Ranking valid topologies of the secondary structure elements using a constraint graph

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6-10 ? resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N(2)2(N)) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.     

Local hydrophobicity stabilizes secondary structures in proteins

The probability of occurrence of helix and β-sheet residues in 47 globular proteins was determined as a function of local hydrophobicity, which was defined by the sum of the Nozaki-Tanford transfer free energies at two nearest-neighbors on both sides of the amino acid sequence. In general, hydrophilic amino acids favor neither helix nor β-sheet formations when neighbor residues are also hydrophilic but favor helix formation at higher local hydrophobicity. On the other hand, some hydrophobic amino acids such as Met, Leu, and Ile favor helix formation when neighbor residues are hydrophilic. None of the hydrophobic amino acids favor β-sheet formation with hydrophilic neighbors, but most of them strongly favor β-sheet formation at high local hydrophobicity. When the average of 20 amino acids is taken, both helix and β-sheet residue probabilities are higher at higher local hydrophobicity, although the increase is steeper for β-sheets. Therefore, β-sheet formation is more influenced by local hydrophobicity than helix formation. Generally, helices are nearer the surface and tend to have hydrophilic and hydrophobic faces at opposite sides. The tendency of alternating regions of hydrophilic and hydrophobic residues in a helical sequence was revealed by calculating the correlation of the Nozaki-Tanford values. Such amphipathic helices may be important in protein–protein and protein–lipid interactions and in forming hydrophilic channels in the membrane. The choice of 30 nonhomologous proteins as the data set did not alter the above results.     

Outcome of the first electron microscopy validation task force meeting

This Meeting Review describes the proceedings and conclusions from the inaugural meeting of the Electron Microscopy Validation Task Force organized by the Unified Data Resource for 3DEM (http://www.emdatabank.org) and held at Rutgers University in New Brunswick, NJ on September 28 and 29, 2010. At the workshop, a group of scientists involved in collecting electron microscopy data, using the data to determine three-dimensional electron microscopy (3DEM) density maps, and building molecular models into the maps explored how to assess maps, models, and other data that are deposited into the Electron Microscopy Data Bank and Protein Data Bank public data archives. The specific recommendations resulting from the workshop aim to increase the impact of 3DEM in biology and medicine.     

Determination method of the balance of the secondary-structure-forming tendencies of force fields

We propose a new method of optimisation of backbone torsion-energy parameters in the force field for molecular simulations of protein systems. This method is based on the idea of balancing the secondary-structure-forming tendencies, namely, those of α-helix and β-sheet structures. We perform a minimisation of the backbone dihedral angle-based root-mean-square deviation of the helix and β structure regions in many protein structures. As an example, we optimised the backbone torsion-energy parameters of AMBER parm96 force field using 100 protein molecules from the Protein Data Bank. We then performed folding simulations of α-helical and β-hairpin peptides, using the optimised force field. The results imply that the new force-field parameters give structures more consistent with the experimental implications than the original AMBER parm96 force field.     

Automatic determination of the handedness of single-particle maps of macromolecules solved by CryoEM

Single-Particle Analysis by Cryo-Electron Microscopy is a well-established technique to elucidate the three-dimensional (3D) structure of biological macromolecules. The orientation of the acquired projection images must be initially estimated without any reference to the final structure. In this step, algorithms may find a mirrored version of all the orientations resulting in a mirrored 3D map. It is as compatible with the acquired images as its unmirrored version from the image processing point of view, only that it is not biologically plausible.In this article, we introduce HaPi (Handedness Pipeline), the first method to automatically determine the hand of electron density maps of macromolecules solved by CryoEM. HaPi is built by training two 3D convolutional neural networks. The first determines α-helices in a map, and the second determines whether the α-helix is left-handed or right-handed. A consensus strategy defines the overall map hand. The pipeline is trained on simulated and experimental data. The handedness can be detected only for maps whose resolution is better than 5 Å. HaPi can identify the hand in 89% of new simulated maps correctly. Moreover, we evaluated all the maps deposited at the Electron Microscopy Data Bank and 11 structures uploaded with the incorrect hand were identified.     

Deriving topology and sequence alignment for the helix skeleton in low-resolution protein density maps

Cryoelectron microscopy (cryoEM) is an experimental technique to determine the three-dimensional (3D) structure of large protein complexes. Currently, this technique is able to generate protein density maps at 6-9 A resolution, at which the skeleton of the structure (which is composed of alpha-helices and beta-sheets) can be visualized. As a step towards predicting the entire backbone of the protein from the protein density map, we developed a method to predict the topology and sequence alignment for the skeleton helices. Our method combines the geometrical information of the skeleton helices with the Rosetta ab initio structure prediction method to derive a consensus topology and sequence alignment for the skeleton helices. We tested the method with 60 proteins. For 45 proteins, the majority of the skeleton helices were assigned a correct topology from one of our top ten predictions. The offsets of the alignment for most of the assigned helices were within +/-2 amino acids in the sequence. We also analyzed the use of the skeleton helices as a clustering tool for the decoy structures generated by Rosetta. Our comparison suggests that the topology clustering is a better method than a general overlap clustering method to enrich the ranking of decoys, particularly when the decoy pool is small.     

Effects of aligned α‐helix peptide dipoles on experimental electrostatic potentials

Aligned protein α‐helix dipoles have been implicated in protein function and structure. The recent breakthroughs in high‐resolution electron microscopy (EM) of macromolecules makes it possible to explore fundamental aspects of structural biology at the detailed molecular level. The electrostatic potential (ESP) generated by aligned protein α‐helix dipole should be observable in high‐resolution EM maps despite the fact that the effect may be partially screened by induced electric fields. Here, we show that aligned backbone dipoles in protein α‐helices account for long‐range features in the protein ESP functions. Our results are consistent with experimental EM maps and density functional theory calculations, including direct Fourier summation for proper calculation of the ESP due to the nonlocal nature of the ESP function from aligned dipoles and other partial atomic charges.     

Deep learning for reconstructing protein structures from cryo-EM density maps: Recent advances and future directions

Cryo-Electron Microscopy (cryo-EM) has emerged as a key technology to determine the structure of proteins, particularly large protein complexes and assemblies in recent years. A key challenge in cryo-EM data analysis is to automatically reconstruct accurate protein structures from cryo-EM density maps. In this review, we briefly overview various deep learning methods for building protein structures from cryo-EM density maps, analyze their impact, and discuss the challenges of preparing high-quality data sets for training deep learning models. Looking into the future, more advanced deep learning models of effectively integrating cryo-EM data with other sources of complementary data such as protein sequences and AlphaFold-predicted structures need to be developed to further advance the field.     

Structure determination of archaea-specific ribosomal protein L46a reveals a novel protein fold

Three archaea-specific ribosomal proteins recently identified show no sequence homology with other known proteins. Here we determined the structure of L46a, the most conserved one among the three proteins, from Sulfolobus solfataricus P2 using NMR spectroscopy. The structure presents a twisted β-sheet formed by the N-terminal part and two helices at the C-terminus. The L46a structure has a positively charged surface which is conserved in the L46a protein family and is the potential rRNA-binding site. Searching homologous structures in Protein Data Bank revealed that the structure of L46a represents a novel protein fold. The backbone dynamics identified by NMR relaxation experiments reveal significant flexibility at the rRNA binding surface. The potential position of L46a on the ribosome was proposed by fitting the structure into a previous electron microscopy map of the ribosomal 50S subunit, which indicated that L46a contacts to domain I of 23S rRNA near a multifunctional ribosomal protein L7ae.     

Uniformity,ideality, and hydrogen bonds in transmembrane alpha-helices

Protein environments substantially influence the balance of molecular interactions that generate structural stability. Transmembrane helices exist in the relatively uniform low dielectric interstices of the lipid bilayer, largely devoid of water and with a very hydrophobic distribution of amino acid residues. Here, through an analysis of bacteriorhodopsin crystal structures and the transmembrane helix structure from M2 protein of influenza A, some helices are shown to be exceptionally uniform in hydrogen bond geometry, peptide plane tilt angle, and backbone torsion angles. Evidence from both the x-ray crystal structures and solid-state NMR structure suggests that the intramolecular backbone hydrogen bonds are shorter than their counterparts in water-soluble proteins. Moreover, the geometry is consistent with a dominance of electrostatic versus covalent contributions to these bonds. A comparison of structure as a function of resolution shows that as the structures become better characterized the helices become much more uniform, suggesting that there is a possibility that many more uniform helices will be observed, even among the moderate resolution membrane protein structures that are currently in the Protein Data Bank that do not show such features.     

Conformational prediction and circular dichroism studies on the lac repressor

Using the protein predictive model of Chou & Fasman (1974b), the secondary structure of the lac repressor has been elucidated from its amino acid sequence of 347 residues. The conformation is predicted to contain 37% α-helix and 35% β-sheet for the repressor, and 29% helix and 41% β-sheet for the trypsin-resistant core (residues 60 to 327). Circular dichroism studies indicate that native lac repressor contains 40% helix and 42% β-sheet, while the core has 16% helix and 54% β-sheet, in general agreement with the predicted conformation. The sharp reduction in helicity for the trypsinized lac repressor could be due to the loss of two long helical regions, 26–45 and 328–344, predicted at both terminals. There are extensive β-sheets predicted in the 215–324 region, which may be responsible for tetrameric stabilization found in both the lac repressor and the core. Residues 17 to 33 were previously predicted by Adler et al. (1972) to be helical and were proposed to bind in the major groove of DNA. However, the present analysis shows that there are two anti-parallel β-sheet regions: 4–7 and 17–24 at the N-terminal as well as 315–318 and 321–324 at the C-terminal of the lac repressor. These β-sheet pairs may assume the twisted “polypeptide double helix” conformation (Carter & Kraut, 1974) and bind to complementary regions in the major groove of DNA. The OH groups of Tyr at the N-terminal and those of Thr and Ser side chains, in both β-sheets at the N and C-terminal ends, could form hydrogen bonds to specific sites on the lac operator. There are 23 reverse β-turns predicted that may control the tertiary folding of the lac repressor, which is essential for operator binding. The behavior of several lac repressor mutants can be satisfactorily explained in terms of polar to non-polar group replacements as well as conformational changes in light of the present predicted model.     

Synthesis and β-sheet propensity of constrained N-amino peptides

The stabilization of β-sheet secondary structure through peptide backbone modification represents an attractive approach to protein mimicry. Here, we present strategies toward stable β-hairpin folds based on peptide strand N-amination. Novel pyrazolidinone and tetrahydropyridazinone dipeptide constraints were introduced via on-resin Mitsunobu cyclization between α-hydrazino acid residues and a serine or homoserine side chain. Acyclic and cyclic N-amino peptide building blocks were then evaluated for their effect on β-hairpin stability in water using a GB1-derived model system. Our results demonstrate the strong β-sheet stabilizing effect of the peptide N-amino substituent, and provide useful insights into the impact of covalent dipeptide constraint on β-sheet folding.     

Analysis and prediction of helix shift errors in homology modeling

High sequence identity between two proteins (e.g. > 60%) is a strong evidence for high structural similarity. However, internal shifts in one of the two proteins can sometimes give rise to unexpectedly high structural differences. This, in turn, causes unreliable structure predictions when two such proteins are used in homology modeling. Here, we perform a computational analysis of helix shifts and we show that their occurrence can be predicted with statistical learning methods. Our results indicate that helix shifts increase the RMS error by factor 2.6 compared to those protein pairs without a helix shift. Although helix shifts are rare (1.6% of helices and a commensurately higher number of proteins are affected), they therefore pose a significant problem for reliable structure prediction systems. In this paper, we prototype a new approach for model quality assessment and demonstrate that it can successfully warn against helix shifts. A support vector machine trained on a wide range of sequence and structure properties predicts the occurrence of helix shifts with a sensitivity of 74.2% and a specificity of 83.6%. On an equalized test dataset, this corresponds to an accuracy of 78.9%. Projected to the full dataset, it translates to an accuracy of 83.4%. Our analysis shows that helix shift detection is a valuable building block for highly reliable structure prediction systems. Furthermore, the statistical learning based approach to helix shift detection that we employ here is orthogonal to well-established model quality assessment methods (which use geometric constraint checking or mean force potentials). Therefore, a further increase of prediction accuracy is expected from the combination of these methods.     

The extended left-handed helix: a simple nucleic acid-binding motif

The poly-proline type II extended left-handed helical structure is well represented in proteins. In an effort to determine the helix's role in nucleic acid recognition and binding, a survey of 258 nucleic acid-binding protein structures from the Protein Data Bank was conducted. Results indicate that left-handed helices are commonly found at the nucleic acid interfacial regions. Three examples are used to illustrate the utility of this structural element as a recognition motif. The third K homology domain of NOVA-2, the Epstein-Barr nuclear antigen-1, and the Drosophila paired protein homeodomain all contain left-handed helices involved in nucleic acid interactions. In each structure, these helices were previously unidentified as left-handed helices by secondary structure algorithms but, rather, were identified as either having small amounts of hydrogen bond patterns to the rest of the protein or as being "unstructured." Proposed mechanisms for nucleic acid interactions by the extended left-handed helix include both nonspecific and specific recognition. The observed interactions indicate that this secondary structure utilizes an increase in protein backbone exposure for nucleic acid recognition. Both main-chain and side-chain atoms are involved in specific and nonspecific hydrogen bonding to nucleobases or sugar-phosphates, respectively. Our results emphasize the need to classify the left-handed helix as a viable nucleic acid recognition and binding motif, similar to previously identified motifs such as the helix-turn-helix, zinc fingers, leucine zippers, and others.     

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.     

Differential backbone dynamics of companion helices in the extended helical coiled‐coil domain of a bacterial chemoreceptor

Cytoplasmic domains of transmembrane bacterial chemoreceptors are largely extended four‐helix coiled coils. Previous observations suggested the domain was structurally dynamic. We probed directly backbone dynamics of this domain of the transmembrane chemoreceptor Tar from Escherichia coli using site‐directed spin labeling and electron paramagnetic resonance (EPR) spectroscopy. Spin labels were positioned on solvent‐exposed helical faces because EPR spectra for such positions reflect primarily polypeptide backbone movements. We acquired spectra for spin‐labeled, intact receptor homodimers solubilized in detergent or inserted into native E. coli lipid bilayers in Nanodiscs, characterizing 16 positions distributed throughout the cytoplasmic domain and on both helices of its helical hairpins, one amino terminal to the membrane‐distal tight turn (N‐helix), and the other carboxyl terminal (C‐helix). Detergent solubilization increased backbone dynamics for much of the domain, suggesting that loss of receptor activities upon solubilization reflects wide‐spread destabilization. For receptors in either condition, we observed an unanticipated difference between the N‐ and C‐helices. For bilayer‐inserted receptors, EPR spectra from sites in the membrane‐distal protein‐interaction region and throughout the C‐helix were typical of well‐structured helices. In contrast, for approximately two‐thirds of the N‐helix, from its origin as the AS‐2 helix of the membrane‐proximal HAMP domain to the beginning of the membrane‐distal protein‐interaction region, spectra had a significantly mobile component, estimated by spectral deconvolution to average approximately 15%. Differential helical dynamics suggests a four‐helix bundle organization with a pair of core scaffold helices and two more dynamic partner helices. This newly observed feature of chemoreceptor structure could be involved in receptor function.     

Simulation Studies on the Stabilities of Aggregates Formed by Fibril-Forming Segments of α-Synuclein

Abstract

We performed molecular dynamics simulations for various oligomers with different β-sheet conformations consisting of α-Synuclein 71–82 residues using an all atom force field and explicit water model. Tetramers of antiparallel β-sheet are shown to be stable, whereas parallel sheets are highly unstable due to the repulsive interactions between bulky and polar side chains as well as the weaker backbone hydrogen bonds. We also investigated the stabilities of double antiparallel β-sheets stacked with asymmetric and symmetric geometries. Our results show that this 12 amino acid residue peptide can form stable β-sheet conformers at 320K and higher temperatures. The backbone hydrogen bonds in β-sheet and the steric packing between hydrophobic side chains between β-sheets are shown to give conformational stabilities.     

Stabilization of short helices by intramolecular cluster formation

The intramolecular formation of multiple clusters of interacting helices has been characterized in a homopolymer. The configuration partition function permits the formation of clusters in which the number of interacting helices may be as large as the greatest integer in n/2, where n denotes the number of amino acid residues in the chain. The theoretical formulation has its origin in a recent [Mattice, W. L. & Scheraga, H. A. (1984) Biopolymers 23 , 1701–1724], tractable matrix expression for the configuration partition function for intramolecular antiparallel β-sheet formation. Reassignment of the expression for one of the n(n+3)/2 elements in the sparse statistical weight matrix, along with a simple change in notation, converts that treatment into a matrix formulation of the configuration partition function for a chain containing multiple clusters of interacting antiparallel helices. The five statistical weights used are δ, f_l, w, and the Zimm-Bragg σ and s. Each tight bend that connects two interacting helices contributes a factor of δ, f_l is used in the weight for larger loops between interacting helices, and w arises from helix–helix interaction. The influence of the helix–helix interaction is well illustrated by two helix–coil transitions in a chain with n = 156 and σ = 0.001. In the absence of helix–helix interaction, the transition occurs by the nucleation and subsequent elongation of a small number of helices. When helix–helix interaction is attractive, the transition can occur by a different mechanism. Formation of a single pair of interacting helices is followed by addition of new helices to the initial cluster. In the latter process, individual helices experience relatively little growth after they are formed.     

Influence of the g− conformation of Ser and Thr on the structure of transmembrane helices

In order to study the influence of Ser and Thr on the structure of transmembrane helices we have analyzed a database of helix stretches extracted from crystal structures of membrane proteins and an ensemble of model helices generated by molecular dynamics simulations. Both complementary analyses show that Ser and Thr in the g? conformation induce and/or stabilize a structural distortion in the helix backbone. Using quantum mechanical calculations, we have attributed this effect to the electrostatic repulsion between the side chain Oγ atom of Ser and Thr and the backbone carbonyl oxygen at position i ? 3. In order to minimize the repulsive force between these negatively charged oxygens, there is a modest increase of the helix bend angle as well as a local opening of the helix turn preceding Ser/Thr. This small distortion can be amplified through the helix, resulting in a significant displacement of the residues located at the other side of the helix. The crystal structures of aquaporin Z and the β₂-adrenergic receptor are used to illustrate these effects. Ser/Thr-induced structural distortions can be implicated in processes as diverse as ligand recognition, protein function and protein folding.     

High-resolution prediction of protein helix positions and orientations

We have developed a new method for predicting helix positions in globular proteins that is intended primarily for comparative modeling and other applications where high precision is required. Unlike helix packing algorithms designed for ab initio folding, we assume that knowledge is available about the qualitative placement of all helices. However, even among homologous proteins, the corresponding helices can demonstrate substantial differences in positions and orientations, and for this reason, improperly positioned helices can contribute significantly to the overall backbone root-mean-square deviation (RMSD) of comparative models. A helix packing algorithm for use in comparative modeling must obtain high precision to be useful, and for this reason we utilize an all-atom protein force field (OPLS) and a Generalized Born continuum solvent model. To reduce the computational expense associated with using a detailed, physics-based energy function, we have developed new hierarchical and multiscale algorithms for sampling the helices and flanking loops. We validate the method using a test suite of 33 cases, which are drawn from a diverse set of high-resolution crystal structures. The helix positions are reproduced with an average backbone RMSD of 0.6 A, while the average backbone RMSD of the complete loop-helix-loop region (i.e., the helix with the surrounding loops, which are also repredicted) is 1.3 A.