Protein Design by Sampling an Undirected Graphical Model of Residue Constraints

This paper develops an approach for designing protein variants by sampling sequences that satisfy residue constraints encoded in an undirected probabilistic graphical model. Due to evolutionary pressures on proteins to maintain structure and function, the sequence record of a protein family contains valuable information regarding position-specific residue conservation and coupling (or covariation) constraints. Representing these constraints with a graphical model provides two key benefits for protein design: a probabilistic semantics enabling evaluation of possible sequences for consistency with the constraints, and an explicit factorization of residue dependence and independence supporting efficient exploration of the constrained sequence space. We leverage these benefits in developing two complementary MCMC algorithms for protein design: constrained shuffling mixes wild-type sequences positionwise and evaluates graphical model likelihood, while component sampling directly generates sequences by sampling clique values and propagating to other cliques. We apply our methods to design WW domains. We demonstrate that likelihood under a model of wild-type WWs is highly predictive of foldedness of new WWs. We then show both theoretical and rapid empirical convergence of our algorithms in generating high-likelihood, diverse new sequences. We further show that these sequences capture the original sequence constraints, yielding a model as predictive of foldedness as the original one.     

Effect of pressure on helix‐coil transition of an alanine‐based peptide: An FTIR study

Protein–protein interactions are mediated by complementary amino acids defining complementary surfaces. Typically not all members of a family of related proteins interact equally well with all members of a partner family; thus analysis of the sequence record can reveal the complementary amino acid partners that confer interaction specificity. This article develops methods for learning and using probabilistic graphical models of such residue “cross‐coupling” constraints between interacting protein families, based on multiple sequence alignments and information about which pairs of proteins are known to interact. Our models generalize traditional consensus sequence binding motifs, and provide a probabilistic semantics enabling sound evaluation of the plausibility of new possible interactions. Furthermore, predictions made by the models can be explained in terms of the underlying residue interactions. Our approach supports different levels of prior knowledge regarding interactions, including both one‐to‐one (e.g., pairs of proteins from the same organism) and many‐to‐many (e.g., experimentally identified interactions), and we present a technique to account for possible bias in the represented interactions. We apply our approach in studies of PDZ domains and their ligands, fundamental building blocks in a number of protein assemblies. Our algorithms are able to identify biologically interesting cross‐coupling constraints, to successfully identify known interactions, and to make explainable predictions about novel interactions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Learning generative models for protein fold families

We introduce a new approach to learning statistical models from multiple sequence alignments (MSA) of proteins. Our method, called GREMLIN (Generative REgularized ModeLs of proteINs), learns an undirected probabilistic graphical model of the amino acid composition within the MSA. The resulting model encodes both the position-specific conservation statistics and the correlated mutation statistics between sequential and long-range pairs of residues. Existing techniques for learning graphical models from MSA either make strong, and often inappropriate assumptions about the conditional independencies within the MSA (e.g., Hidden Markov Models), or else use suboptimal algorithms to learn the parameters of the model. In contrast, GREMLIN makes no a priori assumptions about the conditional independencies within the MSA. We formulate and solve a convex optimization problem, thus guaranteeing that we find a globally optimal model at convergence. The resulting model is also generative, allowing for the design of new protein sequences that have the same statistical properties as those in the MSA. We perform a detailed analysis of covariation statistics on the extensively studied WW and PDZ domains and show that our method out-performs an existing algorithm for learning undirected probabilistic graphical models from MSA. We then apply our approach to 71 additional families from the PFAM database and demonstrate that the resulting models significantly out-perform Hidden Markov Models in terms of predictive accuracy.     

Evolutionary information hidden in a single protein structure

The knowledge of conserved sequences in proteins is valuable in identifying functionally or structurally important residues. Generating the conservation profile of a sequence requires aligning families of homologous sequences and having knowledge of their evolutionary relationships. Here, we report that the conservation profile at the residue level can be quantitatively derived from a single protein structure with only backbone information. We found that the reciprocal packing density profiles of protein structures closely resemble their sequence conservation profiles. For a set of 554 nonhomologous enzymes, 74% (408/554) of the proteins have a correlation coefficient > 0.5 between these two profiles. Our results indicate that the three-dimensional structure, instead of being a mere scaffold for positioning amino acid residues, exerts such strong evolutionary constraints on the residues of the protein that its profile of sequence conservation essentially reflects that of its structural characteristics.     

Protein-DNA interactions: amino acid conservation and the effects of mutations on binding specificity

We investigate the conservation of amino acid residue sequences in 21 DNA-binding protein families and study the effects that mutations have on DNA-sequence recognition. The observations are best understood by assigning each protein family to one of three classes: (i) non-specific, where binding is independent of DNA sequence; (ii) highly specific, where binding is specific and all members of the family target the same DNA sequence; and (iii) multi-specific, where binding is also specific, but individual family members target different DNA sequences. Overall, protein residues in contact with the DNA are better conserved than the rest of the protein surface, but there is a complex underlying trend of conservation for individual residue positions. Amino acid residues that interact with the DNA backbone are well conserved across all protein families and provide a core of stabilising contacts for homologous protein-DNA complexes. In contrast, amino acid residues that interact with DNA bases have variable levels of conservation depending on the family classification. In non-specific families, base-contacting residues are well conserved and interactions are always found in the minor groove where there is little discrimination between base types. In highly specific families, base-contacting residues are highly conserved and allow member proteins to recognise the same target sequence. In multi-specific families, base-contacting residues undergo frequent mutations and enable different proteins to recognise distinct target sequences. Finally, we report that interactions with bases in the target sequence often follow (though not always) a universal code of amino acid-base recognition and the effects of amino acid mutations can be most easily understood for these interactions.     

Entropy calculator: getting the best from your multiple protein alignments

Amino acid sequence alignment is an extremely useful tool in protein family analysis. Most family characteristics, such as the localization of functional residues, structural constraints and evolutionary relationships may be retrieved through the observation of the conservation pattern highlighted by the alignments. A quantitative score for the conservation in the alignment allows different stages of an alignment to be compared and consequently the alignment information to be efficiently exploited. Many scoring methods have been proposed during the last three decades. Claude Shannon's theory of communication (1948) paved the way for a consistent scoring of protein alignments by considering the residue (or symbol) frequency. A number of modifications have been proposed since that time, but the core statistical approach is still considered one of the best. By combining many database managing tools for treatment of protein sequences, a ClustalW software integration, a flexible symbols treatment and gap normalization functions, Entropy Calculator software has been developed. This new tool provides a global and optimal approach to multiple sequence alignment scoring by offering an easy graphic interface and a series of modification options that help in interpreting alignments and allow conservation pattern inferences to be performed.     

A Sequence Alignment-Independent Method for Protein Classification

Annotation of the rapidly accumulating body of sequence data relies heavily on the detection of remote homologues and functional motifs in protein families. The most popular methods rely on sequence alignment. These include programs that use a scoring matrix to compare the probability of a potential alignment with random chance and programs that use curated multiple alignments to train profile hidden Markov models (HMMs). Related approaches depend on bootstrapping multiple alignments from a single sequence. However, alignment-based programs have limitations. They make the assumption that contiguity is conserved between homologous segments, which may not be true in genetic recombination or horizontal transfer. Alignments also become ambiguous when sequence similarity drops below 40%. This has kindled interest in classification methods that do not rely on alignment. An approach to classification without alignment based on the distribution of contiguous sequences of four amino acids (4-grams) was developed. Interest in 4-grams stemmed from the observation that almost all theoretically possible 4-grams (20(4)) occur in natural sequences and the majority of 4-grams are uniformly distributed. This implies that the probability of finding identical 4-grams by random chance in unrelated sequences is low. A Bayesian probabilistic model was developed to test this hypothesis. For each protein family in Pfam-A and PIR-PSD, a feature vector called a probe was constructed from the set of 4-grams that best characterised the family. In rigorous jackknife tests, unknown sequences from Pfam-A and PIR-PSD were compared with the probes for each family. A classification result was deemed a true positive if the probe match with the highest probability was in first place in a rank-ordered list. This was achieved in 70% of cases. Analysis of false positives suggested that the precision might approach 85% if selected families were clustered into subsets. Case studies indicated that the 4-grams in common between an unknown and the best matching probe correlated with functional motifs from PRINTS. The results showed that remote homologues and functional motifs could be identified from an analysis of 4-gram patterns.     

Multiple Profile Models Extract Features from Protein Sequence Data and Resolve Functional Diversity of Very Different Protein Families

Functional classification of proteins from sequences alone has become a critical bottleneck in understanding the myriad of protein sequences that accumulate in our databases. The great diversity of homologous sequences hides, in many cases, a variety of functional activities that cannot be anticipated. Their identification appears critical for a fundamental understanding of the evolution of living organisms and for biotechnological applications. ProfileView is a sequence-based computational method, designed to functionally classify sets of homologous sequences. It relies on two main ideas: the use of multiple profile models whose construction explores evolutionary information in available databases, and a novel definition of a representation space in which to analyze sequences with multiple profile models combined together. ProfileView classifies protein families by enriching known functional groups with new sequences and discovering new groups and subgroups. We validate ProfileView on seven classes of widespread proteins involved in the interaction with nucleic acids, amino acids and small molecules, and in a large variety of functions and enzymatic reactions. ProfileView agrees with the large set of functional data collected for these proteins from the literature regarding the organization into functional subgroups and residues that characterize the functions. In addition, ProfileView resolves undefined functional classifications and extracts the molecular determinants underlying protein functional diversity, showing its potential to select sequences towards accurate experimental design and discovery of novel biological functions. On protein families with complex domain architecture, ProfileView functional classification reconciles domain combinations, unlike phylogenetic reconstruction. ProfileView proves to outperform the functional classification approach PANTHER, the two k-mer-based methods CUPP and eCAMI and a neural network approach based on Restricted Boltzmann Machines. It overcomes time complexity limitations of the latter.     

Sequence and structure conservation in a protein core

In order to study structural aspects of sequence conservation in families of homologous proteins, we have analyzed structurally aligned sequences of 585 proteins grouped into 128 homologous families. The conservation of a residue in a family is defined as the average residue similarity in a given position of aligned sequences. The residue similarities were expressed in the form of log-odd substitution tables that take into account the environments of amino acids in three-dimensional structures. The protein core is defined as those residues that have less then 7% solvent accessibility. The density of a protein core is described in terms of atom packing, which is investigated as a criterion for residue substitution and conservation. Although there is no significant correlation between sequence conservation and average atom packing around nonpolar residues such as leucine, valine and isoleucine, a significant correlation is observed for polar residues in the protein core. This may be explained by the hydrogen bonds in which polar residues are involved; the better their protection from water access the more stable should be the structure in that position. Proteins 33:358–366, 1998. © 1998 Wiley-Liss, Inc.     

Using a strategy based on the concept of convergent evolution to identify residue substitutions responsible for thermal adaptation

Factors that are related to thermostability of proteins have been extensively studied in recent years, especially by comparing thermophiles and mesophiles. However, most of them are global characters. It is still not clear how to identify specific residues or fragments which may be more relevant to protein thermostability. Moreover, some of the differences among the thermophiles and mesophiles may be due to phylogenetic differences instead of thermal adaptation. To resolve these problems, I adopted a strategy to identify residue substitutions evolved convergently in thermophiles or mesophiles. These residues may therefore be responsible for thermal adaptation. Four classes of genomes were utilized in this study, including thermophilic archaea, mesophilic archaea, thermophilic bacteria, and mesophilic bacteria. For most clusters of orthologous groups (COGs) with sequences from all of these four classes of genomes, I can identify specific residues or fragments that may potentially be responsible for thermal adaptation. Functional or structural constraints (represented as sequence conservation) were suggested to have higher impact on thermal adaptation than secondary structure or solvent accessibility does. I further compared thermophilic archaea and mesophilic bacteria, and found that the most diverged fragments may not necessarily correspond to the thermostability-determining ones. The usual approach to compare thermophiles and mesophiles without considering phylogenetic relationships may roughly identify sequence features contributing to thermostability; however, to specifically identify residue substitutions responsible for thermal adaptation, one should take sequence evolution into consideration.     

UPSEC: an algorithm for classifying unaligned protein sequences into functional families.

To classify proteins into functional families based on their primary sequences, popular algorithms such as the k-NN-, HMM-, and SVM-based algorithms are often used. For many of these algorithms to perform their tasks, protein sequences need to be properly aligned first. Since the alignment process can be error-prone, protein classification may not be performed very accurately. To improve classification accuracy, we propose an algorithm, called the Unaligned Protein SEquence Classifier (UPSEC), which can perform its tasks without sequence alignment. UPSEC makes use of a probabilistic measure to identify residues that are useful for classification in both positive and negative training samples, and can handle multi-class classification with a single classifier and a single pass through the training data. UPSEC has been tested with real protein data sets. Experimental results show that UPSEC can effectively classify unaligned protein sequences into their corresponding functional families, and the patterns it discovers during the training process can be biologically meaningful.     

A Bayesian network model for protein fold and remote homologue recognition

MOTIVATION: The Bayesian network approach is a framework which combines graphical representation and probability theory, which includes, as a special case, hidden Markov models. Hidden Markov models trained on amino acid sequence or secondary structure data alone have been shown to have potential for addressing the problem of protein fold and superfamily classification. RESULTS: This paper describes a novel implementation of a Bayesian network which simultaneously learns amino acid sequence, secondary structure and residue accessibility for proteins of known three-dimensional structure. An awareness of the errors inherent in predicted secondary structure may be incorporated into the model by means of a confusion matrix. Training and validation data have been derived for a number of protein superfamilies from the Structural Classification of Proteins (SCOP) database. Cross validation results using posterior probability classification demonstrate that the Bayesian network performs better in classifying proteins of known structural superfamily than a hidden Markov model trained on amino acid sequences alone.     

Characterization of sequence variability in nucleosome core histone folds

The three-helix, approximately 65-residue histone fold domain is the most structurally conserved part of the core histones H2A, H2B, H3, and H4. However, it evinces a notable degree of sequence variation within and between histone classes. We used two approaches to characterize sequence variation in these histone folds, toward elucidating their structure/function relationships and evolution. On the one hand we asked how much of the sequence variation seen in structure-based alignments of the folds maintains physicochemical properties at a position, and on the other, whether conservation correlates to structural importance, as measured by the number of residue-to-residue contacts a position makes. Strong physicochemical conservation or correlation of conservation to contacts would support the idea that functional constraints, rather than genetic drift, determines the observed range of variants at a given position. We used an 11-state table of physicochemical properties to classify each position in the core histone fold (CHF) alignments, and a public website (http://www.ebi.ac.uk/thornton-srv/databases/cgi-bin/valdar/scorecons_server.pl) to score conservation. We found that, depending on histone class, from 38 to 77% of CHF positions are maximally conserved physicochemically, and that for H2B, H3, and H4 the degree to which a position is conserved correlates positively to the number of contacts made by the residue at that position in the crystal structure of the nucleosome core particle. We also examined the correlation between conservation and the type of contact (e.g., inter- or intrachain, histone-histone, or histone-DNA, etc.). For H2B, H3, and H4 we found a positive correlation between conservation and number of interchain protein contacts. No such correlation or statistical significance was found for DNA or intrachain contacts. This suggests that variations in the CHF sequences could be functionally constrained by requirements to make sufficient interchain histone contacts. We also suggest that inventory of histone residue variants can augment functional studies of histones. An example is presented for histone H3.     

Analysis and prediction of functionally important sites in proteins

The rapidly increasing volume of sequence and structure information available for proteins poses the daunting task of determining their functional importance. Computational methods can prove to be very useful in understanding and characterizing the biochemical and evolutionary information contained in this wealth of data, particularly at functionally important sites. Therefore, we perform a detailed survey of compositional and evolutionary constraints at the molecular and biological function level for a large set of known functionally important sites extracted from a wide range of protein families. We compare the degree of conservation across different functional categories and provide detailed statistical insight to decipher the varying evolutionary constraints at functionally important sites. The compositional and evolutionary information at functionally important sites has been compiled into a library of functional templates. We developed a module that predicts functionally important columns (FIC) of an alignment based on the detection of a significant "template match score" to a library template. Our template match score measures an alignment column's similarity to a library template and combines a term explicitly representing a column's residue composition with various evolutionary conservation scores (information content and position-specific scoring matrix-derived statistics). Our benchmarking studies show good sensitivity/specificity for the prediction of functional sites and high accuracy in attributing correct molecular function type to the predicted sites. This prediction method is based on information derived from homologous sequences and no structural information is required. Therefore, this method could be extremely useful for large-scale functional annotation.     

Assessing annotation transfer for genomics: quantifying the relations between protein sequence, structure and function through traditional and probabilistic scores

Measuring in a quantitative, statistical sense the degree to which structural and functional information can be "transferred" between pairs of related protein sequences at various levels of similarity is an essential prerequisite for robust genome annotation. To this end, we performed pairwise sequence, structure and function comparisons on approximately 30,000 pairs of protein domains with known structure and function. Our domain pairs, which are constructed according to the SCOP fold classification, range in similarity from just sharing a fold, to being nearly identical. Our results show that traditional scores for sequence and structure similarity have the same basic exponential relationship as observed previously, with structural divergence, measured in RMS, being exponentially related to sequence divergence, measured in percent identity. However, as the scale of our survey is much larger than any previous investigations, our results have greater statistical weight and precision. We have been able to express the relationship of sequence and structure similarity using more "modern scores," such as Smith-Waterman alignment scores and probabilistic P-values for both sequence and structure comparison. These modern scores address some of the problems with traditional scores, such as determining a conserved core and correcting for length dependency; they enable us to phrase the sequence-structure relationship in more precise and accurate terms. We found that the basic exponential sequence-structure relationship is very general: the same essential relationship is found in the different secondary-structure classes and is evident in all the scoring schemes. To relate function to sequence and structure we assigned various levels of functional similarity to the domain pairs, based on a simple functional classification scheme. This scheme was constructed by combining and augmenting annotations in the enzyme and fly functional classifications and comparing subsets of these to the Escherichia coli and yeast classifications. We found sigmoidal relationships between similarity in function and sequence, with clear thresholds for different levels of functional conservation. For pairs of domains that share the same fold, precise function appears to be conserved down to approximately 40 % sequence identity, whereas broad functional class is conserved to approximately 25 %. Interestingly, percent identity is more effective at quantifying functional conservation than the more modern scores (e.g. P-values). Results of all the pairwise comparisons and our combined functional classification scheme for protein structures can be accessed from a web database at http://bioinfo.mbb.yale.edu/alignCopyright 2000 Academic Press.     

A Web-based classification system of DNA-binding protein families

Rational classification of proteins encoded in sequenced genomes is critical for making the genome sequences maximally useful for functional and evolutionary studies. The family of DNA-binding proteins is one of the most populated and studied amongst the various genomes of bacteria, archaea and eukaryotes and the Web-based system presented here is an approach to their classification. The DnaProt resource is an annotated and searchable collection of protein sequences for the families of DNA-binding proteins. The database contains 3238 full-length sequences (retrieved from the SWISS-PROT database, release 38) that include, at least, a DNA-binding domain. Sequence entries are organized into families defined by PROSITE patterns, PRINTS motifs and de novo excised signatures. Combining global similarities and functional motifs into a single classification scheme, DNA-binding proteins are classified into 33 unique classes, which helps to reveal comprehensive family relationships. To maximize family information retrieval, DnaProt contains a collection of multiple alignments for each DNA-binding family while the recognized motifs can be used as diagnostically functional fingerprints. All available structural class representatives have been referenced. The resource was developed as a Web-based management system for online free access of customized data sets. Entries are fully hyperlinked to facilitate easy retrieval of the original records from the source databases while functional and phylogenetic annotation will be applied to newly sequenced genomes. The database is freely available for online search of a library containing specific patterns of the identified DNA-binding protein classes and retrieval of individual entries from our WWW server (http://kronos.biol.uoa.gr/~mariak/dbDNA.html).     

A method for probabilistic mapping between protein structure and function taxonomies through cross training

Background

Prediction of function of proteins on the basis of structure and vice versa is a partially solved problem, largely in the domain of biophysics and biochemistry. This underlies the need of computational and bioinformatics approach to solve the problem. Large and organized latent knowledge on protein classification exists in the form of independently created protein classification databases. By creating probabilistic maps between classes of structural classification databases (e.g. SCOP [1]) and classes of functional classification databases (e.g. PROSITE [2]), structure and function of proteins could be probabilistically related.

Results

We demonstrate that PROSITE and SCOP have significant semantic overlap, in spite of independent classification schemes. By training classifiers of SCOP using classes of PROSITE as attributes and vice versa, accuracy of Support Vector Machine classifiers for both SCOP and PROSITE was improved. Novel attributes, 2-D elastic profiles and Blocks were used to improve time complexity and accuracy. Many relationships were extracted between classes of SCOP and PROSITE using decision trees.

Conclusion

We demonstrate that presented approach can discover new probabilistic relationships between classes of different taxonomies and render a more accurate classification. Extensive mappings between existing protein classification databases can be created to link the large amount of organized data. Probabilistic maps were created between classes of SCOP and PROSITE allowing predictions of structure using function, and vice versa. In our experiments, we also found that functions are indeed more strongly related to structure than are structure to functions.     

Robustness of the residue conservation score reflecting both frequencies and physicochemistries

Measuring residue conservation at aligned positions has many applications in biology. Recently, a new conservation score has been defined. Unlike the previous methods, the new approach considers both residue frequencies and physicochemistries. Specifically, it measures physicochemistries based on BLOSUM matrices disregarding the meaning of the entries in such matrices, which may involve the problem of log–log probability. In this paper we present a conservation measure that also reflects both frequencies and physicochemistries while considering the fact that the entries of BLOSUM matrices are already interpreted as log probability. When the supposed score is applied to 14 protein examples, the results show that these two conservation scores are equivalent aside from the different score ranges. The method is also used to score the functional sites of three protein families. Compared with the widely used entropy-based methods, the resulting scores are more robust and consistent in the sense that the functional sites are much more conserved because of functional constraints.     

Protein simple sequence conservation

Protein simple sequences, a subset of low-complexity sequences, are regions of sequence highly enriched in one or a few residue types. Simple sequences are exceedingly common, the average being more than one per protein sequence. Despite being so common, such sequences are not well-studied. The simple sequences that have been subjected to detailed study are often found to possess important functions. Here we present a survey of protein simple sequences, generally enriched in a single residue type, with the aim of studying their conservation. We find that the majority of such simple sequences are not conserved. However, conserved protein simple sequences are relatively common, with approximately 11% of the surveyed protein families possessing a conserved simple sequence. The data obtained in this study support the idea that simple sequences are conserved for functional reasons. Such functions can range from substrate binding, to mediating protein-protein interactions, to structural integrity. A perhaps surprising finding is that the residue enriching a conserved simple sequence is itself not necessarily conserved. Neither is the length of many of the highly conserved simple sequences. In the few cases where structural and functional data is available it is found that the conserved simple sequences are consistent with both local structure and function. The data presented support the idea that protein simple sequences can be conserved and have important roles in protein structure and function.