Evolutionary significance of metabolic network properties

Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein–protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, such as small average path length, large clustering coefficient, heavy-tail degree distribution and hierarchical organization, viewed as requirements for efficient and robust system architectures. However, for biological networks, it is unclear to what extent these properties reflect the evolutionary history of the represented systems. Here, we show that the salient structural properties of six metabolic networks from all kingdoms of life may be inherently related to the evolution and functional organization of metabolism by employing network randomization under mass balance constraints. Contrary to the results from the common Markov-chain switching algorithm, our findings suggest the evolutionary importance of the small-world hypothesis as a fundamental design principle of complex networks. The approach may help us to determine the biologically meaningful properties that result from evolutionary pressure imposed on metabolism, such as the global impact of local reaction knockouts. Moreover, the approach can be applied to test to what extent novel structural properties can be used to draw biologically meaningful hypothesis or predictions from structure alone

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

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

Systematic Analysis of Stability Patterns in Plant Primary Metabolism

Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM) is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models

Identification of significant properties of metabolic networks

<p>Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein–protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, such as small average path length, large clustering coefficient, heavy-tail degree distribution and hierarchical organization, viewed as requirements for efficient and robust system architectures. However, for biological networks, it is unclear to what extent these properties reflect the evolutionary history of the represented systems. Here, we show that the salient structural properties of six metabolic networks from all kingdoms of life may be inherently related to the evolution and functional organization of metabolism by employing network randomization under mass balance constraints. Contrary to the results from the common Markov-chain switching algorithm, our findings suggest the evolutionary importance of the small-world hypothesis as a fundamental design principle of complex networks. The approach may help us to determine the biologically meaningful properties that result from evolutionary pressure imposed on metabolism, such as the global impact of local reaction knockouts. Moreover, the approach can be applied to test to what extent novel structural properties can be used to draw biologically meaningful hypothesis or predictions from structure alone.</p

Published online at the

Towards structure and dynamics of metabolic network

Metabolic networks are NP-hard to reconstruct.

High-throughput data from various omics and sequencing techniques have rendered the automated metabolic network reconstruction a highly relevant problem. Our approach reflects the inherent probabilistic nature of the steps involved in metabolic network reconstruction. Here, the goal is to arrive at networks which combine probabilistic information with the possibility to obtain a small number of disconnected network constituents by reduction of a given preliminary probabilistic metabolic network. We define automated metabolic network reconstruction as an optimization problem on four-partite graph (nodes representing genes, enzymes, reactions, and metabolites) which integrates: (1) probabilistic information obtained from the existing process for metabolic reconstruction from a given genome, (2) connectedness of the raw metabolic network, and (3) clustering of components in the reconstructed metabolic network. The practical implications of our theoretical analysis refer to the quality of reconstructed metabolic networks and shed light on the problem of finding more efficient and effective methods for automated reconstruction. Our main contributions include: a completeness result for the defined problem, polynomial-time approximation algorithm, and an optimal polynomial-time algorithm for trees. Moreover, we exemplify our approach by the reconstruction of the sucrose biosynthesis pathway in Chlamydomonas reinhardtii

Cocoa bean fermentation model

Datasets and codes supporting the article: "A mathematical model of cocoa bean fermentation" by Mauricio Moreno-Zambrano, Sergio Grimbs, Matthias S. Ullrich and Marc-Thorsten Hüt

Network underlying the SK-model of the CBC and related pathways.

<p>Compounds written in italics represent external substances the concentrations of which are kept constant in the model. Dotted lines indicate the reactions of cofactors. Dashed lines connect metabolites that are assumed to be in equilibrium so that their concentration changes are directly proportional to each other. The proportions of the individual concentrations of these metabolites then depend solely on their equilibrium constants.</p

Example patterns with a) two or b) three stability conditions each.

<p>For each enzyme-metabolite pair, a threshold for the saturation is given. Enzymes are marked in red, their reactants are marked in green. Pattern 1 exhibited an average Laplace ratio of (, ). Pattern 2 affected less training samples because of its less strict threshold on the parameter associated with PGK and GAPDH but also produced more training errors and a lower Laplace value ( , ). Pattern 3 affected an even larger number of hits but nevertheless, it produced fewer training errors than pattern 2. As a consequence, it exhibited the highest Laplace value of all the depicted patterns (, , ).</p