Modelling and analysis of the sugar cataract development process using stochastic hybrid systems

Area of Science:

• Biochemical Systems Analysis
• Computational Biology
• Systems Biology

Background:

• Modeling biochemical systems is crucial for understanding complex biological processes.
• Sugar cataract development (SCD) involves intricate, coupled chemical reactions that are challenging to study experimentally.
• Existing models often lack the ability to incorporate drug treatment effects on system dynamics.

Purpose of the Study:

• To present a novel stochastic hybrid system (SHS) framework for modeling biochemical systems.
• To demonstrate the framework's application to sugar cataract development (SCD).
• To introduce a probabilistic verification method for assessing SCD formation probability under varying chemical concentrations.

Main Methods:

• Development of a stochastic hybrid system (SHS) framework.
• Simulation of SCD models using two distinct algorithms for validation.
• Application of safety and reachability analysis for probabilistic verification.
• Implementation of a parallel dynamic programming approach to address the curse of dimensionality.

Main Results:

• The SHS framework successfully models biochemical systems, including SCD.
• The framework allows for the simulation of drug treatment effects on system dynamics.
• A probabilistic verification method was developed and applied to SCD, demonstrating feasibility for realistic systems.
• Parallel dynamic programming implementation showed promise for handling large-scale biochemical models.

Conclusions:

• The proposed SHS framework is a viable approach for modeling and analyzing complex biochemical systems like SCD.
• The framework facilitates the study of drug interventions and probabilistic outcomes in biological systems.
• While scalability remains a challenge, the methods are applicable to realistic biochemical system analysis.