(568o) Matrix and Optimization Approach to Kinetic Modeling of Lipid Pathways

There is increasing recognition of the role of lipids in signaling and disease pathways. The LIPID MAPS consortium (www.lipidmaps.org) has developed methods to quantitatively measure the composition of lipids in RAW 264.7 macrophage cells. Time-course data in response to treatment with KDO2 lipid A (a lipopolysaccharide analogue) has been collected for several lipids. Towards systems modeling and analysis, we have developed a framework for kinetic modeling of various lipid pathways. First we generate the reaction network using information from KEGG pathways and literature. Then we develop the mathematical model and estimate the rate parameters using experimental data through a two-step approach.

The system is modeled as a set of ordinary differential equations. The flux expressions are based on law of mass action kinetics. Thus, the flux expressions are linear in rate parameters and nonlinear in metabolite concentrations. In order to use linear algebra-based methods for estimating the rate constants, the pathway map is simplified to retain only the measured metabolites and discretization is used to convert the differential relationships into algebraic relationships. In the first step, the matrix-approach uses Matlab's optimization functions lsqlin (constrained least squares-based optimization). These initial estimates serve as the starting point for the second step in which they are further refined using a general constrained nonlinear optimization (Matlab function fmincon). This makes the overall process computationally efficient. Further, in the second step, numerical integration is used to compute the time-courses to eliminate discretization errors [1].

We have applied this approach to three lipid pathways: (1) eicosanoid pathways involving arachidonic acid metabolism, (2) sphingolipid pathway involving the metabolism of ceramides, and (3) sterol pathway involving cholesterol and its derivatives. In each case, the resulting models fitted the experimental data well and demonstrated that the integrated metabolic and signaling networks and the experimental data are consistent with each other. Further, the estimated activities for main enzymes were similar to their literature values. These quantitative models can be used for making predictions and designing further experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.

References

1. Gupta, S., M. R. Maurya, D. L. Stephens, E. A. Dennis, and S. Subramaniam. 2009. An integrated model of eicosanoid metabolism and signaling based on lipidomics flux analysis. Biophys J. 96:4542-51.