Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Assessment of flexible backbone protein design methods for sequence library prediction in the therapeutic antibody Herceptin-HER2 interface

Computational protein design methods can complement experimental screening and selection techniques by predicting libraries of low-energy sequences compatible with a desired structure and function. Incorporating backbone flexibility in computational design allows conformational adjustments that should broaden the range of predicted low-energy sequences. Here, we evaluate computational predictions of sequence libraries from different protocols for modeling backbone flexibility using the complex between the therapeutic antibody Herceptin and its target human epidermal growth factor receptor 2 (HER2) as a model system. Within the program RosettaDesign, three methods are compared: The first two use ensembles of structures generated by Monte Carlo protocols for near-native conformational sampling: kinematic closure (KIC) and backrub, and the third method uses snapshots from molecular dynamics (MD) simulations. KIC or backrub methods were better able to identify the amino acid residues experimentally observed by phage display in the Herceptin-HER2 interface than MD snapshots, which generated much larger conformational and sequence diversity. KIC and backrub, as well as fixed backbone simulations, captured the key mutation Asp98Trp in Herceptin, which leads to a further threefold affinity improvement of the already subnanomolar parental Herceptin-HER2 interface. Modeling subtle backbone conformational changes may assist in the design of sequence libraries for improving the affinity of antibody-antigen interfaces and could be suitable for other protein complexes for which structural information is available.     

Energy minimization in low-frequency normal modes to efficiently allow for global flexibility during systematic protein-protein docking

Protein-protein association can frequently involve significant backbone conformational changes of the protein partners. A computationally rapid method has been developed that allows to approximately account for global conformational changes during systematic protein-protein docking starting from many thousands of start configurations. The approach employs precalculated collective degrees of freedom as additional variables during protein-protein docking minimization. The global collective degrees of freedom are obtained from normal mode analysis using a Gaussian network model for the protein. Systematic docking searches were performed on 10 test systems that differed in the degree of conformational change associated with complex formation and in the degree of overlap between observed conformational changes and precalculated flexible degrees of freedom. The results indicate that in case of docking searches that minimize the influence of local side chain conformational changes inclusion of global flexibility can significantly improve the agreement of the near-native docking solutions with the corresponding experimental structures. For docking of unbound protein partners in several cases an improved ranking of near native docking solutions was observed. This was achieved at a very modest ( approximately 2-fold) increase of computational demands compared to rigid docking. For several test cases the number of docking solutions close to experiment was also significantly enhanced upon inclusion of soft collective degrees of freedom. This result indicates that inclusion of global flexibility can facilitate in silico protein-protein association such that a greater number of different start configurations results in favorable complex formation.     

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a–p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and β-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.     

How much can physics do for protein design?

Physics and physical chemistry are an important thread in computational protein design, complementary to knowledge-based tools. They provide molecular mechanics scoring functions that need little or no ad hoc parameter readjustment, methods to thoroughly sample equilibrium ensembles, and different levels of approximation for conformational flexibility. They led recently to the successful redesign of a small protein using a physics-based folded state energy. Adaptive Monte Carlo or molecular dynamics schemes were discovered where protein variants are populated as per their ligand-binding free energy or catalytic efficiency. Molecular dynamics have been used for backbone flexibility. Implicit solvent models have been refined, polarizable force fields applied, and many physical insights obtained.     

Constructing ensembles of flexible fragments in native proteins by iterative stochastic elimination is relevant to protein-protein interfaces

We investigate the extent to which ensembles of flexible fragments (FF), generated by our loop conformational search method, include conformations that are near experimental and reflect conformational changes that these FFs undergo when binary protein-protein complexes are formed. Twenty-eight FFs, which are located in protein-protein interfaces and have different conformations in the bound structure (BS) and unbound structure (UbS) were extracted. The conformational space of these fragments in the BS and UbS was explored with our method which is based on the iterative stochastic elimination (ISE) algorithm. Conformational search of BSs generated bound ensembles and conformational search of UbSs produced unbound ensembles. ISE samples conformations near experimental (less than 1.05 A root mean square deviation, RMSD) for 51 out of the 56 examined fragments in the bound and unbound ensembles. In 14 out of the 28 unbound fragments, it also samples conformations within 1.05 A from the BS in the unbound ensemble. Sampling the bound conformation in the unbound ensemble demonstrates the potential biological relevance of the predicted ensemble. The 10 lowest energy conformations are the best choice for docking experiments, compared with any other 10 conformations of the ensembles. We conclude that generating conformational ensembles for FFs with ISE is relevant to FF conformations in the UbS and BS. Forming ensembles of the isolated proteins with our method prior to docking represents more comprehensively their inherent flexibility and is expected to improve docking experiments compared with results obtained by docking only UbSs.     

Multistate approaches in computational protein design

Computational protein design (CPD) is a useful tool for protein engineers. It has been successfully applied towards the creation of proteins with increased thermostability, improved binding affinity, novel enzymatic activity, and altered ligand specificity. Traditionally, CPD calculations search and rank sequences using a single fixed protein backbone template in an approach referred to as single-state design (SSD). While SSD has enjoyed considerable success, certain design objectives require the explicit consideration of multiple conformational and/or chemical states. Cases where a "multistate" approach may be advantageous over the SSD approach include designing conformational changes into proteins, using native ensembles to mimic backbone flexibility, and designing ligand or oligomeric association specificities. These design objectives can be efficiently tackled using multistate design (MSD), an emerging methodology in CPD that considers any number of protein conformational or chemical states as inputs instead of a single protein backbone template, as in SSD. In this review article, recent examples of the successful design of a desired property into proteins using MSD are described. These studies employing MSD are divided into two categories-those that utilized multiple conformational states, and those that utilized multiple chemical states. In addition, the scoring of competing states during negative design is discussed as a current challenge for MSD.     

Improving the accuracy of protein stability predictions with multistate design using a variety of backbone ensembles

Multistate computational protein design (MSD) with backbone ensembles approximating conformational flexibility can predict higher quality sequences than single‐state design with a single fixed backbone. However, it is currently unclear what characteristics of backbone ensembles are required for the accurate prediction of protein sequence stability. In this study, we aimed to improve the accuracy of protein stability predictions made with MSD by using a variety of backbone ensembles to recapitulate the experimentally measured stability of 85 Streptococcal protein G domain β1 sequences. Ensembles tested here include an NMR ensemble as well as those generated by molecular dynamics (MD) simulations, by Backrub motions, and by PertMin, a new method that we developed involving the perturbation of atomic coordinates followed by energy minimization. MSD with the PertMin ensembles resulted in the most accurate predictions by providing the highest number of stable sequences in the top 25, and by correctly binning sequences as stable or unstable with the highest success rate (≈90%) and the lowest number of false positives. The performance of PertMin ensembles is due to the fact that their members closely resemble the input crystal structure and have low potential energy. Conversely, the NMR ensemble as well as those generated by MD simulations at 500 or 1000 K reduced prediction accuracy due to their low structural similarity to the crystal structure. The ensembles tested herein thus represent on‐ or off‐target models of the native protein fold and could be used in future studies to design for desired properties other than stability. Proteins 2014; 82:771–784. © 2013 Wiley Periodicals, Inc.     

Residue-level global and local ensemble-ensemble comparisons of protein domains

Many methods of protein structure generation such as NMR-based solution structure determination and template-based modeling do not produce a single model, but an ensemble of models consistent with the available information. Current strategies for comparing ensembles lose information because they use only a single representative structure. Here, we describe the ENSEMBLATOR and its novel strategy to directly compare two ensembles containing the same atoms to identify significant global and local backbone differences between them on per-atom and per-residue levels, respectively. The ENSEMBLATOR has four components: eePREP (ee for ensemble-ensemble), which selects atoms common to all models; eeCORE, which identifies atoms belonging to a cutoff-distance dependent common core; eeGLOBAL, which globally superimposes all models using the defined core atoms and calculates for each atom the two intraensemble variations, the interensemble variation, and the closest approach of members of the two ensembles; and eeLOCAL, which performs a local overlay of each dipeptide and, using a novel measure of local backbone similarity, reports the same four variations as eeGLOBAL. The combination of eeGLOBAL and eeLOCAL analyses identifies the most significant differences between ensembles. We illustrate the ENSEMBLATOR''s capabilities by showing how using it to analyze NMR ensembles and to compare NMR ensembles with crystal structures provides novel insights compared to published studies. One of these studies leads us to suggest that a “consistency check” of NMR-derived ensembles may be a useful analysis step for NMR-based structure determinations in general. The ENSEMBLATOR 1.0 is available as a first generation tool to carry out ensemble-ensemble comparisons.     

Flexibility and inhibitor binding in cdc25 phosphatases

Cdc25 phosphatases involved in cell cycle checkpoints are now active targets for the development of anti‐cancer therapies. Rational drug design would certainly benefit from detailed structural information for Cdc25s. However, only apo‐ or sulfate‐bound crystal structures of the Cdc25 catalytic domain have been described so far. Together with previously available crystalographic data, results from molecular dynamics simulations, bioinformatic analysis, and computer‐generated conformational ensembles shown here indicate that the last 30–40 residues in the C‐terminus of Cdc25B are partially unfolded or disordered in solution. The effect of C‐terminal flexibility upon binding of two potent small molecule inhibitors to Cdc25B is then analyzed by using three structural models with variable levels of flexibility, including an equilibrium distributed ensemble of Cdc25B backbone conformations. The three Cdc25B structural models are used in combination with flexible docking, clustering, and calculation of binding free energies by the linear interaction energy approximation to construct and validate Cdc25B‐inhibitor complexes. Two binding sites are identified on top and beside the Cdc25B active site. The diversity of interaction modes found increases with receptor flexibility. Backbone flexibility allows the formation of transient cavities or compact hydrophobic units on the surface of the stable, folded protein core that are unexposed or unavailable for ligand binding in rigid and densely packed crystal structures. The present results may help to speculate on the mechanisms of small molecule complexation to partially unfolded or locally disordered proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Conformational dynamics of α-1 acid glycoprotein (AGP) in cancer: A comparative study of glycosylated and unglycosylated AGP

α-1 acid glycoprotein (AGP) is one of the most abundant plasma proteins. It fulfills two important functions: immunomodulation, and binding to various drugs and receptors. These different functions are closely associated and modulated via changes in glycosylation and cancer missense mutations. From a structural point of view, glycans alter the local biophysical properties of the protein leading to a diverse ligand-binding spectrum. However, glycans can typically not be observed in the resolved X-ray crystallography structure of AGP due to their high flexibility and microheterogeneity, so limiting our understanding of AGP's conformational dynamics 70 years after its discovery. We here investigate how mutations and glycosylation interfere with AGP's conformational dynamics changing its biophysical behavior, by using molecular dynamics (MD) simulations and sequence-based dynamics predictions. The MD trajectories show that glycosylation decreases the local backbone flexibility of AGP and increases the flexibility of distant regions through allosteric effects. We observe that mutations near the glycosylation site affect glycan's conformational preferences. Thus, we conclude that mutations control glycan dynamics which modulates the protein's backbone flexibility directly affecting its accessibility. These findings may assist in the drug design targeting AGP's glycosylation and mutations in cancer.     

Optimal ratio between the average conformational entropy and the average energy of interaction between residues for fast protein folding

Based on available experimental data and using a theoretical model of protein folding, we demonstrate that there is an optimal ratio between the average conformational entropy and the average contact energy per residue for fast protein folding. A statistical analysis of the conformational entropy and the number of contacts per residue for 5829 protein domains from four main classes (α, β, α/β, α+β) shows that each class has its own characteristic average number of contacts per residue and average conformational entropy per residue. These class-specific characteristics determine the protein folding rates: α-proteins are the fastest to fold, β-proteins are the second fastest, α+β-proteins are the third, and α/β-proteins are the last to fold.     

An empirical energy function for threading protein sequence through the folding motif

In this paper we present a new residue contact potantial derived by statistical analysis of protein crystal structures. This gives mean hydrophobic and pairwise contact energies as a function of residue type and distance interval. To test the accuracy of this potential we generate model structures by “threading” different sequences through backbone folding motifs found in the structural data base. We find that conformational energies calculated by summing contact potentials show perfect specificity in matching the correct sequences with each globular folding motif in a 161-protcin data set. They also identify correct models with the core folding motifs of heme-rythrin and immunoglobulin McPC603 V₁-do- main, among millions of alternatives possible when we align subsequences with α-helices and β-strands, and allow for variation in the lengths of intervening loops. We suggest that contact potentials reflect important constraints on nonbonded interaction in native proteins, and that “threading” may be useful for structure prediction by recognition of folding motif. © 1993 Wiley-Liss, Inc.     

Structural characterization of unfolded states of apomyoglobin using residual dipolar couplings

The conformational propensities of unfolded states of apomyoglobin have been investigated by measurement of residual dipolar couplings between (15)N and (1)H in backbone amide groups. Weak alignment of apomyoglobin in acid and urea-unfolded states was induced with both stretched and compressed polyacrylamide gels. In 8 M urea solution at pH 2.3, conditions under which apomyoglobin contains no detectable secondary or tertiary structure, significant residual dipolar couplings of uniform sign were observed for all residues. At pH 2.3 in the absence of urea, a change in the magnitude and/or sign of the residual dipolar couplings occurs in local regions of the polypeptide where there is a high propensity for helical secondary structure. These results are interpreted on the basis of the statistical properties of the unfolded polypeptide chain, viewed as a polymer of statistical segments. For a folded protein, the magnitude and sign of the residual dipolar couplings depend on the orientation of each bond vector relative to the alignment tensor of the entire molecule, which reorients as a single entity. For unfolded proteins, there is no global alignment tensor; instead, residual dipolar couplings are attributed to alignment of the statistical segments or of transient elements of secondary structure. For apomyoglobin in 8 M urea, the backbone is highly extended, with phi and psi dihedral angles favoring the beta or P(II) regions. Each statistical segment has a highly anisotropic shape, with the N-H bond vectors approximately perpendicular to the long axis, and becomes weakly aligned in the anisotropic environment of the strained acrylamide gels. Local regions of enhanced flexibility or chain compaction are characterized by a decrease in the magnitude of the residual dipolar couplings. The formation of a small population of helical structure in the acid-denatured state of apomyoglobin leads to a change in sign of the residual dipolar couplings in local regions of the polypeptide; the population of helix estimated from the residual dipolar couplings is in excellent agreement with that determined from chemical shifts. The alignment model described here for apomyoglobin can also explain the pattern of residual dipolar couplings reported previously for denatured states of staphylococcal nuclease and other proteins. In conjunction with other NMR experiments, residual dipolar couplings can provide valuable insights into the dynamic conformational propensities of unfolded and partly folded states of proteins and thereby help to chart the upper reaches of the folding landscape.     

Determination of protein global folds using backbone residual dipolar coupling and long-range NOE restraints

We report the determination of the global fold of human ubiquitin using protein backbone NMR residual dipolar coupling and long-range nuclear Overhauser effect (NOE) data as conformational restraints. Specifically, by use of a maximum of three backbone residual dipolar couplings per residue (N_i-H^N _i, N_i-C_i–1, H^N _i - C_i–1) in two tensor frames and only backbone H^N-H^N NOEs, a global fold of ubiquitin can be derived with a backbone root-mean-square deviation of 1.4 Å with respect to the crystal structure. This degree of accuracy is more than adequate for use in databases of structural motifs, and suggests a general approach for the determination of protein global folds using conformational restraints derived only from backbone atoms.     

Structural origins of high apparent dielectric constants experienced by ionizable groups in the hydrophobic core of a protein

The side chains of Lys66, Asp66, and Glu66 in staphylococcal nuclease are fully buried and surrounded mainly by hydrophobic matter, except for internal water molecules associated with carboxylic oxygen atoms. These ionizable side chains titrate with pK_a values of 5.7, 8.8, and 8.9, respectively. To reproduce these pK_a values with continuum electrostatics calculations, we treated the protein with high dielectric constants. We have examined the structural origins of these high apparent dielectric constants by using NMR spectroscopy to characterize the structural response to the ionization of these internal side chains. Substitution of Val66 with Lys66 and Asp66 led to increased conformational fluctuations of the microenvironments surrounding these groups, even under pH conditions where Lys66 and Asp66 are neutral. When Lys66, Asp66, and Glu66 are charged, the proteins remain almost fully folded, but resonances for a few backbone amides adjacent to the internal ionizable residues are broadened. This suggests that the ionization of the internal groups promotes a local increase in dynamics on the intermediate timescale, consistent with either partial unfolding or increased backbone fluctuations of helix 1 near residue 66, or, less likely, with increased fluctuations of the charged side chains at position 66. These experiments confirm that the high apparent dielectric constants reported by internal Lys66, Asp66, and Glu66 reflect localized changes in conformational fluctuations without incurring detectable global structural reorganization. To improve structure-based pK_a calculations in proteins, we will need to learn how to treat this coupling between ionization of internal groups and local changes in conformational fluctuations explicitly.     

Local motions in a benchmark of allosteric proteins

Allosteric proteins have been studied extensively in the last 40 years, but so far, no systematic analysis of conformational changes between allosteric structures has been carried out. Here, we compile a set of 51 pairs of known inactive and active allosteric protein structures from the Protein Data Bank. We calculate local conformational differences between the two structures of each protein using simple metrics, such as backbone and side-chain Cartesian displacement, and torsion angle change and rearrangement in residue-residue contacts. Thresholds for each metric arise from distributions of motions in two control sets of pairs of protein structures in the same biochemical state. Statistical analysis of motions in allosteric proteins quantifies the magnitude of allosteric effects and reveals simple structural principles about allostery. For example, allosteric proteins exhibit substantial conformational changes comprising about 20% of the residues. In addition, motions in allosteric proteins show strong bias toward weakly constrained regions such as loops and the protein surface. Correlation functions show that motions communicate through protein structures over distances averaging 10-20 residues in sequence space and 10-20 A in Cartesian space. Comparison of motions in the allosteric set and a set of 21 nonallosteric ligand-binding proteins shows that nonallosteric proteins also exhibit bias of motion toward weakly constrained regions and local correlation of motion. However, allosteric proteins exhibit twice as much percent motion on average as nonallosteric proteins with ligand-induced motion. These observations may guide efforts to design flexibility and allostery into proteins.     

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.