Draft:ATM-Wip1 (Cancer) Oscillator Model

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Instructions · What links here · ATM-Wip1 (Cancer) Oscillator Model (talk: + · bio) · (log) · Copyvios report · reFill · Citation Bot · (Search: Google, Bing, Wikipedia) · Submitted 2 months ago by Gokhan.Demirkiran (talk: D · +) · Last edited 2 months ago by Gokhan.Demirkiran

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

$dx/dt=-x(rx^{2}-r(a+b)x+ab+cy-rd)/\tau _{1}$

$dy/dt=(z+mx-ny)/\tau _{2}$

where

$x$ represents ATM protein concentration levels in arbitrary units.
$y$ 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 $a,b,c,d,n,z,\tau _{1},\tau _{2}$ and they take only positive values. The control parameters are $r$ and $m$ . $r$ represents the damage severity and is restricted to $0<r<1$ , with 0 representing no damage and 1 representing the most severe situation. $m$ represents inversely the duration of the DNA repair and is controlled by proapoptotic genes via mechanisms similar to the "death by integration^[3]". Normally, $m$ stays at a high value indicated as $m_{0}$ 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.

[Demirkıran1-1] 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.

[2] Krishna, S., Semsey, S., & Jensen, M. H. (2009). Frustrated bistability as a means to engineer oscillations in biological systems. Physical biology, 6(3), 036009.

[3] 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.

[4] 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.

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