Revealing determinants of two-phase dynamics of P53 network under gamma irradiation based on a reduced 2D relaxation oscillator model

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root-locus method

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non-linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root-locus-based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner's genetic toggle switch and p53 gene network possessing two-phase (mono-stable/oscillation) dynamics.

Two-dimensional polynomial type canonical relaxation oscillator model for p53 dynamics

p53 network, which is responsible for DNA damage response of cells, exhibits three distinct qualitative behaviours; low state, oscillation and high state, which are associated with normal cell cycle progression, cell cycle arrest and apoptosis, respectively. The experimental studies demonstrate that these dynamics of p53 are due to the ATM and Wip1 interaction. This paper proposes a simple two-dimensional canonical relaxation oscillator model based on the identified topological structure of ATM and Wip1 interaction underlying these qualitative behaviours of p53 network. The model includes only polynomial terms that have the interpretability of known ATM and Wip1 interaction. The introduced model is useful for understanding relaxation oscillations in gene regulatory networks. Through mathematical analysis, we investigate the roles of ATM and Wip1 in forming of these three essential behaviours, and show that ATM and Wip1 constitute the core mechanism of p53 dynamics. In agreement with biological findings, we show that Wip1 degradation term is a highly sensitive parameter, possibly related to mutations. By perturbing the corresponding parameters, our model characterizes some mutations such as ATM deficiency and Wip1 overexpression. Finally, we provide intervention strategies considering our observation that Wip1 seems to be an important target to conduct therapies for these mutations.