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    Area of Science:

    • Computational Biology
    • Systems Biology
    • Mathematical Modeling

    Background:

    • Identifying unknown parameters in dynamical biological systems is crucial for understanding complex biological processes.
    • Ordinary differential equations (ODEs) and delay differential equations (DDEs) are commonly used to model these systems.
    • Experimental data often contains noise, posing challenges for accurate parameter estimation.

    Purpose of the Study:

    • To develop and evaluate a robust two-stage approach for parameter identification in dynamical biological systems.
    • To formulate the parameter estimation problem as an optimization problem with algebraic constraints.
    • To introduce a new differential evolution (DE) algorithm for efficiently finding feasible solutions.

    Main Methods:

    • A two-stage approach combining spline theory and Nonlinear Programming (NLP) to transform parameter estimation into an optimization problem.
    • Development and application of a novel differential evolution (DE) algorithm to solve the formulated optimization problem.
    • Validation using benchmark models with known structures and parameters, and a biological system with an unknown structure.

    Main Results:

    • Successful identification of parameters for all tested systems, including those with noisy data and unknown structures.
    • The proposed method demonstrated capability for fast estimation with good precision.
    • Achieved identification using a reasonable amount of experimental data within acceptable computation time.

    Conclusions:

    • The presented two-stage approach, integrating spline theory, NLP, and a novel DE algorithm, is effective for parameter identification in dynamical biological systems.
    • The method is robust to noisy data and capable of handling systems with unknown structures.
    • This approach offers a computationally efficient and precise solution for a common challenge in systems biology research.