An expert system to identify co-regulated gene groups from time-lagged gene clusters using cell cycle expression data

Abstract

Motivation

The analysis of time series gene expression data can provide us with the opportunity to find co-regulated genes that show a similar expression patterns under a contiguous subset of experimental conditions. However, these co-regulated genes may behave almost independently under other conditions. Furthermore, the similarity in the expression pattern might be time-shifted. In that case, we need to be concerned with grouping genes that share similar expression patterns under a contiguous subset of conditions and where the similarity in expression pattern might have time lags. In addition, to be considered a time-shifted similar pattern, because co-regulated genes in a biological process may show a periodic pattern in their cell cycle expression, we also should group genes with periodic similar patterns over multiple cell cycles. If this is carried out, we can regard such grouped genes as cell-cycle regulated genes.

Results

We propose a method that follows the q-cluster concept [Ji, L., & Tan, K. L. (2005). Identifying time-lagged gene clusters using gene expression data. Bioinformatics, 21(4), 509–516] and further advances this approach towards the identification of cell-cycle regulated genes using cell cycle microarray data. We used our method to cluster a microarray time series of yeast genes to assess the statistically biological significance of the obtained clusters we used the p-value obtained from the hypergeometric distribution. We found that several clusters provided findings suggesting a TF–target relationship. In order to test whether our method could group related genes that other methods have found difficult to group, we compared our method with other measures such as Spearman Rank Correlation and Pearson Correlation. The results of the comparison demonstrate that our method indeed could group known related genes that these measures regard as having only a weak association.

Introduction

DNA microarray technology enables the simultaneous study of gene expression levels on a large scale. Expression level is the logarithm of the abundance of the mRNA of a gene under a specific condition. The gene expression data of a microarray is arranged as a data matrix. Each gene corresponds to one row and each condition to one column. Each element of this matrix represents the expression level of a gene under a specific condition. The conditions of a microarray may be different time points, different environmental conditions or different organs. The analysis of microarray data has facilitated the study of genetic regulatory networks. The correlation patterns of genes with experimental conditions can be used to identify the networks that are comprised of correlated genes and thus how the correlated genes interact with each other.

Clustering methods can be applied to either the genes or the conditions of the microarray matrix separately. However, some problems occur when applying clustering to the analysis of gene expression data. A set of genes may simultaneously activate a particular biological process over certain contiguous conditions but behave independently under other condition. Therefore, we need to group genes that have similar behavior under a specific subset of the conditions. Clustering can not satisfy this requirement. The biclustering method is a technique that makes this possible and allows the grouping of genes and conditions simultaneously within a data matrix. The goal of biclustering is to find a bicluster that is a subset of genes that show similar behavior under a specific subset of the conditions (Cheng & Church, 2000). Thus, genes in the same bicluster are co-expressed and further are likely to be co-regulated.

In the analysis of time-series expression data, a set of genes may activates a particular biological process over a certain contiguous set of conditions instead under a discrete condition. In such a case, we should find biclusters for a contiguous subset of conditions. However, in fact, co-expressed genes do not regulate each other simultaneously but only after a certain time lag. That is to say, there is a transcriptional time lag whereby the regulator gene takes time to express its protein product and a further delay occurs as the target gene responds to the regulator protein. Hence, because of the transcriptional time lag of co-regulated genes, we need to take time-lagged co-regulated genes into consideration when forming biclusters. In addition, when considering time-lagged similarity of expression patterns between genes, it is necessary to consider biclusters with coherent values for both the rows and columns of the expression matrix. This is because their expression relies on a promoter that is a structural regulatory sequence recognized by a TF of the RNA polymerase holoenzyme. The reason that co-expressed genes share a common sequence within their promoter will therefore result in shared expression. However, the recognition efficiency of this TF is not the same for every gene having the same promoter. This condition leads to biclusters having a variety of coherence values. There are two kinds of coherence values for a bicluster. The first is a shifted similarity pattern that can be viewed as based on an additive model. The second is a scaled similarity pattern that can be viewed as based on a multiplicative model. In a mathematical sense, scaling and vertical shifting of the expression level can be referred to as linear transformations. Consider two time-series x and y. In this case y is a linear transformation of x if it can be expressed as $y=\mathit{mx}+b$.

Many biological processes show periodic pattern such as the cell cycle process, therefore it is useful to find periodically regulated genes with similar periodic patterns of expression. We can then use these cell-cycle regulated genes to map the transcriptional regulatory network that controls the cell cycle.

A suffix tree is a data structure that contains all suffixes of a string s. It has been widely used for string matching and exact sequence comparison (Ukkonen, 1995). This approach was used to develop an algorithm for building a suffix tree that runs in time $O(n)$. Once a suffix tree is built, most problems can be solved in linear-time using it. The suffix tree built for a set of strings is called a generalized suffix tree (Gusfield, 1997). In order to avoid creating empty suffixes, we usually append to s an extra character $ before the building of the suffix tree. The key feature of the generalized suffix tree is that any leaves in this tree contain two pieces of information: The first is the string number and the second is the starting position of a suffix that makes up this string.