Variability of the canonical loop conformations in serine proteinases inhibitors and other proteins

Canonical loops of protein inhibitors of serine proteinases occur in proteins having completely different folds. In this article, conformations of the loops have been analyzed for inhibitors belonging to 10 structurally different families. Using deviation in C_α-C_α distances as a criterion for loop similarity, we found that the P3-P3′ segment defines most properly the length of the loop. When conformational differences among loops of individual inhibitors were compared using root mean square deviation (rmsd) in atomic coordinates for all main chain atoms (Δr method) and rmsd operating in main chain torsion angles (Δt method), differences of up to 2.1 Å and 72.3°, respectively, were observed. Such large values indicate significant conformational differences among individual loops. Nevertheless, the overall geometry of the inhibitor-proteinase interaction is very well preserved, as judged from the similarity of C_α-C_α distances between C_α of catalytic Ser and C_α of P3-P3′ residues in various enzyme-inhibitor complexes. The mode of interaction is very well preserved both in the chymotrypsin and subtilisin families, as distances calculated for subtilisin-inhibitor complexes are almost always within the range of those for chymotrypsin-inhibitor complexes. Complex formation leads to conformational changes of up to 160° for χ₁ angle. Side chains of residue P1 and P2′ adopt in different complexes a similar orientation (χ₁ angle = −60° and −180°, respectively). To check whether the canonical conformation can be found among non–proteinase-inhibitor Brookhaven Protein Data Bank structures, two selection criteria—the allowed main chain dihedral angles and C_α-C_α distances for the P3-P3′ segment—were applied to all these structures. This procedure detected 132 unique hexapeptide segments in 121 structurally and functionally unrelated proteins. Partial preferences for certain amino acids occurring at particular positions in these hexapeptides could be noted. Further restriction of this set to hexapeptides with a highly exposed P1 residue side chain resulted in 40 segments. The possibility of complexes formation between these segments and serine proteinases was ruled out in molecular modeling due to steric clashes. Several structural features that determine the canonical conformation of the loop both in inhibitors and in other proteins can be distinguished. They include main chain hydrogen bonds both within the P3-P3′ segment and with the scaffold region, P3-P4 and P3′-P4′ hydrophobic interactions, and finally either hydrophobic or polar interactions involving the P1′ residue. Proteins 32:459–474, 1998. © 1998 Wiley-Liss, Inc.     

DNP-Enhanced MAS NMR: A Tool to Snapshot Conformational Ensembles of α-Synuclein in Different States

Intrinsically disordered proteins dynamically sample a wide conformational space and therefore do not adopt a stable and defined three-dimensional conformation. The structural heterogeneity is related to their proper functioning in physiological processes. Knowledge of the conformational ensemble is crucial for a complete comprehension of this kind of proteins. We here present an approach that utilizes dynamic nuclear polarization-enhanced solid-state NMR spectroscopy of sparsely isotope-labeled proteins in frozen solution to take snapshots of the complete structural ensembles by exploiting the inhomogeneously broadened line-shapes. We investigated the intrinsically disordered protein α-synuclein (α-syn), which plays a key role in the etiology of Parkinson’s disease, in three different physiologically relevant states. For the free monomer in frozen solution we could see that the so-called “random coil conformation” consists of α-helical and β-sheet-like conformations, and that secondary chemical shifts of neighboring amino acids tend to be correlated, indicative of frequent formation of secondary structure elements. Based on these results, we could estimate the number of disordered regions in fibrillar α-syn as well as in α-syn bound to membranes in different protein-to-lipid ratios. Our approach thus provides quantitative information on the propensity to sample transient secondary structures in different functional states. Molecular dynamics simulations rationalize the results.     

Discrete Molecular Dynamics Can Predict Helical Prestructured Motifs in Disordered Proteins

Intrinsically disordered proteins (IDPs) lack a stable tertiary structure, but their short binding regions termed Pre-Structured Motifs (PreSMo) can form transient secondary structure elements in solution. Although disordered proteins are crucial in many biological processes and designing strategies to modulate their function is highly important, both experimental and computational tools to describe their conformational ensembles and the initial steps of folding are sparse. Here we report that discrete molecular dynamics (DMD) simulations combined with replica exchange (RX) method efficiently samples the conformational space and detects regions populating α-helical conformational states in disordered protein regions. While the available computational methods predict secondary structural propensities in IDPs based on the observation of protein-protein interactions, our ab initio method rests on physical principles of protein folding and dynamics. We show that RX-DMD predicts α-PreSMos with high confidence confirmed by comparison to experimental NMR data. Moreover, the method also can dissect α-PreSMos in close vicinity to each other and indicate helix stability. Importantly, simulations with disordered regions forming helices in X-ray structures of complexes indicate that a preformed helix is frequently the binding element itself, while in other cases it may have a role in initiating the binding process. Our results indicate that RX-DMD provides a breakthrough in the structural and dynamical characterization of disordered proteins by generating the structural ensembles of IDPs even when experimental data are not available.     

Structural Interpretation of Paramagnetic Relaxation Enhancement-Derived Distances for Disordered Protein States

Paramagnetic relaxation enhancement (PRE) is a powerful technique for studying transient tertiary organizations of unfolded and partially folded proteins. The heterogeneous and dynamic nature of disordered protein states, together with the r⁻⁶ dependence of PRE, presents significant challenges for reliable structural interpretation of PRE-derived distances. Without additional knowledge of accessible conformational substates, ensemble-simulation-based protocols have been used to calculate structure ensembles that appear to be consistent with the PRE distance restraints imposed on the ensemble level with the proper r⁻⁶ weighting. However, rigorous assessment of the reliability of such protocols has been difficult without intimate knowledge of the true nature of disordered protein states. Here we utilize sets of theoretical PRE distances derived from simulated structure ensembles that represent the folded, partially folded and unfolded states of a small protein to investigate the efficacy of ensemble-simulation-based structural interpretation of PRE distances. The results confirm a critical limitation that, due to r⁻⁶ weighting, only one or a few members need to satisfy the distance restraints and the rest of the ensemble are essentially unrestrained. Consequently, calculated structure ensembles will appear artificially heterogeneous no matter whether the PRE distances are derived from the folded, partially unfolded or unfolded state. Furthermore, the nature of the heterogeneous ensembles is largely determined by the protein model employed in structure calculation and reflects little on the true nature of the underlying disordered state. These findings suggest that PRE measurements on disordered protein states alone generally do not contain enough information for a reliable structural interpretation and that the latter will require additional knowledge of accessible conformational substates. Interestingly, when a very large number of PRE measurements is available, faithful structural interpretation might be possible with intermediate ensemble sizes under ideal conditions.     

Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes

Conformational transitions between open/closed or free/bound states in proteins possess functional importance. We propose a technique in which the collective modes obtained from an anisotropic network model (ANM) are used in conjunction with a Monte Carlo (MC) simulation approach, to investigate conformational transition pathways and pathway intermediates. The ANM-MC technique is applied to adenylate kinase (AK) and hemoglobin. The iterative method, in which normal modes are continuously updated during the simulation, proves successful in accomplishing the transition between open-closed conformations of AK and tense-relaxed forms of hemoglobin (C^α− root mean square deviations between two end structures of 7.13 Å and 3.55 Å, respectively). Target conformations are reached by root mean-square deviations of 2.27 Å and 1.90 Å for AK and hemoglobin, respectively. The intermediate conformations overlap with crystal structures from the AK family within a 3.0-Å root mean-square deviation. In the case of hemoglobin, the transition of tense-to-relaxed passes through the relaxed state. In both cases, the lowest-frequency modes are effective during transitions. The targeted Monte Carlo approach is used without the application of collective modes. Both the ANM-MC and targeted Monte Carlo techniques can explore sequences of events in transition pathways with an efficient yet realistic conformational search.     

Segmental conformational disorder and dynamics in the intrinsically disordered protein α-synuclein and its chain length dependence

Conformational ensembles of fully disordered natural polypeptides represent the starting point of protein refolding initiated by transfer to folding conditions. Thus, understanding the transient properties and dimensions of such peptides under folding conditions is a necessary step in the understanding of their subsequent folding behavior. Such ensembles can also undergo alternative folding and form amyloid structures, which are involved in many neurological degenerative diseases. Here, we performed a structural study of this initial state using time-resolved fluorescence resonance energy transfer analysis of a series of eight partially overlapping double-labeled chain segments of the N-terminal and NAC domains of the α-synuclein molecule. The distributions of end-to-end distance and segmental intramolecular diffusion coefficients were simultaneously determined for eight labeled chain segments. We used the coefficient of variation, C_v, as a measure of the conformational heterogeneity (i.e., structural disorder). With the exception of two segments, the C_vs were characteristic of a fully disordered state of the chain. Subtle deviations from this behavior at the segment labeled in the NAC domain and the segment at the N termini reflected subtle conformational bias that might be related to the initiation of transition to amyloid aggregates. The chain length dependence of the mean segmental end-to-end distance followed a power law as predicted by Flory, but the dependence was steeper than previously predicted, probably due to the contribution of the excluded volume effect, which is more dominant for shorter-chain segments. The observed intramolecular diffusion coefficients (< 10 to ∼ 25 ?²/ns) are only an order of magnitude lower than the common diffusion coefficients of low molecular weight probes. This diffusion coefficient increased with chain length, probably due to the cumulative contributions of minor bond rotations along the chain. These results gave us a reference both for characteristics of a natural unfolded polypeptide at the moment of initiation of folding and for detection of possible initiation sites of the amyloid transition.     

Conversion from a virtual-bond chain to a complete polypeptide backbone chain

A method for generating a complete polypeptide backbone structure from a set of C^α coordinates is presented. Initial trial values of ? and ψ for a selected residue are chosen (essentially from an identification of the conformational region of the virtual-bond backbone, e.g., and α-helical region), and values of ? and ψ for the remaining residues (both towards the N- and C-terminus) are then computed, subject to the constraint that the chain have the same virtual-bond angles and virtual-bond dihedral angles as the given set of C^α coordinates. The conversion from C^α coordinates to full backbone dihedral angles (?,ψ) involves the solution of a set of algebraic equations relating the virtual-bond angles and virtual-bond dihedral angles to standard peptide geometry and backbone dihedral angles. The procedure has been tested successfully on C^α coordinates taken from standard-geometry full-atom structures of bovine pancreatic trypsin inhibitor (BPTI). Some difficulty was encountered with error-sensitive residues, but on the whole the backbone generation was successful. Application of the method to C^α coordinates for BPTI derived from simplified model calculations (involving nonstandard geometry) showed that such coordinates may be inconsistent with the requirement that ?_Pro be near ?75°. In such a case, i.e., for residues for which the algebraic method failed, a leastsquares minimizer was then used in conjunction with the algebraic method; the mean-square deviation of the calculated C^α coordinates from the given ones was minimized by varying the backbone dihedral angles. Thus, these inconsistencies were circumvented and a full backbone structure whose C^α coordinates had an rms deviation of 0.26 Å from the given set of C^α coordinates was obtained.     

Kinetics of Contact Formation and End-to-End Distance Distributions of Swollen Disordered Peptides

Unstructured polypeptide chains are subject to various degrees of swelling or compaction depending on the combination of solvent condition and amino acid sequence. Highly denatured proteins generally behave like random-coils with excluded volume repulsion, whereas in aqueous buffer more compact conformations have been observed for the low-populated unfolded state of globular proteins as well as for naturally disordered sequences. To quantitatively account for the different mechanisms inducing the swelling of polypeptides, we have examined three 14-residues peptides in aqueous buffer and in denaturant solutions, including the well characterized AGQ repeat as a reference and two variants, in which we have successively introduced charged side chains and removed the glycines. Quenching of the triplet state of tryptophan by close contact with cysteine has been used in conjunction with Förster resonance energy transfer to study the equilibrium and kinetic properties of the peptide chains. The experiments enable accessing end-to-end root mean-square distance, probability of end-to-end contact formation and intrachain diffusion coefficient. The data can be coherently interpreted on the basis of a simple chain model with backbone angles obtained from a library of coil segments of proteins and hard sphere repulsion at each C_α position. In buffered water, we find that introducing charges in a glycine-rich sequence induces a mild chain swelling and a significant speed-up of the intrachain dynamics, whereas the removal of the glycines results in almost a two-fold increase of the chain volume and a drastic slowing down. In denaturants we observe a pronounced swelling of all the chains, with significant differences between the effect of urea and guanidinium chloride.     

Identification of minimally interacting modules in an intrinsically disordered protein

The conformational characterization of intrinsically disordered proteins (IDPs) is complicated by their conformational heterogeneity and flexibility. If an IDP could somehow be divided into smaller fragments and reconstructed later, theoretical and spectroscopic studies could probe its conformational variability in detail. Here, we used replica molecular-dynamics simulations and network theory to explore whether such a divide-and-conquer strategy is feasible for α-synuclein, a prototypical IDP. We characterized the conformational variability of α-synuclein by conducting >100 unbiased all-atom molecular-dynamics simulations, for a total of >10 μs of trajectories. In these simulations, α-synuclein formed a heterogeneous ensemble of collapsed coil states in an aqueous environment. These states were stabilized by heterogeneous contacts between sequentially distant regions. We find that α-synuclein contains residual secondary structures in the collapsed states, and the heterogeneity in the collapsed state makes it feasible to split α-synuclein into sequentially contiguous minimally interacting fragments. This study reveals previously unknown characteristics of α-synuclein and provides a new (to our knowledge) approach for studying other IDPs.     

Structure and Disorder in an Unfolded State under Nondenaturing Conditions from Ensemble Models Consistent with a Large Number of Experimental Restraints

Obtaining detailed structural models of disordered states of proteins under nondenaturing conditions is important for a better understanding of both functional intrinsically disordered proteins and unfolded states of folded proteins. Extensive experimental characterization of the drk N-terminal SH3 domain unfolded state has shown that, although it appears to be highly disordered, it possesses significant nonrandom secondary and tertiary structure. In our previous attempts to generate structural models of the unfolded state using the program ENSEMBLE, we were limited by insufficient experimental restraints and conformational sampling. In this study, we have vastly expanded our experimental restraint set to include ¹H-¹⁵N residual dipolar couplings, small-angle X-ray scattering measurements, nitroxide paramagnetic relaxation enhancements, O₂-induced ¹³C paramagnetic shifts, hydrogen-exchange protection factors, and ¹⁵N R₂ data, in addition to the previously used nuclear Overhauser effects, amino terminal Cu²⁺-Ni²⁺ binding paramagnetic relaxation enhancements, J-couplings, chemical shifts, hydrodynamic radius, and solvent accessibility restraints. We have also implemented a new ensemble calculation methodology that uses iterative conformational sampling and seeks to calculate the simplest possible ensemble models. As a result, we can now generate ensembles that are consistent with much larger experimental data sets than was previously possible. Although highly heterogeneous and having broad molecular size distributions, the calculated drk N-terminal SH3 domain unfolded-state ensembles have very different properties than expected for random or statistical coils and possess significant nonnative α-helical structure and both native-like and nonnative tertiary structure.     

Ensembles from Ordered and Disordered Proteins Reveal Similar Structural Constraints during Evolution

The conformations accessible to proteins are determined by the inter-residue interactions between amino acid residues. During evolution, structural constraints that are required for protein function providing biologically relevant information can exist. Here, we studied the proportion of sites evolving under structural constraints in two very different types of ensembles, those coming from ordered and disordered proteins. Using a structurally constrained model of protein evolution, we found that both types of ensembles show comparable, near 40%, number of positions evolving under structural constraints. Among these sites, ~ 68% are in disordered regions and ~ 57% of them show long-range inter-residue contacts. Also, we found that disordered ensembles are redundant in reference to their structurally constrained evolutionary information and could be described on average with ~ 11 conformers. Despite the different complexity of the studied ensembles and proteins, the similar constraints reveal a comparable level of selective pressure to maintain their biological functions. These results highlight the importance of the evolutionary information to recover meaningful biological information to further characterize conformational ensembles.     

Structural ensembles of disordered proteins from hierarchical chain growth and simulation

Disordered proteins and nucleic acids play key roles in cellular function and disease. Here, we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. While atomistic molecular dynamics (MD) simulation has seen a lot of improvement in recent years, large-scale computing resources and careful validation are required to simulate full-length disordered biopolymers in solution. As a computationally efficient alternative, hierarchical chain growth (HCG) combines pre-sampled chain fragments in a statistically reproducible manner into ensembles of full-length atomically detailed biomolecular structures. Experimental data can be integrated during and after chain assembly. Applications to the neurodegeneration-linked proteins α-synuclein, tau, and TDP-43, including as condensate, illustrate the use of HCG. We conclude by highlighting the emerging connections to AI-based structural modeling including AlphaFold2.     

Bayesian Energy Landscape Tilting: Towards Concordant Models of Molecular Ensembles

Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and ³J measurements gives convergent values of the peptide’s α, β, and PP_II conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT’s principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data.     

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the C_α-only elastic network models, which assume elastic interactions between pairs of residues whose C_α atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between C_α atoms or heavy atoms derived from a large set of protein crystal structures.     

Assignment of secondary structure from Cα coordinates

A multiple regression analysis has established a nonlinear relationship between the backbone dihedral angles and the C^α coordinates obtained from the x-ray crystal structures of 14 proteins. The regression equations have been applied to predict specific dihedral angles of each residue in the backbone of 24 proteins. Overall this method (Nonlinear Regression Distance Torsion) predicts values of ϕ and ψ within a ±45° window of those found in the x-ray structure with an accuracy of 94 and 91% and within a ±30° window of 88 and 81%. Two methods for the assignment of motif from C^α coordinates are reported. For the first method, motif is assigned from the dihedral angles predicted using the regression equations. By the second method, motif of the ith residue is assigned from the distance C^α_i-1 to C^α_i+2 (v₆) and torsional angle C^α_i-1, C^α_i, C^α_i+1, C^α_i+2 (v₁₃). For the 24 proteins, 23.7% of the residues by the former method and 19.6% by the latter method are assigned differently than in the Protein Data Bank. © 1997 John Wiley & Sons, Inc.     

Ensemble models of proteins and protein domains based on distance distribution restraints

Conformational ensembles of intrinsically disordered peptide chains are not fully determined by experimental observations. Uncertainty due to lack of experimental restraints and due to intrinsic disorder can be distinguished if distance distributions restraints are available. Such restraints can be obtained from pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy applied to pairs of spin labels. Here, we introduce a Monte Carlo approach for generating conformational ensembles that are consistent with a set of distance distribution restraints, backbone dihedral angle statistics in known protein structures, and optionally, secondary structure propensities or membrane immersion depths. The approach is tested with simulated restraints for a terminal and an internal loop and for a protein with 69 residues by using sets of sparse restraints for underlying well‐defined conformations and for published ensembles of a premolten globule‐like and a coil‐like intrinsically disordered protein. Proteins 2016; 84:544–560. © 2016 Wiley Periodicals, Inc.     

Surface wax of Andreaea and Pogonatum species

The mosses Andreaea rupestris, Pogonatum aloides and P. urnigerum contain surface waxes in amounts of 0.05–0.12% dry wt. The waxes consisted of esters (C₃₈-C₅₄), primary alcohols (C₂₀-C₃₂), free fatty acids (C₁₆-C₃₀), and alkanes (C₂₁-C₃₁). Additionally, aldehydes (C₂₂-C₃₀) were major constituents in the wax of P. urnigerum. The classes and their chain length distributions in the surface waxes of these mosses are comparable to those of epicuticular waxes of higher plants.     

Using a FRET Library with Multiple Probe Pairs To Drive Monte Carlo Simulations of α-Synuclein

We describe a strategy for experimentally-constraining computational simulations of intrinsically disordered proteins (IDPs), using α-synuclein, an IDP with a central role in Parkinson’s disease pathology, as an example. Previously, data from single-molecule Förster Resonance Energy Transfer (FRET) experiments have been effectively utilized to generate experimentally constrained computational models of IDPs. However, the fluorophores required for single-molecule FRET experiments are not amenable to the study of short-range (<30 Å) interactions. Using ensemble FRET measurements allows one to acquire data from probes with multiple distance ranges, which can be used to constrain Monte Carlo simulations in PyRosetta. To appropriately employ ensemble FRET data as constraints, we optimized the shape and weight of constraining potentials to afford ensembles of structures that are consistent with experimental data. We also used this approach to examine the structure of α-synuclein in the presence of the compacting osmolyte trimethylamine-N-oxide. Despite significant compaction imparted by 2 M trimethylamine-N-oxide, the underlying ensemble of α-synuclein remains largely disordered and capable of aggregation, also in agreement with experimental data. These proof-of-concept experiments demonstrate that our modeling protocol enables one to efficiently generate experimentally constrained models of IDPs that incorporate atomic-scale detail, allowing one to study an IDP under a variety of conditions.