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Kinetic modelling of complex metabolic networks - a central goal of computational systems biology - is currently hampered by the lack of reliable rate equations for the majority of the underlying biochemical reactions and membrane transporters. On the basis of biochemically substantiated evidence that metabolic control is exerted by a narrow set of key regulatory enzymes, we propose here a hybrid modelling approach in which only the central regulatory enzymes are described by detailed mechanistic rate equations, and the majority of enzymes are approximated by simplified (nonmechanistic) rate equations (e.g. mass action, LinLog, Michaelis-Menten and power law) capturing only a few basic kinetic features and hence containing only a small number of parameters to be experimentally determined. To check the reliability of this approach, we have applied it to two different metabolic networks, the energy and redox metabolism of red blood cells, and the purine metabolism of hepatocytes, using in both cases available comprehensive mechanistic models as reference standards. Identification of the central regulatory enzymes was performed by employing only information on network topology and the metabolic data for a single reference state of the network [Grimbs S, Selbig J, Bulik S, Holzhutter HG & Steuer R (2007) Mol Syst Biol3, 146, doi:10.1038/msb4100186]. Calculations of stationary and temporary states under various physiological challenges demonstrate the good performance of the hybrid models. We propose the hybrid modelling approach as a means to speed up the development of reliable kinetic models for complex metabolic networks.
Refined elasticity sampling for Monte Carlo-based identification of stabilizing network patterns
(2015)
Motivation: Structural kinetic modelling (SKM) is a framework to analyse whether a metabolic steady state remains stable under perturbation, without requiring detailed knowledge about individual rate equations. It provides a representation of the system's Jacobian matrix that depends solely on the network structure, steady state measurements, and the elasticities at the steady state. For a measured steady state, stability criteria can be derived by generating a large number of SKMs with randomly sampled elasticities and evaluating the resulting Jacobian matrices. The elasticity space can be analysed statistically in order to detect network positions that contribute significantly to the perturbation response. Here, we extend this approach by examining the kinetic feasibility of the elasticity combinations created during Monte Carlo sampling.
Results: Using a set of small example systems, we show that the majority of sampled SKMs would yield negative kinetic parameters if they were translated back into kinetic models. To overcome this problem, a simple criterion is formulated that mitigates such infeasible models. After evaluating the small example pathways, the methodology was used to study two steady states of the neuronal TCA cycle and the intrinsic mechanisms responsible for their stability or instability. The findings of the statistical elasticity analysis confirm that several elasticities are jointly coordinated to control stability and that the main source for potential instabilities are mutations in the enzyme alpha-ketoglutarate dehydrogenase.
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.
Integration of high-throughput data with functional annotation by graph-theoretic methods has been postulated as promising way to unravel the function of unannotated genes. Here, we first review the existing graph-theoretic approaches for automated gene function annotation and classify them into two categories with respect to their relation to two instances of transductive learning on networks - with dynamic costs and with constant costs - depending on whether or not ontological relationship between functional terms is employed. The determined categories allow to characterize the computational complexity of the existing approaches and establish the relation to classical graph-theoretic problems, such as bisection and multiway cut. In addition, our results point out that the ontological form of the structured functional knowledge does not lower the complexity of the transductive learning with dynamic costs - one of the key problems in modern systems biology. The NP-hardness of automated gene annotation renders the development of heuristic or approximation algorithms a priority for additional research.
Spatiotemporal dynamics of the Calvin cycle multistationarity and symmetry breaking instabilities
(2011)
The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle. Unlike the existing simulation-based studies, our approach is based on a sound mathematical framework, chemical reaction network theory and algebraic geometry, which results in provable results for the investigated model of the Calvin cycle in which we embed a hierarchy of realistic kinetic laws. Our theoretical findings demonstrate that there is a possibility for multistationarity resulting from two sources, homogeneous and inhomogeneous instabilities, which partially settle the debate on multistability of the Calvin cycle. In addition, our tractable analytical treatment of the bifurcation parameters can be employed in the design of validation experiments.
Motivation: Metabolic engineering aims at modulating the capabilities of metabolic networks by changing the activity of biochemical reactions. The existing constraint-based approaches for metabolic engineering have proven useful, but are limited only to reactions catalogued in various pathway databases.
Results: We consider the alternative of designing synthetic strategies which can be used not only to characterize the maximum theoretically possible product yield but also to engineer networks with optimal conversion capability by using a suitable biochemically feasible reaction called 'stoichiometric capacitance'. In addition, we provide a theoretical solution for decomposing a given stoichiometric capacitance over a set of known enzymatic reactions. We determine the stoichiometric capacitance for genome-scale metabolic networks of 10 organisms from different kingdoms of life and examine its implications for the alterations in flux variability patterns. Our empirical findings suggest that the theoretical capacity of metabolic networks comes at a cost of dramatic system's changes.
Structural kinetic modeling (SKM) enables the analysis of dynamical properties of metabolic networks solely based on topological information and experimental data. Current SKM-based experiments are hampered by the time-intensive process of assigning model parameters and choosing appropriate sampling intervals for MonteCarlo experiments. We introduce a toolbox for the automatic and efficient construction and evaluation of structural kinetic models (SK models). Quantitative and qualitative analyses of network stability properties are performed in an automated manner. We illustrate the model building and analysis process in detailed example scripts that provide toolbox implementations of previously published literature models.
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.