(458b) A System Identification Based Approach for Phenotype Phase Plane Analysis

Systems biology is a rapidly evolving discipline that seeks to determine how complex biological systems function by integrating experimentally derived information through mathematical modeling.  Genome-scale metabolic network models represent the link between the genotype and phenotype of the organism, where they are usually reconstructed based on the genome sequence annotation and relevant biochemical and physiological information. These models provide a holistic view of the organism’s metabolism, and constraint-based metabolic flux analysis methods have been used extensively to study genome-wide cellular metabolic networks. 

A prevalent method to dissect genome-scale metabolic models is phenotype phase plane (PhPP) analysis, which breaks down metabolic behavior in distinct phases through shadow prices analysis.  The shadow price is defined as the effect of the metabolite concentration on the objective function.  Two independent variables, typically the carbon and oxygen source, are varied, and the shadow price is calculated for each metabolite. Shadow price analysis has the capability to find if metabolites were limited or in excess, and if metabolite were expelled from the network.  However, due to the scale and complexity involved in genome-scale models, many times only knowing whether a metabolite is limited or excess and whether it is expelled from the network is not sufficient in understanding the network. It would be very helpful to figure out how different pathways interact with each other for a given phenotype, and how such interactions differ from different phenotypes.

To address this challenge, we have developed a system identification based framework to extract qualitative biological information (such as how different pathways interact with each other) from quantitative numerical results by performing carefully designed in silico experiments. The basic idea of the developed framework is to treat the genome-scale metabolic network model as a black-box model, and to use designed input sequences (such as a series of carbon substrate pick up rates that keep increasing or decreasing) to perturb the network; then to apply multivariate statistical analysis tools in order to extract information on how such perturbations propagate through the network. We have applied this framework to genome-scale model evaluation, as well guiding the development of an improved genome-scale model of Scheffersomyces stipitis. Our experience show that this framework can effectively extract valuable biological information embedded in the numerical in silico experiments.

In this work, we extended this work to PhPP analysis. Several in silico experiments have been designed to obtain the same findings provided by shadow price analysis. In addition, the system identification approach can further provide how different pathways are affected by perturbing the substrates that are in interest, and highlight the metabolic differences among different phenotypes. The same illustrative example provided in the original PhPP analysis paper (Edwards, Ramakrishna, Palsson, Biotechnology & Bioengineering, Vol 77(1), 27-36, 2002) and the genome-scale metabolic network model of E. coli were used to demonstrate the effectiveness of the proposed phenotype phase plane analysis. Our results show that using phenotype phase plane analysis and system identification method in combination provides a powerful tool for revealing the metabolic capability of a genome-scale metabolic network model.  The phenotype phase plane analysis provides a global view of each phenotype, while the system identification method extracts the key metabolic details by proper design of experiments.  In summary, integrating the PhPP analysis with the system identification approach allow improved systems level understanding, which provides the foundation for improved strain development.