Info! This is a derivative of the model jones1
Info! This is a derivative of the model smallbone14

zatorskye

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000159). Biomodels notes: "The model reproduces the time profile of p53 and Mdm2 as depicted in Fig 6B of the plot for model 1. Results obtained on MathSBML." JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Oscillations and variability in the p53 system.

  • Naama Geva-Zatorsky
  • Nitzan Rosenfeld
  • Shalev Itzkovitz
  • Ron Milo
  • Alex Sigal
  • Erez Dekel
  • Talia Yarnitzky
  • Yuvalal Liron
  • Paz Polak
  • Galit Lahav
  • Uri Alon
Mol. Syst. Biol. 2006; 2 :
Abstract
Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1.0 item
3600.0 second
Id Name Spatial dimensions Size
compartment cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
x p53 0.0 compartment (cell)
y Mdm2 0.0 compartment (cell)
y0 precursor Mdm2 0.0 compartment (cell)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
R1 p53 production ∅ > x

compartment * beta_x * psi
R2 Mdm2 independent p53 degradation x > ∅

compartment * alpha_x * x
R3 Mdm2 dependent p53 degradation x > ∅

compartment * alpha_xy * y * x
R4 p53 dependent Mdm2 precursor production ∅ > y0

compartment * beta_y * x * psi
R5 Mdm2 synthesis from precursor y0 > y

compartment * alpha_0 * y0
R6 Mdm2 degradation y = ∅

compartment * alpha_y * y

Global parameters

Id Value
alpha_0 0.1
alpha_x 0.0
alpha_xy 3.2
alpha_y 0.1
beta_x 0.3
beta_y 0.4
psi 1.0

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments