Modeling metabolism has been generally based on the numerous cellular reactions to be in steady state with respect to the external fluxes on the cell boundary. The essence of this “steady state” approach is the identification of all the reaction rates (fluxes), both external and internal to the cell, that together constitute metabolism. This quest reduces to elucidating the null space of the metabolic stoichiometric matrix, which has many more reactions (columns) than species (rows), yielding a highly underdetermined system of homogeneous algebraic equations.

Flux balance approaches have dealt with this circumstance by seeking to identify fluxes that are experimentally accessible, a strategy that continues to grow in scope (such as by the systematic use of isotopic tracers), as a means to enable estimation of other fluxes that are not accessible. Resolution of the indeterminacy, however, has depended on fortification with additional conceptual tools such as maximizing the biomass yield. Regulatory processes, which are a vital component of metabolism in that they determine what reactions are in fact active in metabolism, are not an explicit aspect of flux balance approaches. They are, however, implicitly contained in the measured fluxes, as well as in the optimality criterion used to compute fluxes, as in cybernetic modeling, although perhaps in a much less sophisticated way.

We contend that a rational framework for modeling metabolism must accommodate the prediction of all fluxes and in particular the external fluxes which must reflect the consequences of metabolic regulation. Such a framework is therefore forced to address regulatory processes in a comprehensive way. In this regard, the cybernetic modeling concept developed by our research group, that has been evolving since the early eighties, has progressively accommodated features of regulation that have not been within the scope of other modeling approaches. While the cybernetic models have fared well with coarse-grained views of microbial processes, the extension to large metabolic pathways has had many complex features in need of resolution. Of these, in particular, the stable control of large networks of reactions in the course of metabolism has challenged large dynamic models. A second basic issue has been a view of the metabolic network which would allow the formulation of global and local cybernetic variables within a suitably designed optimal framework. A resolution of both the foregoing issues has become available from the recent dissertation of Young (2005) that has paved the way for a rational framework of metabolic systems.

In this paper, we outline the various advances that we have made in enabling the rationality of the foregoing framework. First and foremost, the cybernetic laws have been established on the basis of optimal control theory, which has rendered an anticipatory quality to the cybernetic variables that allows robust dynamic behavior of the models. Second, the development of the concept of elementary modes into which a metabolic network can be decomposed provides a rational view of how substances in the abiotic environment are converted into products as a result of metabolism. Thus by viewing global cybernetic variables as those that govern the optimal distribution of cellular resources to direct uptake of nutrients so that some global perspective such as maximizing biomass productivity (rather than yield) is achieved, a strategy has been made possible. Furthermore, this optimal strategy is reinforced in each of the elementary modes by a resource-distribution strategy that maximizes the flux throughput of each mode. A complete dynamic model is thus the outcome of such a development.

Finally, we report also a hybrid model development that represents a dynamic extension of the flux balance approach, in which the external fluxes are predicted with the global cybernetic variables above for elementary modes, while using the linear programming approach to predict the internal fluxes.

This paper will outline the various ingredients of both the cybernetic models of Young (2005) and the hybrid models that are currently under investigation at Purdue University along with their major predictions.

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