Energetically significant networks of coupled interactions within an unfolded protein

BAD-NEUS: Rapidly converging trajectory stratification

An issue for molecular dynamics simulations is that events of interest often involve timescales that are much longer than the simulation time step, which is set by the fastest timescales of the model. Because of this timescale separation, direct simulation of many events is prohibitively computationally costly. This issue can be overcome by aggregating information from many relatively short simulations that sample segments of trajectories involving events of interest. This is the strategy of Markov state models (MSMs) and related approaches, but such methods suffer from approximation error because the variables defining the states generally do not capture the dynamics fully. By contrast, once converged, the weighted ensemble (WE) method aggregates information from trajectory segments so as to yield unbiased estimates of both thermodynamic and kinetic statistics. Unfortunately, errors decay no faster than unbiased simulation in WE as originally formulated and commonly deployed. Here, we introduce a theoretical framework for describing WE that shows that the introduction of an approximate stationary distribution on top of the stratification, as in nonequilibrium umbrella sampling (NEUS), accelerates convergence. Building on ideas from MSMs and related methods, we generalize the NEUS approach in such a way that the approximation error can be reduced systematically. We show that the improved algorithm can decrease the simulation time required to achieve the desired precision by orders of magnitude.

When MELD Meets GaMD: Accelerating Biomolecular Landscape Exploration

We introduce Gaussian accelerated MELD (GaMELD) as a new method for exploring the energy landscape of biomolecules. GaMELD combines the strengths of Gaussian accelerated molecular dynamics (GaMD) and modeling employing limited data (MELD) to navigate complex energy landscapes. MELD uses replica-exchange molecular simulations to integrate limited and uncertain data into simulations via Bayesian inference. MELD has been successfully applied to problems of structure prediction like protein folding and complex structure prediction. However, the computational cost for MELD simulations has limited its broader applicability. The synergy of GaMD and MELD surmounts this limitation efficiently sampling the energy landscape at a lower computational cost (reducing the computational cost by a factor of 2 to six). Effectively, GaMD is used to shift energy distributions along replicas to increase the overlap in energy distributions across replicas, facilitating a random walk in replica space. We tested GaMELD on a benchmark set of 12 small proteins that have been previously studied through MELD and conventional MD. GaMELD consistently achieves accurate predictions with fewer replicas. By increasing the efficacy of replica exchange, GaMELD effectively accelerates convergence in the conformational space, enabling improved sampling across a diverse set of systems.

High-Accuracy Prediction of Stabilizing Surface Mutations to the Three-Helix Bundle, UBA(1), with EmCAST

The accurate modeling of energetic contributions to protein structure is a fundamental challenge in computational approaches to protein analysis and design. We describe a general computational method, EmCAST (empirical Cα stabilization), to score and optimize the sequence to the structure in proteins. The method relies on an empirical potential derived from the database of the Cα dihedral angle preferences for all possible four-residue sequences, using the data available in the Protein Data Bank. Our method produces stability predictions that naturally correlate one-to-one with the experimental results for solvent-exposed mutation sites. EmCAST predicted four mutations that increased the stability of a three-helix bundle, UBA(1), from 2.4 to 4.8 kcal/mol by optimizing residues in both helices and turns. For a set of eight variants, the predicted and experimental stabilizations correlate very well (R2 = 0.97) with a slope near 1 and with a 0.16 kcal/mol standard error for EmCAST predictions. Tests against literature data for the stability effects of surface-exposed mutations show that EmCAST outperforms the existing stability prediction methods. UBA(1) variants were crystallized to verify and analyze their structures at an atomic resolution. Thermodynamic and kinetic folding experiments were performed to determine the magnitude and mechanism of stabilization. Our method has the potential to enable the rapid, rational optimization of natural proteins, expand the analysis of the sequence/structure relationship, and supplement the existing protein design strategies.

Improving Estimation of the Koopman Operator with Kolmogorov-Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. We apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

Linking Gas-Phase and Solution-Phase Protein Unfolding via Mobile Proton Simulations

Native mass spectrometry coupled to ion mobility (IM-MS) combined with collisional activation (CA) of ions in the gas phase (in vacuo) is an important method for the study of protein unfolding. It has advantages over classical biophysical and structural techniques as it can be used to analyze small volumes of low-concentration heterogeneous mixtures while maintaining solution-like behavior and does not require labeling with fluorescent or other probes. It is unclear, however, whether the unfolding observed during collision activation experiments mirrors solution-phase unfolding. To bridge the gap between in vacuo and in-solution behavior, we use unbiased molecular dynamics (MD) to create in silico models of in vacuo unfolding of a well-studied protein, the N-terminal domain of ribosomal L9 (NTL9) protein. We utilize a mobile proton algorithm (MPA) to create 100 thermally unfolded and coulombically unfolded in silico models for observed charge states of NTL9. The unfolding behavior in silico replicates the behavior in-solution and is in line with the in vacuo observations; however, the theoretical collision cross section (CCS) of the in silico models was lower compared to that of the in vacuo data, which may reflect reduced sampling.

Oncogenic Mutations in the DNA-Binding Domain of FOXO1 that Disrupt Folding: Quantitative Insights from Experiments and Molecular Simulations

FOXO1, a member of the family of winged-helix motif Forkhead box (FOX) transcription factors, is the most abundantly expressed FOXO member in mature B cells. Sequencing of diffuse large B-cell lymphoma (DLBCL) tumors and cell lines identified specific mutations in the forkhead domain linked to loss of function. Differential scanning calorimetry and thermal shift assays were used to characterize how eight of these mutations affect the stability of the FOX domain. Mutations L183P and L183R were found to be particularly destabilizing. Electrophoresis mobility shift assays show these same mutations also disrupt FOXO1 binding to their canonical DNA sequences, suggesting that the loss of function is due to destabilization of the folded structure. Computational modeling of the effect of mutations on FOXO1 folding was performed using alchemical free energy perturbation (FEP), and a Markov model of the entire folding reaction was constructed from massively parallel molecular simulations, which predicts folding pathways involving the late folding of helix α3. Although FEP can qualitatively predict the destabilization from L183 mutations, we find that a simple hydrophobic transfer model, combined with estimates of unfolded-state solvent-accessible surface areas from molecular simulations, is able to more accurately predict changes in folding free energies due to mutations. These results suggest that the atomic detail provided by simulations is important for the accurate prediction of mutational effects on folding stability. Corresponding disease-associated mutations in other FOX family members support further experimental and computational studies of the folding mechanism of FOX domains.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules

Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Suppressing Nonspecific Binding in Biolayer Interferometry Experiments for Weak Ligand-Analyte Interactions

Quantitative analysis of protein-protein interactions (PPIs) using biolayer interferometry (BLI) requires effective suppression of nonspecific binding (NSB) between analytes and biosensors. In particular, the study of weak interactions (i.e., K _D > 1 μM) requires high concentrations of analytes, which substantially increases NSB. However, there are only a few so-called NSB blockers compatible with biomolecules, which limits the use of BLI in the accurate analysis of weak interactions. The present study aims to identify a new NSB blocker for the quantitative analysis of weak PPIs using BLI. We find that saccharides, especially sucrose, are potent NSB blockers and demonstrate their compatibility with other blocking additives. We also demonstrate the effects of the new NSB blocker by characterizing the binding between nonstructural protein 1 of the influenza A virus and human phosphoinositide 3-kinase. We anticipate that the new NSB-blocking admixture will find broad applications in studying weak interactions using BLI.

Selection of representative structures from large biomolecular ensembles

Despite the incredible progress of experimental techniques, protein structure determination still remains a challenging task. Due to the rapid improvements of computer technology, simulations are often used to complement or interpret experimental data, in particular for sparse or low-resolution data. Many such in silico methods allow to obtain highly accurate models of a protein structure either de novo or via refinement of a physical model with experimental restraints. One crucial question is how to select a representative member or ensemble out of vast number of computationally generated structures. Here, we introduce such a method. As a representative task, we add co-evolutionary contact pairs as distance restraints to a physical force field and want to select a good characterization of the resulting native-like ensemble. To generate large ensembles, we run replica-exchange molecular dynamics (REMD) on five mid-sized test proteins and over a wide temperature range. High temperatures allow overcoming energetic barriers while low temperatures perform local searches of native-like conformations. The integrated bias is based on co-evolutionary contact pairs derived from a deep residual neural network to guide the simulation towards native-like conformations. We shortly compare and discuss the achieved model precision of contact-guided REMD for mid-sized proteins. Lastly, we discuss four robust ensemble-selection algorithms in great detail which are capable to extract the representative structure models with a high certainty. To assess the performance of the selection algorithms we exemplarily mimic a "blind scenario', i.e. where the target structure is unknown, and select a representative structural ensemble of native-like folds.

FSATOOL 2.0: An integrated molecular dynamics simulation and trajectory data analysis program

Molecular dynamics simulation is important in the computational study of the biomolecules. In this paper, we upgrade our previous FSATOOL to version 2.0. It is no longer a plugin as before. Besides the existed enhanced sampling and Markov state model analysis module, FSATOOL 2.0 has three new features now. First, it contains a molecular dynamics simulation engine on both CPU and GPU device. The engine works with an embedded enhanced sampling module. Second, it can do the free energy calculation by various practical methods, including the weighted histogram analysis method and Gaussian mixture model. Third, it has many subroutines to process the trajectory data, such as principal component analysis, time-structure based independent component analysis, contact analysis, and Φ-value analysis. Most importantly, all these calculations are integrated into one package. The trajectory data format is compatible with all the modules. With a proper input parameter file, users can do the molecular dynamics simulation and data analysis work by only a few simplified commands. The capabilities and theoretical backgrounds of FSATOOL 2.0 are introduced in the paper.

Denatured State Conformational Biases in Three-Helix Bundles Containing Divergent Sequences Localize near Turns and Helix Capping Residues

Rhodopseudomonas palustris cytochrome c', a four-helix bundle, and the second ubiquitin-associated domain, UBA(2), a three-helix bundle from the human homologue of yeast Rad23, HHR23A, deviate from random coil behavior under denaturing conditions in a fold-specific manner. The random coil deviations in each of these folds occur near interhelical turns and loops in their tertiary structures. Here, we examine an additional three-helix bundle with an identical fold to UBA(2), but a highly divergent sequence, the first ubiquitin-associated domain, UBA(1), of HHR23A. We use histidine-heme loop formation methods, employing eight single histidine variants, to probe for denatured state conformational bias of a UBA(1) domain fused to the N-terminus of iso-1-cytochrome c (iso-1-Cytc). Guanidine hydrochloride (GuHCl) denaturation shows that the iso-1-Cytc domain unfolds first, followed by the UBA(1) domain. Denatured state (4 and 6 M GuHCl) histidine-heme loop formation studies show that as the size of the histidine-heme loop increases, loop stability decreases, as expected for the Jacobson-Stockmayer relationship. However, loops formed with His35, His31, and His15, of UBA(1), are 0.6-1.1 kcal/mol more stable than expected from the Jacobson-Stockmayer relationship, confirming the importance of deviations of the denatured state from random coil behavior near interhelical turns of helical domains for facilitating folding to the correct topology. For UBA(1) and UBA(2), hydrophobic clusters on either side of the turns partially explain deviations from random coil behavior; however, helix capping also appears to be important.

Understanding the Binding Transition State After the Conformational Selection Step: The Second Half of the Molecular Recognition Process Between NS1 of the 1918 Influenza Virus and Host p85β

Biomolecular recognition often involves conformational changes as a prerequisite for binding (i.e., conformational selection) or concurrently with binding (i.e., induced-fit). Recent advances in structural and kinetic approaches have enabled the detailed characterization of protein motions at atomic resolution. However, to fully understand the role of the conformational dynamics in molecular recognition, studies on the binding transition state are needed. Here, we investigate the binding transition state between nonstructural protein 1 (NS1) of the pandemic 1918 influenza A virus and the human p85β subunit of PI3K. 1918 NS1 binds to p85β via conformational selection. We present the free-energy mapping of the transition and bound states of the 1918 NS1:p85β interaction using linear free energy relationship and ϕ-value analyses. We find that the binding transition state of 1918 NS1 and p85β is structurally similar to the bound state with well-defined binding orientation and hydrophobic interactions. Our finding provides a detailed view of how protein motion contributes to the development of intermolecular interactions along the binding reaction coordinate.

Charge Interactions in a Highly Charge-Depleted Protein

Electrostatic forces are important for protein folding and are favored targets of protein engineering. However, interactions between charged residues are difficult to study because of the complex network of interactions found in most proteins. We have designed a purposely simple system to investigate this problem by systematically introducing individual and pairs of charged and titratable residues in a protein otherwise free of such residues. We used constant pH molecular dynamics simulations, NMR spectroscopy, and thermodynamic double mutant cycles to probe the structure and energetics of the interaction between the charged residues. We found that the partial burial of surface charges contributes to a shift in pK_a value, causing an aspartate to titrate in the neutral pH range. Additionally, the interaction between pairs of residues was found to be highly context dependent, with some pairs having no apparent preferential interaction, while other pairs would engage in coupled titration forming a highly stabilized salt bridge. We find good agreement between experiments and simulations and use the simulations to rationalize our observations and to provide a detailed mechanistic understanding of the electrostatic interactions.

The use of consensus sequence information to engineer stability and activity in proteins

The goal of protein design is to create proteins that are stable, soluble, and active. Here we focus on one approach to protein design in which sequence information is used to create a "consensus" sequence. Such consensus sequences comprise the most common residue at each position in a multiple sequence alignment (MSA). After describing some general ideas that relate MSA and consensus sequences and presenting a statistical thermodynamic framework that relates consensus and non-consensus sequences to stability, we detail the process of designing a consensus sequence and survey reports of consensus design and characterization from the literature. Many of these consensus proteins retain native biological activities including ligand binding and enzyme activity. Remarkably, in most cases the consensus protein shows significantly higher stability than extant versions of the protein, as measured by thermal or chemical denaturation, consistent with the statistical thermodynamic model. To understand this stability increase, we compare various features of consensus sequences with the extant MSA sequences from which they were derived. Consensus sequences show enrichment in charged residues (most notably glutamate and lysine) and depletion of uncharged polar residues (glutamine, serine, and asparagine). Surprisingly, a survey of stability changes resulting from point substitutions show little correlation with residue frequencies at the corresponding positions within the MSA, suggesting that the high stability of consensus proteins may result from interactions among residue pairs or higher-order clusters. Whatever the source, the large number of reported successes demonstrates that consensus design is a viable route to generating active and in many cases highly stabilized proteins.

Adaptive Markov state model estimation using short reseeding trajectories

In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.

Dissecting the Energetics of Intrinsically Disordered Proteins via a Hybrid Experimental and Computational Approach

Intrinsically disordered proteins (IDPs) play important roles in biology, but little is known about the energetics of their inter-residue interactions. Methods that have been successfully applied to analyze the energetics of globular proteins are not applicable to the fluctuating partially ordered ensembles populated by IDPs. A combined computational experimental strategy is introduced for analyzing the energetic role of individual residues in the free state of IDPs. The approach combines experimental measurements of the binding of wild-type and mutant IDPs to their partners with alchemical free energy calculations of the structured complexes. These data allow quantitative information to be deduced about the free state via a thermodynamic cycle. The approach is validated by the analysis of the effects of mutations upon the binding free energy of the ovomucoid inhibitor third binding domain to its partners and is applied to the C-terminal domain of the measles virus nucleoprotein, a 125-residue IDP involved in the RNA transcription and replication of measles virus. The analysis reveals significant inter-residue interactions in the unbound IDP and suggests a biological role for them. The work demonstrates that advances in force fields and computational hardware have now led to the point where it is possible to develop methods, which integrate experimental and computational techniques to reveal insights that cannot be studied using either technique alone.

Unfolded states under folding conditions accommodate sequence-specific conformational preferences with random coil-like dimensions

Proteins are marginally stable molecules that fluctuate between folded and unfolded states. Here, we provide a high-resolution description of unfolded states under refolding conditions for the N-terminal domain of the L9 protein (NTL9). We use a combination of time-resolved Förster resonance energy transfer (FRET) based on multiple pairs of minimally perturbing labels, time-resolved small-angle X-ray scattering (SAXS), all-atom simulations, and polymer theory. Upon dilution from high denaturant, the unfolded state undergoes rapid contraction. Although this contraction occurs before the folding transition, the unfolded state remains considerably more expanded than the folded state and accommodates a range of local and nonlocal contacts, including secondary structures and native and nonnative interactions. Paradoxically, despite discernible sequence-specific conformational preferences, the ensemble-averaged properties of unfolded states are consistent with those of canonical random coils, namely polymers in indifferent (theta) solvents. These findings are concordant with theoretical predictions based on coarse-grained models and inferences drawn from single-molecule experiments regarding the sequence-specific scaling behavior of unfolded proteins under folding conditions.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

Heterogeneity in the Folding of Villin Headpiece Subdomain HP36

Small single domain proteins that fold on the microsecond time scale have been the subject of intense interest as models for probing the complexity of folding energy landscapes. The villin headpiece subdomain (HP36) has been extensively studied because of its simple three helix structure, ultrafast folding lifetime of a few microseconds, and stable native fold. We have previously shown that folding as measured by a single ¹³C═¹⁸O isotopic label on residue A57 in helix 2 occurs at a different rate than that measured by global probes of folding, indicating noncooperative complexity in the folding of HP36. In order to determine whether this complexity reflects intermediates or parallel pathways over a small activation barrier, ¹³C═¹⁸O labels were individually incorporated at six different positions in HP36, including into all 3 helices. The equilibrium thermal unfolding transitions and the folding/unfolding dynamics were monitored using the unique IR signature of the ¹³C═¹⁸O label by temperature dependent FTIR and temperature jump IR spectroscopy, respectively. Equilibrium experiments reveal that the ¹³C═¹⁸O labels at different positions in HP36 show drastic differences in the midpoint of their transitions ( T_m), ranging from 45 to 67 °C. Heterogeneity is also observed in the relaxation kinetics; there are differences in the microsecond phase when different labeled positions are probed. At a final temperature of 45 °C, the relaxation rate for ¹³C═¹⁸O A57 is 2.4e + 05 s^-1 whereas for ¹³C═¹⁸O L69 HP36 the relaxation rate is 5.1e + 05 s^-1, two times faster. The observation of site-dependent midpoints for the equilibrium unfolding transitions and differences in the relaxation rates of the labeled positions enables us to probe the progressive accumulation of the folded structure, providing insight into the microscopic details of the folding mechanism.

SAFlex: A structural alphabet extension to integrate protein structural flexibility and missing data information

In this paper, we describe SAFlex (Structural Alphabet Flexibility), an extension of an existing structural alphabet (HMM-SA), to better explore increasing protein three dimensional structure information by encoding conformations of proteins in case of missing residues or uncertainties. An SA aims to reduce three dimensional conformations of proteins as well as their analysis and comparison complexity by simplifying any conformation in a series of structural letters. Our methodology presents several novelties. Firstly, it can account for the encoding uncertainty by providing a wide range of encoding options: the maximum a posteriori, the marginal posterior distribution, and the effective number of letters at each given position. Secondly, our new algorithm deals with the missing data in the protein structure files (concerning more than 75% of the proteins from the Protein Data Bank) in a rigorous probabilistic framework. Thirdly, SAFlex is able to encode and to build a consensus encoding from different replicates of a single protein such as several homomer chains. This allows localizing structural differences between different chains and detecting structural variability, which is essential for protein flexibility identification. These improvements are illustrated on different proteins, such as the crystal structure of an eukaryotic small heat shock protein. They are promising to explore increasing protein redundancy data and obtain useful quantification of their flexibility.

A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding

Structure-based coarse-grained Gō-like models have been used extensively in deciphering protein folding mechanisms because of their simplicity and tractability. Meanwhile, explicit-solvent molecular dynamics (MD) simulations with physics-based all-atom force fields have been applied successfully to simulate folding/unfolding transitions for several small, fast-folding proteins. To explore the degree to which coarse-grained Gō-like models and their extensions to incorporate nonnative interactions are capable of producing folding processes similar to those in all-atom MD simulations, here we systematically compare the computed unfolded states, transition states, and transition paths obtained using coarse-grained models and all-atom explicit-solvent MD simulations. The conformations in the unfolded state in common Gō models are more extended, and are thus more in line with experiment, than those from all-atom MD simulations. Nevertheless, the structural features of transition states obtained by the two types of models are largely similar. In contrast, the folding transition paths are significantly more sensitive to modeling details. In particular, when common Gō-like models are augmented with nonnative interactions, the predicted dimensions of the unfolded conformations become similar to those computed using all-atom MD. With this connection, the large deviations of all-atom MD from simple diffusion theory are likely caused in part by the presence of significant nonnative effects in folding processes modelled by current atomic force fields. The ramifications of our findings to the application of coarse-grained modeling to more complex biomolecular systems are discussed.

Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Proteins can collapse into compact globules or form expanded, solvent-accessible, coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

Hypothesis: structural heterogeneity of the unfolded proteins originating from the coupling of the local clusters and the long-range distance distribution

We propose a hypothesis that explains two apparently contradicting observations for the heterogeneity of the unfolded proteins. First, the line confocal method of the single-molecule Förster resonance energy transfer (sm-FRET) spectroscopy revealed that the unfolded proteins possess broad peaks in the FRET efficiency plot, implying the significant heterogeneity that lasts longer than milliseconds. Second, the fluorescence correlation method demonstrated that the unfolded proteins fluctuate in the time scale shorter than 100 ns. To formulate the hypothesis, we first summarize the recent consensus for the structure and dynamics of the unfolded proteins. We next discuss the conventional method of the sm-FRET spectroscopy and its limitations for the analysis of the unfolded proteins, followed by the advantages of the line confocal method that revealed the heterogeneity. Finally, we propose that the structural heterogeneity formed by the local clustering of hydrophobic residues modulates the distribution of the long-range distance between the labeled chromophores, resulting in the broadening of the peak in the FRET efficiency plot. A clustering of hydrophobic residues around the chromophore might further contribute to the broadening. The proposed clusters are important for the understanding of protein folding mechanism.

The N-Terminal Domain of Ribosomal Protein L9 Folds via a Diffuse and Delocalized Transition State

The N-terminal domain of L9 (NTL9) is a 56-residue mixed α-β protein that lacks disulfides, does not bind cofactors, and folds reversibly. NTL9 has been widely used as a model system for experimental and computational studies of protein folding and for investigations of the unfolded state. The role of side-chain interactions in the folding of NTL9 is probed by mutational analysis. ϕ-values, which represent the ratio of the change in the log of the folding rate upon mutation to the change in the log of the equilibrium constant for folding, are reported for 25 point mutations and 15 double mutants. All ϕ-values are small, with an average over all sites probed of only 0.19 and a largest value of 0.4. The effect of modulating unfolded-state interactions is studied by measuring ϕ-values in second- site mutants and under solvent conditions that perturb unfolded-state energetics in a defined way. Neither of these alterations significantly affects the distribution of ϕ-values. The results, combined with those of earlier studies that probe the role of hydrogen-bond formation in folding and the burial of surface area, reveal that the transition state for folding contains extensive backbone structure and buries a significant fraction of hydrophobic surface area, but lacks well developed side-chain-side-chain interactions. The folding transition state for NTL9 does not contain a specific "nucleus" consisting of a few key residues; rather, it involves extensive backbone hydrogen bonding and partially formed structure delocalized over almost the entire domain. The potential generality of these observations is discussed.

Kinetic Insights into the Binding between the nSH3 Domain of CrkII and Proline-Rich Motifs in cAbl

The interaction between CrkII and cAbl is implicated in diverse cellular processes. This interaction starts with the binding of the N-terminal Src homology 3 (nSH3) domain of CrkII to the proline-rich motifs of cAbl (PRMs^cAbl). Despite its critical importance, the detailed binding mechanism between the nSH3 domain and PRMs remains elusive. In this study, we used nuclear magnetic resonance Carr-Purcell-Meiboom-Gill relaxation dispersion experiment to study the binding kinetics between the nSH3 domain of CrkII and PRMs^cAbl. Our results highlight that the nSH3 domain binds to three PRMs^cAbl with very high on- and off-rate constants, indicating the transient nature of the binding. To further characterize the binding transition state, we conducted the Eyring and linear free energy relationship analyses using temperature-dependent kinetic data. These data indicate that the binding transition state of the nSH3 domain and PRM is accompanied by small activation enthalpy, owing to partial desolvation of the transition state. These results also highlight the similarity between the transition and free states, in terms of structure and energetics. Although the binding of the nSH3 domain and PRM displays the features consistent with a diffusion-limited process within our experimental conditions, further tests are necessary to determine if the binding is a true diffusion-limited process.

Intrinsically disordered inhibitor of glutamine synthetase is a functional protein with random-coil-like pKa values

The sequential action of glutamine synthetase (GS) and glutamate synthase (GOGAT) in cyanobacteria allows the incorporation of ammonium into carbon skeletons. In the cyanobacterium Synechocystis sp. PCC 6803, the activity of GS is modulated by the interaction with proteins, which include a 65-residue-long intrinsically disordered protein (IDP), the inactivating factor IF7. This interaction is regulated by the presence of charged residues in both IF7 and GS. To understand how charged amino acids can affect the binding of an IDP with its target and to provide clues on electrostatic interactions in disordered states of proteins, we measured the pK_a values of all IF7 acidic groups (Glu32, Glu36, Glu38, Asp40, Asp58, and Ser65, the backbone C-terminus) at 100 mM NaCl concentration, by using NMR spectroscopy. We also obtained solution structures of IF7 through molecular dynamics simulation, validated them on the basis of previous experiments, and used them to obtain theoretical estimates of the pK_a values. Titration values for the two Asp and three Glu residues of IF7 were similar to those reported for random-coil models, suggesting the lack of electrostatic interactions around these residues. Furthermore, our results suggest the presence of helical structure at the N-terminus of the protein and of conformational changes at acidic pH values. The overall experimental and in silico findings suggest that local interactions and conformational equilibria do not play a role in determining the electrostatic features of the acidic residues of IF7.

Experimental and Computational Analysis of Protein Stabilization by Gly-to-d-Ala Substitution: A Convolution of Native State and Unfolded State Effects

The rational and predictable enhancement of protein stability is an important goal in protein design. Most efforts target the folded state, however stability is the free energy difference between the folded and unfolded states thus both are suitable targets. Strategies directed at the unfolded state usually seek to decrease chain entropy by introducing cross-links or by replacing glycines. Cross-linking has led to mixed results. Replacement of glycine with an l-amino acid, while reducing the entropy of the unfolded state, can introduce unfavorable steric interactions in the folded state, since glycine is often found in conformations that require a positive φ angle such as helical C-capping motifs or type I' and II″ β-turns. l-Amino acids are strongly disfavored in these conformations, but d-amino acids are not. However, there are few reported examples and conflicting results have been obtained when glycines are replaced with d-Ala. We critically examine the effect of Gly-to-d-Ala substitutions on protein stability using experimental approaches together with molecular dynamics simulations and free energy calculations. The data, together with a survey of high resolution structures, show that the vast majority of proteins can be stabilized by substitution of C-capping glycines with d-Ala. Sites suitable for substitutions can be identified via sequence alignment with a high degree of success. Steric clashes in the native state due to the new side chain are rarely observed, but are likely responsible for the destabilizing or null effect observed for the small subset of Gly-to-d-Ala substitutions which are not stabilizing. Changes in backbone solvation play less of a role. Favorable candidates for d-Ala substitution can be identified using a rapid algorithm based on molecular mechanics.

Mechanism of Phosphorylation-Induced Folding of 4E-BP2 Revealed by Molecular Dynamics Simulations

Site-specific phosphorylation of an intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can suppress its native function by folding it into a four-stranded β-sheet, but the mechanism of this phosphorylation-induced folding is unclear. In this work, we use all-atom molecular dynamics simulations to investigate both the folded and unfolded states of 4E-BP2 under different phosphorylation states of T37 and T46. The results show that the phosphorylated forms of both T37 and T46 play important roles in stabilizing the folded structure, especially for the β-turns and the sequestered binding motif. The phosphorylated residues not only guide the folding of the protein through several intermediate states but also affect the conformational distribution of the unfolded ensemble. Significantly, the phosphorylated residues can function as nucleation sites for the folding of the protein by forming certain local structures that are stabilized by hydrogen bonding involving the phosphate group. The region around phosphorylated T46 appears to fold before that around phosphorylated T37. These findings provide new insight into the intricate effects of protein phosphorylation.

Negative Charge Neutralization in the Loops and Turns of Outer Membrane Phospholipase A Impacts Folding Hysteresis at Neutral pH

Hysteresis in equilibrium protein folding titrations is an experimental barrier that must be overcome to extract meaningful thermodynamic quantities. Traditional approaches to solving this problem involve testing a spectrum of solution conditions to find ones that achieve path independence. Through this procedure, a specific pH of 3.8 was required to achieve path independence for the water-to-bilayer equilibrium folding of outer membrane protein OmpLA. We hypothesized that the neutralization of negatively charged side chains (Asp and Glu) at pH 3.8 could be the physical basis for path-independent folding at this pH. To test this idea, we engineered variants of OmpLA with Asp → Asn and Glu → Gln mutations to neutralize the negative charges within various regions of the protein and tested for reversible folding at neutral pH. Although not fully resolved, our results show that these mutations in the periplasmic turns and extracellular loops are responsible for 60% of the hysteresis in wild-type folding. Overall, our study suggests that negative charges impact the folding hysteresis in outer membrane proteins and their neutralization may aid in protein engineering applications.

NTL9 Folding at Constant pH: The Importance of Electrostatic Interaction and pH Dependence

The folding process of the N-terminal domain of ribosomal protein L9 (NTL9) was investigated at constant-pH computer simulations. Evaluation of the role of electrostatic interaction during folding was carried out by including a Debye-Hückel potential into a Cα structure-based model (SBM). In this study, the charges of the ionizable residues and the electrostatic potential are susceptible to the solution conditions, such as pH and ionic strength, as well as to the presence of charged groups. Simulations were performed under different pHs, and the results were validated by comparing them with experimental values of pKa and with denaturation experiment data. Also, the free energy profiles, Φ-values, and folding routes were calculated for each condition. It was shown how charges vary along the folding under different pH, which is subject to different scenarios. This study reveals how simplified models can capture essential physical features, reproducing experimental results, and presenting the role of electrostatic interactions before, during, and after the transition state.

Residual structures in the unfolded state of starch-binding domain of glucoamylase revealed by near-UV circular dichroism and protein engineering techniques

Protein folding is a thermodynamic process driven by energy gaps between the native and unfolded states. Although a wealth of information is available on the structure of folded species, there is a paucity of data on unfolded species. Here, we analyzed the structural properties of the unfolded state of the starch-binding domain of glucoamylase from Aspergillus niger (SBD) formed in the presence of guanidinium hydrochloride (GuHCl). Although far-UV CD and intrinsic tryptophan fluorescence spectra as well as small angle X-ray scattering suggested that SBD assumes highly unfolded structures in the presence of GuHCl, near-UV circular dichroism of wild-type SBD suggested the presence of residual structures in the unfolded state. Analyses of the unfolded states of tryptophan mutants (W543L, W563A, W590A and W615L) using Similarity Parameter, a modified version of root mean square deviation as a measure of similarity between two spectra, suggested that W543 and W563 have preferences to form native-like residual structures in the GuHCl-unfolded state. In contrast, W615 was entirely unstructured, while W590 tended to form non-native ordered structures in the unfolded state. These data and the amino acid sequence of SBD suggest that local structural propensities in the unfolded state can be determined by the probability of the presence of hydrophobic or charged residues nearby tryptophan residues.

Nascent β-Hairpin Formation of a Natively Unfolded Peptide Reveals the Role of Hydrophobic Contacts

Despite the important role of the unfolded states in protein stability, folding, and aggregation, they remain poorly understood due to the lack of residue-specific experimental data. Here, we explore features of the unfolded state of the NTL9 protein by applying all-atom replica-exchange simulations to the two fragment peptides NTL9(1–22) and NTL9(6–17). We found that while NTL9(6–17) is unstructured, NTL9(1–22) transiently folds as various β-hairpins, a fraction of which contain a native β-sheet. Interestingly, despite a large number of charged residues, the formation of backbone hydrogen bonds is concomitant with hydrophobic but not electrostatic contacts. Although the fragment peptides lack a proposed specific contact between Asp⁸ and Lys¹², the individually weak, nonspecific interactions with lysines together stabilize the charged Asp⁸, leading to a pK_a shift of nearly 0.5 units, in agreement with the NMR data. Taken together, our data suggest that the unfolded state of NTL9 likely contains a β-hairpin in segment 1–22 with sequence-distant hydrophobic contacts, thus lending support to a long-standing hypothesis that the unfolded states of proteins exhibit native-like topology with hydrophobic clusters.

Determinants of the pKa values of ionizable residues in an intrinsically disordered protein

Intrinsically disordered proteins (IDPs) are prevalent in eukaryotes; in humans, they are often associated with diseases. The protein NUPR1 is a multifunctional IDP involved in the development and progression of pancreatic cancer; therefore, it constitutes a target for drug design. In an effort to contribute to the understanding of the conformational features of NUPR1 and to provide clues on amino acid interactions in disordered states of proteins, we measured the pKa values of all its acidic groups (aspartic and glutamic residues, and backbone C terminus) by using NMR spectroscopy at low (100 mM) and high (500 mM) NaCl concentration. At low ionic strength, the pKa values were similar to those reported for random-coil models, except for Glu18 and Asp19, suggesting electrostatic interactions around these residues. Molecular modelling and simulation indicate an additional, significant role of nearby proline residues in determining the polypeptide conformational features and water accessibility in the region around Glu18, modulating the titration properties of these amino acids. In the other acidic residues of NUPR1, the small deviations of pKa values (compared to those expected for a random-coil) are likely due to electrostatic interactions with charged adjacent residues, which should be reduced at high NaCl concentrations. In fact, at high ionic strength, the pKa values of the aspartic residues were similar to those in a random coil, but there were still small differences for those of glutamic acids, probably due to hydrogen-bond formation. The overall findings suggest that local interactions and hydrophobic effects play a major role in determining the electrostatic features of NUPR1, whereas long-range charge contributions appear to be of lesser importance.

Can I solve my structure by SAD phasing? Planning an experiment, scaling data and evaluating the useful anomalous correlation and anomalous signal

A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. Here, algorithms and tools for evaluating and optimizing the useful anomalous correlation and the anomalous signal in a SAD experiment are described. A simple theoretical framework [Terwilliger et al. (2016), Acta Cryst. D72, 346-358] is used to develop methods for planning a SAD experiment, scaling SAD data sets and estimating the useful anomalous correlation and anomalous signal in a SAD data set. The phenix.plan_sad_experiment tool uses a database of solved and unsolved SAD data sets and the expected characteristics of a SAD data set to estimate the probability that the anomalous substructure will be found in the SAD experiment and the expected map quality that would be obtained if the substructure were found. The phenix.scale_and_merge tool scales unmerged SAD data from one or more crystals using local scaling and optimizes the anomalous signal by identifying the systematic differences among data sets, and the phenix.anomalous_signal tool estimates the useful anomalous correlation and anomalous signal after collecting SAD data and estimates the probability that the data set can be solved and the likely figure of merit of phasing.

Using Kinetic Network Models To Probe Non-Native Salt-Bridge Effects on α-Helix Folding

Salt-bridge interactions play an important role in stabilizing many protein structures, and have been shown to be designable features for protein design. In this work, we study the effects of non-native salt bridges on the folding of a soluble alanine-based peptide (Fs peptide) using extensive all-atom molecular dynamics simulations performed on the Folding@home distributed computing platform. Using Markov State Models, we show how non-native salt-bridges affect the folding kinetics of Fs peptide by perturbing specific conformational states. Furthermore, we present methods for the automatic detection and analysis of such states. These results provide insight into helix folding mechanisms and useful information to guide simulation-based computational protein design.

Correlation Analysis of Trp-Cage Dynamics in Folded and Unfolded States

A fundamental and still debated problem is how folded structures of proteins are related to their unfolded state. Besides the classical view, in which a large number of conformations characterize the unfolded state while the folded one is dominated by a single structure, recently a reassessment of the denatured state has been suggested. A growing amount of evidence indicates that not only the folded but also the unfolded state is at least partially organized. Here, we try to answer the question of how different protein dynamics is in folded and unfolded states by performing all-atom molecular dynamics simulations on the model protein Trp-cage. Random matrix theory inspired analysis of the correlation matrices has been carried out. The spectra of these correlation matrices show that the low rank modes of Trp-cage dynamics are outside of the limit expected for a random system both in folded and in unfolded conditions. These findings shed light on the nature of the unfolded state of the proteins, suggesting that it is much less random than previously thought.

Where the complex things are: single molecule and ensemble spectroscopic investigations of protein folding dynamics

Progress in our understanding of the simple folding dynamics of small proteins and the complex dynamics of large proteins is reviewed. Recent characterizations of the folding transition path of small proteins revealed a simple dynamics explainable by the native centric model. In contrast, the accumulated data showed the substates containing residual structures in the unfolded state and partially populated intermediates, causing complexity in the early folding dynamics of small proteins. The size of the unfolded proteins in the absence of denaturants is likely expanded but still controversial. The steady progress in the observation of folding of large proteins has clarified the rapid formation of long-range contacts that seem inconsistent with the native centric model, suggesting that the folding strategy of large proteins is distinct from that of small proteins.

Topological and sequence information predict that foldons organize a partially overlapped and hierarchical structure

It has been suggested that proteins have substructures, called foldons, which can cooperatively fold into the native structure. However, several prior investigations define foldons in various ways, citing different foldon characteristics, thereby making the concept of a foldon ambiguous. In this study, we perform a Gō model simulation and analyze the characteristics of substructures that cooperatively fold into the native-like structure. Although some results do not agree well with the experimental evidence due to the simplicity of our coarse-grained model, our results strongly suggest that cooperatively folding units sometimes organize a partially overlapped and hierarchical structure. This view makes us easy to interpret some different proposal about the foldon as a difference of the hierarchical structure. On the basis of this finding, we present a new method to assign foldons and their hierarchy, using structural and sequence information. The results show that the foldons assigned by our method correspond to the intermediate structures identified by some experimental techniques. The new method makes it easy to predict whether a protein folds sequentially into the native structure or whether some foldons fold into the native structure in parallel.

Fast-folding proteins under stress

Proteins are subject to a variety of stresses in biological organisms, including pressure and temperature, which are the easiest stresses to simulate by molecular dynamics. We discuss the effect of pressure and thermal stress on very-fast-folding model proteins, whose in vitro folding can be fully simulated on computers and compared with experiments. We then discuss experiments that can be used to subject proteins to low- and high-temperature unfolding, as well as low- and high-pressure unfolding. Pressure and temperature are prototypical perturbations that illustrate how close many proteins are to instability, a property that cells can exploit to control protein function. We conclude by reviewing some recent in-cell experiments, and progress being made in simulating and measuring protein stability and function inside live cells.

High-resolution structure of the Escherichia coli ribosome

Protein synthesis by the ribosome is highly dependent on the ionic conditions in the cellular environment, but the roles of ribosome solvation remain poorly understood. Moreover, the function of modifications to ribosomal RNA and ribosomal proteins are unclear. Here we present the structure of the Escherichia coli 70S ribosome to 2.4 Å resolution. The structure reveals details of the ribosomal subunit interface that are conserved in all domains of life, and suggest how solvation contributes to ribosome integrity and function. The structure also suggests how the conformation of ribosomal protein uS12 likely impacts its contribution to messenger RNA decoding. This structure helps to explain the phylogenetic conservation of key elements of the ribosome, including posttranscriptional and posttranslational modifications and should serve as a basis for future antibiotic development.

Quantitative assessments of the distinct contributions of polypeptide backbone amides versus side chain groups to chain expansion via chemical denaturation

In aqueous solutions with high concentrations of chemical denaturants such as urea and guanidinium chloride (GdmCl) proteins expand to populate heterogeneous conformational ensembles. These denaturing environments are thought to be good solvents for generic protein sequences because properties of conformational distributions align with those of canonical random coils. Previous studies showed that water is a poor solvent for polypeptide backbones, and therefore, backbones form collapsed globular structures in aqueous solvents. Here, we ask if polypeptide backbones can intrinsically undergo the requisite chain expansion in aqueous solutions with high concentrations of urea and GdmCl. We answer this question using a combination of molecular dynamics simulations and fluorescence correlation spectroscopy. We find that the degree of backbone expansion is minimal in aqueous solutions with high concentrations of denaturants. Instead, polypeptide backbones sample conformations that are denaturant-specific mixtures of coils and globules, with a persistent preference for globules. Therefore, typical denaturing environments cannot be classified as good solvents for polypeptide backbones. How then do generic protein sequences expand in denaturing environments? To answer this question, we investigated the effects of side chains using simulations of two archetypal sequences with amino acid compositions that are mixtures of charged, hydrophobic, and polar groups. We find that side chains lower the effective concentration of backbone amides in water leading to an intrinsic expansion of polypeptide backbones in the absence of denaturants. Additional dilution of the effective concentration of backbone amides is achieved through preferential interactions with denaturants. These effects lead to conformational statistics in denaturing environments that are congruent with those of canonical random coils. Our results highlight the role of side chain-mediated interactions as determinants of the conformational properties of unfolded states in water and in influencing chain expansion upon denaturation.

Theoretical perspectives on nonnative interactions and intrinsic disorder in protein folding and binding

The diverse biological functions of intrinsically disordered proteins (IDPs) have markedly raised our appreciation of protein conformational versatility, whereas the existence of energetically favorable yet functional detrimental nonnative interactions underscores the physical limitations of evolutionary optimization. Here we survey recent advances in using biophysical modeling to gain insight into experimentally observed nonnative behaviors and IDP properties. Simulations of IDP interactions to date focus mostly on coupled folding-binding, which follows essentially the same organizing principle as the local-nonlocal coupling mechanism in cooperative folding of monomeric globular proteins. By contrast, more innovative theories of electrostatic and aromatic interactions are needed for the conceptually novel but less-explored 'fuzzy' complexes in which the functionally bound IDPs remain largely disordered.