Separation of phylogenetic and functional associations in biological sequences by using the parametric bootstrap

Abstract

Quantitative analyses of biological sequences generally proceed under the assumption that individual DNA or protein sequence elements vary independently. However, this assumption is not biologically realistic because sequence elements often vary in a concerted manner resulting from common ancestry and structural or functional constraints. We calculated intersite associations among aligned protein sequences by using mutual information. To discriminate associations resulting from common ancestry from those resulting from structural or functional constraints, we used a parametric bootstrap algorithm to construct replicate data sets. These data are expected to have intersite associations resulting solely from phylogeny. By comparing the distribution of our association statistic for the replicate data against that calculated for empirical data, we were able to assign a probability that two sites covaried resulting from structural or functional constraint rather than phylogeny. We tested our method by using an alignment of 237 basic helix-loop-helix (bHLH) protein domains. Comparison of our results against a solved three-dimensional structure confirmed the identification of several sites important to function and structure of the bHLH domain. This analytical procedure has broad utility as a first step in the identification of sites that are important to biological macromolecular structure and function when a solved structure is unavailable.Q uantitative analyses of biological sequences are the cornerstone for studies in bioinformatics and molecular evolution. Such analyses generally proceed assuming that the sites in individual DNA or protein sequences vary independently, i.e., amino acid replacements at site X occur independently of those at site Y (1). Biochemical and biophysical studies show this assumption is not biologically realistic because sequence elements often change in a concerted manner (2-6). Nonrandom associations among sites within sequences arise from at least three sources: (i) chance, (ii) common ancestry (ϭ phylogeny), and (iii) structural or functional constraints. (For simplicity, associations resulting from structure and function are considered to be equivalent.) Effectively discriminating among these underlying causes facilitates understanding the origin and magnitude of associations observed among sites in biological sequences and clarifying the role of such associations in evolution.The first step in resolving questions about the origins of associations among sequence elements is to generate replicate data sets that vary according to specific underlying evolutionary models. For biological sequences, the typical model components are a reconstructed phylogeny and a nucleotide or amino acid substitution matrix. These components are relevant because sequence diversity has been generated by a process of descent with modification from a common ancestor.Historical associations between sequences are represented by the reconstructed phylogeny. The topology of the evolutionary tree specifies the cladis...

In silico Discovery of Enzyme–Substrate Specificity-determining Residue Clusters

“…convergent evolution, differing affinities for more than one substrate, variations in conservation among functional residues and multi-functional proteins) which cannot be easily captured by the phylogenetic tree. [29][30][31][32] Thus, Hannenhalli & Russell 33 and Li et al 23 use experimentally predefined functional subtypes, rather than those derived from a tree, and then find individual positions that are conserved within each subtype but vary between different subtypes using hidden Markov models (HMMs) and relative entropy, together with Dirichlet mixture priors. Landgraf et al 34 expanded this with spatially neighboring amino acids around each residue, and then identified functional residues as those whose variations deviate significantly from the average in the protein family.…”

Using Mutual Information and Models of Evolution for Improved Pattern Detection

“…Classical MI calculation has already proven to be an adequate measure for identifying coevolving positions within an alignment as well as for identifying associations between sites [12], [1]. By considering the models of evolution in the calculation new patterns have emerged.…”

“…As pointed out by Wollenberg and Atchley [12], the amino acids along a column are just symbols with no underlying metric, disallowing some conventional statistical methods for estimating correlation. By counting the number of each amino acid within a site and estimating a probability we can use the MI to estimate the distance between sites.…”

“…Taking the log to the base 20 is a common approach [1], [12] when dealing with amino acid sequences as it scales the entropies between 0 and 1, even if all 20 amino acids happen to occur in a given column. Next we define, the joint entropy H ij of two columns i and j:…”

“…The mutual information has found several applications in bioinformatics, and analysing sequence alignments in particular, as it provides us with a usable metric of dependency between the sites in the alignment. Wollenberg and Atchley [12] used MI to calculate the magnitude of association between pairs of sites, arguing that statistical methods such as correlation cannot be used, as the members of the sequence are symbols with no underlying metric. More recent applications of MI include: finding and analysing coevolving positions [1], [6], scoring pairwise sequence alignments [14], clustering [13] and discovering characteristic sites in homologous alignments [15].…”