Flexibility of beta-sheets: principal component analysis of database protein structures

Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold (e.g., coiled coils and beta-barrels). Recent work has quantified the flexibility of alpha-helices using a principal component analysis (PCA) of database helical structures (J. Mol. Bio. 2003, 327, pp. 229-237). Here, we extend the analysis to beta-sheet flexibility using PCA on a database of beta-sheet structures. For sheets of varying dimension and geometry, we find two dominant modes of flexibility: twist and bend. The distributions of amplitudes for these modes are found to be Gaussian and independent, suggesting that the PCA twist and bend modes can be identified as the soft elastic normal modes of sheets. We consider the scaling of mode eigenvalues with sheet size and find that parallel beta-sheets are more rigid than antiparallel sheets over the entire range studied. Finally, we discuss the application of our PCA results to modeling and design of beta-sheet proteins.     

A study of the membrane-water interface region of membrane proteins

The most conspicuous structural characteristic of the alpha-helical membrane proteins is their long transmembrane alpha-helices. However, other structural elements, as yet largely ignored in statistical studies of membrane protein structure, are found in those parts of the protein that are located in the membrane-water interface region. Here, we show that this region is enriched in irregular structure and in interfacial helices running roughly parallel with the membrane surface, while beta-strands are extremely rare. The average amino acid composition is different between the interfacial helices, the parts of the transmembrane helices located in the interface region, and the irregular structures. In this region, hydrophobic and aromatic residues tend to point toward the membrane and charged/polar residues tend to point away from the membrane. The interface region thus imposes different constraints on protein structure than do the central hydrocarbon core of the membrane and the surrounding aqueous phase.     

Interactions of alpha-helices with lipid bilayers: a review of simulation studies

Membrane proteins, of which the majority seem to contain one or more alpha-helix, constitute approx. 30% of most genomes. A complete understanding of the nature of helix/bilayer interactions is necessary for an understanding of the structural principles underlying membrane proteins. This review describes computer simulation studies of helix/bilayer interactions. Key experimental studies of the interactions of alpha-helices and lipid bilayers are briefly reviewed. Surface associated helices are found in some membrane-bound enzymes (e.g. prostaglandin synthase), and as stages in the mechanisms of antimicrobial peptides and of pore-forming bacterial toxins. Transmembrane alpha-helices are found in most integral membrane proteins, and also in channels formed by amphipathic peptides or by bacterial toxins. Mean field simulations, in which the lipid bilayer is approximated as a hydrophobic continuum, have been used in studies of membrane-active peptides (e.g. alamethicin, melittin, magainin and dermaseptin) and of simple membrane proteins (e.g. phage Pf1 coat protein). All atom molecular dynamics simulations of fully solvated bilayers with transmembrane helices have been applied to: the constituent helices of bacteriorhodopsin; peptide-16 (a simple model TM helix); and a number of pore-lining helices from ion channels. Surface associated helices (e.g. melittin and dermaseptin) have been simulated, as have alpha-helical bundles such as bacteriorhodopsin and alamethicin. From comparison of the results from the two classes of simulation, it emerges that a major theoretical challenge is to exploit the results of all atom simulations in order to improve the mean field approach.     

Geometry of proline-containing alpha-helices in proteins.

Crystal structure analysis of proline-containing alpha-helices in proteins has been carried out. High resolution crystal structures were selected from the Protein Data Bank. Apart from the standard internal parameters, some parameters which are specifically related to the bend in the helix due to proline have been developed and analyzed. Finally the position and nature of these helices and their interactions with the rest of the protein have been analyzed.     

How protein transmembrane segments sense the lipid environment

Integral membrane proteins have central roles in a vast number of vital cellular processes. A structural feature that most membrane proteins have in common is the presence of one or more alpha-helices with which they traverse the lipid bilayer. Because of the interaction with the surrounding lipids, the organization of these transmembrane helices will be sensitive to lipid properties like lateral packing, hydrophobic thickness, and headgroup charge. The helices may adapt to the lipids in different ways, which in turn can influence the structure and function of the intact membrane protein. In this review, we will focus on how the lipid environment influences two specific properties of transmembrane segments: their lateral association and their tilt with respect to the bilayer normal.     

Role of stabilization centers in 4 helix bundle proteins

Stabilization centers (SCs) were shown to play an important role in preventing decay of three-dimensional protein structures. These residue clusters, stabilized by cooperative long-range interactions, were proposed to serve as anchoring points for arranging secondary structure elements. In all-alpha proteins, SC elements appear less frequently than in all-beta, alpha/beta, and alpha+beta proteins suggesting that tertiary structure formation of all-alpha proteins is governed by different principles than in other protein classes. Here we analyzed the relation between the formation of stabilization centers and the inter-axial angles (Omega) of alpha-helices in 4 helix bundle proteins. In the distance range, where dipoles have dominant effect on the helix pair arrangement, those helix pairs, where residues from both helices participate in SC elements, appear as parallel more frequently than those helices where no SC elements are present. For SC containing helix pairs, the energetic difference between the parallel and anti-parallel states decreases considerably from 1.1 kcal/mol to 0.4 kcal/mol. Although the observed effect is weak for more distant helices, a competition between the SC element formation and the optimal dipole-dipole interaction of alpha-helices is proposed as a mechanism for tertiary structure formation in 4 helix bundle proteins. The SC-forming potential of different arrangements as well as the pitfalls of the SC definition are also discussed.     

Conformational dynamics of helix S6 from Shaker potassium channel: simulation studies

Prolines in transmembrane (TM) alpha-helices are believed to play an important structural and/or functional role in membrane proteins. At a structural level a proline residue distorts alpha-helical structure due to the loss of at least one stabilizing backbone hydrogen bond, and introduces flexibility in the helix that may result in substantial kink and swivel motions about the effective "hinge." At a functional level, for example in Kv channels, it is believed that proline-induced molecular hinges may have a direct role in gating, i.e., the conformational change linked to opening/closing the channel to movement of ions. In this article we study the conformational dynamics of the S6 TM helix from of the Kv channel Shaker, which possesses the motif PVP--a motif that is conserved in Kv channels. We perform multiple molecular dynamics simulations of single S6 helices in a membrane-mimetic environment in order to effectively map the kink-swivel conformational space of the protein, exploiting the ability of multiple simulations to achieve greater sampling. We show that the presence of proline locally perturbs the helix, disrupting local dihedral angles and producing local twist and unwinding in the region of the hinge--an effect that is relaxed with distance from the PVP motif. We furthermore show that motions about the hinge are highly anisotropic, reflecting a preferred region of kink-swivel conformation space that may have implications for the gating process.     

Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic

We investigated protein motions using normal modes within a database framework, determining on a large sample the degree to which normal modes anticipate the direction of the observed motion and were useful for motions classification. As a starting point for our analysis, we identified a large number of examples of protein flexibility from a comprehensive set of structural alignments of the proteins in the PDB. Each example consisted of a pair of proteins that were considerably different in structure given their sequence similarity. On each pair, we performed geometric comparisons and adiabatic-mapping interpolations in a high-throughput pipeline, arriving at a final list of 3,814 putative motions and standardized statistics for each. We then computed the normal modes of each motion in this list, determining the linear combination of modes that best approximated the direction of the observed motion. We integrated our new motions and normal mode calculations in the Macromolecular Motions Database, through a new ranking interface at http://molmovdb.org. Based on the normal mode calculations and the interpolations, we identified a new statistic, mode concentration, related to the mathematical concept of information content, which describes the degree to which the direction of the observed motion can be summarized by a few modes. Using this statistic, we were able to determine the fraction of the 3,814 motions where one could anticipate the direction of the actual motion from only a few modes. We also investigated mode concentration in comparison to related statistics on combinations of normal modes and correlated it with quantities characterizing protein flexibility (e.g., maximum backbone displacement or number of mobile atoms). Finally, we evaluated the ability of mode concentration to automatically classify motions into a variety of simple categories (e.g., whether or not they are "fragment-like"), in comparison to motion statistics. This involved the application of decision trees and feature selection (particular machine-learning techniques) to training and testing sets derived from merging the "list" of motions with manually classified ones.     

Bundles of amphipathic transmembrane alpha-helices as a structural motif for ion-conducting channel proteins: studies on sodium channels and acetylcholine receptors

Channel proteins are transmembrane symmetric (or pseudosymmetric) oligomers organized around a central ionic pore. We present here a molecular model of the pore forming structures of two channel proteins with different primary structures and oligomeric size: the voltage-sensitive sodium channel and the nicotinic cholinergic receptor. We report low-energy arrangements of alpha-helical bundles calculated by semiempiricial potential energy functions and optimization routines and further refined using molecular dynamics. The ion-conducting pore is considered to be a symmetric or pseudosymmetric homooligomer of 3-5 amphipathic alpha-helices arranged such that the polar residues line a central hydrophilic pathway and the apolar residues face the hydrophobic bilayer interior. The channel lining exposes either charged (Asp, Glu, Arg, Lys) or polar-neutral (Ser, Thr) residues. A bundle of four parallel helices constrained to C4 symmetry, the helix axis aligned with the symmetry axis, and the helices constrained to idealized dihedral angles, produces a structure with a pore of the size inferred for the sodium channel protein (area approximately 16 A2). Similarly, a pentameric array optimized with constraints to maintain C5 symmetry and backbone torsions characteristic of alpha-helices adopts a structure that appears well suited to form the lining of the nicotinic cholinergic receptor (pore area approximately 46 A2). Thus, bundles of amphipathic alpha-helices satisfy the structural, energetic, and dynamic requirements to be the molecular structural motif underlying the function of ionic channels.     

Proline-induced distortions of transmembrane helices

Proline residues in the transmembrane (TM) alpha-helices of integral membrane proteins have long been suspected to play a key role for helix packing and signal transduction by inducing regions of helix distortion and/or dynamic flexibility (hinges). In this study we try to characterise the effect of proline on the geometric properties of TM alpha-helices. We have examined 199 transmembrane alpha-helices from polytopic membrane proteins of known structure. After examining the location of proline residues within the amino acid sequences of TM helices, we estimated the helix axes either side of a hinge and hence identified a hinge residue. This enabled us to calculate helix kink and swivel angles. The results of this analysis show that proline residues occur with a significant concentration in the centre of sequences of TM alpha-helices. In this location, they may induce formation of molecular hinges, located on average about four residues N-terminal to the proline residue. A superposition of proline-containing TM helices structures shows that the distortion induced is anisotropic and favours certain relative orientations (defined by helix kink and swivel angles) of the two helix segments.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Comparison of the structures of cro and lambda repressor proteins from bacteriophage lambda

The three-dimensional structures of cro repressor protein and of the amino-terminal domain of lambda repressor protein, both from bacteriophage lambda, are compared. The second and third alpha-helices, alpha 2 and alpha 3, are shown to have essentially identical conformations in the two proteins, confirming the significance of the amino acid sequence homology previously noted between these and other DNA binding proteins in the region corresponding to these helices. The correspondence between the two-helical units in cro and lambda repressor protein is better than the striking agreement noted previously between two-helical units in cro and catabolite gene-activator protein. Parts of the first alpha-helices of repressor and cro show a structural correspondence that suggests a revised sequence homology between the two proteins in their extreme amino-terminal regions. In particular, there is a short loop between the alpha 1 and alpha 2 helices of lambda repressor that is missing from cro. This structural difference may account for the observed differences found with different cros and repressors in the pattern of phosphates whose ethylation prevents the binding of these proteins to their specific recognition sites. Although the two proteins have strikingly similar alpha 2-alpha 3 helical units that are presumed to bind to DNA in an essentially similar manner, stereochemical restrictions prevent the alpha 2-alpha 3 units of the respective proteins aligning on the DNA in exactly the same way.     

Limited tendency of alpha-helical residues to form disulfide bridges: a structural explanation.

Disulfide bridges have an enormous impact on the structure of a large number of proteins and polypeptides. Understanding the structural basis that regulates their formation may be important for the design of novel peptide-based molecules with a specific fold and stability. Here we report a statistical analysis of the relationships between secondary structure and disulfide bond formation, carried out using a large database of protein structures. Our analyses confirm the observation sporadically reported in previous investigations that cysteine residues located in alpha-helices display a limited tendency to form disulfide bridges. The very low occurrence of the disulfide bond in all alpha-chains compared to all beta-chains indicates that this property is also evident when proteins with different topologies are investigated. Taking advantage of the large database that endorsed the analysis on relatively rare motifs, we demonstrate that cysteine residues embedded in 3(10) helices present a good tendency to form disulfide bonds. This result is somewhat surprising since 3(10) helices are commonly assimilated into alpha-helices. A plausible structural explanation for the observed data has been derived combining analyses of disulfide bond sequence separation and of the length of the different secondary structure elements.     

Domain-elongation NMR spectroscopy yields new insights into RNA dynamics and adaptive recognition

By simplifying the interpretation of nuclear magnetic resonance spin relaxation and residual dipolar couplings data, recent developments involving the elongation of RNA helices are providing new atomic insights into the dynamical properties that allow RNA structures to change functionally and adaptively. Domain elongation, in concert with spin relaxation measurements, has allowed the detailed characterization of a hierarchical network of local and collective motional modes occurring at nanosecond timescale that mirror the structural rearrangements that take place following adaptive recognition. The combination of domain elongation with residual dipolar coupling measurements has allowed the experimental three-dimensional visualization of very large amplitude rigid-body helix motions in HIV-1 transactivation response element (TAR) that trace out a highly choreographed trajectory in which the helices twist and bend in a correlated manner. The dynamic trajectory allows unbound TAR to sample many of its ligand bound conformations, indicating that adaptive recognition occurs by “conformational selection” rather than “induced fit.” These studies suggest that intrinsic flexibility plays essential roles directing RNA conformational changes along specific pathways.     

Protein folding and wring resonances

The polypeptide chain of a protein is shown to obey topological constraints which enable long range excitations in the form of wring modes of the protein backbone. Wring modes of proteins of specific lengths can therefore resonate with molecular modes present in the cell. It is suggested that protein folding takes place when the amplitude of a wring excitation becomes so large that it is energetically favorable to bend the protein backbone. The condition under which such structural transformations can occur is found, and it is shown that both cold and hot denaturation (the unfolding of proteins) are natural consequences of the suggested wring mode model. Native (folded) proteins are found to possess an intrinsic standing wring mode.     

Coils in the membrane core are conserved and functionally important

With the increasing number of available α-helical transmembrane (TM) protein structures, the traditional picture of membrane proteins has been challenged. For example, reentrant regions, which enter and exit the membrane at the same side, and interface helices, which lie parallel with the membrane in the membrane-water interface, are common. Furthermore, TM helices are frequently kinked, and their length and tilt angle vary. Here, we systematically analyze 7% of all residues within the deep membrane core that are in coil state. These coils can be found in TM-helix kinks as major breaks in TM helices and as parts of reentrant regions.Coil residues are significantly more conserved than other residues. Due to the polar character of the coil backbone, they are either buried or located near aqueous channels. Coil residues are frequently found within channels and transporters, where they introduce the flexibility and polarity required for transport across the membrane. Therefore, we believe that coil residues in the membrane core, while constituting a structural anomaly, are essential for the function of proteins.     

Polyproline helices in protein structures: A statistical survey

A statistical survey of polyproline II (PPII) helices extracted from protein crystal structures is here reported. The average hydrophobicity of these helices is intermediate between those displayed by beta-strands and coil regions and is similar to that of alpha-helices. PPII helices with amphipathic properties have been identified and classified. Amino acid propensities for PPII helices derived in this study differ significantly from those previously reported. They show a little albeit significant correlation with propensities for alpha-helices whereas they are fully non-correlated to propensities for beta-sheets. Finally, PPII propensities have been correlated with amino acid frequencies in structural proteins, such as collagen and extensins.     

Helix kinks are equally prevalent in soluble and membrane proteins

Helix kinks are a common feature of α‐helical membrane proteins, but are thought to be rare in soluble proteins. In this study we find that kinks are a feature of long α‐helices in both soluble and membrane proteins, rather than just transmembrane α‐helices. The apparent rarity of kinks in soluble proteins is due to the relative infrequency of long helices (≥20 residues) in these proteins. We compare length‐matched sets of soluble and membrane helices, and find that the frequency of kinks, the role of Proline, the patterns of other amino acid around kinks (allowing for the expected differences in amino acid distributions between the two types of protein), and the effects of hydrogen bonds are the same for the two types of helices. In both types of protein, helices that contain Proline in the second and subsequent turns are very frequently kinked. However, there are a sizeable proportion of kinked helices that do not contain a Proline in either their sequence or sequence homolog. Moreover, we observe that in soluble proteins, kinked helices have a structural preference in that they typically point into the solvent. Proteins 2014; 82:1960–1970. © 2014 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

Structures, basins, and energies: a deconstruction of the Protein Coil Library

Globular proteins adopt complex folds, composed of organized assemblies of alpha-helix and beta-sheet together with irregular regions that interconnect these scaffold elements. Here, we seek to parse the irregular regions into their structural constituents and to rationalize their formative energetics. Toward this end, we dissected the Protein Coil Library, a structural database of protein segments that are neither alpha-helix nor beta-strand, extracted from high-resolution protein structures. The backbone dihedral angles of residues from coil library segments are distributed indiscriminately across the phi,psi map, but when contoured, seven distinct basins emerge clearly. The structures and energetics associated with the two least-studied basins are the primary focus of this article. Specifically, the structural motifs associated with these basins were characterized in detail and then assessed in simple simulations designed to capture their energetic determinants. It is found that conformational constraints imposed by excluded volume and hydrogen bonding are sufficient to reproduce the observed ,psi distributions of these motifs; no additional energy terms are required. These three motifs in conjunction with alpha-helices, strands of beta-sheet, canonical beta-turns, and polyproline II conformers comprise approximately 90% of all protein structure.