Analyzing site heterogeneity during protein evolution

New computational models of the kinetics of natural site substitutions in proteins are described based on the underlying physical chemical properties of the amino acids. The corresponding reduction in the number of adjustable parameters allows us to analyze site-heterogeneity. Applying this evolutionary model to various data sets allows us to identify the important factors constraining molecular evolution, providing insight into the relationship between amino acid properties and protein structure.

Major structural determinants of transmembrane proteins identified by principal component analysis

We identify amino acid characteristics important in determining the secondary structures of transmembrane proteins, and compare them with characteristics important for cytoplasmic proteins. Using information derived from multiple sequence alignments, we perform a principal component analysis (PCA) to identify the directions in the 20-dimensional amino acid frequency space that comprise the most variance within each protein secondary structure. These vectors represent the important position-specific properties of the amino acids for coils, turns, beta sheets, and alpha helices. As expected, the most important axis for most of the datasets was hydrophobicity. Additional axes, distinct from hydrophobicity, are surprising, especially in the case of transmembrane alpha helices, where the effects of aromaticity and beta-branching are the next two most significant characteristics. The axis representing beta-branching also has equal importance in cytoplasmic and transmembrane helices, a finding that contrasts with some experimental results in membrane-like environments. In a further analysis, we examine trends for some of the PCA axes over averaged transmembrane alpha helices, and find interesting results for aromaticity.

Using physical-chemistry-based substitution models in phylogenetic analyses of HIV-1 subtypes

HIV-1 subtype phylogeny is investigated using a previously developed computational model of natural amino acid site substitutions. This model, based on Boltzmann statistics and Metropolis kinetics, involves an order of magnitude fewer adjustable parameters than traditional substitution matrices and deals more effectively with the issue of protein site heterogeneity. When optimized for sequences of HIV-1 envelope (env) proteins from a few specific subtypes, our model is more likely to describe the evolutionary record for other subtypes than are methods using a single substitution matrix, even a matrix optimized over the same data. Pairwise distances are calculated between various probabilistic ancestral subtype sequences, and a distance matrix approach is used to find the optimal phylogenetic tree. Our results indicate that the relationships between subtypes B, C, and D and those between subtypes A and H may be closer than previously thought.

Models of natural mutations including site heterogeneity

New computational models of natural site mutations are developed that account for the different selective pressures acting on different locations in the protein. The number of adjustable parameters is greatly reduced by basing the models on the underlying physical-chemical properties of the amino acids. This allows us to use our method on small data sets built of specific protein types. We demonstrate that with this approach we can represent the evolutionary patterns in HIV envelope proteins far better than with more traditional methods.

Correlating structure-dependent mutation matrices with physical-chemical properties

We have investigated how structure-dependent mutation matrices derived in previous work correlate with various physical-chemical properties of the 20 naturally occurring amino acids. Among the properties we investigated were delta G of transfer from water to octanol and cyclohexane, alpha helical and beta sheet propensity, size, and charge. We found that the delta G of transfer to octanol had a high correlation with matrices for all categories of residues, especially the matrices for buried and exposed positions. This result suggests that octanol is a good model for understanding both the changes in stability resulting from substitutions of buried residues and changes in foldability resulting from varying exposed residues. We also found the correlations of the matrices with size and charge varied with the local environment, and that neither alpha helical nor beta sheet propensity had high correlations with most matrices. Thus, conservation of size and charge appear to be important in specific environments, and conservation of alpha helix and beta sheet propensity do not seem to be key factors.

Mutation matrices and physical-chemical properties: correlations and implications

To investigate how the properties of individual amino acids result in proteins with particular structures and functions, we have examined the correlations between previously derived structure-dependent mutation rates and changes in various physical-chemical properties of the amino acids such as volume, charge, alpha-helical and beta-sheet propensity, and hydrophobicity. In most cases we found the delta G of transfer from octanol to water to be the best model for evolutionary constraints, in contrast to the much weaker correlation with the delta G of transfer from cyclohexane to water, a property found to be highly correlated to changes in stability in site-directed mutagenesis studies. This suggests that natural evolution may follow different rules than those suggested by results obtained in the laboratory. A high degree of conservation of a surface residue's relative hydrophobicity was also observed, a fact that cannot be explained by constraints on protein stability but that may reflect the consequences of the reverse-hydrophobic effect. Local propensity, especially alpha-helical propensity, is rather poorly conserved during evolution, indicating that non-local interactions dominate protein structure formation. We found that changes in volume were important in specific cases, most significantly in transitions among the hydrophobic residues in buried locations. To demonstrate how these techniques could be used to understand particular protein families, we derived and analyzed mutation matrices for the hypervariable and framework regions of antibody light chain V regions. We found surprisingly high conservation of hydrophobicity in the hypervariable region, possibly indicating an important role for hydrophobicity in antigen recognition.

Probabilistic reconstruction of ancestral protein sequences

Using a maximum-likelihood formalism, we have developed a method with which to reconstruct the sequences of ancestral proteins. Our approach allows the calculation of not only the most probable ancestral sequence but also of the probability of any amino acid at any given node in the evolutionary tree. Because we consider evolution on the amino acid level, we are better able to include effects of evolutionary pressure and take advantage of structural information about the protein through the use of mutation matrices that depend on secondary structure and surface accessibility. The computational complexity of this method scales linearly with the number of homologous proteins used to reconstruct the ancestral sequence.

Context-dependent optimal substitution matrices

Substitution matrices are a key tool in important applications such as identifying sequence homologies, creating sequence alignments and more recently using evolutionary patterns for the prediction of protein structure. We have derived a novel approach to the derivation of these matrices that utilizes not only multiple sequence alignments, but also the associated evolutionary trees. The key to our method is the use of a Bayesian formalism to calculate the probability that a given substitution matrix fits the tree structures and multiple sequence alignment data. Using this procedure, we can determine optimal substitution matrices for various local environments, depending on parameters such as secondary structure and surface accessibility.