Global analysis of phase locking in gene expression during cell cycle: the potential in network modeling

Abstract

Background: In nonlinear dynamic systems, synchrony through oscillation and frequency modulation is a general control strategy to coordinate multiple modules in response to external signals. Conversely, the synchrony information can be utilized to infer interaction. Increasing evidence suggests that frequency modulation is also common in transcription regulation.

Results: In this study, we investigate the potential of phase locking analysis, a technique to study the synchrony patterns, in the transcription network modeling of time course gene expression data. Using the yeast cell cycle data, we show that significant phase locking exists between transcription factors and their targets, between gene pairs with prior evidence of physical or genetic interactions, and among cell cycle genes. When compared with simple correlation we found that the phase locking metric can identify gene pairs that interact with each other more efficiently. In addition, it can automatically address issues of arbitrary time lags or different dynamic time scales in different genes, without the need for alignment. Interestingly, many of the phase locked gene pairs exhibit higher order than 1:1 locking, and significant phase lags with respect to each other. Based on these findings we propose a new phase locking metric for network reconstruction using time course gene expression data. We show that it is efficient at identifying network modules of focused biological themes that are important to cell cycle regulation.

Conclusions: Our result demonstrates the potential of phase locking analysis in transcription network modeling. It also suggests the importance of understanding the dynamics underlying the gene expression patterns.

Figure 1

Distribution of the phase locking index λ.

Figure 2

The efficiency of using r and λ to distinguish targets from non-targets of transcription factors. Overall, λ is significantly better than either r (p < 1e-9) or a random classifier (p < 1e-3). Plotted are data from the alpha factor dataset.

Figure 3

AUC of ROC of the nine TFs. Including the consideration of higher order locking significantly improved the performance.

Figure 4

Significantly enhanced presence of phase locking in BioGRID gene pairs.

Figure 5

The cell cycle genes form a densely connected subnetwork according phase locking. Presented here are 2 D colormaps of the adjacency matrix A as defined by the phase locking index λ and the correlation coefficient r. Pixels are represented by black color if A_{i, j} = 1, white if A_{i, j} = 0. The diagonal elements A_{i, j} were set to zero to avoid obscuring the interaction pattern between different genes.

Figure 6

Comparison of network degrees in the networks of random genes and cell cycle genes. According to λ, the cell cycle genes clearly form a highly connected subnetwork, while random genes are sparsely connected. In contract, the two groups of genes show no connectivity difference according to r. Data presented are from the alpha factor synchronization dataset.

Figure 7

Distribution of phase lags between TF and phase locked targets.

Figure 8

Higher order phase locking in gene expression changes. The number of phase locked gene pairs decrease exponentially with max{m, n}.

Figure 9

Examples of BioGRID pairs that are 1:2 or 2:1 phase locked in their expression time series. The frequency of the slower time series has been doubled. The PubMed ID gives the literature that contains evidence of their interaction. Data from the ELU experiment.

Figure 10

Agreement among the 4 datasets. A. Venn diagram of sharing of the phase locked pairs in the four datasets. (B) A TF-target pair that shows phase locking across three datasets, but exhibits low correlation consistently.

Figure 11

Genes of higher network degree are more likely to be essential genes. (A). Fraction of essential genes goes up linearly with increasing network degree (r = 0.59, p ~ 7e-5). (B) Cumulative distribution fraction (CDF) plot shows that the network degree distribution of essential genes is skewed toward having higher network degrees (p < 1e-5, KS test).

Figure 12

Network modules identified based on phase locking in the alpha factor dataset.