An effective all-atom potential for proteins

Impact of N-Terminal Domain Conformation and Domain Interactions on RfaH Fold Switching

RfaH is a two-domain metamorphic protein involved in transcription regulation and translation initiation. To carry out its dual functions, RfaH relies on two coupled structural changes: Domain dissociation and fold switching. In the free state, the C-terminal domain (CTD) of RfaH adopts an all-α fold and is tightly associated with the N-terminal domain (NTD). Upon binding to RNA polymerase (RNAP), the domains dissociate and the CTD transforms into an all-β fold while the NTD remains largely, but not entirely, unchanged. We test the idea that a change in the conformation of an extended β-hairpin (β3-β4) located on the NTD, helps trigger domain dissociation. To this end, we use homology modeling to construct a structure, H1, which is similar to free RfaH but with a remodeled β3-β4 hairpin. We then use an all-atom physics-based model enhanced with a dual basin structure-based potential to simulate domain separation driven by the thermal unfolding of the CTD with NTD in a fixed, folded conformation. We apply our model to both free RfaH and H1. For H1 we find, in line with our hypothesis, that the CTD exhibits lower stability and the domains dissociate at a lower temperature T, as compared to free RfaH. We do not, however, observe complete refolding to the all-β state in these simulations, suggesting that a change in β3-β4 orientation aids in, but is not sufficient for, domain dissociation. In addition, we study the reverse fold switch in which RfaH returns from a domain-open all-β state to its domain-closed all-α state. We observe a T-dependent transition rate; fold switching is slow at low T, where the CTD tends to be kinetically trapped in its all-β state, and at high-T, where the all-α state becomes unstable. Consequently, our simulations suggest an optimal T at which fold switching is most rapid. At this T, the stabilities of both folds are reduced. Overall, our study suggests that both inter-domain interactions and conformational changes within NTD may be important for the proper functioning of RfaH.

NPEX: Never give up protein exploration with deep reinforcement learning

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

Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions

Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ_16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ_16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.

The C-terminal domain of transcription factor RfaH: Folding, fold switching and energy landscape

We simulate the folding and fold switching of the C-terminal domain (CTD) of the transcription factor RfaH using an all-atom physics-based model augmented with a dual-basin structure-based potential energy term. We show that this hybrid model captures the essential thermodynamic behavior of this metamorphic domain, that is, a change in the global free energy minimum from an α-helical hairpin to a 5-stranded β-barrel upon the dissociation of the CTD from the rest of the protein. Using Monte Carlo sampling techniques, we then analyze the energy landscape of the CTD in terms of progress variables for folding toward the two folds. We find that, below the folding transition, the energy landscape is characterized by a single, dominant funnel to the native β-barrel structure. The absence of a deep funnel to the α-helical hairpin state reflects a negligible population of this fold for the isolated CTD. We observe, however, a higher α-helix structure content in the unfolded state compared to results from a similar but fold switch-incompetent version of our model. Moreover, in folding simulations started from an extended chain conformation we find transiently formed α-helical structure, occurring early in the process and disappearing as the chain progresses toward the thermally stable β-barrel state.

When a foreign gene meets its native counterpart: computational biophysics analysis of two PgiC loci in the grass Festuca ovina

Duplicative horizontal gene transfer may bring two previously separated homologous genes together, which may raise questions about the interplay between the gene products. One such gene pair is the “native” PgiC1 and “foreign” PgiC2 in the perennial grass Festuca ovina. Both PgiC1 and PgiC2 encode cytosolic phosphoglucose isomerase, a dimeric enzyme whose proper binding is functionally essential. Here, we use biophysical simulations to explore the inter-monomer binding of the two homodimers and the heterodimer that can be produced by PgiC1 and PgiC2 in F. ovina. Using simulated native-state ensembles, we examine the structural properties and binding tightness of the dimers. In addition, we investigate their ability to withstand dissociation when pulled by a force. Our results suggest that the inter-monomer binding is tighter in the PgiC2 than the PgiC1 homodimer, which could explain the more frequent occurrence of the foreign PgiC2 homodimer in dry habitats. We further find that the PgiC1 and PgiC2 monomers are compatible with heterodimer formation; the computed binding tightness is comparable to that of the PgiC1 homodimer. Enhanced homodimer stability and capability of heterodimer formation with PgiC1 are properties of PgiC2 that may contribute to the retaining of the otherwise redundant PgiC2 gene.

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

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

Slow Dissolution Kinetics of Model Peptide Fibrils

Understanding the kinetics of peptide self-assembly is important because of the involvement of peptide amyloid fibrils in several neurodegenerative diseases. In this paper, we have studied the dissolution kinetics of self-assembled model peptide fibrils after a dilution quench. Due to the low concentrations involved, the experimental method of choice was isothermal titration calorimetry (ITC). We show that the dissolution is a strikingly slow and reaction-limited process, that can be timescale separated from other rapid processes associated with dilution in the ITC experiment. We argue that the rate-limiting step of dissolution involves the breaking up of inter-peptide β–sheet hydrogen bonds, replacing them with peptide–water hydrogen bonds. Complementary pH experiments revealed that the self-assembly involves partial deprotonation of the peptide molecules.

Structural fluctuations and mechanical stabilities of the metamorphic protein RfaH

RfaH is a compact two-domain bacterial transcription factor that functions both as a regulator of transcription and an enhancer of translation. Underpinning the dual functional roles of RfaH is a partial but dramatic fold switch, which completely transforms the ~50-amino acid C-terminal domain (CTD) from an all-α state to an all-β state. The fold switch of the CTD occurs when RfaH binds to RNA polymerase (RNAP), however, the details of how this structural transformation is triggered is not well understood. Here we use all-atom Monte Carlo simulations to characterize structural fluctuations and mechanical stability properties of the full-length RfaH and the CTD as an isolated fragment. In agreement with experiments, we find that interdomain contacts are crucial for maintaining a stable, all-α CTD in free RfaH. To probe mechanical properties, we use pulling simulations to measure the work required to inflict local deformations at different positions along the chain. The resulting mechanical stability profile reveals that free RfaH can be divided into a "rigid" part and a "soft" part, with a boundary that nearly coincides with the boundary between the two domains. We discuss the potential role of this feature for how fold switching may be triggered by interaction with RNAP.

Glutenin and Gliadin, a Piece in the Puzzle of their Structural Properties in the Cell Described through Monte Carlo Simulations

Gluten protein crosslinking is a predetermined process where specific intra- and intermolecular disulfide bonds differ depending on the protein and cysteine motif. In this article, all-atom Monte Carlo simulations were used to understand the formation of disulfide bonds in gliadins and low molecular weight glutenin subunits (LMW-GS). The two intrinsically disordered proteins appeared to contain mostly turns and loops and showed "self-avoiding walk" behavior in water. Cysteine residues involved in intramolecular disulfide bonds were located next to hydrophobic peptide sections in the primary sequence. Hydrophobicity of neighboring peptide sections, synthesis chronology, and amino acid chain flexibility were identified as important factors in securing the specificity of intramolecular disulfide bonds formed directly after synthesis. The two LMW-GS cysteine residues that form intermolecular disulfide bonds were positioned next to peptide sections of lower hydrophobicity, and these cysteine residues are more exposed to the cytosolic conditions, which influence the crosslinking behavior. In addition, coarse-grained Monte Carlo simulations revealed that the protein folding is independent of ionic strength. The potential molecular behavior associated with disulfide bonds, as reported here, increases the biological understanding of seed storage protein function and provides opportunities to tailor their functional properties for different applications.

Protein thermal stability

Proteins, in general, fold to a well-organized three-dimensional structure in order to function. The stability of this functional shape can be perturbed by external environmental conditions, such as temperature. Understanding the molecular factors underlying the resistance of proteins to the thermal stress has important consequences. First of all, it can aid the design of thermostable enzymes able to perform efficient catalysis in the high-temperature regime. Second, it is an essential brick of knowledge required to decipher the evolutionary pathways of life adaptation on Earth. Thanks to the development of atomistic simulations and ad hoc enhanced sampling techniques, it is now possible to investigate this problem in silico, and therefore provide support to experiments. After having described the methodological aspects, the chapter proposes an extended discussion on two problems. First, we focus on thermophilic proteins, a perfect model to address the issue of thermal stability and molecular evolution. Second, we discuss the issue of how protein thermal stability is affected by crowded in vivo-like conditions.

Systematically Scrutinizing the Impact of Substitution Sites on Thermostability and Detergent Tolerance for Bacillus subtilis Lipase A

Improving an enzyme's (thermo-)stability or tolerance against solvents and detergents is highly relevant in protein engineering and biotechnology. Recent developments have tended toward data-driven approaches, where available knowledge about the protein is used to identify substitution sites with high potential to yield protein variants with improved stability, and subsequently, substitutions are engineered by site-directed or site-saturation (SSM) mutagenesis. However, the development and validation of algorithms for data-driven approaches have been hampered by the lack of availability of large-scale data measured in a uniform way and being unbiased with respect to substitution types and locations. Here, we extend our knowledge on guidelines for protein engineering following a data-driven approach by scrutinizing the impact of substitution sites on thermostability or/and detergent tolerance for Bacillus subtilis lipase A (BsLipA) at very large scale. We systematically analyze a complete experimental SSM library of BsLipA containing all 3439 possible single variants, which was evaluated as to thermostability and tolerances against four detergents under respectively uniform conditions. Our results provide systematic and unbiased reference data at unprecedented scale for a biotechnologically important protein, identify consistently defined hot spot types for evaluating the performance of data-driven protein-engineering approaches, and show that the rigidity theory and ensemble-based approach Constraint Network Analysis yields hot spot predictions with an up to ninefold gain in precision over random classification.

Probing the Basis of α-Synuclein Aggregation by Comparing Simulations to Single-Molecule Experiments

Intrinsically disordered proteins often play an important role in protein aggregation. However, it is challenging to determine the structures and interactions that drive the early stages of aggregation because they are transient and obscured in a heterogeneous mixture of disordered states. Even computational methods are limited because the lack of ordered structure makes it difficult to ensure that the relevant conformations are sampled. We address these challenges by integrating atomistic simulations with high-resolution single-molecule measurements reported previously, using the measurements to help discern which parts of the disordered ensemble of structures in the simulations are most probable while using the simulations to identify residues and interactions that are important for oligomer stability. This approach was applied to α-synuclein, an intrinsically disordered protein that aggregates in the context of Parkinson's disease. We simulated single-molecule pulling experiments on dimers, the minimal oligomer, and compared them to force spectroscopy measurements. Force-extension curves were simulated starting from a set of 66 structures with substantial structured content selected from the ensemble of dimer structures generated at zero force via Monte Carlo simulations. The pattern of contour length changes as the structures unfolded through intermediate states was compared to the results from optical trapping measurements on the same dimer to discern likely structures occurring in the measurements. Simulated pulling curves were generally consistent with experimental data but with a larger number of transient intermediates. We identified an ensemble of β-rich dimer structures consistent with the experimental data from which dimer interfaces could be deduced. These results suggest specific druggable targets in the structural motifs of α-synuclein that may help prevent the earliest steps of oligomerization.

Twisted Ribbon Aggregates in a Model Peptide System

The model peptides A₈K and A₁₀K self-assemble in water into ca. 100 nm long ribbon-like aggregates. These structures can be described as β-sheets laminated into a ribbon structure with a constant elliptical cross-section of 4 by 8 nm, where the longer axis corresponds to a finite number, N ≈ 15, of laminated sheets, and 4 nm corresponds to a stretched peptide length. The ribbon cross-section is strikingly constant and independent of the peptide concentration. High-contrast transmission electron microscopy shows that the ribbons are twisted with a pitch λ ≈ 15 nm. The self-assembly is analyzed within a simple model taking into account the interfacial free energy of the hydrophobic β-sheets and a free energy penalty arising from an increased stretching of hydrogen bonds within the laminated β-sheets, arising from the twist of the ribbons. The model predicts an optimal value N, in agreement with the experimental observations.

Stability and Local Unfolding of SOD1 in the Presence of Protein Crowders

Using NMR and Monte Carlo (MC) methods, we investigate the stability and dynamics of superoxide dismutase 1 (SOD1) in homogeneous crowding environments, where either bovine pancreatic trypsin inhibitor (BPTI) or the B1 domain of streptococcal protein G (PGB1) serves as a crowding agent. By NMR, we show that both crowders, and especially BPTI, cause a drastic loss in the overall stability of SOD1 in its apo monomeric form. Additionally, we determine chemical shift perturbations indicating that SOD1 interacts with the crowder proteins in a residue-specific manner that further depends on the identity of the crowding protein. Furthermore, the specificity of SOD1-crowder interactions is reciprocal: chemical shift perturbations on BPTI and PGB1 identify regions that interact preferentially with SOD1. By MC simulations, we investigate the local unfolding of SOD1 in the absence and presence of the crowders. We find that the crowders primarily interact with the long flexible loops of the folded SOD1 monomer. The basic mechanisms by which the SOD1 β-barrel core unfolds remain unchanged when adding the crowders. In particular, both with and without the crowders, the second β-sheet of the barrel is more dynamic and unfolding-prone than the first. Notably, the MC simulations (exploring the early stages of SOD1 unfolding) and the NMR experiments (under equilibrium conditions) identify largely the same set of PGB1 and BPTI residues as prone to form SOD1 contacts. Thus, contacts stabilizing the unfolded state of SOD1 in many cases appear to form early in the unfolding reaction.

Markov modeling of peptide folding in the presence of protein crowders

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Structure of the Bacterial Cytoskeleton Protein Bactofilin by NMR Chemical Shifts and Sequence Variation

Bactofilins constitute a recently discovered class of bacterial proteins that form cytoskeletal filaments. They share a highly conserved domain (DUF583) of which the structure remains unknown, in part due to the large size and noncrystalline nature of the filaments. Here, we describe the atomic structure of a bactofilin domain from Caulobacter crescentus. To determine the structure, we developed an approach that combines a biophysical model for proteins with recently obtained solid-state NMR spectroscopy data and amino acid contacts predicted from a detailed analysis of the evolutionary history of bactofilins. Our structure reveals a triangular β-helical (solenoid) conformation with conserved residues forming the tightly packed core and polar residues lining the surface. The repetitive structure explains the presence of internal repeats as well as strongly conserved positions, and is reminiscent of other fibrillar proteins. Our work provides a structural basis for future studies of bactofilin biology and for designing molecules that target them, as well as a starting point for determining the organization of the entire bactofilin filament. Finally, our approach presents new avenues for determining structures that are difficult to obtain by traditional means.

Bayesian inference of protein ensembles from SAXS data

The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble.

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches

Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein’s folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the G_A all-α and G_B α+β folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between G_A and G_B. In agreement with experiment, we observe conformational switching from G_A to G_B upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp G_A/G_B switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.

The biological functions of globular proteins are intimately related to their folded structures and their associated conformational fluctuations. Evolution of new structures is an important avenue to new functions. Although many mutations do not change the folded state, experiments indicate that a single amino acid substitution can lead to a drastic change in the folded structure. The physics of this switch-like behavior remains to be elucidated. Here we develop a computational model for the relevant physical forces, showing that mutations can lead to new folds by passing through intermediate sequences where the old and new folds occur with varying probabilities. Our approach helps provide a general physical account of conformational switching in evolution and mutational effects on conformational dynamics.

Peptide folding in the presence of interacting protein crowders

Using Monte Carlo methods, we explore and compare the effects of two protein crowders, BPTI and GB1, on the folding thermodynamics of two peptides, the compact helical trp-cage and the β-hairpin-forming GB1m3. The thermally highly stable crowder proteins are modeled using a fixed backbone and rotatable side-chains, whereas the peptides are free to fold and unfold. In the simulations, the crowder proteins tend to distort the trp-cage fold, while having a stabilizing effect on GB1m3. The extent of the effects on a given peptide depends on the crowder type. Due to a sticky patch on its surface, BPTI causes larger changes than GB1 in the melting properties of the peptides. The observed effects on the peptides stem largely from attractive and specific interactions with the crowder surfaces, and differ from those seen in reference simulations with purely steric crowder particles.

A Monte Carlo Study of the Early Steps of Functional Amyloid Formation

In addition to their well-known roles in neurodegenerative diseases and amyloidoses, amyloid structures also assume important functional roles in the cell. Although functional amyloid shares many physiochemical properties with its pathogenic counterpart, it is evolutionarily optimized to avoid cytotoxicity. This makes it an interesting study case for aggregation phenomenon in general. One of the most well-known examples of a functional amyloid, E. coli curli, is an essential component in the formation of bacterial biofilm, and is primarily formed by aggregates of the protein CsgA. Previous studies have shown that the minor sequence variations observed in the five different subrepeats (R1-R5), which comprise the CsgA primary sequence, have a substantial influence on their individual aggregation propensities. Using a recently described diffusion-optimized enhanced sampling approach for Monte Carlo simulations, we here investigate the equilibrium properties of the monomeric and dimeric states of these subrepeats, to probe whether structural properties observed in these early stage oligomers are decisive for the characteristics of the resulting aggregate. We show that the dimerization propensities of these peptides have strong correlations with their propensity for amyloid formation, and provide structural insights into the inter- and intramolecular contacts that appear to be essential in this process.

Molecular basis for structural heterogeneity of an intrinsically disordered protein bound to a partner by combined ESI-IM-MS and modeling

Intrinsically disordered proteins (IDPs) form biologically active complexes that can retain a high degree of conformational disorder, escaping structural characterization by conventional approaches. An example is offered by the complex between the intrinsically disordered N(TAIL) domain and the phosphoprotein X domain (P(XD)) from measles virus (MeV). Here, distinct conformers of the complex are detected by electrospray ionization-mass spectrometry (ESI-MS) and ion mobility (IM) techniques yielding estimates for the solvent-accessible surface area (SASA) in solution and the average collision cross-section (CCS) in the gas phase. Computational modeling of the complex in solution, based on experimental constraints, provides atomic-resolution structural models featuring different levels of compactness. The resulting models indicate high structural heterogeneity. The intermolecular interactions are predominantly hydrophobic, not only in the ordered core of the complex, but also in the dynamic, disordered regions. Electrostatic interactions become involved in the more compact states. This system represents an illustrative example of a hydrophobic complex that could be directly detected in the gas phase by native mass spectrometry. This work represents the first attempt to modeling the entire N(TAIL) domain bound to P(XD) at atomic resolution.

Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts

Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.

Conformational and aggregation properties of the 1-93 fragment of apolipoprotein A-I

Several disease-linked mutations of apolipoprotein A-I, the major protein in high-density lipoprotein (HDL), are known to be amyloidogenic, and the fibrils often contain N-terminal fragments of the protein. Here, we present a combined computational and experimental study of the fibril-associated disordered 1-93 fragment of this protein, in wild-type and mutated (G26R, S36A, K40L, W50R) forms. In atomic-level Monte Carlo simulations of the free monomer, validated by circular dichroism spectroscopy, we observe changes in the position-dependent β-strand probability induced by mutations. We find that these conformational shifts match well with the effects of these mutations in thioflavin T fluorescence and transmission electron microscopy experiments. Together, our results point to molecular mechanisms that may have a key role in disease-linked aggregation of apolipoprotein A-I.

β-hairpin-mediated formation of structurally distinct multimers of neurotoxic prion peptides

Protein misfolding disorders are associated with conformational changes in specific proteins, leading to the formation of potentially neurotoxic amyloid fibrils. During pathogenesis of prion disease, the prion protein misfolds into β-sheet rich, protease-resistant isoforms. A key, hydrophobic domain within the prion protein, comprising residues 109-122, recapitulates many properties of the full protein, such as helix-to-sheet structural transition, formation of fibrils and cytotoxicity of the misfolded isoform. Using all-atom, molecular simulations, it is demonstrated that the monomeric 109-122 peptide has a preference for α-helical conformations, but that this peptide can also form β-hairpin structures resulting from turns around specific glycine residues of the peptide. Altering a single amino acid within the 109-122 peptide (A117V, associated with familial prion disease) increases the prevalence of β-hairpin formation and these observations are replicated in a longer peptide, comprising residues 106-126. Multi-molecule simulations of aggregation yield different assemblies of peptide molecules composed of conformationally-distinct monomer units. Small molecular assemblies, consistent with oligomers, comprise peptide monomers in a β-hairpin-like conformation and in many simulations appear to exist only transiently. Conversely, larger assemblies are comprised of extended peptides in predominately antiparallel β-sheets and are stable relative to the length of the simulations. These larger assemblies are consistent with amyloid fibrils, show cross-β structure and can form through elongation of monomer units within pre-existing oligomers. In some simulations, assemblies containing both β-hairpin and linear peptides are evident. Thus, in this work oligomers are on pathway to fibril formation and a preference for β-hairpin structure should enhance oligomer formation whilst inhibiting maturation into fibrils. These simulations provide an important new atomic-level model for the formation of oligomers and fibrils of the prion protein and suggest that stabilization of β-hairpin structure may enhance cellular toxicity by altering the balance between oligomeric and fibrillar protein assemblies.

Mechanical resistance in unstructured proteins

Single-molecule pulling experiments on unstructured proteins linked to neurodegenerative diseases have measured rupture forces comparable to those for stable folded proteins. To investigate the structural mechanisms of this unexpected force resistance, we perform pulling simulations of the amyloid β-peptide (Aβ) and α-synuclein (αS), starting from simulated conformational ensembles for the free monomers. For both proteins, the simulations yield a set of rupture events that agree well with the experimental data. By analyzing the conformations occurring shortly before rupture in each event, we find that the mechanically resistant structures share a common architecture, with similarities to the folds adopted by Aβ and αS in amyloid fibrils. The disease-linked Arctic mutation of Aβ is found to increase the occurrence of highly force-resistant structures. Our study suggests that the high rupture forces observed in Aβ and αS pulling experiments are caused by structures that might have a key role in amyloid formation.

Application of the maximum entropy principle to determine ensembles of intrinsically disordered proteins from residual dipolar couplings

We present a method based on the maximum entropy principle that can re-weight an ensemble of protein structures based on data from residual dipolar couplings (RDCs).

Inference of structure ensembles of flexible biomolecules from sparse, averaged data

We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution with respect to the experimental data and its uncertainty. This principle generalizes the successful inferential structure determination method and recently proposed maximum entropy methods. Tractability of the protocol is demonstrated through the analysis of simulated nuclear magnetic resonance spectroscopy data of a small peptide.

Variational Optimization of an All-Atom Implicit Solvent Force Field to Match Explicit Solvent Simulation Data

The development of accurate implicit solvation models with low computational cost is essential for addressing many large-scale biophysical problems. Here, we present an efficient solvation term based on a Gaussian solvent-exclusion model (EEF1) for simulations of proteins in aqueous environment, with the primary aim of having a good overlap with explicit solvent simulations, particularly for unfolded and disordered states - as would be needed for multiscale applications. In order to achieve this, we have used a recently proposed coarse-graining procedure based on minimization of an entropy-related objective function to train the model to reproduce the equilibrium distribution obtained from explicit water simulations. Via this methodology, we have optimized both a charge screening parameter and a backbone torsion term against explicit solvent simulations of an α-helical and a β-stranded peptide. The performance of the resulting effective energy function, termed EEF1-SB, is tested with respect to the properties of folded proteins, the folding of small peptides or fast-folding proteins, and NMR data for intrinsically disordered proteins. The results show that EEF1-SB provides a reasonable description of a wide range of systems, but its key advantage over other methods tested is that it captures very well the structure and dimension of disordered or weakly structured peptides. EEF1-SB is thus a computationally inexpensive (~ 10 times faster than Generalized-Born methods) and transferable approximation for treating solvent effects.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

Local unfolding and aggregation mechanisms of SOD1: a Monte Carlo exploration

Copper, zinc superoxide dismutase 1 (SOD1) is a ubiquitous homodimeric enzyme, whose misfolding and aggregation play a potentially key role in the neurodegenerative disease amyotrophic lateral sclerosis (ALS). SOD1 aggregation is thought to be preceded by dimer dissociation and metal loss, but the mechanisms by which the metal-free monomer aggregates remain incompletely understood. Here we use implicit solvent all-atom Monte Carlo (MC) methods to investigate the local unfolding dynamics of the β-barrel-forming SOD1 monomer. Although event-to-event variations are large, on average, we find clear differences in dynamics among the eight strands forming the β-barrel. Most dynamic is the eighth strand, β8, which is located in the dimer interface of native SOD1. For the four strands in or near the dimer interface (β1, β2, β7, and β8), we perform aggregation simulations to assess the propensity of these chain segments to self-associate. We find that β1 and β2 readily self-associate to form intermolecular parallel β-sheets, whereas β8 shows a very low aggregation propensity.

SS-map: Visualizing cooperative secondary structure elements in protein ensembles

We present SS-map, a tool to visualize the secondary structure content of ensembles of proteins. When generating ensembles of intrinsically disordered proteins, we lose the understanding a single native structure gives for folded proteins. It then becomes difficult to visualize the composition of the ensembles or to detect transient helices such as MoRFs. Conformational propensities for single residues also hide the nature of cooperative structures. Here we show how SS-map describes folded and unfolded ensembles of some peptides and gives a new view of the ensembles used to describe intrinsically disordered proteins with residual structure in computational and NMR experiments. This tool is implemented in an open-source python code located at code.google.com/p/ss-map

PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Binding of two intrinsically disordered peptides to a multi-specific protein: a combined Monte Carlo and molecular dynamics study

The unique ability of intrinsically disordered proteins (IDPs) to fold upon binding to partner molecules makes them functionally well-suited for cellular communication networks. For example, the folding-binding of different IDP sequences onto the same surface of an ordered protein provides a mechanism for signaling in a many-to-one manner. Here, we study the molecular details of this signaling mechanism by applying both Molecular Dynamics and Monte Carlo methods to S100B, a calcium-modulated homodimeric protein, and two of its IDP targets, p53 and TRTK-12. Despite adopting somewhat different conformations in complex with S100B and showing no apparent sequence similarity, the two IDP targets associate in virtually the same manner. As free chains, both target sequences remain flexible and sample their respective bound, natively -helical states to a small extent. Association occurs through an intermediate state in the periphery of the S100B binding pocket, stabilized by nonnative interactions which are either hydrophobic or electrostatic in nature. Our results highlight the importance of overall physical properties of IDP segments, such as net charge or presence of strongly hydrophobic amino acids, for molecular recognition via coupled folding-binding.

A substantial fraction of our proteins are believed to be partly or completely disordered, meaning that they contain regions that lack a stable folded structure under typical physiological conditions. This is a feature which plays a key role in their functions. For example, it allows them to have many structurally different binding partners which in turn permits the construction of the intricate signaling and regulatory networks necessary to sustain complex biological organisms such as ourselves. Whereas measuring the binding strengths of associations involving disordered proteins is routine, the binding process itself is today still not fully understood. We use two different computational models to study the interactions of a folded protein, S100B, which can bind various disordered peptides. In particular, we compare two peptides whose structures are known when in complex with S100B. Our results suggest that, although the peptides assume different structures in the bound state, there are similarities in how they associate with S100B. The possibility to computationally model the interplay between proteins is an important complement to experiments, by identifying crucial steps in the binding process. This is essential to understand, e.g., how single mutations sometimes lead to serious diseases.

Binding free energy landscape of domain-peptide interactions

Peptide recognition domains (PRDs) are ubiquitous protein domains which mediate large numbers of protein interactions in the cell. How these PRDs are able to recognize peptide sequences in a rapid and specific manner is incompletely understood. We explore the peptide binding process of PDZ domains, a large PRD family, from an equilibrium perspective using an all-atom Monte Carlo (MC) approach. Our focus is two different PDZ domains representing two major PDZ classes, I and II. For both domains, a binding free energy surface with a strong bias toward the native bound state is found. Moreover, both domains exhibit a binding process in which the peptides are mostly either bound at the PDZ binding pocket or else interact little with the domain surface. Consistent with this, various binding observables show a temperature dependence well described by a simple two-state model. We also find important differences in the details between the two domains. While both domains exhibit well-defined binding free energy barriers, the class I barrier is significantly weaker than the one for class II. To probe this issue further, we apply our method to a PDZ domain with dual specificity for class I and II peptides, and find an analogous difference in their binding free energy barriers. Lastly, we perform a large number of fixed-temperature MC kinetics trajectories under binding conditions. These trajectories reveal significantly slower binding dynamics for the class II domain relative to class I. Our combined results are consistent with a binding mechanism in which the peptide C terminal residue binds in an initial, rate-limiting step.

The complex biological processes occurring in living organisms are enabled by numerous networks of interacting proteins. It is therefore of great interest to understand the physical interplay between proteins and, in particular, how this process gives rise to highly specific network connectivities. For a long time, the dominant molecular view of protein-protein interactions was the docking of more or less static folded structures, with specificity obtained from a complementarity in shape and charge distributions. Lately it has been realized that many of the links in protein networks are mediated by interactions between folded domains, on the one hand, and disordered polypeptide segments, on the other. We use an all-atom Monte Carlo based approach which attempts to capture this domain-peptide binding process in full and apply it to representative members of a common domain family. This allows us to examine and compare detailed aspects of the binding free energy landscapes which underlie specificity and affinity. Being able to model domain-peptide binding in a physically sound, yet computationally tractable way is essential for identifying molecular binding mechanisms and opens up possibilities for modifying interaction networks in a controlled way.

Monte Carlo study of the formation and conformational properties of dimers of Aβ42 variants

Small soluble oligomers, and dimers in particular, of the amyloid β-peptide (Aβ) are believed to play an important pathological role in Alzheimer's disease. Here, we investigate the spontaneous dimerization of Aβ42, with 42 residues, by implicit solvent all-atom Monte Carlo simulations, for the wild-type peptide and the mutants F20E, E22G and E22G/I31E. The observed dimers of these variants share many overall conformational characteristics but differ in several aspects at a detailed level. In all four cases, the most common type of secondary structure is intramolecular antiparallel β-sheets. Parallel, in-register β-sheet structure, as in models for Aβ fibrils, is rare. The primary force driving the formation of dimers is hydrophobic attraction. The conformational differences that we do see involve turns centered in the 20-30 region. The probability of finding turns centered in the 25-30 region, where there is a loop in Aβ fibrils, is found to increase upon dimerization and to correlate with experimentally measured rates of fibril formation for the different Aβ42 variants. Our findings hint at reorganization of this part of the molecule as a potentially critical step in Aβ aggregation.