A structural property for reduction of biochemical networks

Abstract

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

The hidden simplicity of metabolic networks is revealed by multireaction dependencies

“…Our first contribution consists of showing that concordant complexes can be efficiently identified in large-scale biochemical networks by linear fractional programming (see Methods). We note that complexes whose activity is zero in every steady state in S are referred to as balanced and have been used in reduction of metabolic networks ( 18 ). For instance, complex A + E is balanced because species E occurs in only this complex; as a result, the complex 2A is also balanced.…”

“…Next, we show that the concept of concordance module has important implications with respect to decomposability of metabolic networks. First, we note that a balanced complex that has out-degree of one can be removed without affecting the steady-state supported by the rewired network ( 18 ), because this amounts to substitution of the flux of the outgoing reaction by the sum of fluxes of the incoming reactions. On the basis of the number of reactions incoming and outgoing to a concordance module in the network obtained by removal of such balanced complexes, we define four classes of concordance modules: (i) source modules that have no input from any complex outside of the concordant module but have output to other concordant modules, (ii) sink modules that have no output to any complex outside of the concordant module but have some inputs from other concordant modules, (iii) intermediate modules that have input and output from complexes outside of the concordant module, and (iv) closed modules that have no input or output from any complex outside of the concordant module.…”

“…In the next step, the blocked reactions, i.e., reactions with absolute flux values below 10 −6 mmol/gDW per hour in any feasible steady state supported by network [as determined by Flux Variability Analysis ( 36 )], were removed from the original models. Note that the threshold to consider a reaction blocked can influence the number of identified balanced complexes [compare results of ( 18 ) where balanced complexes are identified using threshold 10 −9 ]. Optimum specific growth rate was determined per flux balance analysis ( 37 ) with the assumed reaction reversibility.…”

The unraveling of balanced complexes in metabolic networks

“…However, balanced complexes are not only present in complex balanced networks. For instance, under the steady-state assumption, a complex including a species that does not occur in any other complex of a given network is balanced 12 , 13 . For instance, the network on Fig.…”

A universal dynamical metabolic model representing mixotrophic growth of Chlorella sp. on wastes

“…Our increasing understanding of genomic information led to the construction of more complex genome scale networks. This has motivated the field of bioinformatics to research new ways to reduce and analyze metabolic models, consequently new methods are still being developed (Küken et al, 2021, Hameri et al, 2021. The choice of the reduction method will depend on the intentions of the modeler, the wished degree of flexibility of the phenotype prediction and the final size of the model.…”