Effect of Linearization in a WNT Signaling Model

Area of Science:

• Systems biology
• Computational biology
• Mathematical oncology

Background:

• Nonlinear ordinary differential equations (ODEs) model complex biological processes, including cancer development.
• Linearization simplifies ODE models but its accuracy depends on perturbation magnitude.
• The wingless/integrated (WNT) signaling pathway is a key pathway in cancer development.

Purpose of the Study:

• To investigate the accuracy of linearizing a nonlinear ODE model of a cancer-related biological process (WNT pathway).
• To analyze the impact of input perturbation magnitude on linearization accuracy.
• To assess the utility of linearization for computational efficiency and analytical problem-solving.

Main Methods:

• A nonlinear ODE system describing the WNT pathway was linearized using Taylor series expansion.
• The linearized model was tested against various input perturbation magnitudes.
• A Monte Carlo-based error testing workflow quantified deviations between nonlinear and linearized systems.

Main Results:

• Linearization accuracy was high for perturbations within 10% of the base input vector.
• Deviations between nonlinear and linearized systems increased polynomially with perturbation magnitude.
• Analytical properties like steady-state existence and initial value sensitivity were compared.

Conclusions:

• Linearization is a valid approximation for WNT pathway models under small perturbations.
• The method can accelerate drug response computations and aid in determining required drug concentrations.
• Understanding linearization limits is crucial for reliable computational and analytical biological modeling.