Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

Area of Science:

• Computational Chemistry
• Chemical Kinetics
• Mathematical Modeling

Background:

• Sensitivity analysis is crucial for understanding complex reaction kinetics models.
• Traditional methods for ordinary differential equations (ODEs) can be computationally intensive, especially for nonlinear systems.
• Existing techniques may not fully capture nonlinear dynamical effects.

Purpose of the Study:

• To present a unified approach for both linear and nonlinear sensitivity analysis of reaction kinetics models.
• To reformulate ordinary differential equation (ODE) models as a density transport problem solvable by a Fokker-Planck equation.
• To extend the TRAIL algorithm for efficient solution of the resulting partial differential equation.

Main Methods:

• Reformulation of ODEs into a Fokker-Planck equation.
• Extension of the TRAIL algorithm for solving multidimensional partial differential equations.
• Comparison with established Monte Carlo techniques.
• Application to an enzyme-substrate model for sensitivity analysis.

Main Results:

• The extended TRAIL approach provides a unified framework for sensitivity analysis.
• The method is fully adaptive and capable of studying nonlinear dynamical effects.
• Demonstrated effectiveness on an enzyme-substrate model for sensitivity analysis concerning initial concentrations and parameters.

Conclusions:

• The proposed unified approach offers an efficient and adaptive method for sensitivity analysis in reaction kinetics.
• The reformulation and extended TRAIL algorithm effectively handle nonlinear dynamics.
• This method enhances the understanding of parameter and initial condition influences in biochemical models.