Stability and rigidity/flexibility—Two sides of the same coin?

Protein molecules require both flexibility and rigidity for functioning. The fast and accurate prediction of protein rigidity/flexibility is one of the important problems in protein science. We have determined flexible regions for four homologous pairs from thermophilic and mesophilic organisms by two methods: the fast FoldUnfold which uses amino acid sequence and the time consuming MDFirst which uses three-dimensional structures. We demonstrate that both methods allow determining flexible regions in protein structure. For three of the four thermophile–mesophile pairs of proteins, FoldUnfold predicts practically the same flexible regions which have been found by the MD/First method. As expected, molecular dynamics simulations show that thermophilic proteins are more rigid in comparison to their mesophilic homologues. Analysis of rigid clusters and their decomposition provides new insights into protein stability. It has been found that the local networks of salt bridges and hydrogen bonds in thermophiles render their structure more stable with respect to fluctuations of individual contacts. Such network includes salt bridge triads Agr-Glu-Lys and Arg-Glu-Arg, or salt bridges (such as Arg-Glu) connected with hydrogen bonds. This ionic network connects alpha helices and rigidifies the structure. Mesophiles can be characterized by stand alone salt bridges and hydrogen bonds or small ionic clusters. Such difference in the network of salt bridges results in different flexibility of homologous proteins. Combining both approaches allows characterizing structural features in atomic detail that determine the rigidity/flexibility of a protein structure. This article is a part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.     

Wiggle—Predicting Functionally Flexible Regions from Primary Sequence

The Wiggle series are support vector machine–based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

Wiggle-predicting functionally flexible regions from primary sequence

The Wiggle series are support vector machine-based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

Protein flexibility and rigidity predicted from sequence

Structural flexibility has been associated with various biological processes such as molecular recognition and catalytic activity. In silico studies of protein flexibility have attempted to characterize and predict flexible regions based on simple principles. B-values derived from experimental data are widely used to measure residue flexibility. Here, we present the most comprehensive large-scale analysis of B-values. We used this analysis to develop a neural network-based method that predicts flexible-rigid residues from amino acid sequence. The system uses both global and local information (i.e., features from the entire protein such as secondary structure composition, protein length, and fraction of surface residues, and features from a local window of sequence-consecutive residues). The most important local feature was the evolutionary exchange profile reflecting sequence conservation in a family of related proteins. To illustrate its potential, we applied our method to 4 different case studies, each of which related our predictions to aspects of function. The first 2 were the prediction of regions that undergo conformational switches upon environmental changes (switch II region in Ras) and the prediction of surface regions, the rigidity of which is crucial for their function (tunnel in propeller folds). Both were correctly captured by our method. The third study established that residues in active sites of enzymes are predicted by our method to have unexpectedly low B-values. The final study demonstrated how well our predictions correlated with NMR order parameters to reflect motion. Our method had not been set up to address any of the tasks in those 4 case studies. Therefore, we expect that this method will assist in many attempts at inferring aspects of function.     

Molecular dynamics simulations of polypeptide conformations in water: A comparison of alpha, beta, and poly(pro)II conformations.

A significant fraction of the so-called "random coil" residues in globular proteins exists in the left-handed poly(Pro)II conformation. In order to compare the behavior of this secondary structure with that of the other regular secondary structures, molecular dynamics simulations, with the GROMOS suite of programs, of an alanine octapeptide in water, in alpha-helix, beta-strand, and left-handed poly(Pro)II conformations, have been performed. Our results indicate a limited flexibility for the alpha-helix conformation and a relatively larger flexibility for the beta-strand and poly(Pro)II conformations. The behavior of oligopeptides with a starting configuration of beta-strand and poly(Pro)II conformations, both lacking interchain hydrogen bonds, were similar. The (phi, psi) angles reflect a continuum of structures including both beta and P(II) conformations, but with a preference for local P(II) regions. Differences in the network of water molecules involved in hydrogen bonding with the backbone of the polypeptide were observed in local regions of beta and P(II) conformations. Such water bridges help stabilize the P(II) conformation relative to the beta conformation. Proteins 1999;36:400-406.     

One nanosecond molecular dynamics simulation of the N-terminal domain of the lambda repressor protein

We have carried out molecular dynamics simulation of the N-terminal domain of the lambda repressor protein in a surrounding environment including explicit waters and ions. We observe two apparent dynamics substates in the nanosecond protein simulation, the transition occurring around 500 ps. The existence of these two apparent substates results from a high flexibility of the arm in each monomer, a relative flexibility of both arms with respect to each other, and a relative displacement of the recognition helices from 30 to 40 A of interhelical distance. Many amino acid residues, including those involved in DNA recognition, undergo a simultaneous transition in their side-chain conformations, consistent with the relationship between side-chain conformation and secondary structural elements, as observed in protein crystal structures. This result suggests plausible conformational changes experienced by the protein upon DNA binding. On the whole, the non-consensus monomer appears to be more flexible than its consensus counterpart.     

Analysis of protein main-chain solvation as a function of secondary structure

We have analysed the hydration of main-chain carbonyl and amide groups in 24 high-resolution well-refined protein structures as a function of the secondary structure in which these polar groups occur. We find that main-chain atoms in beta-sheets are as hydrated as those in alpha-helices, with most interactions involving "free" amide and carbonyl groups that do not participate in secondary structure hydrogen bonds. The distributions of water molecules around these non-bonded carbonyl groups reflect specific steric interactions due to the local secondary structure. Approximately 20% and 4%, respectively of bonded carbonyl and amide groups interact with solvent. These include interactions with carbonyl groups on the exposed faces of alpha-helices that have been correlated previously with bending of the helix. Water molecules interacting with alpha-helices occur mainly at the amino and carbonyl termini of the helices, in which case the solvent sites maintain the hydrogen bonding by bridging between residues i and i-3 or i-4 at the amino terminus and between i and i+3 or i+4 at the carbonyl terminus. We also see a number of solvent-mediated Ncap and Ccap interactions. The water molecules interacting with beta-sheets occur mainly at the edges, in which case they extend the sheet structure, or at the ends of strands, in which case they extend the beta-ladder. In summary, the solvent networks appear to extend the hydrogen-bonding structure of the secondary structures. In beta-turns, which usually occur at the surface of a protein, exposed amide and carbonyl groups are often hydrated, especially close to glycine residues. Occasionally water molecules form a bridge between residues i and i+3 in the turn and this may provide extra stabilization.     

HingeProt: automated prediction of hinges in protein structures

Proteins are highly flexible molecules. Prediction of molecular flexibility aids in the comprehension and prediction of protein function and in providing details of functional mechanisms. The ability to predict the locations, directions, and extent of molecular movements can assist in fitting atomic resolution structures to low-resolution EM density maps and in predicting the complex structures of interacting molecules (docking). There are several types of molecular movements. In this work, we focus on the prediction of hinge movements. Given a single protein structure, the method automatically divides it into the rigid parts and the hinge regions connecting them. The method employs the Elastic Network Model, which is very efficient and was validated against a large data set of proteins. The output can be used in applications such as flexible protein-protein and protein-ligand docking, flexible docking of protein structures into cryo-EM maps, and refinement of low-resolution EM structures. The web server of HingeProt provides convenient visualization of the results and is available with two mirror sites at http://www.prc.boun.edu.tr/appserv/prc/HingeProt3 and http://bioinfo3d.cs.tau.ac.il/HingeProt/.     

Control of protein functional dynamics by peptide linkers

Control of structural flexibility is essential for the proper functioning of a large number of proteins and multiprotein complexes. At the residue level, such flexibility occurs due to local relaxation of peptide bond angles whose cumulative effect may result in large changes in the secondary, tertiary or quaternary structures of protein molecules. Such flexibility, and its absence, most often depends on the nature of interdomain linkages formed by oligopeptides. Both flexible and relatively rigid peptide linkers are found in many multidomain proteins. Linkers are thought to control favorable and unfavorable interactions between adjacent domains by means of variable softness furnished by their primary sequence. Large-scale structural heterogeneity of multidomain proteins and their complexes, facilitated by soft peptide linkers, is now seen as the norm rather than the exception. Biophysical discoveries as well as computational algorithms and databases have reshaped our understanding of the often spectacular biomolecular dynamics enabled by soft linkers. Absence of such motion, as in so-called molecular rulers, also has desirable functional effects in protein architecture. We review here the historic discovery and current understanding of the nature of domains and their linkers from a structural, computational, and biophysical point of view. A number of emerging applications, based on the current understanding of the structural properties of peptides, are presented in the context of domain fusion of synthetic multifunctional chimeric proteins.     

Internal dynamics of the tryptophan repressor (TrpR) and two functionally distinct TrpR variants, L75F-TrpR and A77V-TrpR, in their l-Trp-bound forms

Backbone amide dynamics of the Escherichia coli tryptophan repressor protein (WT-TrpR) and two functionally distinct variants, L75F-TrpR and A77V-TrpR, in their holo (l-tryptophan corepressor-bound) form have been characterized using (15)N nuclear magnetic resonance (NMR) relaxation. The three proteins possess very similar structures, ruling out major conformational differences as the source of their functional differences, and suggest that changes in protein flexibility are at the origin of their distinct functional properties. Comparison of site specific (15)N-T(1), (15)N-T(2), (15)N-{(1)H} nuclear Overhauser effect, reduced spectral density, and generalized order (S(2)) parameters indicates that backbone dynamics in the three holo-repressors are overall very similar with a few notable and significant exceptions for backbone atoms residing within the proteins' DNA-binding domain. We find that flexibility is highly restricted for amides in core α-helices (i.e., helices A-C and F), and a comparable "stiffening" is observed for residues in the DNA recognition helix (helix E) of the helix D-turn-helix E (HTH) DNA-binding domain of the three holo-repressors. Unexpectedly, amides located in helix D and in adjacent turn regions remain flexible. These data support the concept that residual flexibility in TrpR is essential for repressor function, DNA binding, and molecular recognition of target operators. Comparison of the (15)N NMR relaxation parameters of the holo-TrpRs with those of the apo-TrpRs indicates that the single-point amino acid substitutions, L75F and A77V, perturb the flexibility of backbone amides of TrpR in very different ways and are most pronounced in the apo forms of the three repressors. Finally, we present these findings in the context of other DNA-binding proteins and the role of protein flexibility in molecular recognition.     

Side-chain flexibility in proteins upon ligand binding

Ligand binding may involve a wide range of structural changes in the receptor protein, from hinge movement of entire domains to small side-chain rearrangements in the binding pocket residues. The analysis of side chain flexibility gives insights valuable to improve docking algorithms and can provide an index of amino-acid side-chain flexibility potentially useful in molecular biology and protein engineering studies. In this study we analyzed side-chain rearrangements upon ligand binding. We constructed two non-redundant databases (980 and 353 entries) of "paired" protein structures in complexed (holo-protein) and uncomplexed (apo-protein) forms from the PDB macromolecular structural database. The number and identity of binding pocket residues that undergo side-chain conformational changes were determined. We show that, in general, only a small number of residues in the pocket undergo such changes (e.g., approximately 85% of cases show changes in three residues or less). The flexibility scale has the following order: Lys > Arg, Gln, Met > Glu, Ile, Leu > Asn, Thr, Val, Tyr, Ser, His, Asp > Cys, Trp, Phe; thus, Lys side chains in binding pockets flex 25 times more often then do the Phe side chains. Normalizing for the number of flexible dihedral bonds in each amino acid attenuates the scale somewhat, however, the clear trend of large, polar amino acids being more flexible in the pocket than aromatic ones remains. We found no correlation between backbone movement of a residue upon ligand binding and the flexibility of its side chain. These results are relevant to 1. Reduction of search space in docking algorithms by inclusion of side-chain flexibility for a limited number of binding pocket residues; and 2. Utilization of the amino acid flexibility scale in protein engineering studies to alter the flexibility of binding pockets.     

Multiple Molecular Dynamics Simulations of TEM β-Lactamase: Dynamics and Water Binding of the Ω-Loop

The Ω-loop of TEM β-lactamase is involved in substrate recognition and catalysis. Its dynamical properties and interaction with water molecules were investigated by performing multiple molecular dynamics simulations of up to 50 ns. Protein flexibility was assessed by calculating the root mean-square fluctuations and the generalized order parameter, S². The residues in secondary structure elements are highly ordered, whereas loop regions are more flexible, which is in agreement with previous experimental observations. Interestingly, the Ω-loop (residues 161-179) is rigid with order parameters similar to secondary structure elements, with the exception of the tip of the loop (residues 173-177) that has a considerably higher flexibility and performs an opening and closing motion on the 50-ns timescale. The rigidity of the main part of the Ω-loop is mediated by stabilizing and highly conserved water bridges inside a cavity lined by the Ω-loop and residues 65-69 of the protein core. In contrast, the flexible tip of the Ω-loop lacks these interactions. Hydration of the cavity and exchange of the water molecules with the bulk solvent occurs via two pathways: the flexible tip that serves as a door to the cavity, and a temporary water channel involving the side chain of Arg¹⁶⁴.     

Large-scale networks of hydration water molecules around proteins investigated by cryogenic X-ray crystallography.

The structures at protein-water interface, i.e. the hydration structure of proteins, have been investigated by cryogenic X-ray crystal structure analyses. Hydration structures appeared far clearer at cryogenic temperature than at ambient temperature, presumably because the motions of hydration water molecules were quenched by cooling. Based on the structural models obtained, the hydration structures were systematically analyzed with respect to the amount of water molecules, the interaction modes between water molecules and proteins, the local and the global distribution of them on the surface of proteins. The standard tetrahedral interaction geometry of water in bulk retained at the interface and enabled the three-dimensional chain connection of hydrogen bonds between hydration water molecules and polar protein atoms. Large-scale networks of hydrogen bonds covering the entire surface of proteins were quite flexible to accommodate to the large-scale conformational changes of proteins and seemed to have great influences on the dynamics and function of proteins. The present observation may provide a new concept for discussing the dynamics of proteins in aqueous solution.     

A comparison of structural relationships among α-crystallin, human Hsp27, γ-crystallins and βB2-crystallin

The 3D structures of α-crystallin, a major eye lens protein, and related small heat shock proteins are unresolved. It has been assumed that α-crystallin is primarily a β-sheet globular protein similar to γ-crystallin (Siezen and Argos, Biochim. Biophys. Acta, 1983, 748, 56–67) containing sequence repeats in its two domains (Wistow, FEBS Lett. 1985, 181, 1–6). Positional flexibility of amino acid residues and far UV-circular dichroism spectroscopy were used to investigate structural relationships among these proteins. The utility of flexibility plots for predicting protein structure is demonstrated by the excellent correlation of these plots with the known 3D X-ray structures of β/γ-crystallins. Similar analyses of α-crystallin subunits, αA and αB, and human heat shock protein 27 show that the C-terminal domains and connecting segments of these proteins are very similar while the N-terminal domains have significant structural differences. Unlike β/γ-crystallins, both Hsp27 and α-crystallin subunits are asymmetrical with highly flexible C-terminal domains. Flexibility is considered essential for protein functional activity. Therefore, the C-terminal region may play an active role in α-crystallin and small heat shock protein function. Differences in flexibility profiles and estimated secondary structure distribution in α-crystallin by three recent/updated algorithms from far UV-CD spectra support our predicted 3D structure and the concept that α-crystallin and members of β/γ-superfamily are structurally dissimilar.     

Investigating the local flexibility of functional residues in hemoproteins

It is now widely accepted that protein function depends not only on structure, but also on flexibility. However, the way mechanical properties contribute to catalytic mechanisms remains unclear. Here, we propose a method for investigating local flexibility within protein structures that combines a reduced protein representation with Brownian dynamics simulations. An analysis of residue fluctuations during the dynamics simulation yields a rigidity profile for the protein made up of force constants describing the ease of displacing each residue with respect to the rest of the structure. This approach has been applied to the analysis of a set of hemoproteins, one of the functionally most diverse protein families. Six proteins containing one or two heme groups have been studied, paying particular attention to the mechanical properties of the active-site residues. The calculated rigidity profiles show that active site residues are generally associated with high force constants and thus rigidly held in place. This observation also holds for diheme proteins if their mechanical properties are analyzed domain by domain. We note, however, that residues other than those in the active site can also have high force constants, as in the case of residues belonging to the folding nucleus of c-type hemoproteins.     

Fluctuations in ion pairs and their stabilities in proteins

This report investigates the effect of systemic protein conformational flexibility on the contribution of ion pairs to protein stability. Toward this goal, we use all NMR conformer ensembles in the Protein Data Bank (1) that contain at least 40 conformers, (2) whose functional form is monomeric, (3) that are nonredundant, and (4) that are large enough. We find 11 proteins adhering to these criteria. Within these proteins, we identify 22 ion pairs that are close enough to be classified as salt bridges. These are identified in the high-resolution crystal structures of the respective proteins or in the minimized average structures (if the crystal structures are unavailable) or, if both are unavailable, in the "most representative" conformer of each of the ensembles. We next calculate the electrostatic contribution of each such ion pair in each of the conformers in the ensembles. This results in a comprehensive study of 1,201 ion pairs, which allows us to look for consistent trends in their electrostatic contributions to protein stability in large sets of conformers. We find that the contributions of ion pairs vary considerably among the conformers of each protein. The vast majority of the ion pairs interconvert between being stabilizing and destabilizing to the structure at least once in the ensembles. These fluctuations reflect the variabilities in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other, and with respect to other charged groups in the remainder of the protein. The higher crystallographic B-factors for the respective side-chains are consistent with these fluctuations. The major conclusion from this study is that salt bridges observed in crystal structure may break, and new salt bridges may be formed. Hence, the overall stabilizing (or, destabilizing) contribution of an ion pair is conformer population dependent.     

Relationships between protein structure and dynamics from a database of NMR-derived backbone order parameters

The amplitude of protein backbone NH group motions on a time-scale faster than molecular tumbling may be determined by analysis of (15)N NMR relaxation data according to the Lipari-Szabo model free formalism. An internet-accessible database has been compiled containing 1855 order parameters from 20 independent NMR relaxation studies on proteins whose three-dimensional structures are known. A series of statistical analyses has been performed to identify relationships between the structural features and backbone dynamics of these proteins. Comparison of average order parameters for different amino acid types indicates that amino acids with small side-chains tend to have greater backbone flexibility than those with large side-chains. In addition, the motions of a given NH group are also related to the sizes of the neighboring amino acids in the primary sequence. The secondary structural environment appears to influence backbone dynamics relatively weakly, with only subtle differences between the order parameter distributions of loop structures and regular hydrogen bonded secondary structure elements. However, NH groups near helix termini are more mobile on average than those in the central regions of helices. Tertiary structure influences are also relatively weak but in the expected direction, with more exposed residues being more flexible on average than residues that are relatively inaccessible to solvent.     

Protein interactions and fluctuations in a proteomic network using an elastic network model

A set of protein conformations are analyzed by normal mode analysis. An elastic network model is used to obtain fluctuation and cooperativity of residues with low amplitude fluctuations across different species. Slow modes that are associated with the function of proteins have common features among different protein structures. We show that the degree of flexibility of the protein is important for proteins to interact with other proteins and as the species gets more complex its proteins become more flexible. In the complex organism, higher cooperativity arises due to protein structure and connectivity.     

A method for biomolecular structural recognition and docking allowing conformational flexibility.

In this work, we present an algorithm developed to handle biomolecular structural recognition problems, as part of an interdisciplinary research endeavor of the Computer Vision and Molecular Biology fields. A key problem in rational drug design and in biomolecular structural recognition is the generation of binding modes between two molecules, also known as molecular docking. Geometrical fitness is a necessary condition for molecular interaction. Hence, docking a ligand (e.g., a drug molecule or a protein molecule), to a protein receptor (e.g., enzyme), involves recognition of molecular surfaces. Conformational transitions by "hinge-bending" involves rotational movements of relatively rigid parts with respect to each other. The generation of docked binding modes between two associating molecules depends on their three dimensional structures (3-D) and their conformational flexibility. In comparison to the particular case of rigid-body docking, the computational difficulty grows considerably when taking into account the additional degrees of freedom intrinsic to the flexible molecular docking problem. Previous docking techniques have enabled hinge movements only within small ligands. Partial flexibility in the receptor molecule is enabled by a few techniques. Hinge-bending motions of protein receptors domains are not addressed by these methods, although these types of transitions are significant, e.g., in enzymes activity. Our approach allows hinge induced motions to exist in either the receptor or the ligand molecules of diverse sizes. We allow domains/subdomains/group of atoms movements in either of the associating molecules. We achieve this by adapting a technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These types of objects consist of rigid parts which are connected by rotary joints (hinges). Our method is based on an extension and generalization of the Hough transform and the Geometric Hashing paradigms for rigid object recognition. We show experimental results obtained by the successful application of the algorithm to cases of bound and unbound molecular complexes, yielding fast matching times. While the "correct" molecular conformations of the known complexes are obtained with small RMS distances, additional, predictive good-fitting binding modes are generated as well. We conclude by discussing the algorithm's implications and extensions, as well as its application to investigations of protein structures in Molecular Biology and recognition problems in Computer Vision.     

Computational approaches for identification of conserved/unique binding pockets in the A chain of ricin

MOTIVATION: Specific and sensitive ligand-based protein detection assays that employ antibodies or small molecules such as peptides, aptamers or other small molecules require that the corresponding surface region of the protein be accessible and that there be minimal cross-reactivity with non-target proteins. To reduce the time and cost of laboratory screening efforts for diagnostic reagents, we developed new methods for evaluating and selecting protein surface regions for ligand targeting. RESULTS: We devised combined structure- and sequence-based methods for identifying 3D epitopes and binding pockets on the surface of the A chain of ricin that are conserved with respect to a set of ricin A chains and unique with respect to other proteins. We (1) used structure alignment software to detect structural deviations and extracted from this analysis the residue-residue correspondence, (2) devised a method to compare corresponding residues across sets of ricin structures and structures of closely related proteins, (3) devised a sequence-based approach to determine residue infrequency in local sequence context and (4) modified a pocket-finding algorithm to identify surface crevices in close proximity to residues determined to be conserved/unique based on our structure- and sequence-based methods. In applying this combined informatics approach to ricin A, we identified a conserved/unique pocket in close proximity (but not overlapping) the active site that is suitable for bi-dentate ligand development. These methods are generally applicable to identification of surface epitopes and binding pockets for development of diagnostic reagents, therapeutics and vaccines.