Universality and flexibility in gene expression from bacteria to human

Abstract

Highly parallel experimental biology is offering opportunities to not just accomplish work more easily, but to explore for underlying governing principles. Recent analysis of the large-scale organization of gene expression has revealed its complex and dynamic nature. However, the underlying dynamics that generate complex gene expression and cellular organization are not yet understood. To comprehensively and quantitatively elucidate these underlying gene expression dynamics, we have analyzed genome-wide gene expression in many experimental conditions in Escherichia coli, Saccharomyces cerevisiae, Arabidopsis thaliana, Drosophila melanogaster, Mus musculus, and Homo sapiens. Here we demonstrate that the gene expression dynamics follows the same and surprisingly simple principle from E. coli to human, where gene expression changes are proportional to their expression levels, and show that this "proportional" dynamics or "rich-travel-more" mechanism can regenerate the observed complex and dynamic organization of the transcriptome. These findings provide a universal principle in the regulation of gene expression, show how complex and dynamic organization can emerge from simple underlying dynamics, and demonstrate the flexibility of transcription across a wide range of expression levels.

Fig. 1.

Evolutional conservation of transcriptional organization. The distributions of gene expression levels in E. coli (A), S. cerevisiae (B), A. thaliana (C), D. melanogaster (D), M. musculus (E), and H. sapiens (F) exhibit a power-law distribution in which the probability that a gene has an expression level k, decays as a power law, P(k) ∝ k^-r. A straight line in each panel represents the estimated power-law distribution. The estimated value of exponent r is indicated in the lower left corner of each panel.

Fig. 2.

Characteristics in gene expression dynamics. (A-H) Transition probability T(k₂, k₁), where a gene with a certain expression level k₁ changes its expression level to k₂, calculated from expression data in E. coli (A), S. cerevisiae (B), A. thaliana (C), heads of D. melanogaster (D), liver and suprachiasmatic nucleus of M. musculus (E and F), 45 tissues of M. musculus (G), and 47 tissues of H. sapiens (H). Colors from red to yellow to green represent transition probability of descending values. Gray indicates the value of zero (the lack of the transition data). (I-P) Proportionality in gene expression dynamics. The absolute expression level change () is plotted along the before-transition expression level k₁ in E. coli (I), S. cerevisiae (J), A. thaliana (K), heads of D. melanogaster (L), liver and suprachiasmatic nucleus of M. musculus (M and N), 45 tissues of M. musculus (O), and 47 tissues of H. sapiens (P) expression data. The estimated values for exponent s from a log-log plot of absolute expression change against the before-transition expression level (i.e., ) are indicated in the lower right corner of each panel.

Fig. 3.

Proportional gene expression dynamics can regenerate the observed transcriptional organization. Shown are the stationary distributions of gene expression levels calculated by using transition probability matrices in Fig. 2 A-H from arbitrary initial distribution of gene expression levels. The stationary distributions of E. coli (A), S. cerevisiae (B), A. thaliana (C), heads of D. melanogaster (D), liver and suprachiasmatic nucleus of M. musculus (E and F), 45 tissues of M. musculus (G), and 47 tissues of H. sapiens (H) exhibit a power-law decay in which the probability that a gene has an expression level k, is P(k) ∝ k^-r. The straight line in each panel represents the estimated power-law distribution. The estimated value of exponent r is indicated in the lower left corner of each panel.

Fig. 4.

Theoretical model of proportional gene expression dynamics. (A) Transition probability matrix representing the theoretical model of proportional gene expression dynamics. The model transition probability T(k₂, k₁) represents the probability of expression change from a certain expression level k₁ to other expression level k₂ during unit time interval. Colors from red to yellow to green represent transition probabilities of descending values. (B) The stationary distribution of gene expression calculated by using the modeled transition probability matrix from arbitrary initial distribution of gene expression levels. The stationary distributions of model proportional exhibit a power-law distribution in which the probability that a gene has an expression level k, decays as a power law. The straight line represents the estimated power-law distribution P(k) ∝ k^-2.