Dynamic sensitivity analysis of biological systems

Area of Science:

• Systems Biology
• Computational Biology
• Chemical Engineering

Background:

• Systems biology relies on mathematical models, typically nonlinear ordinary differential equations (ODEs), to understand and predict biological system behavior.
• Efficient and accurate simulation of dynamic behavior and parameter sensitivities in ODE systems is crucial for practical applications.
• Time-dependent inputs in models, common in systems like fed-batch fermentation, pose challenges for classical dynamic sensitivity analysis, particularly for dynamic log gains.

Purpose of the Study:

• To develop and present an algorithm for simultaneously computing solutions and dynamic parameter sensitivities of autonomous ODE systems.
• To address the limitations of classical methods by enabling dynamic sensitivity analysis for models with time-dependent admissible inputs.
• To evaluate the algorithm's accuracy and applicability on stiff ODE systems and realistic biological models.

Main Methods:

• An algorithm with adaptive step-size control was developed for simultaneous computation of ODE solutions and dynamic sensitivities.
• This algorithm employs a decoupled direct method approach for calculating dynamic sensitivities.
• The method was implemented and tested on chemical reaction systems (ethane pyrolysis, formaldehyde oxidation) and an ethanol fed-batch fermentation system.

Main Results:

• The algorithm accurately computes dynamic parameter sensitivities for stiff ODE systems, even when sensitivity equations are more numerically challenging than model equations.
• Demonstrated moderate accuracy for dynamic sensitivities and time profiles using step sizes determined by model equations.
• Successfully applied to an ethanol fed-batch fermentation system with time-varying feed rates, showcasing its utility for realistic models.

Conclusions:

• The developed algorithm offers an accurate and efficient method for computing dynamic parameter sensitivities in stiff ODE problems.
• It extends the applicability of dynamic sensitivity analysis to models incorporating time-dependent admissible inputs, a significant advancement.
• The method provides a valuable tool for systems biology and related fields requiring robust dynamic modeling and sensitivity analysis.