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

Abstract

This study proposes a two-dimensional (2D) oscillator model of p53 network, which is derived via reducing the multidimensional two-phase dynamics model into a model of ataxia telangiectasia mutated (ATM) and Wip1 variables, and studies the impact of p53-regulators on cell fate decision. First, the authors identify a 6D core oscillator module, then reduce this module into a 2D oscillator model while preserving the qualitative behaviours. The introduced 2D model is shown to be an excitable relaxation oscillator. This oscillator provides a mechanism that leads diverse modes underpinning cell fate, each corresponding to a cell state. To investigate the effects of p53 inhibitors and the intrinsic time delay of Wip1 on the characteristics of oscillations, they introduce also a delay differential equation version of the 2D oscillator. They observe that the suppression of p53 inhibitors decreases the amplitudes of p53 oscillation, though the suppression increases the sustained level of p53. They identify Wip1 and P53DINP1 as possible targets for cancer therapies considering their impact on the oscillator, supported by biological findings. They model some mutations as critical changes of the phase space characteristics. Possible cancer therapeutic strategies are then proposed for preventing these mutations' effects using the phase space approach.

A Canonical 3-D P53 Network Model that Determines Cell Fate by Counting Pulses

“…In this compact motif, oscillations occur due to the interaction between bistable switch of ATM and negative feedback of Wip1 upon the stimulus [19]. The high level is observed when P53DINP1 level accumulates above a certain threshold value which distracts the feedback loop of Wip1.…”

“…These complexes act as external stimuli that excite the system such that [ATM*] (active ATM level) and [Wip1] oscillate. As [ATM*] oscillates, it promotes the accumulation of P53DINP1 protein, which is revealed as an accumulating component in two-phase dynamics model in another paper [19]. If DSBCs disappear, meaning that DSBs are repaired, then the ATM level goes down.…”

“…That is, other variables in the motif control the ATM dynamics. More specifically, i) Wip1 feedback loop allows for oscillations by frustrating bistable ATM [19], ii) P53DINP1 makes ATM switch from oscillations to high level by distracting Wip1 feedback loop (Figure 8), and iii) the extinction of stimulus make ATM switch to low level.…”

“…Recently, Demirkıran et al [18] successfully reduced the two-phase dynamics model by into a 2-dimensional model with rational terms, which is capable of showing these three distinct modes when the critical parameters of the model are changed externally [17,18]. The reduced 2-D model is shown to be a relaxation oscillator model which enhances the understanding of oscillations as well making corrections on the interpretation of the original 17-D model [19].…”

“…Although the reduced 2-D model with rational terms has provided a greater depth of understanding, the terms of the model are too complex [19]. Thus, Demirkıran et al [18] proposed a simple canonical 2-D model of polynomial type, whose parameters are interpreted from p53 network interactions [20].…”