Stochastic Dynamical Systems: Spectral Methods for the Analysis of Dynamics and Predictability

Bert Debusschere, Khachik Sargsyan, Habib Najm

Understanding systems such as gene transcription, cell signaling, and surface catalytic reactions is critical in the areas of bioenergy, biomedicine, and fuel cells. Computational models can be powerful tools to gain deeper insight into these systems and to enable an engineering approach to improved performance. Due to inherent variability, these systems are best described by stochastic reaction networks. While many methods are available to simulate such networks, there is a lack of tools for analyzing their dynamical behavior and uncertainty. This project develops methods to analyze the dynamics and predictability of stochastic reaction networks. These methods will enable a detailed understanding of these systems in terms of their functionality, robustness under experimental data uncertainty and inherent variability, and their core components that may be targets for engineered performance improvement.

Project Goals/Objectives

• Stochastic dynamics play a role in numerous areas such as biochemical and surface catalytic reactions
• Develop methods for analyzing dynamics and predictability of stochastic reaction networks
  • detailed understanding of functionality
  • robustness under experimental data uncertainty and inherent variability.

Approach

• Rely on spectral expansions to represent and probe stochastic processes
• Multiwavelet expansions to represent effect of parametric uncertainties on system observables
• Reduced order modeling and dynamical analysis based on Karhunen-Loève decomposition

Relevance

• Gene transcriptional control of cellular behavior
  • Microbial processes
  • Immune system signaling
  • Metabolic pathways
• Surface catalytic reactions

Accomplishments

• Performed sensitivity analysis in intracellular viral infection model system
• Used reduced order model to investigate effect of system volume on dynamics in Schlögl model

Spectral Methods for Parametric Sensitivity in Stochastic Dynamical Systems, Biophysical Journal, Vol 92, Jan 2007

Analysis of Dynamics and Predictability in Stochastic Reaction Networks,
Office of Science, ASCR, FY 2007 Accomplishment


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