P-value based visualization of codon usage data
© Meinicke et al; licensee BioMed Central Ltd. 2006
Received: 13 March 2006
Accepted: 29 June 2006
Published: 29 June 2006
Two important and not yet solved problems in bacterial genome research are the identification of horizontally transferred genes and the prediction of gene expression levels. Both problems can be addressed by multivariate analysis of codon usage data. In particular dimensionality reduction methods for visualization of multivariate data have shown to be effective tools for codon usage analysis. We here propose a multidimensional scaling approach using a novel similarity measure for codon usage tables. Our probabilistic similarity measure is based on P-values derived from the well-known chi-square test for comparison of two distributions. Experimental results on four microbial genomes indicate that the new method is well-suited for the analysis of horizontal gene transfer and translational selection. As compared with the widely-used correspondence analysis, our method did not suffer from outlier sensitivity and showed a better clustering of putative alien genes in most cases.
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 . 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 . 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 , Mycoplasma genitalium , Helicobacter pylori  and Pseudomonas aeruginosa .
Recently, self-organizing maps  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.
P-values for multidimensional scaling
where n a is the number of amino acids. Note that S has unit diagonal elements, i.e. S jj = 1, because the P-value for tables with identical counts is one. Consequently all off-diagonal elements are in the range [0, 1].
In order to derive a suitable low-dimensional point representation of genes we apply classical multidimensional scaling (see e.g. ) to the above similarities. The objective is to find a two-dimensional point configuration with interpoint distances reflecting the codon usage similarities of the corresponding genes. To perform classical scaling based on similarities we first transform the similarity matrix S into a positive semi-definite matrix C by subtracting the smallest eigenvalue λmin of S from all of its diagonal elements:
C = S - λminI (3)
where I is the M × M identity matrix. Note that this transformation preserves the equality of diagonal elements. With the M × M centering matrix H with elements
we finally obtain the matrix
B = HCH. (5)
It can be shown that for a positive semi-definite matrix C the distance matrix D with elements obtained by the standard transformation is Euclidean and B is a centered inner product matrix (, pp. 402). Therefore principal components can be obtained from (partial) eigenvalue decomposition of B. Thus, for 2D-visualization we compute the two leading eigenvectors x1 and x2 of B associated with the largest and second largest eigenvalue, respectively. The M components of x1 and x2 provide the x1 and x2 coordinates for the M genes, which are utilized for scatter plot visualization.
To evaluate our multidimensional scaling (MDS) approach, we focused on visualizations of ribosomal protein genes and putative alien genes for different microbial genomes. Ribosomal protein genes belong to the class of highly expressed genes which tend to use codons associated with the prevalent tRNAs present in the organism. If translational selection is one of the main sources for codon preferences in a particular genome, then codon usage can in turn be used for the prediction of putative highly expressed genes . Another source of codon usage variation in microbial genomes is provided by the insertion of foreign DNA by means of horizontal gene transfer. Thus, putative alien genes may also be predicted on the basis of codon usage analysis [2, 21]. While ribosomal protein genes can be identified from the annotations of completely sequenced genomes, reliable information about putative alien genes is much more difficult to obtain. We combined predictions of the SIGI-HMM tool  with existing references from the literature in order to obtain suitable test sets for our evaluations. SIGI-HMM is based on a Hidden Markov Model for the detection of genomic islands and, in contrast to our MDS-based visualization method, it explicitly uses information about the locations of genes on the corresponding chromosomes. However, unlike MDS, SIGI-HMM does not consider codon usage correlations between different amino acids. Using the two complementary kinds of information exclusively, both methods provide completely different approaches to codon usage analysis .
Number of genes used for the visualization for all species under consideration. Given are the number of putative alien genes, the number of ribosomal protein genes and the total number of genes on the respective chromosomes.
# genes (total)
# ribosomal protein genes
# putative alien genes
V. cholerae Chr1
V. cholerae Chr2
We compared our multidimensional scaling (MDS) approach with the correspondence analysis (CA) method as implemented in the CodonW program  of J. Peden. Computations were based on relative synonymous codon usage (RSCU) values which is the most common way to perform CA on codon usage data . For both methods the resulting coordinates were normalized according to a unit variance of the leading two factors and principal components, respectively.
We proposed an approach for the visualization of codon usage data, using multidimensional scaling (MDS). In that context we introduced a novel similarity measure for codon usage tables, which has been derived from the classical chi-square test. An important feature of our P-value based similarity measure is that it does not involve any hyperparameters. Therefore a subjective "bias" on the visualization due to user-adjusted parameters is effectively avoided. Our comparisons with the widely-used correspondence analysis (CA) method in most cases showed a slightly better clustering of putative alien genes for our P-value based visualization. In particular the results indicate that our approach is more robust than the CA-based visualization method. The outlier-sensitivity of CA becomes apparent in the plots for all species considered here and has already been observed in previous studies . While in most cases the CA-based visualizations are still useful in terms of a suitable clustering of ribosomal protein and putative alien genes, for T. thermophilus that sensitivity results in an inappropriate plot which complicates interpretation.
The work was partially supported by BMBF project MediGrid (01AK803G).
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