Dynamical analysis of cellular ageing by modeling of gene regulatory network based attractor landscape

<div><p>Ageing is a natural phenomenon that is inherently complex and remains a mystery. Conceptual model of cellular ageing landscape was proposed for computational studies of ageing. However, there is a lack of quantitative model of cellular ageing landscape. This study aims to investigate the mechanism of cellular ageing in a theoretical model using the framework of Waddington’s epigenetic landscape. We construct an ageing gene regulatory network (GRN) consisting of the core cell cycle regulatory genes (including p53). A model parameter (activation rate) is used as a measure of the accumulation of DNA damage. Using the bifurcation diagrams to estimate the parameter values that lead to multi-stability, we obtained a conceptual model for capturing three distinct stable steady states (or attractors) corresponding to homeostasis, cell cycle arrest, and senescence or apoptosis. In addition, we applied a Monte Carlo computational method to quantify the potential landscape, which displays: I) one homeostasis attractor for low accumulation of DNA damage; II) two attractors for cell cycle arrest and senescence (or apoptosis) in response to high accumulation of DNA damage. Using the Waddington’s epigenetic landscape framework, the process of ageing can be characterized by state transitions from landscape I to II. By <i>in silico</i> perturbations, we identified the potential landscape of a perturbed network (inactivation of p53), and thereby demonstrated the emergence of a cancer attractor. The simulated dynamics of the perturbed network displays a landscape with four basins of attraction: homeostasis, cell cycle arrest, senescence (or apoptosis) and cancer. Our analysis also showed that for the same perturbed network with low DNA damage, the landscape displays only the homeostasis attractor. The mechanistic model offers theoretical insights that can facilitate discovery of potential strategies for network medicine of ageing-related diseases such as cancer.</p></div

Time-course simulation of p53.

The three vertical dashed lines mark two thresholds for the activation of p53 (a = 1.16 and a = 1.5) and a lower threshold to turn ‘OFF’ p53 (a = 0.7). The timing for the value of a changes is for illustration only (i.e. three different levels of p53 for three cell fates).</p

Emergence of cancer attractor.

<p>For the inactivation of p53 with the deletion of two interactions with p53 (the activation of p53 by ATM and by ARF respectively), the landscape displays an additional attractor with low p53 level and high ATM (<i>a</i> = 1.5, <i>b</i> = 0.05). This attractor represents cancer because low p53 level leads to p53 inactivation that enables cells to acquire the ability to evade cellular senescence or apoptosis.</p

p53 bifurcation diagram.

<p>Red curves represent stable steady states and the black curves represent unstable steady states. The bifurcation diagram shows a tri-stability with hysteresis behavior. The ‘Going up’ means to turn ‘ON’ p53 and the ‘Coming down’ means to turn ‘OFF’ p53.</p

The ageing network model.

<p>The core GRN for ageing (arrows represent activations and bar arrows represent inhibitions).</p

No cancer attractor for low accumulation of DNA damage.

<p>In response to the inactivation of p53 with the deletion of two interactions to p53 (the activation of p53 by ATM and by ARF respectively), the landscape displays only one attractor for homeostasis and no cancer attractor for <i>a</i> = 0.5 and <i>b</i> = 0.05, which might correspond to young cells with low accumulation of DNA damage.</p

The carboxyl terminus of Yorkie is dispensable for its ability to stimulate tissue growth in <i>D. melanogaster</i>.

<p>(a–c) Dorsal views of fly heads expressing the indicated transgenes with the eye-specific <i>GMR-Gal4</i> driver. (d–f) Wings of flies expressing the indicated transgenes using the <i>71B-Gal4</i> driver. (g) Quantification of wing sizes of genotypes displayed in (d–f). Data is presented as mean +/− SD, n = 20 for each genotype, *** indicates p<0.0001. (h and i) Expression of <i>Yki</i> (h) and <i>Yki-ΔC</i> (i) in the posterior compartment of the developing wing (marked by GFP, green) with the <i>en-Gal4</i> driver resulted in upregulation of <i>ex-lacZ</i> (grayscale in single channel, red in overlay). (j–l) <i>yki^B5</i> mutant clones alone or co-expressing a <i>yki</i> transgene in wing discs, marked by GFP (green). Nuclei of cells are marked with DAPI (blue). (j) <i>yki^B5</i> mutant clones. (k) <i>yki^B5</i> mutant clones co-expressing <i>Yki</i>. (l) <i>yki^B5</i> mutant clones co-expressing <i>YkiΔC</i>.</p

Top view of landscape II in Fig 6(B).

<p>There is a line connecting the two attractors. The line is formed by two unstable manifolds representing a kinetic path between the cell cycle arrest and senescence (or apoptosis) basins of attraction.</p

Bistable activation of E2F.

<p>Bifurcation diagram of E2F (y-axis) with respect to growth signals (x-axis).</p

Potential landscapes for cell fate attractors (measured by p53 and ATM).

<p>(A) Landscape I: For low activation rate (<i>a</i> = 0.5, <i>b</i> = 0.05), the landscape displays one attractor (blue color) with low p53 protein corresponding to homeostasis. (B) Landscape II: For high activation rate (<i>a</i> = 1.5, <i>b</i> = 0.05), the landscape displays two attractors, one for cell cycle arrest and the other with high level of p53 protein corresponding to senescence or apoptosis. The senescence (or apoptosis) attractor is a dominant attractor of landscape II and thus a potential biomarker of ageing.</p