Cellular Potts Model Rho GTPase Synchrony (Forced Oscillations)

Parameter beta is randomly chosen for each cell, resulting in a heterogeneous tissue. Therefore, some cells evolve to steady state while others follow limit cycle dynamics. As a consequence of mechanical coupling between cells due to adhesion and volume exclusion, cells in steady state are forced to oscillate.

Simulation Parameters
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Number of Cells: 373
Monte Carlo Steps: 2000
Temperature: 15

Medium-Medium Adhesion Energy: 0.0
Cell-Cell Adhesion Energy: 60.0
Cell-Medium Adhesion Energy: 80.0

Volume (Area in 2D) Constraint Parameter, lambda: 1.0
Surface (Perimeter in 2D) Constraint Parameter, lambda: 0.0

SBML Model
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Rho GTPase Concentration: G
Cell Area: A
Cell Target Area: AT
Time Scale: tau
Time Scale Separation Parameter: eps

dG/dt = tau * ( ( 0.1 + beta * A^10/(AT^10 + A^10) + 1.5 * G^4/(1+G^4) ) * (2 - G) - G )

dAT/dt = -1 * tau * eps * ( AT - 600 * (1 - 0.75 * G^4/(0.3^4 + G^4)) )

Model Parameter Values
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tau: 2000
eps: 0.1
beta: random ~ Unif(0.05,0.3)
ODE Solver step-size: 0.001
Initial GTPase Concentration, G(0): random ~ Unif(0,1)
Initial Cell Target Area, AT(0) = Initial Cell Area, A(0)