in CV trends and clustering these segments using a standard density-based spatial clustering of applications with noise (DBSCAN) scheme. Applied to the MD-based CV trajectories of Chignolin and Trp-Cage proteins, the SLC demonstrates apposite accuracy, validated by comparing standard classification metrics against ground-truth data. These metrics affirm the efficacy of the SLC in capturing intricate protein dynamics and offer a method to evaluate and select the most informative CVs. The practical application of this technique lies in its ability to provide a detailed, quantitative description of protein folding processes, with significant implications for understanding and manipulating protein behavior in industrial and pharmaceutical contexts.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Modeling SARS-CoV-2 spike/ACE2 protein-protein interactions for predicting the binding affinity of new spike variants for ACE2, and novel ACE2 structurally related human protein targets, for COVID-19 handling in the 3PM context

Aims

The rapid spread of new SARS-CoV-2 variants has highlighted the crucial role played in the infection by mutations occurring at the SARS-CoV-2 spike receptor binding domain (RBD) in the interactions with the human ACE2 receptor. In this context, it urgently needs to develop new rapid tools for quickly predicting the affinity of ACE2 for the SARS-CoV-2 spike RBD protein variants to be used with the ongoing SARS-CoV-2 genomic sequencing activities in the clinics, aiming to gain clues about the transmissibility and virulence of new variants, to prevent new outbreaks and to quickly estimate the severity of the disease in the context of the 3PM.

Methods

In our study, we used a computational pipeline for calculating the interaction energies at the SARS-CoV-2 spike RBD/ACE2 protein–protein interface for a selected group of characterized infectious variants of concern/interest (VoC/VoI). By using our pipeline, we built 3D comparative models of the SARS-CoV-2 spike RBD/ACE2 protein complexes for the VoC B.1.1.7-United Kingdom (carrying the mutations of concern/interest N501Y, S494P, E484K at the RBD), P.1-Japan/Brazil (RBD mutations: K417T, E484K, N501Y), B.1.351-South Africa (RBD mutations: K417N, E484K, N501Y), B.1.427/B.1.429-California (RBD mutations: L452R), the B.1.141 (RBD mutations: N439K), and the recent B.1.617.1-India (RBD mutations: L452R; E484Q) and the B.1.620 (RBD mutations: S477N; E484K). Then, we used the obtained 3D comparative models of the SARS-CoV-2 spike RBD/ACE2 protein complexes for predicting the interaction energies at the protein–protein interface.

Results

Along SARS-CoV-2 mutation database screening and mutation localization analysis, it was ascertained that the most dangerous mutations at VoC/VoI spike proteins are located mainly at three regions of the SARS-CoV-2 spike “boat-shaped” receptor binding motif, on the RBD domain. Notably, the P.1 Japan/Brazil variant present three mutations, K417T, E484K, N501Y, located along the entire receptor binding motif, which apparently determines the highest interaction energy at the SARS-CoV-2 spike RBD/ACE2 protein–protein interface, among those calculated. Conversely, it was also observed that the replacement of a single acidic/hydrophilic residue with a basic residue (E484K or N439K) at the “stern” or “bow” regions, of the boat-shaped receptor binding motif on the RBD, appears to determine an interaction energy with ACE2 receptor higher than that observed with single mutations occurring at the “hull” region or with other multiple mutants. In addition, our pipeline allowed searching for ACE2 structurally related proteins, i.e., THOP1 and NLN, which deserve to be investigated for their possible involvement in interactions with the SARS-CoV-2 spike protein, in those tissues showing a low expression of ACE2, or as a novel receptor for future spike variants. A freely available web-tool for the in silico calculation of the interaction energy at the SARS-CoV-2 spike RBD/ACE2 protein–protein interface, starting from the sequences of the investigated spike and/or ACE2 variants, was made available for the scientific community at: https://www.mitoairm.it/covid19affinities.

Conclusion

In the context of the PPPM/3PM, the employment of the described pipeline through the provided webservice, together with the ongoing SARS-CoV-2 genomic sequencing, would help to predict the transmissibility of new variants sequenced from future patients, depending on SARS-CoV-2 genomic sequencing activities and on the specific amino acid replacement and/or on its location on the SARS-CoV-2 spike RBD, to put in play all the possible counteractions for preventing the most deleterious scenarios of new outbreaks, taking into consideration that a greater transmissibility has not to be necessarily related to a more severe manifestation of the disease.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13167-021-00267-w.

Variable-Temperature Native Mass Spectrometry for Studies of Protein Folding, Stabilities, Assembly, and Molecular Interactions

The structures and conformational dynamics of proteins, protein complexes, and their noncovalent interactions with other molecules are controlled specifically by the Gibbs free energy (entropy and enthalpy) of the system. For some organisms, temperature is highly regulated, but the majority of biophysical studies are carried out at room, nonphysiological temperature. In this review, we describe variable-temperature electrospray ionization (vT-ESI) mass spectrometry (MS)-based studies with unparalleled sensitivity, dynamic range, and selectivity for studies of both cold- and heat-induced chemical processes. Such studies provide direct determinations of stabilities, reactivities, and thermodynamic measurements for native and non-native structures of proteins and protein complexes and for protein-ligand interactions. Highlighted in this review are vT-ESI-MS studies that reveal 40 different conformers of chymotrypsin inhibitor 2, a classic two-state (native → unfolded) unfolder, and thermochemistry for a model membrane protein system binding lipid and its regulatory protein. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Effects of Ionic Liquids on Metalloproteins

In the past decade, innovative protein therapies and bio-similar industries have grown rapidly. Additionally, ionic liquids (ILs) have been an area of great interest and rapid development in industrial processes over a similar timeline. Therefore, there is a pressing need to understand the structure and function of proteins in novel environments with ILs. Understanding the short-term and long-term stability of protein molecules in IL formulations will be key to using ILs for protein technologies. Similarly, ILs have been investigated as part of therapeutic delivery systems and implicated in numerous studies in which ILs impact the activity and/or stability of protein molecules. Notably, many of the proteins used in industrial applications are involved in redox chemistry, and thus often contain metal ions or metal-associated cofactors. In this review article, we focus on the current understanding of protein structure-function relationship in the presence of ILs, specifically focusing on the effect of ILs on metal containing proteins.

Molecular forces governing protein-protein interaction: Structure-function relationship of complexes protein in the food industry

The application of protein-protein interaction (PPI) has been widely used in various industries, such as food, nutraceutical, and pharmaceutical. A deeper understanding of PPI is needed, and the molecular forces governing proteins and their interaction must be explained. The design of new structures with improved functional properties, e.g., solubility, emulsion, and gelation, has been fueled by the development of structural and colloidal building blocks. In this review, the molecular forces of protein structures are discussed, followed by the relationship between molecular force and structure, ways of a bind of proteins together in solution or at the interface, and functional properties. A more detailed look is thus taken at the relationship between the various influencing factors on molecular forces involved in PPI. These factors include protein properties, such as types, concentration, and mixing ratio, and solvent conditions, such as ionic strength and pH. This review also summarizes methods tha1t are capable of identifying molecular forces in protein and PPI, as well as characterizing protein structure.

Evidence for Many Unique Solution Structures for Chymotrypsin Inhibitor 2: A Thermodynamic Perspective Derived from vT-ESI-IMS-MS Measurements

Chymotrypsin inhibitor 2 (CI-2) is a classic model for two-state cooperative protein folding and is one of the most extensively studied systems. Alan Fersht, a pioneer in the field of structural biology, has studied the wild-type (wt) and over 100 mutant forms of CI-2 with traditional analytical and biochemical techniques. Here, we examine wt CI-2 and three mutant forms (A16G, K11A, L32A) to demonstrate the utility of variable-temperature (vT) electrospray ionization (ESI) paired with ion mobility spectrometry (IMS) and mass spectrometry (MS) to map the free energy folding landscape. As the solution temperature is increased, the abundance of each of the six ESI charge states for wt CI-2 and each mutant is found to vary independently. These results require that at least six unique types of CI-2 solution conformers are present. Ion mobility analysis reveals that within each charge state there are additional conformers having distinct solution temperature profiles. A model of the data at ∼30 different temperatures for all four systems suggests the presence of 41 unique CI-2 solution conformations. A thermodynamic analysis of this system yields values of ΔC_p as well as ΔG, ΔH, and ΔS for each state at every temperature studied. Detailed energy landscapes derived from these data provide a rare glimpse into Anfinsen's thermodynamic hypothesis and the process of thermal denaturation, normally thought of as a cooperative two-state transition involving the native state and unstructured denatured species. Specifically, as the temperature is varied, the entropies and enthalpies of different conformers undergo dramatic changes in magnitude and relative order to maintain the delicate balance associated with equilibrium.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

Mechanistic Insights into Protein Stability and Self-aggregation in GLUT1 Genetic Variants Causing GLUT1-Deficiency Syndrome

Human sodium-independent glucose cotransporter 1 (hGLUT1) has been studied for its tetramerization and multimerization at the cell surface. Homozygous or compound heterozygous mutations in hGLUT1 elicit GLUT1-deficiency syndrome (GLUT1-DS), a metabolic disorder, which results in impaired glucose transport into the brain. The reduced cell surface expression or loss of function have been shown for some GLUT1 mutants. However, the mechanism by which deleterious mutations affect protein structure, conformational stability and GLUT1 oligomerization is not known and require investigation. In this review, we combined previous knowledge of GLUT1 mutations with hGLUT1 crystal structure to analyze native interactions and several natural single-point mutations. The modeling of native hGLUT1 structure confirmed the roles of native residues in forming a range of side-chain interactions. Interestingly, the modeled mutants pointed to the formation of a variety of non-native novel interactions, altering interaction networks and potentially eliciting protein misfolding. Self-aggregation of the last part of hGLUT1 was predicted using protein aggregation prediction tool. Furthermore, an increase in aggregation potential in the aggregation-prone regions was estimated for several mutants suggesting increased aggregation of misfolded protein. Protein stability change analysis predicted that GLUT1 mutant proteins are unstable. Combining GLUT1 oligomerization behavior with our modeling, aggregation prediction, and protein stability analyses, this work provides state-of-the-art view of GLUT1 genetic mutations that could destabilize native interactions, generate novel interactions, trigger protein misfolding, and enhance protein aggregation in a disease state.

Atomic clusters with addressable complexity

A general formulation for constructing addressable atomic clusters is introduced, based on one or more reference structures. By modifying the well depths in a given interatomic potential in favour of nearest-neighbour interactions that are defined in the reference(s), the potential energy landscape can be biased to make a particular permutational isomer the global minimum. The magnitude of the bias changes the resulting potential energy landscape systematically, providing a framework to produce clusters that should self-organise efficiently into the target structure. These features are illustrated for small systems, where all the relevant local minima and transition states can be identified, and for the low-energy regions of the landscape for larger clusters. For a 55-particle cluster, it is possible to design a target structure from a transition state of the original potential and to retain this structure in a doubly addressable landscape. Disconnectivity graphs based on local minima that have no direct connections to a lower minimum provide a helpful way to visualise the larger databases. These minima correspond to the termini of monotonic sequences, which always proceed downhill in terms of potential energy, and we identify them as a class of biminimum. Multiple copies of the target cluster are treated by adding a repulsive term between particles with the same address to maintain distinguishable targets upon aggregation. By tuning the magnitude of this term, it is possible to create assemblies of the target cluster corresponding to a variety of structures, including rings and chains.

Distance-dependent hydrophobic-hydrophobic contacts in protein folding simulations

Successful prediction of protein folding from an amino acid sequence is a challenge in computational biology. In order to reveal the geometric constraints that drive protein folding, highlight those constraints kept or missed by distinct lattices and for establishing which class of intra- and inter-secondary structure element interactions is the most relevant for the correct folding of proteins, we have calculated inter-alpha carbon distances in a set of 42 crystal structures consisting of mainly helix, sheet or mixed conformations. The inter-alpha carbon distances were also calculated in several lattice "hydrophobic-polar" models built from the same protein set. We found that helix structures are more prone to form "hydrophobic-hydrophobic" contacts than beta-sheet structures. At a distance lower than or equal to 3.8 Å (very short-range interactions), "hydrophobic-hydrophobic" contacts are almost absent in the native structures, while they are frequent in all the analyzed lattice models. At distances in-between 3.8 and 9.5 Å (short-/medium-range interactions), the best performing lattice for reproducing mainly helix structures is the body-centered-cubic lattice. If protein structures contain sheet portions, lattice performances get worse, with few exceptions observed for double-tetrahedral and body-centered-cubic lattices. Finally, we can observe that ab initio protein folding algorithms, i.e. those based on the employment of lattices and Monte Carlo simulated annealings, can be improved simply and effectively by preventing the generation of "hydrophobic-hydrophobic" contacts shorter than 3.8 Å, by monitoring the "hydrophobic-hydrophobic/polar-polar" contact ratio in short-/medium distance ranges and by using preferentially a body-centered-cubic lattice.

Single H5N1 influenza A neuraminidase mutation develops resistance to oseltamivir due to distorted conformational and drug binding landscape: multiple molecular dynamics analyses

Clinical studies showed that a single mutation, I117V, develops severe resistance to oseltamivir, the first orally active influenza A neuraminidase inhibitor, in highly pathogenic H5N1 influenza A viruses.

A hydrophobic gold surface triggers misfolding and aggregation of the amyloidogenic Josephin domain in monomeric form, while leaving the oligomers unaffected

Protein misfolding and aggregation in intracellular and extracellular spaces is regarded as a main marker of the presence of degenerative disorders such as amyloidoses. To elucidate the mechanisms of protein misfolding, the interaction of proteins with inorganic surfaces is of particular relevance, since surfaces displaying different wettability properties may represent model systems of the cell membrane. Here, we unveil the role of surface hydrophobicity/hydrophilicity in the misfolding of the Josephin domain (JD), a globular-shaped domain of ataxin-3, the protein responsible for the spinocerebellar ataxia type 3. By means of a combined experimental and theoretical approach based on atomic force microscopy, Fourier transform infrared spectroscopy and molecular dynamics simulations, we reveal changes in JD morphology and secondary structure elicited by the interaction with the hydrophobic gold substrate, but not by the hydrophilic mica. Our results demonstrate that the interaction with the gold surface triggers misfolding of the JD when it is in native-like configuration, while no structural modification is observed after the protein has undergone oligomerization. This raises the possibility that biological membranes would be unable to affect amyloid oligomeric structures and toxicity.

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

Describing a potential energy surface in terms of local minima and the transition states that connect them provides a conceptual and computational framework for understanding and predicting observable properties. Visualizing the potential energy landscape using disconnectivity graphs supplies a graphical connection between different structure-seeking systems, which can relax efficiently to a particular morphology. Landscapes involving competing morphologies support multiple potential energy funnels, which may exhibit characteristic heat capacity features and relaxation time scales. These connections between the organization of the potential energy landscape and structure, dynamics and thermodynamics are common to all the examples presented, ranging from atomic and molecular clusters to biomolecules and soft and condensed matter. Further connections between motifs in the energy landscape and the interparticle forces can be developed using symmetry considerations and results from catastrophe theory.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

Enhancement of the hydrolysis activity of β-galactosidase from Geobacillus stearothermophilus by saturation mutagenesis

Thermostable β-galactosidase (BgaB) from Geobacillus stearothermophilus is characterized by its thermoactivity in the hydrolysis of lactose to produce lactose-free milk products. However, BgaB has limited activity toward lactose. We established a method for screening evolved mutants with high hydrolysis activity based on prediction of substrate binding sites. Seven amino acid residues were identified as candidates for substrate binding to galactose. To study the hydrolysis activity of these residues, we constructed mutants by site-saturation mutagenesis of these residue sites, and each variant was screened for its hydrolysis activity. The first round of mutagenesis showed that changes in amino acid residues of Arg109, Tyr272, and Glu351 resulted in altered hydrolysis activity, including greater activity toward ortho-nitrophenyl-β-d-galactopyranoside (oNPG). The mutants R109V and R109L displayed changes in the optimum pH from 7.0 to 6.5, and the mutant R109V/L displayed different substrate affinity and catalytic efficiency (k(cat)/K(m)). Mutant R109G showed complete loss of BgaB enzymatic activity, suggesting that Arg109 plays a significant role in maintaining hydrolysis activity. The optimum pH of mutant E351R increased from 7.0 to 7.5 and this mutant showed a prominent increase in catalytic efficiency with oNPG and lactose as substrates.

Balancing simulation accuracy and efficiency with the Amber united atom force field

We have analyzed the quality of a recently proposed Amber united-atom model and its overall efficiency in ab initio folding and thermodynamic sampling of two stable beta-hairpins. It is found that the mean backbone structures are quite consistent between the simulations in the united-atom and its corresponding all-atom models in Amber. More importantly, the simulated beta turns are also consistent between the two models. Finally, the chemical shifts on H alpha are highly consistent between simulations in the two models, although the simulated chemical shifts are lower than experiment, indicating less structured peptides, probably due to the omission of the hydrophobic term in the simulations. More interestingly, the stabilities of both beta-hairpins at room temperature are similar to those derived from the NMR measurement, whether the united-atom or the all-atom model is used. Detailed analysis shows high percentages of backbone torsion angles within the beta region and high percentages of native contacts. Given the reasonable quality of the united-atom model with respect to experimental data, we have further studied the simulation efficiency of the united-atom model over the all-atom model. Our data shows that the united-atom model is a factor of 6-8 faster than the all-atom model as measured with the ab initio first pass folding time for the two tested beta-hairpins. Detailed structural analysis shows that all ab initio folded trajectories enter the native basin, whether the united-atom model or the all-atom model is used. Finally, we have also studied the simulation efficiency of the united-atom model as measured in terms of how fast thermodynamic convergence can be achieved. It is apparent that the united-atom simulations reach convergence faster than the all-atom simulations with respect to both mean potential energies and mean native contacts. These findings show that the efficiency of the united-atom model is clearly beyond the per-step dynamics simulation of about 2 over the all-atom model. Thus, reasonable reduction of a protein model can be achieved with improved sampling efficiency while still preserving a high level of accuracy for applications in both ab initio folding and thermodynamic sampling. This study motivates us to develop more simplified protein models with sufficient consistency with the all-atom models for enhanced conformational sampling.

Mechanism of formation of the C-terminal beta-hairpin of the B3 domain of the immunoglobulin-binding protein G from Streptococcus. IV. Implication for the mechanism of folding of the parent protein

A 34-residue alpha/beta peptide [IG(28-61)], derived from the C-terminal part of the B3 domain of the immunoglobulin binding protein G from Streptoccocus, was studied using CD and NMR spectroscopy at various temperatures and by differential scanning calorimetry. It was found that the C-terminal part (a 16-residue-long fragment) of this peptide, which corresponds to the sequence of the beta-hairpin in the native structure, forms structure similar to the beta-hairpin only at T = 313 K, and the structure is stabilized by non-native long-range hydrophobic interactions (Val47-Val59). On the other hand, the N-terminal part of IG(28-61), which corresponds to the middle alpha-helix in the native structure, is unstructured at low temperature (283 K) and forms an alpha-helix-like structure at 305 K, and only one helical turn is observed at 313 K. At all temperatures at which NMR experiments were performed (283, 305, and 313 K), we do not observe any long-range connectivities which would have supported packing between the C-terminal (beta-hairpin) and the N-terminal (alpha-helix) parts of the sequence. Such interactions are absent, in contrast to the folding pathway of the B domain of protein G, proposed recently by Kmiecik and Kolinski (Biophys J 2008, 94, 726-736), based on Monte-Carlo dynamics studies. Alternative folding mechanisms are proposed and discussed.

Thermodynamics and folding pathways of trpzip2: an accelerated molecular dynamics simulation study

In this paper, we apply an enhanced sampling method introduced earlier to study the folding mechanism of a beta-hairpin, trpzip2, using an all-atom potential for the protein and an implicit model for the solvent. The enhanced sampling method allows us to obtain multiple protein folding and unfolding trajectories in relatively short simulations. The sufficient sampling of folding and unfolding events of trpzip2 makes possible a more detailed investigation of its folding landscape and thermodynamics, leading to the identification of folding pathways. The analysis of the thermodynamics involved in the folding of trpzip2 showed that this polypeptide folds by two stages: a downhill hydrophobic collapse followed by formation of native hydrogen bonds. During the hydrogen bond formation, a transition state can be identified with only one native hydrogen bond being formed, which is more consistent with a 'zip-out' mechanism. To address the dynamics in a more reliable way, explicit solvent was used for the estimation of the diffusion constant, which was used in the Kramer's theory, together with the free energy profile calculated using the enhanced sampling and the implicit solvent, to calculate the folding rate. The calculated folding time agrees well with the experimental value of 2.5 micros.

Pseudocounts for transcription factor binding sites

To represent the sequence specificity of transcription factors, the position weight matrix (PWM) is widely used. In most cases, each element is defined as a log likelihood ratio of a base appearing at a certain position, which is estimated from a finite number of known binding sites. To avoid bias due to this small sample size, a certain numeric value, called a pseudocount, is usually allocated for each position, and its fraction according to the background base composition is added to each element. So far, there has been no consensus on the optimal pseudocount value. In this study, we simulated the sampling process by artificially generating binding sites based on observed nucleotide frequencies in a public PWM database, and then the generated matrix with an added pseudocount value was compared to the original frequency matrix using various measures. Although the results were somewhat different between measures, in many cases, we could find an optimal pseudocount value for each matrix. These optimal values are independent of the sample size and are clearly correlated with the entropy of the original matrices, meaning that larger pseudocount vales are preferable for less conserved binding sites. As a simple representative, we suggest the value of 0.8 for practical uses.

Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

To provide evidence for the interpretation of temperature-dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz-Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One-dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's beta-sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable beta-strands I and II and those of the less stable strands III-V. Although the original ME model successfully captures folding features of zipper-like one-dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the beta-strands III-V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T-jump experiment at high temperature. The calculation also reports a high stability for the alpha-helix of ubiquitin.

A shorter peptide model from staphylococcal nuclease for the folding-unfolding equilibrium of a beta-hairpin shows that unfolded state has significant contribution from compact conformational states

It is important to understand the conformational features of the unfolded state in equilibrium with folded state under physiological conditions. In this paper, we consider a short peptide model LMYKGQPM from staphylococcal nuclease to model the conformational equilibrium between a hairpin conformation and its unfolded state using molecular dynamics simulation under NVT conditions at 300K using GROMOS96 force field. The free energy landscape has overall funnel-like shape with hairpin conformations sampling the minima. The "unfolded" state has a higher free energy of approximately 12kJ/mol with respect to native hairpin minimum and occupies a plateau region. We find that the unfolded state has significant contributions from compact conformations. Many of these conformations have hairpin-like topology. Further, these compact conformational forms are stabilized by hydrophobic interactions. Conversion between native and non-native hairpins occurs via unfolded states. Frequent conversions between folded and unfolded hairpins are observed with single exponential kinetics. We compare our results with the emerging picture of unfolded state from both experimental and theoretical studies.

Distinct unfolding and refolding pathways of ribonuclease a revealed by heating and cooling temperature jumps

Heating and cooling temperature jumps (T-jumps) were performed using a newly developed technique to trigger unfolding and refolding of wild-type ribonuclease A and a tryptophan-containing variant (Y115W). From the linear Arrhenius plots of the microscopic folding and unfolding rate constants, activation enthalpy (DeltaH(#)), and activation entropy (DeltaS(#)) were determined to characterize the kinetic transition states (TS) for the unfolding and refolding reactions. The single TS of the wild-type protein was split into three for the Y115W variant. Two of these transition states, TS1 and TS2, characterize a slow kinetic phase, and one, TS3, a fast phase. Heating T-jumps induced protein unfolding via TS2 and TS3; cooling T-jumps induced refolding via TS1 and TS3. The observed speed of the fast phase increased at lower temperature, due to a strongly negative DeltaH(#) of the folding-rate constant. The results are consistent with a path-dependent protein folding/unfolding mechanism. TS1 and TS2 are likely to reflect X-Pro(114) isomerization in the folded and unfolded protein, respectively, and TS3 the local conformational change of the beta-hairpin comprising Trp(115). A very fast protein folding/unfolding phase appears to precede both processes. The path dependence of the observed kinetics is suggestive of a rugged energy protein folding funnel.

Folding and unfolding of gammaTIM monomers and dimers

Kinetic simulations of the folding and unfolding of triosephosphate isomerase (TIM) from yeast were conducted using a single monomer gammaTIM polypeptide chain that folds as a monomer and two gammaTIM chains that fold to the native dimer structure. The basic protein model used was a minimalist Gō model using the native structure to determine attractive energies in the protein chain. For each simulation type--monomer unfolding, monomer refolding, dimer unfolding, and dimer refolding--thirty simulations were conducted, successfully capturing each reaction in full. Analysis of the simulations demonstrates four main conclusions. First, all four simulation types have a similar "folding order", i.e., they have similar structures in intermediate stages of folding between the unfolded and folded state. Second, despite this similarity, different intermediate stages are more or less populated in the four different simulations, with 1), no intermediates populated in monomer unfolding; 2), two intermediates populated with beta(2)-beta(4) and beta(1)-beta(5) regions folded in monomer refolding; 3), two intermediates populated with beta(2)-beta(3) and beta(2)-beta(4) regions folded in dimer unfolding; and 4), two intermediates populated with beta(1)-beta(5) and beta(1)-beta(5) + beta(6) + beta(7) + beta(8) regions folded in dimer refolding. Third, simulations demonstrate that dimer binding and unbinding can occur early in the folding process before complete monomer-chain folding. Fourth, excellent agreement is found between the simulations and MPAX (misincorporation proton alkyl exchange) experiments. In total, this agreement demonstrates that the computational Gō model is accurate for gammaTIM and that the energy landscape of gammaTIM appears funneled to the native state.

Structural analysis of kinetic folding intermediates for a TIM barrel protein, indole-3-glycerol phosphate synthase, by hydrogen exchange mass spectrometry and Gō model simulation

The structures of partially folded states appearing during the folding of a (betaalpha)(8) TIM barrel protein, the indole-3-glycerol phosphate synthase from Sulfolobus solfataricus (sIGPS), was assessed by hydrogen exchange mass spectrometry (HX-MS) and Gō model simulations. HX-MS analysis of the peptic peptides derived from the pulse-labeled product of the sub-millisecond folding reaction from the urea-denatured state revealed strong protection in the (betaalpha)(4) region, modest protection in the neighboring (betaalpha)(1-3) and (betaalpha)(5)beta(6) segments and no significant protection in the remaining N and C-terminal segments. These results demonstrate that this species is not a collapsed form of the unfolded state under native-favoring conditions nor is it the native state formed via fast-track folding. However, the striking contrast of these results with the strong protection observed in the (betaalpha)(2-5)beta(6) region after 5 s of folding demonstrates that these species represent kinetically distinct folding intermediates that are not identical as previously thought. A re-examination of the kinetic folding mechanism by chevron analysis of fluorescence data confirmed distinct roles for these two species: the burst-phase intermediate is predicted to be a misfolded, off-pathway intermediate, while the subsequent 5 s intermediate corresponds to an on-pathway equilibrium intermediate. Comparison with the predictions using a C(alpha) Gō model simulation of the kinetic folding reaction for sIGPS shows good agreement with the core of the structure offering protection against exchange in the on-pathway intermediate(s). Because the native-centric Gō model simulations do not explicitly include sequence-specific information, the simulation results support the hypothesis that the topology of TIM barrel proteins is a primary determinant of the folding free energy surface for the productive folding reaction. The early misfolding reaction must involve aspects of non-native structure not detected by the Gō model simulation.

Network scaling invariants help to elucidate basic topological principles of proteins

The structural architecture of proteins continues to be an area of active research. Despite the difference in models dealing with the way proteins fold into their tertiary structures, it is recognized that small regions of proteins tend to fold independently and are then stabilized by interactions between these distinct subunits. However, there are a number of different definitions of what comprises an independent subunit. In the belief that an unequivocal definition of a domain must be based on the most fundamental property of protein 3D structure, namely, the adjacency matrix of inter-residues contact, we adopt a network representation of the protein. In this work, we used a well-established, global method for identifying modules in networks, without any specific reference to the kind of network being analyzed. The algorithm converges toward the maximization of the modularity of the given protein network and, in doing so, allows the representation of the residues of the protein in terms of their intramodule degree, z, and participation coefficient, P. We demonstrate that the labeling of residues in terms of these invariants allows for information-rich representations of the studied proteins as well as to sketch a new way to link sequence, structure, and the dynamical properties of proteins. We discovered a strong invariant character of protein molecules in terms of P/z characterization, pointing to a common topological design of all protein structures. This invariant representation, applied to different protein systems, enabled us to identify the possible functional role of high P/z residues during the folding process. Additionally, we observe a hierarchical behavior of protein structural organization that provides a sequence-secondary-tertiary structure link. The discovery of similar and repeatable scaling laws at different level of definitions going from hydrophobicity patterning along the sequence up to the size of an autonomous folding unit (AFU) and general contact distribution of the entire molecule suggest a hierarchical-like behavior of protein architecture. This implies the possibility to select different privileged scales of observation for deriving useful information on protein systems.

Uncovering the topology of configuration space networks

The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical solution is provided to explain the heavy tail of the degree distribution, neighbor connectivity, and clustering coefficient. This derivation allows us to understand the universal CSN topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a two-dimensional lattice heteropolymer. Moreover, CSNs are shown to fall in the general class of complex networks described by the fitness model.

UV resonance Raman measurements of poly-L-lysine's conformational energy landscapes: dependence on perchlorate concentration and temperature

UV resonance Raman spectroscopy has been used to determine the conformational energy landscape of poly-L-lysine (PLL) in the presence of NaClO4 as a function of temperature. At 1 degree C, in the presence of 0.83 M NaClO4, PLL shows an approximately 86% alpha-helix-like content, which contains alpha-helix and pi-bulge/helix conformations. The high alpha-helix-like content of PLL occurs because of charge screening due to strong ion-pair formation between ClO4- and the lysine side chain -NH3+. As the temperature increases from 1 to 60 degrees C, the alpha-helix and pi-bulge/helix conformations melt into extended conformations (PPII and 2.51-helix). We calculate the Psi Ramachandran angle distribution of the PLL peptide bonds from the UV Raman spectra which allows us to calculate the PLL (un)folding energy landscapes along the Psi reaction coordinate. We observe a basin in the Psi angle conformational space associated with alpha-helix and pi-bulge/helix conformations and another basin for the extended PPII and 2.51-helical conformations.

Equilibrium unfolding of DLC8 monomer by urea and guanidine hydrochloride: Distinctive global and residue level features

We present circular dichroism (CD), steady state fluorescence and multidimensional NMR investigations on the equilibrium unfolding of monomeric dynein light chain protein (DLC8) by urea and guanidine hydrochloride (GdnHCl). Quantitative analysis of the CD and fluorescence denaturation curves reveals that urea unfolding is a two-state process, whereas guanidine unfolding is more complex. NMR investigations in the native state and in the near native states created by low denaturant concentrations enabled residue level characterization of the early structural and dynamic perturbations by the two denaturants. Firstly, (15)N transverse relaxation rates in the native state indicate that the regions around N10, Q27, the loop between beta2 and beta4 strands, and K87 at the C-terminal are potential unfolding initiation sites in the protein. Amide and (15)N chemical shift perturbations indicate different accessibilities of the residues along the chain and help identify locations of the early perturbations by the two denaturants. Guanidine and urea are seen to interact at several sites some of which are different in the two cases. Notable among the common interaction site is that around K87 which is in close proximity to W54 on the protein structure, but the interaction modes of the two denaturants are different. The secondary chemical shifts indicate that the structural perturbation by 1M urea is small, compared to that by guanidine which is more encompassing over the length of the chain. The probable (phi, psi) changes at the individual residues have been calculated using the TALOS algorithm. It appears that the helices in the protein are significantly perturbed by guanidine. Further, comparison of the spectral density functions of the native and the two near native states in the two denaturants implicate greater loosening of the structure by guanidine as compared to that by urea, even though the structures are still in the native state ensemble. These differences in the early perturbations of the native state structure and dynamics by the two denaturants might direct the protein along different pathways, as the unfolding progresses on further increasing the denaturant concentration.

Effect of salt bridges on the energy landscape of a model protein

The effect of introducing salt bridges (gatekeepers) into an off-lattice three-color, 46-bead model protein is investigated in terms of the effect on global optimization statistics. The global minima for all the gatekeepers that exhibited faster folding in previous molecular dynamics studies are located more rapidly than for the original potential, although the global minimum itself may change. Visualization of the underlying potential energy surface using disconnectivity graphs reveals that the gatekeepers exhibit structure intermediate between the original potential and a Go model. Competition between low-lying minima and the global minimum is reduced in the gatekeepers compared to the original potential, and interconversion barriers are generally smaller.

Structural Analysis of Human Lysozyme Using Molecular Dynamics Simulations

In this study, various molecular dynamics simulations were conducted to investigate the effects of ethanol and temperature on the conformational changes of human lysozyme, which may lead insights into amyloidosis. The analyses of some important structural characteristics, such as backbone root-mean-square deviation, secondary structural stability, radius of gyration, accessible surface area, and hydrophobic contact of the hydrophobic core all show that ethanol tends to destabilize human lysozyme at high temperatures. It can be attributed to that higher temperatures result in the destruction of the native structure of this protein, leading to the exposure of the interior hydrophobic core. At this stage, ethanol plays a role to destroy this region by forming hydrophobic interactions between protein and solvent due to its lower polarity comparing to water. Such newly formed intermolecular interactions accelerate the unfolding of this protein, starting from the core between the alpha- and beta-domains. Our results are in good agreement with the previous hypothesis suggesting that the distortion of the hydrophobic core at the alpha- and beta-interface putatively results in the formation of the initial "seed" for amyloid fibril. Although the present results cannot directly be linked to fibril formation, they still provide valuable insights into amyloidosis of human lysozyme.

An evidence for the equilibrium unfolding intermediates of ribonuclease A by tritium labeling method

A formation of a molten globule in the unfolding of ribonuclease A could be considered as an evidence supporting a hypothesis on the existence of such intermediates on the pathway of a protein folding. Using a novel technique (tritium labeling method) we have showed that the ribonuclease A equilibrium unfolding in urea and guanidinium chloride (GuCl) solutions proceeds through a formation of intermediates whose properties (compactness, retention of the larger part hydrophobic core, secondary structure, and native-like folding pattern) correspond to the fundamental characteristics of the molten globule state. The both intermediates are the "wet" molten globules (the globule interior contains the water molecules). The results reveal the noticeable distinctions in intermediates structure, first of all, in the extent of their compactness. The urea intermediate is less compact than that in GuCl. It is shown that the refolding of the protein denatured by GuCl results in the formation of the intermediate which enzyme activity is virtually the same as the activity of the native protein.

Symmetry relations in chemical kinetics arising from microscopic reversibility

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding or unfolding are pointed out.