Quantification of expression conservation by local network similarity (LNS). Pair-wise Pearson correlation between genes was calculated for individual S. bayanus and S. cerevisiae datasets, generating a matrix of gene-gene correlations. The data used to create this illustration are the actual diauxic shift, cell cycle synchronization, and alpha factor treatment. The distribution of these correlation values is between −1 and 1, and can be drastically different from one dataset to another. Therefore, Fisher’s z-transformation and normalization of these z-values were applied on each correlation matrix, so that the correlations were comparable across datasets. The resulting correlation matrices are normally distributed and centered at 0 with standard deviation equal to 1. For each orthologous pair i and i’, their z-transformed, normalized correlation to all other matched orthologs form two vectors, indicating the relative positions of this pair of ortholog in their respective expression network. The correlation of these two vectors was taken as LNS. To calculate the correlation matrix for global LNS, the average values of individual datasets for a specific gene-gene pair were used to form a new global correlation matrix. According to the properties of normal distribution, the values within this matrix are still normally distributed and centered at 0 with standard deviation equal to 1. This global matrix was then used to calculate global LNS for each ortholog. To simulate the case of non-conservation, orthologous pairs were randomized along one axis of the expression correlation matrix. Therefore in calculating background LNS, only the ortholog match was disturbed, but not the expression network structure (in contrast to randomizing along both axes).
Guan et al. BMC Genomics 2013 14:33 doi:10.1186/1471-2164-14-33