Preservation of ranking order in the expression of human Housekeeping genes

Abstract

Housekeeping (HK) genes fulfill the basic needs for a cell to survive and function properly. Their ubiquitous expression, originally thought to be constant, can vary from tissue to tissue, but this variation remains largely uncharacterized and it could not be explained by previously identified properties of HK genes such as short gene length and high GC content. By analyzing microarray expression data for human genes, we uncovered a previously unnoted characteristic of HK gene expression, namely that the ranking order of their expression levels tends to be preserved from one tissue to another. Further analysis by tensor product decomposition and pathway stratification identified three main factors of the observed ranking preservation, namely that, compared to those of non-HK (NHK) genes, the expression levels of HK genes show a greater degree of dispersion (less overlap), stableness (a smaller variation in expression between tissues), and correlation of expression. Our results shed light on regulatory mechanisms of HK gene expression that are probably different for different HK genes or pathways, but are consistent and coordinated in different tissues.

Figure 1. HK genes exhibited a significantly more preserved expression ranking order than MR or TS genes.

Frequency is the percentage of tissue pairs with the indicated Kendall's tau (). Each distribution is a compilation of 630 Kendall's tau (; Equation (3 )), where each was for a pair of tissues sampled from a 36-tissue pool and the frequency of at a particular value was computed on a histogram using a bin width of 0.1. The average value () of the distribution for the HK, MR, and TS gene sets was 0.77, 0.59, and 0.41, respectively, and the standard errors were all small, mostly less than 0.01.

Figure 2. Ranking preservation of HK genes was not a random event.

(A) Kendall's tau computed for the manually partitioned HK and MR genes (circles) compared to those generated from two different random distributions: the triangles show the results when the GSE2361 expression data were randomly divided into two sets containing the same number of HK (N_g = 388) and MR (N_g = 11,953) genes, while the squares show the results when expression levels were ignored and rankings were randomly created (see Methods). Each data point is a combination of the two computed for the two gene groups (N_g = 388 and N_g = 11,953) for a particular pair of tissues. (B) The expression of all the genes in any two human tissues (heart and thymus are shown as an example) always has an elliptical shape, resulting in a substantially preserved ranking order with a non-zero (>0.4) even for randomly grouped genes (triangles in (A)). In contrast, randomly assigned rankings would yield a value very close to zero (squares in (A)). Gene expression levels were log2 transformed and were denoted by x_gt.

Figure 3. Schematic illustration of the three factors that contribute to preserve gene expression rankings.

The three factors represent three different types of expression pattern of a pair of genes in different tissues: (A) Co-expression (r_gg′; Equation (5 )), (B) stableness (S_gg′; Equation (7 )), and (C) dispersion (D_{gg′ ;} Equation (8 )).

Figure 4. The contributions to the ranking preservation of the HK, MR, and TS genes.

The three contributing factors were dispersion (solid line), stableness (dashed line), and co-expression (dotted line). For each factor, its contribution (in parenthesis) was the sum of the individual contributions calculated using tensor product decomposing equations, such as Equation (11 )–(13). The contribution of factors other than these three is given in the black box in the upper right corner of each panel.

Figure 5. The contributions to the ranking preservation of the HK genes in seven HK-enriched KEGG pathways.

Shown is the percentage contribution of the three factors, stableness, co-expression, and dispersion to the expression ranking (Kendall's tau, ) computed for the HK genes found in each of the seven HK-enriched KEGG pathways. The black bars are the contributions of other unknown factors.

Figure 6. Range of expression levels of the HK genes in HK-enriched KEGG pathways.

Shown are boxplots of the tissue-wide expression profiles of the HK genes in each of the 7 HK-enriched KEGG pathways. The results for the whole HK set (388 genes) and for the NHK set (12,687 genes) are presented on the right for comparison. Each box is bounded by the 25^th and 75^th percentile of the data, with the solid line within the box marking the median and the dotted line the mean, while the two short horizontal bars indicate the 90^th and 10^th percentile of the data and dots beyond these two bars are outliers. Gene expression levels were log2 transformed and are denoted by x_gt.

Figure 7. The ribosomal HK genes are expressed at different levels in tissues of different embryonic origins.

Shown are boxplots of expression levels on a log2 scale (x_gt) for 79 ribosomal HK genes (94.1% of the 84 ribosomal genes, Table 2) in each human tissue. Each box is bounded by the 25^th and 75^th percentile of the data, the solid line within the box marking the median. The two short horizontal bars indicate the 90^th and 10^th percentile of the data, while the crosses mark the 95^th and the 5^th percentile of the data. The tissues are grouped according to their embryonic origin.

Figure 8. A less coherently regulated subcomplex (β) reduced the overall expression ranking preservation of proteasomal genes.

Shown are gene expression rankings () computed for HK genes coding for proteins involved in different subcomplexes of the proteasome. The value is shown in parenthesis at the bottom of the box. * indicates that the value is significantly different from computed from random sampling using the same number of genes.

Figure 9. The relationships of the contributing components of gene expression rankings.

The four-circle Venn diagram is used to illustrate the intertwined relationships between gene expression ranking () and the three contributing factors of co-expression (, Equation (5 )), stableness (, Equation (7 )), and dispersion (, Equation (8 )). The rectangular box represents the universal set, its 16 components can be deduced from tensor computations (Equation (9 )), e.g., A8 = , A10 = , and A16 = . The equations for computing these components are described in the Methods (Equation (11 – 13 )). Note that each of the four elements (,,, and ) is a composite of eight components.