A specialized ODE integrator for the efficient computation of parameter sensitivities

Area of Science:

• Systems Biology
• Computational Biology
• Mathematical Modeling

Background:

• Dynamic mathematical models, often systems of ordinary differential equations (ODEs), are crucial in systems biology.
• Efficient and accurate numerical integration of ODEs is vital for complex models, particularly for parameter sensitivity analysis in systems identification.
• Existing ODE solvers often lack automatic computation of parameter sensitivities.

Purpose of the Study:

• To develop a novel numerical integration algorithm for systems biology models.
• To improve the speed and accuracy of solving ODEs and computing parameter sensitivities.
• To enhance the efficiency of parameter estimation and optimization in computational biology.

Main Methods:

• A novel integration algorithm based on second derivatives and improved error estimates.
• Implementation within a framework that automatically generates integrator input from SBML descriptions.
• Comparison with established integrators for solving system equations and evaluating parameter sensitivities.

Main Results:

• The new algorithm allows for larger time steps compared to other methods.
• It competes effectively with established integrators in solving system equations.
• The method significantly outperforms existing integrators when evaluating local parameter sensitivities.

Conclusions:

• "Cheap" parameter sensitivities will enable advances in computationally expensive parameter estimation and optimization problems.
• Exploiting domain-specific characteristics can lead to substantial improvements in computational performance.
• Elements of the developed error estimation method may have broader applicability in general numerical algorithms.