The stability and robustness of metabolic states: identifying stabilizing sites in metabolic networks

Abstract

The dynamic behavior of metabolic networks is governed by numerous regulatory mechanisms, such as reversible phosphorylation, binding of allosteric effectors or temporal gene expression, by which the activity of the participating enzymes can be adjusted to the functional requirements of the cell. For most of the cellular enzymes, such regulatory mechanisms are at best qualitatively known, whereas detailed enzyme-kinetic models are lacking. To explore the possible dynamic behavior of metabolic networks in cases of lacking or incomplete enzyme-kinetic information, we present a computational approach based on structural kinetic modeling. We derive statistical measures for the relative impact of enzyme-kinetic parameters on dynamic properties (such as local stability) and apply our approach to the metabolism of human erythrocytes. Our findings show that allosteric enzyme regulation significantly enhances the stability of the network and extends its potential dynamic behavior. Moreover, our approach allows to differentiate quantitatively between metabolic states related to senescence and metabolic collapse of the human erythrocyte. We think that the proposed method represents an important intermediate step on the long way from topological network analysis to detailed kinetic modeling of complex metabolic networks.

Theoretical Description of Metabolism Using Queueing Theory

“…Such approach in general does not introduce new biophysical processes, but is fully probabilistic in its origin and therefore should be described by the laws of probability. Its quantitative description may, in principle, be accomplished by any of the approaches currently developed in literature and cited in the introductory section, e.g., flux-based models (Grimbs et al 2007;Aldridge et al 2006;Stelling et al 2002) or Petri net analysis (Chaouiya 2007;Peleg et al 2002). However, the Pachinko approach introduces the incoming flow of metabolites in general case as a flow of discrete particles, which may create queues near the Pins and Holes and result in deviation from the common mass action law which is most often used in order to quantify the metabolic network by means of kinetic equations (see for example Wagner and Fell 2001;Aldridge et al 2006;Covert et al 2001).…”

“…Theoretical description of metabolism in complex multicellular system in terms of metabolites' distribution is extremely difficult task as it requires detailed knowledge of all metabolic pathways. Numerous approaches for analytical description of metabolism have so far been developed, all of them grounded on the use of concrete metabolic picture, e.g., the flux-based approaches (see Grimbs et al 2007; Aldridge et al 2006;Stelling et al 2002), metabolic network analysis (Jeong et al 2000;Lima-Mendez and Helden 2009), Petri net analysis (Chaouiya 2007;Peleg et al 2002), stochastic approach (De Jong 2002, entropy approach (see Veselkov et al 2010) and others.…”

Erratum to: A coupled thermodynamic and metabolic control analysis methodology and its evaluation on glycerol biosynthesis in Saccharomyces cerevisiae

“…In case (i), we uniformly sampled the scaled elasticities within defined ranges, and correlated the scaled elasticities of the forward and backward fluxes in the same reaction (e.g. E v þ;1 G3P and E v À;1 G3P ; for further details, see Supporting Information, Steuer et al (2006) and Grimbs et al (2007)). In case (ii), we uniformly sampled the degrees of saturation of active sites and calculated the scaled metabolite concentrations as proposed by Wang et al (2004).…”

“…The following discussion focuses on the scaled flux control coefficients of glycerol-3-phosphate dehydrogenase (Gpd p, reaction 1, C v net e 1 ). The coefficients of glycerol-3-phosphatase (Gpp p, reaction 2, C v net e 2 ) are then directly obtained from the summation theorem P i C v net e i ¼ 1: In case (i), the scaled elasticities were uniformly sampled and correlated within defined ranges as described by Steuer et al (2006) and Grimbs et al (2007). This approach exploits the fact that, in typical enzyme reactions, the scaled elasticities are confined to specific ranges.…”

Modeling of uncertainties in biochemical reactions

“…These dependencies imply that the kinetic parameters' space is constrained in a very intricate way, which might reduce the sampling efficiency especially in the case of modeling of large-scale metabolic networks. On the other hand, ignoring possible constraints might result in a population of computed models containing a subset of thermodynamically and physicochemically inconsistent models (Steuer et al, 2006;Grimbs et al, 2007).…”