Maximization of negative correlations in time-course gene expression data for enhancing understanding of molecular pathways

Abstract

Positive correlation can be diversely instantiated as shifting, scaling or geometric pattern, and it has been extensively explored for time-course gene expression data and pathway analysis. Recently, biological studies emerge a trend focusing on the notion of negative correlations such as opposite expression patterns, complementary patterns and self-negative regulation of transcription factors (TFs). These biological ideas and primitive observations motivate us to formulate and investigate the problem of maximizing negative correlations. The objective is to discover all maximal negative correlations of statistical and biological significance from time-course gene expression data for enhancing our understanding of molecular pathways. Given a gene expression matrix, a maximal negative correlation is defined as an activation-inhibition two-way expression pattern (AIE pattern). We propose a parameter-free algorithm to enumerate the complete set of AIE patterns from a data set. This algorithm can identify significant negative correlations that cannot be identified by the traditional clustering/biclustering methods. To demonstrate the biological usefulness of AIE patterns in the analysis of molecular pathways, we conducted deep case studies for AIE patterns identified from Yeast cell cycle data sets. In particular, in the analysis of the Lysine biosynthesis pathway, new regulation modules and pathway components were inferred according to a significant negative correlation which is likely caused by a co-regulation of the TFs at the higher layer of the biological network. We conjecture that maximal negative correlations between genes are actually a common characteristic in molecular pathways, which can provide insights into the cell stress response study, drug response evaluation, etc.

Figure 1.

Notion of negative correlations in biological studies. (a) Reprinted by permission from Macmillan Publishers Ltd: Nature Genetics, 37(5):501–506, ©2005. (b) Reprinted by permission from American Society For Cell Biology: Molecular Biology of the Cell, 16(11):5316–5333, ©2005. (c) Reprinted by permission from Oxford University Press: Bioinformatics, 23(13):i440–i449, ©2007. (d) Reprinted by permission from Elsevier B.V.: Cell, 117(6):721–733, ©2004.

Figure 2.

A suffix-tree and a bi-clique search method are combined for AIE pattern mining.

Figure 3.

Examples of AIE patterns and their up-down trends.

Figure 4.

Biological significance comparison between our AIE patterns and gene clusters by the conventional methods. Here, HCL-x or Kmeans-x stands for x number of clusters being pre-set.

Figure 5.

The generalized pearson’s correlation coefficient and group ratio comparison between AIE pattern mining and the conventional methods.

Figure 6.

Representative examples of AIE pattern from the three data sets. Here, two groups of genes colored in red and blue, show negative correlation during the time points in orange area.

Figure 7.

A subregulatory tree for AIE-Alpha-87.

Figure 8.

An expanded diagram for the pathway lysine biosynthesis after our functional annotation is used to derive new components (shown as dashed lines) based on the negative correlation of AIE-Alpha-87.

Figure 9.

A partial diagram of the pathway ergosterol biosynthesis.

Figure 10.

The expression profiles of the genes in AIE-Alpha-87 under three different conditions (Alpha factor, Cdc15 and Cdc28). The signs following each gene name have specific meanings. -B stands for this gene in the blue group; -BP stands for this gene in the blue group and also belonging to the pathway; and -R stands for this gene in the red group.

Figure 11.

An invariable negative correlation shared by six common genes of two AIE patterns (AIE-BeforeStress-4411 and AIE-AfterStress-3827).