Protein folding by zipping and assembly

A Perspective on Interdicting in Protein Misfolding for Therapeutic Drug Design: Modulating the Formation of Nonlocal Contacts in α-Synuclein as a Strategy against Parkinson's Disease

In recent work we proposed that interdiction in the earliest contact-formation events along the folding pathway of key viral proteins could provide a novel avenue for therapeutic drug design. In this Perspective we explore the potential applicability of the protein folding interdiction strategy in the realm of neurodegenerative diseases with a specific focus on synucleinopathies. In order to fulfill this goal we review the interdiction proposal and its practical challenges, and we present new results concerning design strategies for possible peptide drugs that could be useful in preventing α-synuclein aggregation.

Hairpin trimer transition state of amyloid fibril

Protein fibril self-assembly is a universal transition implicated in neurodegenerative diseases. Although fibril structure/growth are well characterized, fibril nucleation is poorly understood. Here, we use a computational-experimental approach to resolve fibril nucleation. We show that monomer hairpin content quantified from molecular dynamics simulations is predictive of experimental fibril formation kinetics across a tau motif mutant library. Hairpin trimers are predicted to be fibril transition states; one hairpin spontaneously converts into the cross-beta conformation, templating subsequent fibril growth. We designed a disulfide-linked dimer mimicking the transition state that catalyzes fibril formation, measured by ThT fluorescence and TEM, of wild-type motif - which does not normally fibrillize. A dimer compatible with extended conformations but not the transition-state fails to nucleate fibril at any concentration. Tau repeat domain simulations show how long-range interactions sequester this motif in a mutation-dependent manner. This work implies that different fibril morphologies could arise from disease-dependent hairpin seeding from different loci.

Interdiction in the Early Folding of the p53 DNA-Binding Domain Leads to Its Amyloid-Like Misfolding

In this article, we investigate two issues: (a) the initial contact formation events along the folding pathway of the DNA-binding domain of the tumor suppressor protein p53 (core p53); and (b) the intermolecular events leading to its conversion into a prion-like form upon incubation with peptide P8(250-257). In the case of (a), the calculations employ the sequential collapse model (SCM) to identify the segments involved in the initial contact formation events that nucleate the folding pathway. The model predicts that there are several possible initial non-local contacts of comparative stability. The most stable of these possible initial contacts involve the protein segments 159AMAIY163 and 251ILTII255, and it is the only native-like contact. Thus, it is predicted to constitute “Nature’s shortcut” to the native structure of the core domain of p53. In the case of issue (b), these findings are then combined with experimental evidence showing that the incubation of the core domain of p53 with peptide P8(250-257), which is equivalent to the native protein segment 250PILTIITL257, leads to an amyloid conformational transition. It is explained how the SCM predicts that P8(250-257) effectively interdicts in the formation of the most stable possible initial contact and, thereby, disrupts the subsequent normal folding. Interdiction by polymeric P8(250-257) seeds is also studied. It is then hypothesized that enhanced folding through one or several of the less stable contacts could play a role in P8(250-257)-promoted core p53 amyloid misfolding. These findings are compared to previous results obtained for the prion protein. Experiments are proposed to test the hypothesis presented regarding core p53 amyloid misfolding.

Prediction of protein secondary structure based on an improved channel attention and multiscale convolution module

Prediction of the protein secondary structure is a key issue in protein science. Protein secondary structure prediction (PSSP) aims to construct a function that can map the amino acid sequence into the secondary structure so that the protein secondary structure can be obtained according to the amino acid sequence. Driven by deep learning, the prediction accuracy of the protein secondary structure has been greatly improved in recent years. To explore a new technique of PSSP, this study introduces the concept of an adversarial game into the prediction of the secondary structure, and a conditional generative adversarial network (GAN)-based prediction model is proposed. We introduce a new multiscale convolution module and an improved channel attention (ICA) module into the generator to generate the secondary structure, and then a discriminator is designed to conflict with the generator to learn the complicated features of proteins. Then, we propose a PSSP method based on the proposed multiscale convolution module and ICA module. The experimental results indicate that the conditional GAN-based protein secondary structure prediction (CGAN-PSSP) model is workable and worthy of further study because of the strong feature-learning ability of adversarial learning.

Protein Folding Interdiction Strategy for Therapeutic Drug Development in Viral Diseases: Ebola VP40 and Influenza A M1

In a recent paper, we proposed the folding interdiction target region (FITR) strategy for therapeutic drug design in SARS-CoV-2. This paper expands the application of the FITR strategy by proposing therapeutic drug design approaches against Ebola virus disease and influenza A. We predict target regions for folding interdicting drugs on correspondingly relevant structural proteins of both pathogenic viruses: VP40 of Ebola, and matrix protein M1 of influenza A. Identification of the protein targets employs the sequential collapse model (SCM) for protein folding. It is explained that the model predicts natural peptide candidates in each case from which to start the search for therapeutic drugs. The paper also discusses how these predictions could be tested, as well as some challenges likely to be found when designing effective therapeutic drugs from the proposed peptide candidates. The FITR strategy opens a potential new avenue for the design of therapeutic drugs that promises to be effective against infectious diseases.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Identification of Two Early Folding Stage Prion Non-Local Contacts Suggested to Serve as Key Steps in Directing the Final Fold to Be Either Native or Pathogenic

The initial steps of the folding pathway of the C-terminal domain of the murine prion protein mPrP(90–231) are predicted based on the sequential collapse model (SCM). A non-local dominant contact is found to form between the connecting region between helix 1 and β-sheet 1 and the C-terminal region of helix 3. This non-local contact nucleates the most populated molten globule-like intermediate along the folding pathway. A less stable early non-local contact between segments 120–124 and 179–183, located in the middle of helix 2, promotes the formation of a less populated molten globule-like intermediate. The formation of the dominant non-local contact constitutes an example of the postulated Nature’s Shortcut to the prion protein collapse into the native structure. The possible role of the less populated molten globule-like intermediate is explored as the potential initiation point for the folding for three pathogenic mutants (T182A, I214V, and Q211P in mouse prion numbering) of the prion protein.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

Local Interactions That Contribute Minimal Frustration Determine Foldability

Earlier experiments suggest that the evolutionary information (conservation and coevolution) encoded in protein sequences is necessary and sufficient to specify the fold of a protein family. However, there is no computational work to quantify the effect of such evolutionary information on the folding process. Here we explore the role of early folding steps for sequences designed using coevolution and conservation through a combination of computational and experimental methods. We simulated a repertoire of native and designed WW domain sequences to analyze early local contact formation and found that the N-terminal β-hairpin turn would not form correctly due to strong non-native local contacts in unfoldable sequences. Through a maximum likelihood approach, we identified five local contacts that play a critical role in folding, suggesting that a small subset of amino acid pairs can be used to solve the "needle in the haystack" problem to design foldable sequences. Thus, using the contact probability of those five local contacts that form during the early stage of folding, we built a classification model that predicts the foldability of a WW sequence with 81% accuracy. This classification model was used to redesign WW domain sequences that could not fold due to frustration and make them foldable by introducing a few mutations that led to the stabilization of these critical local contacts. The experimental analysis shows that a redesigned sequence folds and binds to polyproline peptides with a similar affinity as those observed for native WW domains. Overall, our analysis shows that evolutionary-designed sequences should not only satisfy the folding stability but also ensure a minimally frustrated folding landscape.

Mapping Distinct Sequences of Structure Formation Differentiating Multiple Folding Pathways of a Small Protein

To determine experimentally how the multiple folding pathways of a protein differ, in the order in which the structural parts are assembled, has been a long-standing challenge. To resolve whether structure formation during folding can progress in multiple ways, the complex folding landscape of monellin has been characterized, structurally and temporally, using the multisite time-resolved FRET methodology. After an initial heterogeneous polypeptide chain collapse, structure formation proceeds on parallel pathways. Kinetic analysis of the population evolution data across various protein segments provides a clear structural distinction between the parallel pathways. The analysis leads to a phenomenological model that describes how and when discrete segments acquire structure independently of each other in different subensembles of protein molecules. When averaged over all molecules, structure formation is seen to progress as α-helix formation, followed by core consolidation, then β-sheet formation, and last end-to-end distance compaction. Parts of the protein that are closer in the primary sequence acquire structure before parts separated by longer sequence.

The Last Secret of Protein Folding: The Real Relationship Between Long-Range Interactions and Local Structures

The protein folding problem has been extensively studied for decades, and hundreds of thousands of protein structures have been solved. Yet, how proteins fold from a linear peptide chain to their unique 3D structures is not fully understood. With key clues having emerged unexpectedly from the field of nanoscience, a "Confined Lowest Energy Fragment" (CLEF) hypothesis was proposed. The CLEF hypothesis states that a protein chain can be divided into CLEFs, the semi-independent folding units, by a small number of key residues that form key long-range interactions. The native structure of a CLEF is the lowest energy state under the constraints of the key long-range interactions, but the native structure of the whole protein is not necessary the lowest energy state as Anfinsen's thermodynamic hypothesis suggested. The CLEF hypothesis proposes a unified CLEF mechanism for protein folding, basically a two-step process. In the first step, the favorable enthalpy of CLEFs for native structures quickly brings those residues for the key long-range interactions together, forming intermediates corresponding to the so-called hydrophobic collapse. In the second step, those collapsed key residues shuffle for the right combination to form the native key long-range interactions. The CLEF hypothesis provides a simple solution to all protein folding paradoxes, and proposes a "CLEF Age" or "Stone Age" for the prebiotic evolution of proteins.

Interdiction of Protein Folding for Therapeutic Drug Development in SARS CoV-2

In this article, we predict the folding initiation events of the ribose phosphatase domain of protein Nsp3 and the receptor binding domain of the spike protein from the severe acute respiratory syndrome (SARS) coronavirus-2. The calculations employ the sequential collapse model and the crystal structures to identify the segments involved in the initial contact formation events of both viral proteins. The initial contact locations may provide good targets for therapeutic drug development. The proposed strategy is based on a drug binding to the contact location, thereby aiming to prevent protein folding. Peptides are suggested as a natural choice for such protein folding interdiction drugs.

Fast and flexible coarse-grained prediction of protein folding routes using ensemble modeling and evolutionary sequence variation

MOTIVATION

Protein folding is a dynamic process through which polypeptide chains reach their native 3D structures. Although the importance of this mechanism is widely acknowledged, very few high-throughput computational methods have been developed to study it.

RESULTS

In this paper, we report a computational platform named P3Fold that combines statistical and evolutionary information for predicting and analyzing protein folding routes. P3Fold uses coarse-grained modeling and efficient combinatorial schemes to predict residue contacts and evaluate the folding routes of a protein sequence within minutes or hours. To facilitate access to this technology, we devise graphical representations and implement an interactive web interface that allows end-users to leverage P3Fold predictions. Finally, we use P3Fold to conduct large and short scale experiments on the human proteome that reveal the broad conservation and variations of structural intermediates within protein families.

AVAILABILITY AND IMPLEMENTATION

A Web server of P3Fold is freely available at http://csb.cs.mcgill.ca/P3Fold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.

Experimental accuracy in protein structure refinement via molecular dynamics simulations

Refinement is the last step in protein structure prediction pipelines to convert approximate homology models to experimental accuracy. Protocols based on molecular dynamics (MD) simulations have shown promise, but current methods are limited to moderate levels of consistent refinement. To explore the energy landscape between homology models and native structures and analyze the challenges of MD-based refinement, eight test cases were studied via extensive simulations followed by Markov state modeling. In all cases, native states were found very close to the experimental structures and at the lowest free energies, but refinement was hindered by a rough energy landscape. Transitions from the homology model to the native states require the crossing of significant kinetic barriers on at least microsecond time scales. A significant energetic driving force toward the native state was lacking until its immediate vicinity, and there was significant sampling of off-pathway states competing for productive refinement. The role of recent force field improvements is discussed and transition paths are analyzed in detail to inform which key transitions have to be overcome to achieve successful refinement.

Hetero-oligomeric Amyloid Assembly and Mechanism: Prion Fragment PrP(106-126) Catalyzes the Islet Amyloid Polypeptide β-Hairpin

Protein aggregation is typically attributed to the association of homologous amino acid sequences between monomers of the same protein. Coaggregation of heterogeneous peptide species can occur, however, and is implicated in the proliferation of seemingly unrelated protein diseases in the body. The prion protein fragment (PrP_106-126) and human islet amyloid polypeptide (hIAPP) serve as an interesting model of nonhomologous protein assembly as they coaggregate, despite a lack of sequence homology. We have applied ion-mobility mass spectrometry, atomic force microscopy, circular dichroism, and high-level molecular modeling to elucidate this important assembly process. We found that the prion fragment not only forms pervasive hetero-oligomeric aggregates with hIAPP but also promotes the transition of hIAPP into its amyloidogenic β-hairpin conformation. Further, when PrP_106-126 was combined with non-amyloidogenic rIAPP, the two formed nearly identical hetero-oligomers to those seen with hIAPP, despite rIAPP containing β-sheet breaking proline substitutions. Additionally, while rIAPP does not natively form the amyloidogenic β-hairpin structure, it did so in the presence of PrP_106-126 and underwent a conformational transition to β-sheet in solution. We also find that PrP_106-126 forms hetero-oligomers with the IAPP_8-20 fragment but not with the "aggregation hot spot" IAPP_20-29 fragment. PrP_106-126 apparently induces IAPP into a β-hairpin structure within the PrP:IAPP heterodimer complex and then, through ligand exchange, catalytically creates the amyloidogenic β-hairpin dimer of IAPP in significantly greater abundance than IAPP does on its own. This is a new mechanistic model that provides a critical foundation for the detailed study of hetero-oligomerization and prion-like proliferation in amyloid systems.

Sixty-five years of the long march in protein secondary structure prediction: the final stretch?

Protein secondary structure prediction began in 1951 when Pauling and Corey predicted helical and sheet conformations for protein polypeptide backbone even before the first protein structure was determined. Sixty-five years later, powerful new methods breathe new life into this field. The highest three-state accuracy without relying on structure templates is now at 82-84%, a number unthinkable just a few years ago. These improvements came from increasingly larger databases of protein sequences and structures for training, the use of template secondary structure information and more powerful deep learning techniques. As we are approaching to the theoretical limit of three-state prediction (88-90%), alternative to secondary structure prediction (prediction of backbone torsion angles and Cα-atom-based angles and torsion angles) not only has more room for further improvement but also allows direct prediction of three-dimensional fragment structures with constantly improved accuracy. About 20% of all 40-residue fragments in a database of 1199 non-redundant proteins have <6 Å root-mean-squared distance from the native conformations by SPIDER2. More powerful deep learning methods with improved capability of capturing long-range interactions begin to emerge as the next generation of techniques for secondary structure prediction. The time has come to finish off the final stretch of the long march towards protein secondary structure prediction.

Helical Propensity Affects the Conformational Properties of the Denatured State of Cytochrome c'

Changing the helical propensity of a polypeptide sequence might be expected to affect the conformational properties of the denatured state of a protein. To test this hypothesis, alanines at positions 83 and 87 near the center of helix 3 of cytochrome c' from Rhodopseudomonas palustris were mutated to serine to decrease the stability of this helix. A set of 13 single histidine variants in the A83S/A87S background were prepared to permit assessment of the conformational properties of the denatured state using histidine-loop formation in 3 M guanidine hydrochloride. The data are compared with previous histidine-heme loop formation data for wild-type cytochrome c'. As expected, destabilization of helix 3 decreases the global stabilities of the histidine variants in the A83S/A87S background relative to the wild-type background. Loop stability versus loop size data yields a scaling exponent of 2.1 ± 0.2, similar to the value of 2.3 ± 0.2 obtained for wild-type cytochrome c'. However, the stabilities of all histidine-heme loops, which contain the helix 3 sequence segment, are increased in the A83S/A87S background compared to the wild-type background. Rate constants for histidine-heme loop breakage are similar for the wild-type and A83S/A87S variants. However, for histidine-heme loops that contain the helix 3 sequence segment, the rate constants for loop formation increase in the A83S/A87S background compared to the wild-type background. Thus, residual helical structure appears to stiffen the polypeptide chain slowing loop formation in the denatured state. The implications of these results for protein folding mechanisms are discussed.

A Data-Driven Perspective on the Hierarchical Assembly of Molecular Structures

Macromolecular systems are composed of a very large number of atomic degrees of freedom. There is strong evidence suggesting that structural changes occurring in large biomolecular systems at long time scale dynamics may be captured by models coarser than atomistic, although a suitable or optimal coarse-graining is a priori unknown. Here we propose a systematic approach to learning a coarse representation of a macromolecule from microscopic simulation data. In particular, the definition of effective coarse variables is achieved by partitioning the degrees of freedom both in the structural (physical) space and in the conformational space. The identification of groups of microscopic particles forming dynamical coherent states in different metastable states leads to a multiscale description of the system, in space and time. The application of this approach to the folding dynamics of two proteins provides a revised view of the classical idea of prestructured regions (foldons) that combine during a protein-folding process and suggests a hierarchical characterization of the assembly process of folded structures.

LRFragLib: an effective algorithm to identify fragments for de novo protein structure prediction

Motivation

The quality of fragment library determines the efficiency of fragment assembly, an approach that is widely used in most de novo protein-structure prediction algorithms. Conventional fragment libraries are constructed mainly based on the identities of amino acids, sometimes facilitated by predicted information including dihedral angles and secondary structures. However, it remains challenging to identify near-native fragment structures with low sequence homology.

Results

We introduce a novel fragment-library-construction algorithm, LRFragLib, to improve the detection of near-native low-homology fragments of 7-10 residues, using a multi-stage, flexible selection protocol. Based on logistic regression scoring models, LRFragLib outperforms existing techniques by achieving a significantly higher precision and a comparable coverage on recent CASP protein sets in sampling near-native structures. The method also has a comparable computational efficiency to the fastest existing techniques with substantially reduced memory usage.

Availability and Implementation

The source code is available for download at http://166.111.152.91/Downloads.html.

Contact

hgong@tsinghua.edu.cn.

Supplementary information

Supplementary data are available at Bioinformatics online.

Equilibrium folding dynamics of meACP in water, heavy water, and low concentration of urea

Many proteins fold in apparent two-state behavior, as partially folded intermediates only transiently accumulate and easily escape detection. Besides a native form and a mainly unfolded form, we captured a partially unfolded form of an acyl carrier protein from Micromonospora echinospora (meACP) in the folding/unfolding equilibrium using chemical exchange saturation transfer NMR experiments. The C-terminal region of the partially unfolded form is mainly folded and the N-terminal is unfolded. Furthermore, to understand how the folding process of meACP is influenced by solvent environments, we compared the folding dynamics of meACP in D₂O, H₂O and low concentration of urea. As the environment becomes more denaturing from D₂O to H₂O and then to urea, the unfolded state becomes increasingly populated, and the folding rate decreases. Adding a small amount of urea, which does not change solvent viscosity, has little effects on the unfolding rates, while changing H₂O to D₂O reduces the unfolding rates possibly due to the increase of solvent viscosity. The quantified solvent effects on the protein folding Gibbs energy and activation energy suggest that the transition state of folding may have a similar structure to the native state of the protein.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template-based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug-design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr-REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native-like structures from a template and to provide a set of persistent contacts to be employed during re-folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled.

Selective refinement and selection of near-native models in protein structure prediction

In recent years in silico protein structure prediction reached a level where fully automated servers can generate large pools of near-native structures. However, the identification and further refinement of the best structures from the pool of models remain problematic. To address these issues, we have developed (i) a target-specific selective refinement (SR) protocol; and (ii) molecular dynamics (MD) simulation based ranking (SMDR) method. In SR the all-atom refinement of structures is accomplished via the Rosetta Relax protocol, subject to specific constraints determined by the size and complexity of the target. The best-refined models are selected with SMDR by testing their relative stability against gradual heating through all-atom MD simulations. Through extensive testing we have found that Mufold-MD, our fully automated protein structure prediction server updated with the SR and SMDR modules consistently outperformed its previous versions.

Discriminating trpzip2 and trpzip4 peptides' folding landscape using the two-dimensional infrared spectroscopy: a simulation study

We analyzed, based on the theoretical spectroscopic modeling, how the differences in the folding landscapes of two β-hairpin peptides trpzip2 and trpzip4 are reflected in their thermal unfolding infrared measurements. The isotope-edited equilibrium FTIR and two dimensional infrared spectra of the two peptides were calculated, using the nonlinear exciton propagation method, at a series of temperatures. The spectra calculations were based on the configuration distributions generated using the GB(OBC) implicit solvent MD simulation and the integrated tempering sampling technique. Conformational analysis revealed the different local thermal stabilities for these two peptides, which suggested the different folding landscapes. Our study further suggested that the ellipticities of the isotope peaks in the coherent IR signals are more sensitive to these local stability differences compared with other spectral features such as the peak intensities. Our technique can thus be combined with the relevant experimental measurements to achieve a better understanding of the peptide folding behaviors.

Fast closure of long loops at the initiation of the folding transition of globular proteins studied by time-resolved FRET-based methods

The protein folding problem would be considered “solved” when it will be possible to “read genes”, i.e., to predict the native fold of proteins, their dynamics, and the mechanism of fast folding based solely on sequence data. The long-term goal should be the creation of an algorithm that would simulate the stepwise mechanism of folding, which constrains the conformational space and in which random search for stable interactions is possible. Here, we focus attention on the initial phases of the folding transition starting with the compact disordered collapsed ensemble, in search of the initial sub-domain structural biases that direct the otherwise stochastic dynamics of the backbone. Our studies are designed to test the “loop hypothesis”, which suggests that fast closure of long loop structures by non-local interactions between clusters of mainly non-polar residues is an essential conformational step at the initiation of the folding transition of globular proteins. We developed and applied experimental methods based on time-resolved resonance excitation energy transfer (trFRET) measurements combined with fast mixing methods and studied the initial phases of the folding of

Computational and theoretical methods for protein folding

A computational approach is essential whenever the complexity of the process under study is such that direct theoretical or experimental approaches are not viable. This is the case for protein folding, for which a significant amount of data are being collected. This paper reports on the essential role of in silico methods and the unprecedented interplay of computational and theoretical approaches, which is a defining point of the interdisciplinary investigations of the protein folding process. Besides giving an overview of the available computational methods and tools, we argue that computation plays not merely an ancillary role but has a more constructive function in that computational work may precede theory and experiments. More precisely, computation can provide the primary conceptual clues to inspire subsequent theoretical and experimental work even in a case where no preexisting evidence or theoretical frameworks are available. This is cogently manifested in the application of machine learning methods to come to grips with the folding dynamics. These close relationships suggested complementing the review of computational methods within the appropriate theoretical context to provide a self-contained outlook of the basic concepts that have converged into a unified description of folding and have grown in a synergic relationship with their computational counterpart. Finally, the advantages and limitations of current computational methodologies are discussed to show how the smart analysis of large amounts of data and the development of more effective algorithms can improve our understanding of protein folding.

Atomic-accuracy prediction of protein loop structures through an RNA-inspired Ansatz

Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and protein design, can become intractable as loop lengths exceed 10 residues and if surrounding side-chain conformations are erased. Current approaches, such as the protein local optimization protocol or kinematic inversion closure (KIC) Monte Carlo, involve stages that coarse-grain proteins, simplifying modeling but precluding a systematic search of all-atom configurations. This article introduces an alternative modeling strategy based on a ‘stepwise ansatz’, recently developed for RNA modeling, which posits that any realistic all-atom molecular conformation can be built up by residue-by-residue stepwise enumeration. When harnessed to a dynamic-programming-like recursion in the Rosetta framework, the resulting stepwise assembly (SWA) protocol enables enumerative sampling of a 12 residue loop at a significant but achievable cost of thousands of CPU-hours. In a previously established benchmark, SWA recovers crystallographic conformations with sub-Angstrom accuracy for 19 of 20 loops, compared to 14 of 20 by KIC modeling with a comparable expenditure of computational power. Furthermore, SWA gives high accuracy results on an additional set of 15 loops highlighted in the biological literature for their irregularity or unusual length. Successes include cis-Pro touch turns, loops that pass through tunnels of other side-chains, and loops of lengths up to 24 residues. Remaining problem cases are traced to inaccuracies in the Rosetta all-atom energy function. In five additional blind tests, SWA achieves sub-Angstrom accuracy models, including the first such success in a protein/RNA binding interface, the YbxF/kink-turn interaction in the fourth ‘RNA-puzzle’ competition. These results establish all-atom enumeration as an unusually systematic approach to ab initio protein structure modeling that can leverage high performance computing and physically realistic energy functions to more consistently achieve atomic accuracy.

Structure and dynamics of the N-terminal domain of the Cu(I) binding protein CusB

CusCFBA is one of the metal efflux systems in Escherichia coli that is highly specific for its substrates, Cu(I) and Ag(I). It serves to protect the bacteria in environments that have lethal concentrations of these metals. The membrane fusion protein CusB is the periplasmic piece of CusCFBA, which has not been fully characterized by crystallography because of its extremely disordered N-terminal region. This region has both structural and functional importance because it has been experimentally proven to transfer the metal by itself from the metallochaperone CusF and to induce a structural change in the rest of CusB to increase Cu(I)/Ag(I) resistance. Understanding metal uptake from the periplasm is critical to gain insight into the mechanism of the whole CusCFBA pump, which makes resolving a structure for the N-terminal region necessary because it contains the metal binding site. We ran extensive molecular dynamics simulations to reveal the structural and dynamic properties of both the apo and Cu(I)-bound versions of the CusB N-terminal region. In contrast to its functional companion CusF, Cu(I) binding to the N-terminus of CusB causes only a slight, local stabilization around the metal site. The trajectories were analyzed in detail, revealing extensive structural disorder in both the apo and holo forms of the protein. CusB was further analyzed by breaking the protein up into three subdomains according to the extent of the observed disorder: the N- and C-terminal tails, the central beta strand motif, and the M21-M36 loop connecting the two metal-coordinating methionine residues. Most of the observed disorder was traced back to the tail regions, leading us to hypothesize that the latter two subdomains (residues 13-45) may form a functionally competent metal-binding domain because the tail regions appear to play no role in metal binding.

Structural similarities and differences between amyloidogenic and non-amyloidogenic islet amyloid polypeptide (IAPP) sequences and implications for the dual physiological and pathological activities of these peptides

IAPP, a 37 amino-acid peptide hormone belonging to the calcitonin family, is an intrinsically disordered protein that is coexpressed and cosecreted along with insulin by pancreatic islet β-cells in response to meals. IAPP plays a physiological role in glucose regulation; however, in certain species, IAPP can aggregate and this process is linked to β-cell death and Type II Diabetes. Using replica exchange molecular dynamics with extensive sampling (16 replicas per sequence and 600 ns per replica), we investigate the structure of the monomeric state of two species of aggregating peptides (human and cat IAPP) and two species of non-aggregating peptides (pig and rat IAPP). Our simulations reveal that the pig and rat conformations are very similar, and consist of helix-coil and helix-hairpin conformations. The aggregating sequences, on the other hand, populate the same helix-coil and helix-hairpin conformations as the non-aggregating sequence, but, in addition, populate a hairpin structure. Our exhaustive simulations, coupled with available peptide-activity data, leads us to a structure-activity relationship (SAR) in which we propose that the functional role of IAPP is carried out by the helix-coil conformation, a structure common to both aggregating and non-aggregating species. The pathological role of this peptide may have multiple origins, including the interaction of the helical elements with membranes. Nonetheless, our simulations suggest that the hairpin structure, only observed in the aggregating species, might be linked to the pathological role of this peptide, either as a direct precursor to amyloid fibrils, or as part of a cylindrin type of toxic oligomer. We further propose that the helix-hairpin fold is also a possible aggregation prone conformation that would lead normally non-aggregating variants of IAPP to form fibrils under conditions where an external perturbation is applied. The SAR relationship is used to suggest the rational design of therapeutics for treating diabetes.

IAPP, a 37 amino-acid peptide hormone belonging to the calcitonin family, is an intrinsically disordered peptide produced along with insulin by pancreatic islet β-cells in response to meals. In its functional form, IAPP acts as a synergic partner of insulin to reduce blood glucose. IAPP can, however, also play a pathological role, contributing to Type II diabetes (T2D). Knowledge of the structural nature of the physiological and pathological forms of IAPP will facilitate the rational design of novel drugs for therapeutic treatment of T2D. However, because IAPP does not fold to a single structure, but rather co-exists between multiple functional (and toxic) structures, it is extremely challenging for experimental methods to gain detailed structural information. Using a computational approach, we were able to obtain detailed structures of four IAPP variants and propose a novel structural hypothesis for the two opposing roles of this peptide.

PRIMO: A Transferable Coarse-grained Force Field for Proteins

We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.

α-helix to β-hairpin transition of human amylin monomer

The human islet amylin polypeptide is produced along with insulin by pancreatic islets. Under some circumstances, amylin can aggregate to form amyloid fibrils, whose presence in pancreatic cells is a common pathological feature of Type II diabetes. A growing body of evidence indicates that small, early stage aggregates of amylin are cytotoxic. A better understanding of the early stages of the amylin aggregation process and, in particular, of the nucleation events leading to fibril growth could help identify therapeutic strategies. Recent studies have shown that, in dilute solution, human amylin can adopt an α-helical conformation, a β-hairpin conformation, or an unstructured coil conformation. While such states have comparable free energies, the β-hairpin state exhibits a large propensity towards aggregation. In this work, we present a detailed computational analysis of the folding pathways that arise between the various conformational states of human amylin in water. A free energy surface for amylin in explicit water is first constructed by resorting to advanced sampling techniques. Extensive transition path sampling simulations are then employed to identify the preferred folding mechanisms between distinct minima on that surface. Our results reveal that the α-helical conformer of amylin undergoes a transformation into the β-hairpin monomer through one of two mechanisms. In the first, misfolding begins through formation of specific contacts near the turn region, and proceeds via a zipping mechanism. In the second, misfolding occurs through an unstructured coil intermediate. The transition states for these processes are identified. Taken together, the findings presented in this work suggest that the inter-conversion of amylin between an α-helix and a β-hairpin is an activated process and could constitute the nucleation event for fibril growth.

The loop hypothesis: contribution of early formed specific non-local interactions to the determination of protein folding pathways

The extremely fast and efficient folding transition (in seconds) of globular proteins led to the search for some unifying principles embedded in the physics of the folding polypeptides. Most of the proposed mechanisms highlight the role of local interactions that stabilize secondary structure elements or a folding nucleus as the starting point of the folding pathways, i.e., a "bottom-up" mechanism. Non-local interactions were assumed either to stabilize the nucleus or lead to the later steps of coalescence of the secondary structure elements. An alternative mechanism was proposed, an "up-down" mechanism in which it was assumed that folding starts with the formation of very few non-local interactions which form closed long loops at the initiation of folding. The possible biological advantage of this mechanism, the "loop hypothesis", is that the hydrophobic collapse is associated with ordered compactization which reduces the chance for degradation and misfolding. In the present review the experiments, simulations and theoretical consideration that either directly or indirectly support this mechanism are summarized. It is argued that experiments monitoring the time-dependent development of the formation of specifically targeted early-formed sub-domain structural elements, either long loops or secondary structure elements, are necessary. This can be achieved by the time-resolved FRET-based "double kinetics" method in combination with mutational studies. Yet, attempts to improve the time resolution of the folding initiation should be extended down to the sub-microsecond time regime in order to design experiments that would resolve the classes of proteins which first fold by local or non-local interactions.

Structural dynamics flexibility informs function and evolution at a proteome scale

Protein structures are dynamic entities with a myriad of atomic fluctuations, side-chain rotations, and collective domain movements. Although the importance of these dynamics to proper functioning of proteins is emerging in the studies of many protein families, there is a lack of broad evidence for the critical role of protein dynamics in shaping the biological functions of a substantial fraction of residues for a large number of proteins in the human proteome. Here, we propose a novel dynamic flexibility index (dfi) to quantify the dynamic properties of individual residues in any protein and use it to assess the importance of protein dynamics in 100 human proteins. Our analyses involving functionally critical positions, disease-associated and putatively neutral population variations, and the rate of interspecific substitutions per residue produce concordant patterns at a proteome scale. They establish that the preservation of dynamic properties of residues in a protein structure is critical for maintaining the protein/biological function. Therefore, structural dynamics needs to become a major component of the analysis of protein function and evolution. Such analyses will be facilitated by the dfi, which will also enable the integrative use of structural dynamics with evolutionary conservation in genomic medicine as well as functional genomics investigations.

Advanced techniques for constrained internal coordinate molecular dynamics

Internal coordinate molecular dynamics (ICMD) methods provide a more natural description of a protein by using bond, angle, and torsional coordinates instead of a Cartesian coordinate representation. Freezing high-frequency bonds and angles in the ICMD model gives rise to constrained ICMD (CICMD) models. There are several theoretical aspects that need to be developed to make the CICMD method robust and widely usable. In this article, we have designed a new framework for (1) initializing velocities for nonindependent CICMD coordinates, (2) efficient computation of center of mass velocity during CICMD simulations, (3) using advanced integrators such as Runge-Kutta, Lobatto, and adaptive CVODE for CICMD simulations, and (4) cancelling out the "flying ice cube effect" that sometimes arises in Nosé-Hoover dynamics. The Generalized Newton-Euler Inverse Mass Operator (GNEIMO) method is an implementation of a CICMD method that we have developed to study protein dynamics. GNEIMO allows for a hierarchy of coarse-grained simulation models based on the ability to rigidly constrain any group of atoms. In this article, we perform tests on the Lobatto and Runge-Kutta integrators to determine optimal simulation parameters. We also implement an adaptive coarse-graining tool using the GNEIMO Python interface. This tool enables the secondary structure-guided "freezing and thawing" of degrees of freedom in the molecule on the fly during molecular dynamics simulations and is shown to fold four proteins to their native topologies. With these advancements, we envision the use of the GNEIMO method in protein structure prediction, structure refinement, and in studying domain motion.

Non-destructive inhibition of metallofullerenol Gd@C(82)(OH)(22) on WW domain: implication on signal transduction pathway

Endohedral metallofullerenol Gd@C₈₂(OH)₂₂ has recently been shown to effectively inhibit tumor growth; however, its potential adverse bioeffects remain to be understood before its wider applications. Here, we present our study on the interaction between Gd@C₈₂(OH)₂₂ and WW domain, a representative protein domain involved in signaling and regulatory pathway, using all-atom explicit solvent molecular dynamics simulations. We find that Gd@C₈₂(OH)₂₂ has an intrinsic binding preference to the binding groove, particularly the key signature residues Y28 and W39. In its binding competition with the native ligand PRM, Gd@C₈₂(OH)₂₂ is shown to easily win the competition over PRM in occupying the active site, implying that Gd@C₈₂(OH)₂₂ can impose a potential inhibitory effect on the WW domain. Further analyses with binding free energy landscapes reveal that Gd@C₈₂(OH)₂₂ can not only directly block the binding site of the WW domain, but also effectively distract the PRM from its native binding pocket.

Further optimization of a hybrid united-atom and coarse-grained force field for folding simulations: Improved backbone hydration and interactions between charged side chains

PACE, a hybrid force field which couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve itse ciency for folding simulations. Backbone hydration parameters have been re-optimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE in order to provide a more realistic description of interactions between charged groups. Using replica exchange molecular dynamics (REMD), ab initio folding using the new PACE has been achieved for seven small proteins (16 - 23 residues) with different structural motifs. Experimental data about folded states, such as their stability at room temperature, melting point and NMR NOE constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temperature has been made with experiments, through standard MD simulations, showing that the new PACE may speed up the actual folding kinetics 5-10 times. Together with the computational speedup benefited from coarse-graining, the force field provides opportunities to study folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, 3D, in multiple 10 - 30 μs simulations, to its native states (C(α) RMSD ~ 0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins.

Charge effects on the fibril-forming peptide KTVIIE: a two-dimensional replica exchange simulation study

The assembly of peptides into ordered nanostructures is increasingly recognized as both a bioengineering tool for generating new materials and a critical aspect of aggregation processes that underlie neurological diseases such as Alzheimer's disease, Parkinson's disease, and Huntington's disease. There is a major problem in understanding how extremely subtle sequence changes can lead to profound and often unexpected differences in self-assembly behavior. To better delineate the complex interplay of different microscopic driving forces in such cases, we develop a methodology to quantify and compare the propensity of different peptide sequences to form small oligomers during early self-assembly stages. This umbrella-sampling replica exchange molecular dynamics method performs a replica exchange molecular dynamics simulation along peptide association reaction coordinates using umbrella restraints. With this method, we study a set of sequence-similar peptides that differ in net charge: K(+)TVIIE(-), K(+)TVIIE, and (+)K(+)TVIIE. Interestingly, experiments show that only the monovalent peptide, K(+)TVIIE, forms fibrils, whereas the others do not. We examine dimer, trimer, and tetramer formation processes of these peptides, and compute high-accuracy potential of mean force association curves. The potential of mean forces recapitulate a higher stability and equilibrium constant of the fibril-forming peptide, similar to experiment, but reveal that entropic contributions to association free energies can play a surprisingly significant role. The simulations also show behavior reminiscent of experimental aggregate polymorphism, revealed in multiple stable conformational states and association pathways. Our results suggest that sequence changes can have significant effects on self-assembly through not only direct peptide-peptide interactions but conformational entropies and degeneracies as well.

De novo prediction of protein folding pathways and structure using the principle of sequential stabilization

Motivated by the relationship between the folding mechanism and the native structure, we develop a unified approach for predicting folding pathways and tertiary structure using only the primary sequence as input. Simulations begin from a realistic unfolded state devoid of secondary structure and use a chain representation lacking explicit side chains, rendering the simulations many orders of magnitude faster than molecular dynamics simulations. The multiple round nature of the algorithm mimics the authentic folding process and tests the effectiveness of sequential stabilization (SS) as a search strategy wherein 2° structural elements add onto existing structures in a process of progressive learning and stabilization of structure found in prior rounds of folding. Because no a priori knowledge is used, we can identify kinetically significant non-native interactions and intermediates, sometimes generated by only two mutations, while the evolution of contact matrices is often consistent with experiments. Moreover, structure prediction improves substantially by incorporating information from prior rounds. The success of our simple, homology-free approach affirms the validity of our description of the primary determinants of folding pathways and structure, and the effectiveness of SS as a search strategy.