Intrahelical side chain interactions in alpha-helices: poor correlation between energetics and frequency

Protposer: the web server that readily proposes protein stabilizing mutations with high PPV

Protein stability is a requisite for most biotechnological and medical applications of proteins. As natural proteins tend to suffer from a low conformational stability ex vivo, great efforts have been devoted toward increasing their stability through rational design and engineering of appropriate mutations. Unfortunately, even the best currently used predictors fail to compute the stability of protein variants with sufficient accuracy and their usefulness as tools to guide the rational stabilisation of proteins is limited. We present here Protposer, a protein stabilising tool based on a different approach. Instead of quantifying changes in stability, Protposer uses structure- and sequence-based screening modules to nominate candidate mutations for subsequent evaluation by a logistic regression model, carefully trained to avoid overfitting. Thus, Protposer analyses PDB files in search for stabilization opportunities and provides a ranked list of promising mutations with their estimated success rates (eSR), their probabilities of being stabilising by at least 0.5 kcal/mol. The agreement between eSRs and actual positive predictive values (PPV) on external datasets of mutations is excellent. When Protposer is used with its Optimal kappa selection threshold, its PPV is above 0.7. Even with less stringent thresholds, Protposer largely outperforms FoldX, Rosetta and PoPMusiC. Indicating the PDB file of the protein suffices to obtain a ranked list of mutations, their eSRs and hints on the likely source of the stabilization expected. Protposer is a distinct, straightforward and highly successful tool to design protein stabilising mutations, and it is freely available for academic use at http://webapps.bifi.es/the-protposer.

Local and macroscopic electrostatic interactions in single α-helices

The noncovalent forces that stabilize protein structures are not fully understood. One way to address this is to study equilibria between unfolded states and α-helices in peptides. Electrostatic forces-which include interactions between side chains, the backbone and side chains, and side chains and the helix macrodipole-are believed to contribute to these equilibria. Here we probe these interactions experimentally using designed peptides. We find that both terminal backbone-side chain and certain side chain-side chain interactions (which include both local effects between proximal charges and interatomic contacts) contribute much more to helix stability than side chain-helix macrodipole electrostatics, which are believed to operate at larger distances. This has implications for current descriptions of helix stability, the understanding of protein folding and the refinement of force fields for biomolecular modeling and simulations. In addition, this study sheds light on the stability of rod-like structures formed by single α-helices, which are common in natural proteins such as non-muscle myosins.

An amino acid packing code for α-helical structure and protein design

This work demonstrates that all packing in α-helices can be simplified to repetitive patterns of a single motif: the knob-socket. Using the precision of Voronoi Polyhedra/Delauney Tessellations to identify contacts, the knob-socket is a four-residue tetrahedral motif: a knob residue on one α-helix packs into the three-residue socket on another α-helix. The principle of the knob-socket model relates the packing between levels of protein structure: the intra-helical packing arrangements within secondary structure that permit inter-helix tertiary packing interactions. Within an α-helix, the three-residue sockets arrange residues into a uniform packing lattice. Inter-helix packing results from a definable pattern of interdigitated knob-socket motifs between two α-helices. Furthermore, the knob-socket model classifies three types of sockets: (1) free, favoring only intra-helical packing; (2) filled, favoring inter-helical interactions; and (3) non, disfavoring α-helical structure. The amino acid propensities in these three socket classes essentially represent an amino acid code for structure in α-helical packing. Using this code, we used a novel yet straightforward approach for the design of α-helical structure to validate the knob-socket model. Unique sequences for three peptides were created to produce a predicted amount of α-helical structure: mostly helical, some helical, and no helix. These three peptides were synthesized, and helical content was assessed using CD spectroscopy. The measured α-helicity of each peptide was consistent with the expected predictions. These results and analysis demonstrate that the knob-socket motif functions as the basic unit of packing and presents an intuitive tool to decipher the rules governing packing in protein structure.

Amino acid pair- and triplet-wise groupings in the interior of α-helical segments in proteins

A statistical approach has been applied to analyse primary structure patterns at inner positions of α-helices in proteins. A systematic survey was carried out in a recent sample of non-redundant proteins selected from the Protein Data Bank, which were used to analyse α-helix structures for amino acid pairing patterns. Only residues more than three positions apart from both termini of the α-helix were considered as inner. Amino acid pairings i, i+k (k=1, 2, 3, 4, 5), were analysed and the corresponding 20×20 matrices of relative global propensities were constructed. An analysis of (i, i+4, i+8) and (i, i+3, i+4) triplet patterns was also performed. These analysis yielded information on a series of amino acid patterns (pairings and triplets) showing either high or low preference for α-helical motifs and suggested a novel approach to protein alphabet reduction. In addition, it has been shown that the individual amino acid propensities are not enough to define the statistical distribution of these patterns. Global pair propensities also depend on the type of pattern, its composition and orientation in the protein sequence. The data presented should prove useful to obtain and refine useful predictive rules which can further the development and fine-tuning of protein structure prediction algorithms and tools.

Residue patterning in helix interiorsThis paper is one of a selection of papers published in this special issue entitled “Canadian Society of Biochemistry, Molecular & Cellular Biology 52nd Annual Meeting — Protein Folding: Principles and Diseases” and has undergone the Journal's usual peer review process

The α-helix remains a focus of research because of its importance to protein folding and structure. Nevertheless, despite numerous empirical, computational, and theoretical studies, the fundamental structural properties governing their formation and stability are still unclear. We have examined the statistical occurrence of polar and apolar residue patterning in helical interiors in a large, non-redundant dataset, and compared these patterns with those found in other structural environments. While the familiar amphipathic distributions for both polar and apolar residues are evident, our analysis also finds significant differences between these distributions. Non-amphipathic signals can also be discerned within both distributions. Most interestingly, among various positional patterning, an analysis of immediate (i,i + 1) helical neighbours found: (i) clear neighbouring preferences, with high (low) occurrences of hydrophobics (hydrophilics) next to Gly, Pro, and short polar residues; (ii) high negative (positive) correlation between residue helical propensities and the degree of neighbouring hydrophobicity (hydrophilicity); and (iii) a preferred ordering among neighbours, implying an inherent helix directionality. Because (i,i + 1) helical pairs have limited side chain – side chain interactions, thermodynamic considerations cannot readily explain these observations, nor can evolutionary pressures that enhance tertiary interactions via amphipathicity, as this particular spacing does not segregate residues onto either the same or opposing helical faces. We suggest that the mechanism of helix formation may be partly responsible for these observations. In particular, the high negative correlation between residue helical propensities and neighbouring hydrophobicity suggests that hydrophobicity may play a more important role in helix formation than currently recognized.

Folding by numbers: primary sequence statistics and their use in studying protein folding

The exponential growth over the past several decades in the quantity of both primary sequence data available and the number of protein structures determined has provided a wealth of information describing the relationship between protein primary sequence and tertiary structure. This growing repository of data has served as a prime source for statistical analysis, where underlying relationships between patterns of amino acids and protein structure can be uncovered. Here, we survey the main statistical approaches that have been used for identifying patterns within protein sequences, and discuss sequence pattern research as it relates to both secondary and tertiary protein structure. Limitations to statistical analyses are discussed, and a context for their role within the field of protein folding is given. We conclude by describing a novel statistical study of residue patterning in β-strands, which finds that hydrophobic (i,i+2) pairing in β-strands occurs more often than expected at locations near strand termini. Interpretations involving β-sheet nucleation and growth are discussed.

Detecting coevolution without phylogenetic trees? Tree-ignorant metrics of coevolution perform as well as tree-aware metrics

BACKGROUND

Identifying coevolving positions in protein sequences has myriad applications, ranging from understanding and predicting the structure of single molecules to generating proteome-wide predictions of interactions. Algorithms for detecting coevolving positions can be classified into two categories: tree-aware, which incorporate knowledge of phylogeny, and tree-ignorant, which do not. Tree-ignorant methods are frequently orders of magnitude faster, but are widely held to be insufficiently accurate because of a confounding of shared ancestry with coevolution. We conjectured that by using a null distribution that appropriately controls for the shared-ancestry signal, tree-ignorant methods would exhibit equivalent statistical power to tree-aware methods. Using a novel t-test transformation of coevolution metrics, we systematically compared four tree-aware and five tree-ignorant coevolution algorithms, applying them to myoglobin and myosin. We further considered the influence of sequence recoding using reduced-state amino acid alphabets, a common tactic employed in coevolutionary analyses to improve both statistical and computational performance.

RESULTS

Consistent with our conjecture, the transformed tree-ignorant metrics (particularly Mutual Information) often outperformed the tree-aware metrics. Our examination of the effect of recoding suggested that charge-based alphabets were generally superior for identifying the stabilizing interactions in alpha helices. Performance was not always improved by recoding however, indicating that the choice of alphabet is critical.

CONCLUSION

The results suggest that t-test transformation of tree-ignorant metrics can be sufficient to control for patterns arising from shared ancestry.

Alpha-helix stabilization by alanine relative to glycine: roles of polar and apolar solvent exposures and of backbone entropy

The energetics of alpha-helix formation are fairly well understood and the helix content of a given amino acid sequence can be calculated with reasonable accuracy from helix-coil transition theories that assign to the different residues specific effects on helix stability. In internal helical positions, alanine is regarded as the most stabilizing residue, whereas glycine, after proline, is the more destabilizing. The difference in stabilization afforded by alanine and glycine has been explained by invoking various physical reasons, including the hydrophobic effect and the entropy of folding. Herein, the contribution of these two effects and that of hydrophilic area burial is evaluated by analyzing Ala and Gly mutants implemented in three helices of apoflavodoxin. These data, combined with available data for similar mutations in other proteins (22 Ala/Gly mutations in alpha-helices have been considered), allow estimation of the difference in backbone entropy between alanine and glycine and evaluation of its contribution and that of apolar and polar area burial to the helical stabilization typically associated to Gly-->Ala substitutions. Alanine consistently stabilizes the helical conformation relative to glycine because it buries more apolar area upon folding and because its backbone entropy is lower. However, the relative contribution of polar area burial (which is shown to be destabilizing) and of backbone entropy critically depends on the approximation used to model the structure of the denatured state. In this respect, the excised-peptide model of the unfolded state, proposed by Creamer and coworkers (1995), predicts a major contribution of polar area burial, which is in good agreement with recent quantitations of the relative enthalpic contribution of Ala and Gly residues to alpha-helix formation.

Energetics of aliphatic deletions in protein cores

Although core residues can sometimes be replaced by shorter ones without introducing significant changes in protein structure, the energetic consequences are typically large and destabilizing. Many efforts have been devoted to understand and predict changes in stability from analysis of the environment of mutated residues, but the relationships proposed for individual proteins have often failed to describe additional data. We report here 17 apoflavodoxin large-to-small mutations that cause overall protein destabilizations of 0.6-3.9 kcal.mol(-1). By comparing two-state urea and three-state thermal unfolding data, the overall destabilizations observed are partitioned into effects on the N-to-I and on the I-to-U equilibria. In all cases, the equilibrium intermediate exerts a "buffering" effect that reduces the impact of the overall destabilization on the N-to-I equilibrium. The performance of several structure-energetics relationships, proposed to explain the energetics of hydrophobic shortening mutations, has been evaluated by using an apoflavodoxin data set consisting of 14 mutations involving branching-conservative aliphatic side-chain shortenings and a larger data set, including similar mutations implemented in seven model proteins. Our analysis shows that the stability changes observed for any of the different types of mutations (LA, IA, IV, and VA) in either data set are best explained by a combination of differential hydrophobicity and of the calculated volume of the modeled cavity (as previously observed for LA and IA mutations in lysozyme T4). In contrast, sequence conservation within the flavodoxin family, which is a good predictor for charge-reversal stabilizing mutations, does not perform so well for aliphatic shortening ones.

Statistical analysis of intrahelical ionic interactions in alpha-helices and coiled coils

There are many controversies concerning whether ionic interactions in alpha-helices and coiled coils actually contribute to the stabilisation and formation of these structures. Here we used a statistical approach to probe this question. We extracted unique alpha-helical and coiled coil structures from the protein database and analysed the ionic interactions between positively and negatively charged residues. The ionic interactions were categorized according to the type, spacing and order of the residues involved. Separate datasets were produced depending on the number of alpha-helices in the coiled coils and the mutual orientation of the helices. We compared the frequency of residue configurations able to form ionic interactions with their probability to form the interaction. We found a correlation between the two variables in alpha-helices, antiparallel two-stranded coiled coils and parallel two-stranded coiled coils. This indicates that some ionic interactions are indeed important for the formation and stabilisation of alpha-helices and coiled coils. We concluded that the configurations, which have simultaneously a large probability to form the ionic interaction and a frequent occurrence, are those, which have the most stabilising effect. These are the 4RE, 3ER and 4ER interactions.

Do Proteins Always Benefit from a Stability Increase? Relevant and Residual Stabilisation in a Three-state Protein by Charge Optimisation

The vast majority of our knowledge on protein stability arises from the study of simple two-state models. However, proteins displaying equilibrium intermediates under certain conditions abound and it is unclear whether the energetics of native/intermediate equilibria is well represented in current knowledge. We consider here that the overall conformational stability of three-state proteins is made of a "relevant" term and a "residual" one, corresponding to the free energy differences of the native to intermediate (N-to-I) and intermediate to denatured (I-to-D) equilibria, respectively. The N-to-I free energy difference is considered to be the relevant stability because protein-unfolding intermediates are likely devoid of biological activity. We use surface charge optimisation to first increase the overall (N-to-D) stability of a model three-state protein (apoflavodoxin) and then investigate whether the stabilisation obtained is realised into relevant or into residual stability. Most of the mutations designed from electrostatic calculations or from simple sequence conservation analysis produce large increases in the overall stability of the protein. However, in most cases, this simply leads to similarly large increases of the residual stability. Two mutations, nevertheless, show a different trend and increase the relevant stability of the protein substantially. When all the mutations are mapped onto the structure of the apoflavodoxin thermal-unfolding intermediate (obtained independently by equilibrium phi-analysis and NMR) they cluster perfectly so that the mutations increasing the relevant stability appear in the small unstructured region of the intermediate and the others in the native-like region. This illustrates the need for specific investigation of N-to-I equilibria and the structure of protein intermediates, and indicates that it is possible to rationally stabilise a protein against partial unfolding once the structure of the intermediate conformation is known, even if at low resolution.

Cation-pi interaction in model alpha-helical peptides

Cation-pi interactions are increasingly recognized as important in chemistry and biology. Here we investigate the cation-pi interaction by determining its effect on the helicity of model peptides using a combination of CD and NMR spectroscopy. The data show that a single Trp/Arg interaction on the surface of a peptide can make a significant net favorable free energy contribution to helix stability if the two residues are positioned with appropriate spacing and orientation. The solvent-exposed Trp-->Arg (i, i + 4) interaction in helices can contribute -0.4 kcal/mol to the helix stability, while no free energy gain is detected if the two residues have the reversed orientation, Arg-->Trp (i, i + 4). The derived free energy is consistent with other experimental results studied in proteins or model peptides on cation-pi interactions. However in the same system the postulated Phe/Arg (i, i + 4) cation-pi interaction provides no net free energy to helix stability. Thus the Trp-->Arg interaction is stronger than Phe-->Arg. The cation-pi interactions are not sensitive to the screening effect by adding neutral salt as indicated by salt titration. Our results are in qualitative agreement with theoretical calculations emphasizing that cation-pi interactions can contribute significantly to protein stability with the order Trp > Phe. However, our and other experimental values are significantly smaller than estimates from theoretical calculations.

Energetics of a hydrogen bond (charged and neutral) and of a cation-pi interaction in apoflavodoxin

Anabaena apoflavodoxin contains a single histidine residue (H34) that interacts with two aromatic residues (F7 and Y47). The histidine and phenylalanine rings are almost coplanar and they can establish a cation-pi interaction when the histidine is protonated. The histidine and tyrosine side-chains are engaged in a hydrogen bond, which is their only contact. We analyse the energetics of these interactions using p Ka-shift analysis, double-mutant cycle analysis at two pH values, and X-ray crystallography. The H/F interaction is very weak when the histidine is neutral, but it is strengthened by 0.5 kcal mol-1on histidine protonation. Supporting this fact, the histidine p Kain a F7L mutant is 0.4 pH units lower than in wild-type. The strength of the H/Y hydrogen bond is 0.7 kcal mol-1when the histidine is charged, and it becomes stronger (1.3 kcal mol-1) when the histidine is neutral. This is consistent with our observation that the (H34)Nepsilon2-OH(Y47) distance is slightly shorter in the apoflavodoxin structure at pH 9.0 than in the previously reported structure at pH 6.0. It is also consistent with a histidine p Kavalue 0.6 pH units higher in a Y47F mutant than in the wild-type protein. We suggest that the higher stability of the neutral hydrogen bond could be due to a higher desolvation penalty of the charged hydrogen bond that would offset its more favourable enthalpy of formation. The relationship between hydrogen bond strength and the contribution of hydrogen bonds to protein stability is discussed.