Draft:ATM-Wip1 (Cancer) Oscillator Model
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Introduction[edit]
The ATM-(p53)-Wip1 oscillator is a parametric relaxation type of oscillator model with polynomial and biologically-interpretable terms introduced to model the topological structure constructed by bistable dynamics of ATM protein and a long negative feedback loop mediated by Wip1 (the product of PPM1D gene) protein[1]. The ATM-Wip1 topological structure resembles the frustrated bistable unit that is known to produce oscillations as well as other modes of dynamics[2].
Model Equations[edit]
where
- represents ATM protein concentration levels in arbitrary units.
- represents Wip1 protein concentration levels in arbitrary units.
p53 protein (concentration) levels are not introduced as a dynamical variable; instead, it is assumed to follow ATM dynamics proportionally and algebraically under the quasy-steady state assumption for p53-Mdm2 interaction.
The constant parameters of the model are and they take only positive values. The control parameters are and . represents the damage severity and is restricted to , with 0 representing no damage and 1 representing the most severe situation. represents inversely the duration of the DNA repair and is controlled by proapoptotic genes via mechanisms similar to the "death by integration[3]". Normally, stays at a high value indicated as and decreased towards 0 as the repair continues [4].
Repertoire of Dynamical Behaviors[edit]
References[edit]
- ^ Demirkıran, Gökhan, Güleser Kalaycı Demir, and Cüneyt Güzeliş. "Two‐dimensional polynomial type canonical relaxation oscillator model for p53 dynamics." IET Systems Biology 12, no. 4 (2018): 138-147.
- ^ Krishna, S., Semsey, S., & Jensen, M. H. (2009). Frustrated bistability as a means to engineer oscillations in biological systems. Physical biology, 6(3), 036009.
- ^ Li, Zhiyuan, Ming Ni, Jikun Li, Yuping Zhang, Qi Ouyang, and Chao Tang. "Decision making of the p53 network: Death by integration." Journal of theoretical biology 271, no. 1 (2011): 205-211.
- ^ DEMİRKIRAN, Gökhan, Güleser KALAYCI DEMİR, and Cüneyt Güzeliş. "A canonical 3-D P53 network model that determines cell fate by counting pulses." Electrica 18, no. 2 (2018): 284-291.