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Abstract:
A nonlinear model consisting of a system of coupled ordinary differential equations (ODE), describing a biological process linkedwith cancer development, is linearized using Taylor series and tested against different magnitudes of input perturbations, in orderto investigate the extent to which the linearization is accurate. )e canonical wingless/integrated (WNT) signaling pathway isconsidered. )e linearization procedure is described, and special considerations for linearization validity are analyzed. )eanalytical properties of nonlinear and linearized systems are studied, including aspects such as existence of steady state and initialvalue sensitivity. Linearization is a useful tool for speeding up drug response computations or for providing analytical answers toproblems such as required drug concentrations. A Monte Carlo-based error testing workflow is employed to study the errorsintroduced by the linearization for different input conditions and parameter vectors. )e deviations between the nonlinear and thelinearized system were found to increase in a polynomial fashion w.r.t. the magnitude of tested perturbations. )e linearizedsystem closely followed the original one for perturbations of magnitude within 10% of the base input vector which yielded thestate-space fixed point used for the linearization
