Correcting for the bias due to expression specificity improves the estimation of constrained evolution of expression between mouse and human

Abstract

Motivation: Comparative analyses of gene expression data from different species have become an important component of the study of molecular evolution. Thus methods are needed to estimate evolutionary distances between expression profiles, as well as a neutral reference to estimate selective pressure. Divergence between expression profiles of homologous genes is often calculated with Pearson's or Euclidean distance. Neutral divergence is usually inferred from randomized data. Despite being widely used, neither of these two steps has been well studied. Here, we analyze these methods formally and on real data, highlight their limitations and propose improvements.

Results: It has been demonstrated that Pearson's distance, in contrast to Euclidean distance, leads to underestimation of the expression similarity between homologous genes with a conserved uniform pattern of expression. Here, we first extend this study to genes with conserved, but specific pattern of expression. Surprisingly, we find that both Pearson's and Euclidean distances used as a measure of expression similarity between genes depend on the expression specificity of those genes. We also show that the Euclidean distance depends strongly on data normalization. Next, we show that the randomization procedure that is widely used to estimate the rate of neutral evolution is biased when broadly expressed genes are abundant in the data. To overcome this problem, we propose a novel randomization procedure that is unbiased with respect to expression profiles present in the datasets. Applying our method to the mouse and human gene expression data suggests significant gene expression conservation between these species.

Fig. 1.

The distribution of expression similarity between human replicates depends on their organ specificity. (A) d_E^M and (B) d_E^E are significantly lower for broadly expressed genes (group 1) than for organ-specific genes (group 3). For randomly permuted gene pairs d_E^M and d_E^E also differ between the three τ-groups. They are significantly lower for random pairs in group 1 than in group 3. (C) d_E^Z is significantly higher for broadly expressed genes (group 1) than for organ-specific genes (group 3). d_E^Z for randomly permuted pairs is high in all three groups, even in the first τ-group, where random pairs consist of two broadly expressed genes (this is a consequence of low r for uniformly expressed genes). Note that the scale of the x-axis differs strongly between graphs.

Fig. 2.

Overrepresentation of broadly expressed human genes causes underestimation of the conservation of expression when randomly permuted pairs are used to approximate the neutral evolution rate. (A, B) For most randomly permuted pairs (grey) the distance (d_E^M and d_E^E) is small, indistinguishable from the distances between replicates (green). For τ-uniform random pairs (blue) d_E^E and d_E^M are higher, which is more consistent with the assumption about neutral evolution (Jordan et al., 2005). (C) d_E^Z is high both for randomly permuted gene pairs and for the group of replicates. The distribution of d_E^Z does not change with the new random pairs set.

Fig. 3.

Random gene pairs have their τ values differently distributed depending on the randomization procedure used. (A) τ distribution for human replicates. The τ pairs are distributed along the diagonal, which is expected for replicates. (B) τ distribution for randomly permuted gene pairs. The τ pairs are biased towards low values, which are the most frequent values in human datasets. (C) τ distribution for τ-uniform random pairs. The τ pairs are uniformly distributed, and not biased towards the low values.

Fig. 4.

The choice of the randomization method changes the conclusions about gene expression evolution between mouse and human. There is no clear evidence for constrained evolution if we compare the distribution of d_E^E for orthologous (green) and randomly permuted gene pairs (grey). Whereas, comparison of d_E^E distribution for orthologous (green) and τ-uniform random pairs (blue) suggest that expression evolution is far from neutral.