Understanding and reducing complex systems pharmacology models based on a novel input-response index.

Area of Science:

• Systems Biology
• Pharmacology
• Biophysics

Background:

• Complex biological systems are increasingly modeled using large-scale mechanistic approaches.
• Understanding input-response relationships in these models is challenging due to intricate interactions and model size.
• Efficient methods are needed to quantify component importance and simplify model dynamics.

Purpose of the Study:

• To introduce a novel state- and time-dependent "input-response index" for quantifying the importance of model constituents.
• To demonstrate the utility of this index for reducing large-scale mechanistic models.
• To apply the method to the brown snake venom-fibrinogen network for biological insights.

Main Methods:

• The input-response index is based on time-bounded controllability and observability relative to a reference dynamics.
• A two-step model reduction procedure involves state elimination and subsequent lumping.
• The method was applied to a large-scale model of the brown snake venom-fibrinogen network.

Main Results:

• The input-response indices revealed the coordinated action of coagulation factors and identified less influential ones in the venom-Fg network.
• Model reduction of the venom-fibrinogen network decreased the number of state variables from 62 to 8, then to 5.
• The sequence of reduction steps impacts the final reduced model, with input-response indices guiding an informed sequence.

Conclusions:

• The input-response index is a powerful tool for analyzing complex biological dynamics.
• This novel measure enables highly efficient model order reduction for nonlinear systems.
• The approach provides valuable insights into biological networks and facilitates the development of simplified, yet accurate, models.