The effects of model complexity and size on metabolic flux distribution and control: case study in Escherichia coli.

Background: Significant efforts have been made in building large-scale kinetic models of cellular metabolism in the past two decades. However, most kinetic models published to date, remain focused around central carbon pathways or are built around ad hoc reduced models without clear justification on their derivation and usage. Systematic algorithms exist for reducing genome-scale metabolic reconstructions to build thermodynamically feasible and consistently reduced stoichiometric models. However, it is important to study how network complexity affects conclusions derived from large-scale kinetic models built around consistently reduced models before we can apply them to study biological systems.

Results: We reduced the iJO1366 Escherichia Coli genome-scale metabolic reconstruction systematically to build three stoichiometric models of different size. Since the reduced models are expansions around the core subsystems for which the reduction was performed, the models are nested. We present a method for scaling up the flux profile and the concentration vector reference steady-states from the smallest model to the larger ones, whilst preserving maximum equivalency. Populations of kinetic models, preserving similarity in kinetic parameters, were built around the reference steady-states and their metabolic sensitivity coefficients (MSCs) were computed. The MSCs were sensitive to the model complexity. We proposed a metric for measuring the sensitivity of MSCs to these structural changes.

Conclusions: We proposed for the first time a workflow for scaling up the size of kinetic models while preserving equivalency between the kinetic models. Using this workflow, we demonstrate that model complexity in terms of networks size has significant impact on sensitivity characteristics of kinetic models. Therefore, it is essential to account for the effects of network complexity when constructing kinetic models. The presented metric for measuring MSC sensitivity to structural changes can guide modelers and experimentalists in improving model quality and guide synthetic biology and metabolic engineering. Our proposed workflow enables the testing of the suitability of a kinetic model for answering certain study-specific questions. We argue that the model-based metabolic design targets that are common across models of different size are of higher confidence, while those that are different could be the objective of investigations for model improvement.