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Global genetic response in a cancer cell: Self-organized coherent expression dynamics

PLoS ONE (2014) 9(5)
DOI: 10.1371/journal.pone.0097411
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Abstract

Understanding the basic mechanism of the spatio-temporal self-control of genome-wide gene expression engaged with the complex epigenetic molecular assembly is one of major challenges in current biological science. In this study, the genome-wide dynamical profile of gene expression was analyzed for MCF-7 breast cancer cells induced by two distinct ErbB receptor ligands: epidermal growth factor (EGF) and heregulin (HRG), which drive cell proliferation and differentiation, respectively. We focused our attention to elucidate how global genetic responses emerge and to decipher what is an underlying principle for dynamic self-control of genome-wide gene expression. The whole mRNA expression was classified into about a hundred groups according to the root mean square fluctuation ( rmsf). These expression groups showed characteristic time-dependent correlations, indicating the existence of collective behaviors on the ensemble of genes with respect to mRNA expression and also to temporal changes in expression. All-or-none responses were observed for HRG and EGF (biphasic statistics) at around 10-20 min. The emergence of time-dependent collective behaviors of expression occurred through bifurcation of a coherent expression state (CES). In the ensemble of mRNA expression, the self-organized CESs reveals distinct characteristic expression domains for biphasic statistics, which exhibits notably the presence of criticality in the expression profile as a route for genomic transition. In time-dependent changes in the expression domains, the dynamics of CES reveals that the temporal development of the characteristic domains is characterized as autonomous bistable switch, which exhibits dynamic criticality (the temporal development of criticality) in the genome-wide coherent expression dynamics. It is expected that elucidation of the biophysical origin for such critical behavior sheds light on the underlying mechanism of the control of whole genome. © 2014 Tsuchiya et al.

Figures

  • Figure 1. Emergence of biphasic dynamic emergent averaging behaviors (DEABs) of the expression and the expression change. The transition from scattered expression (first row; N = 22035) to time-dependent correlation (second row) is shown as the collective behavior of ensemble groups: DEAB of A) the expression (symbolically represented by ln(e(t)); called simply ‘the expression’) and B) the expression change (ln(e(ti)/
  • Figure 2. Unimodal to bimodal frequency distribution for DEAB of the expression. The profiles of the frequency distribution of the expression (ln(e(t))) from 15 min to 20 min change from unimodal to bimodal for A) high-variance expression (the root mean square fluctuation, rmsf .0.42) and B) low-variance expression (rmsf ,0.42). First row: the HRG response for rmsf .0.42 shows a peak-shift of unimodal profiles from t = 15 min (blue histogram) to t = 20 min (red) with a change in the lower to higher value of the expression, while binomial frequency distributions between 15 min (blue polygonal line) and 20 min (red histogram) almost perfectly overlap each other for rmsf ,0.42. Second row: the EGF response shows almost the perfect overlap of profiles for both unimodal (rmsf .0.42) and bimodal (rmsf ,0.42) distributions, which suggests that there is no temporal averaging response, consistent with DEAB of the expression for the EGF response (Figure 1A). For all histograms in this report, the bin size is set to 0.05. doi:10.1371/journal.pone.0097411.g002
  • Figure 3. Existence of coherent expression states (CESs) as hill-like functions. Plots of single mRNA expression for rmsf .0.42 (blue dot: 15 min and red dot: 20 min) are superimposed in the left panel (first row: 3269 expressions for HRG; second row: 1482 for EGF). In the right panel, the probability density function (PDF) using a Gaussian kernel by Mathematica 9 (default setting) for each point (left panel) reveals hill-like functions in pseudo-3-dimensional space (genetic landscape; z-axis: probability density). Superimposition of the genetic landscapes between ti–1 = 15 min and ti = 20 min - first row: the HRG response has three CESs; two independent CESs plus one CES that results from the overlap of CESs between 15 min (darker color) and 20 min (lighter color) around a zero change in expression at the y-axis; second row: the EGF response has a single CES as the overlap of two CESs around a zero change in expression. The legend shows a lighter (darker) color bar at 20 min (at 15 min) for PDF. doi:10.1371/journal.pone.0097411.g003
  • Figure 4. Onset of the bifurcation of CES for DEAB of the expression (HRG). The onset of bifurcation of a new CES as the growth of a hill-like function is shown. In the first row, the profile of the frequency distribution of expression changes from unimodal (0.26, rmsf ,0.66; left) to bimodal (0.17, rmsf ,0.57; right) through a flattened unimodal profile (0.22, rmsf ,0.62; center). The genetic landscape (second row) for 15–20 min for each region of rmsf illustrates that the onset of bifurcation of CES transforms from a unimodal to bimodal profile; the red arrow (second row) points to the formation of CES and the blue arrow points to the formation of a valley, which gives rise to a low-expression state (LES). The peaks of the bimodal frequency distribution coincide with the highest density of CESs at around ln(e) = 1.7 and 2.2 (black dash lines). doi:10.1371/journal.pone.0097411.g004
  • Figure 5. Bifurcation of CESs in DEAB of the expression. The bifurcations of CESs in DEAB of the expression for 15–20 min are examined with an incremental change in a segment, v , rmsf , v + r, as an extension of Figure 4, where the range r is set to 0.4 and v is a variable of rmsf. The bifurcation diagrams of the expression (v against the expression; first row) at t = 20 min, and the expression change (v against the change in the expression for 15–20 min; second row) are plotted for HRG (left panel) and EGF (right). The bifurcation diagram of the expression defines the expression level at ln(e) = 2.075 (lower: low- and upper: high-expression) because of the existence of a valley, which separates the low and high CESs (Figure 6), whereas the bifurcation diagram of the expression change shows three activity levels of CES: ON (positive change in the expression), EQ (near zero) and OFF (negative change in the expression). The bifurcation diagrams clearly show distinct characteristic expression domains between HRG and EGF: static, transit and dynamic domains for rmsf ,0.21, 0.21, rmsf ,0.42, and 0.42, rmsf for HRG, and static and transit domains for rmsf ,0.16 and 0.16, rmsf for EGF (see details in the main text). doi:10.1371/journal.pone.0097411.g005
  • Figure 6. Genetic landscape of the characteristic expression domains. Each row (A: HRG and B: EGF) corresponds to frequency distributions of mRNA expression (first) and genetic landscapes (second: side view). In the genetic landscape, a static domain with a valley is characterized by two CESs: A) HES1(EQ) and LES1(OFF) for rmsf ,0.21; and B) HES(EQ) and LES(EQ) for rmsf ,0.16, a transit domain is characterized by A) HES1(EQ) for
  • Table 1. Bifurcations of CES, Characteristic Domains and Criticality at 15–20 min.
  • Figure 7. Dynamic motion of the characteristic HRG domains in DEAB of the expression change. The coordinated expression dynamics around an equilibrated high-expression state exhibit the pendulum oscillation of CES (autonomous bistable switch) between different time periods (10–15 min, 15 min–20 min, and 20–30 min): A) in the static domain (9059 mRNAs) LES1 shows ON-OFF-EQ oscillation around HES1(EQ) through a

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Tsuchiya, M., Hashimoto, M., Takenaka, Y., Motoike, I. N., & Yoshikawa, K. (2014). Global genetic response in a cancer cell: Self-organized coherent expression dynamics. PLoS ONE, 9(5). https://doi.org/10.1371/journal.pone.0097411

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