Background
The standard genetic code of protein coding DNA sequences shows a redundancy, since different triplet codons may be used to code for the same amino acid. In general, codon usages show organism-specific patterns. However, codon usage variation within a single genome can be an important source of information about gene expression levels and events of horizontal gene transfer. In particular, dimensionality reduction methods have widely been used for the analysis of codon usage patterns in microbial genomes. These methods provide a low-dimensional point representation of genes, where the proximity of gene-specific points indicates a similar codon usage of the associated genes. Hence, the resulting two-dimensional scatter plots enable a total view on the genome which may reveal a clustering of genes according to groups of nearby points. These clusters can for instance provide evidence for horizontal gene transfer according to groups of putative alien genes [1,2] or for translational selection according to groups of highly expressed genes [3,4].
As a standard method for scatter plot visualization of codon usage data, researchers mostly resort to the so-called correspondence analysis (CA) which has originally been developed for the analysis of contingency tables [5]. From the original formulation it is not completely clear how CA applies to codon counts. Because different preprocessing and normalization schemes have been proposed, the use of CA in codon usage studies has not been without controversy [6]. Nevertheless, CA has been applied for the analysis of many bacterial genomes, including those of Escherichia coli [1,3], Bacillus subtilis [4,7,8], Borrelia burgdorferi [9,10], Chlamydia trachomatis [11], Mycoplasma genitalium [12], Helicobacter pylori [13] and Pseudomonas aeruginosa [14].
Recently, self-organizing maps [15] have been proposed as an alternative visualization method for codon usage data [2,16,17]. Although this method provides a simultaneous clustering of the data which may be useful in certain contexts, it requires to choose the size of a discrete grid on which the genes are mapped in a non-linear way. The grid-size is a critical parameter of the method and directly controls the final clustering in the visualization. Unfortunately, the grid-size of self-organizing maps is a so-called hyperparameter which usually cannot be inferred from the data in an unsupervised manner. Therefore the resulting visualizations bare the risk of being highly subjective.
Here we present a visualization method, which has been tailored to the analysis of codon usage data while not depending on difficult to tune hyperparameters. Our visualization method is based on multidimensional scaling and a new similarity measure for codon usage data. In the following we first introduce our probabilistic similarity measure for codon usage tables and outline the corresponding algorithm for multidimensional scaling based on P-values. Then we provide some visualizations for the analysis of four microbial genomes and discuss our results in comparison with the results obtained from the classical correspondence analysis method.