(490f) Abstraction of Kinetic Models (AKM) Using Function and Parameter Co-Estimation Exploration

Kinetic modeling attempts to describe the time-dependent behavior of every enzyme-catalyzed reaction in the network. Systems of ordinary differential equations express each reaction rate as a function of metabolite concentrations and rate constant parameters. The mechanistic knowledge of enzyme kinetics however is not always available.  Furthermore, estimating a consistent set of rate parameters from time-series data requires a large experimental effort for even a moderately-sized network. This work develops approximate kinetic expressions for a module (connected groups of reactions) instead of developing kinetic expressions for eachreaction within the module.  The approximate kinetic expressions are thus derived only for the exchange metabolites, and not for the internal (non-exchange) metabolites or reactions.  The two relevant questions are: (1) Does this approach yield a predictive module model? (2) Which metabolite concentrations (and measurements) can be eliminated when constructing such a model? 

To explore the first question, we develop a systematic method for creating and evaluating module expressions, we refer to as ABK (Abstraction of Kinetic Models).  We assume expressions will have the format of convenience kinetics [1], where each metabolite can influence another, by acting as either a reactant, product, activator, or inhibitor.  Initially, we assume all metabolites are of interest and calculate kinetic expressions for each, tuning the expression parameters using a genetic algorithm.   Next, we eliminate a metabolite from consideration, and recalculate all kinetic expressions, ranking resulting models based on smallest mean square error between measured and computed data points for exchange metabolites.  Exhaustive elimination of all metabolite combinations is not computationally feasible. We thus use selective elimination, successively reducing the number of internal metabolites used in the expressions, creating new solutions.   

The method was applied to two case studies.  The first case study consists of reactions catalyzed by three glycolytic enzymes in E. coli (Glk, Pgi, and PfkA) for which detailed kinetic parameters have been determined.  The second case study consists of reactions carrying mass flow and regulated through complex mechanistic interactions.   The ABK algorithm generates a number of solutions, reported as a Pareto front, that trade prediction accuracy for complexity (number of metabolites used in the expressions).   The benefits of reduced kinetic models are twofold:  (1) reducing the number of measurements required for fitting the model, and (2) the resulting number of mathematical expressions is smaller compared to the number of equations needed to describe every reaction of the original network with equal detail.    The presented method and the case studies show that expression simplification is possible while maintaining an overall predictive model.  Our reduced models are suitable for building fast and predictive genome-scale kinetic models.

 [1] W. Liebermeister and E. Klipp.  (2006) Theor Biol Med Model 3: 41.