Enzyme States Allow Identification of Rate-Limiting Steps

A precise quantification of the effect of perturbations in a metabolic network depends on explicit knowledge of the kinetic properties of the enzymes of the individual reactions. However, a comprehensive knowledge of enzymes kinetics in a metabolic network is very difficult, if not impossible, to obtain. Furthermore, experimental data obtained under different conditions introduce uncertainty in enzyme kinetic parameters. In this work, we model the uncertainty in the kinetic data and we predict quantitatively the responses of metabolic networks in the presence of genetic, biochemical, and environmental variations. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physicochemical and thermodynamic constraints and is based on formalism from process control and metabolic control. The method employs a novel, efficient Monte Carlo sampling procedure that allows us to simulate all possible meaningful states of a metabolic network and to compute the corresponding values of the kinetic constants of the individual reaction steps. We demonstrate the properties of the proposed framework through a number of case studies.

Modeling of uncertainties in biochemical reactions

Vassily Hatzimanikatis, Ljubisa Miskovic

Mathematical modeling is an indispensable tool for research and development in biotechnology and bioengineering. The formulation of kinetic models of biochemical networks depends on knowledge of the kinetic properties of the enzymes of the individual reactions. However, kinetic data acquired from experimental observations bring along uncertainties due to various experimental conditions and measurement methods. In this contribution, we propose a novel way to model the uncertainty in the enzyme kinetics and to predict quantitatively the responses of metabolic reactions to the changes in enzyme activities under uncertainty. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physico-chemical and thermodynamic constraints, and is based on formalism from systems theory and metabolic control analysis. We achieve this by observing that kinetic responses of metabolic reactions depend: (i) on the distribution of the enzymes among their free form and all reactive states; (ii) on the equilibrium displacements of the overall reaction and that of the individual enzymatic steps; and (iii) on the net fluxes through the enzyme. Relying on this observation, we develop a novel, efficient Monte Carlo sampling procedure to generate all states within a metabolic reaction that satisfy imposed constrains. Thus we derive the statistics of the expected responses of the metabolic reactions to changes in enzyme levels and activities, in the levels of metabolites, and in the values of the kinetic parameters. We present aspects of the proposed framework through an example of the fundamental three-step reversible enzymatic reaction mechanism. We demonstrate that the equilibrium displacements of the individual enzymatic steps have an important influence on kinetic responses of the enzyme. Furthermore, we derive the conditions that must be satisfied by a reversible three-step enzymatic reaction operating far away from the equilibrium in order to respond to changes in metabolite levels according to the irreversible Michelis-Menten kinetics. The efficient sampling procedure allows easy, scalable, implementation of this methodology to modeling of large-scale biochemical networks.

Wiley-Blackwell2010

Quantitative Analysis of Metabolic Networks Through the Explicit Consideration of Kinetic Mechanisms

Vassily Hatzimanikatis, Ljubisa Miskovic

Engineering of large-scale metabolic pathways to maximize production of a certain substance or to minimize creation of undesired chemicals require explicit information about the underlying enzyme kinetics. Unfortunately, such information is frequently not available, or when available, it involves uncertainty due to biological variability and to differences in experimental conditions and measurement techniques. In this contribution, we present a computational framework that allows us to characterize the kinetic responses of metabolic network in the presence of uncertainty. The proposed methodology uses Monte Carlo sampling to explore the kinetic data space, and it accounts explicitly for mechanistic properties of enzymes and physico-chemical and thermodynamic constraints. In our bottom-up approach, we start by modeling the kinetic responses of the individual reactions, and then we integrate this mechanistic information with the thermodynamically feasible pairs of substrate and product concentrations to build a population of all biochemically and thermodynamically meaningful models of the metabolic network. In the integration procedure, we exploit the fact that the control coefficients computed for a kinetic mechanism are the elasticities of the enclosing reaction of a metabolic network. The employed sampling method benefits from the specific structure of the underlying constraints and its effectiveness allows implementing the proposed methodology for modeling of large-scale metabolic networks. We demonstrate the properties of the proposed framework through a case study for the identification of rate limiting steps in the central carbon pathway in S. cerevisiae.

2010

Kinetic reconstruction and analysis of sphingolipid metabolism

Vassily Hatzimanikatis, Howard Riezman, Georgios Savoglidis

Lipids are major constituents of the cell. They are responsible for major properties of the cellular membranes: hydrophobicity, selective permeability and being the scaffold of signaling proteins. Many diseases are associated with alterations in the lipid distribution in the cell and the composition of membrane domains. Metabolic syndrome, obesity, atherosclerosis, as well as Alzheimer’s, Huntington’s diseases and cancer, have an impact in the levels of lipids, with observed alterations in their concentrations compared to the healthy state. Applying computational techniques along with systematic modeling of lipid metabolism can provide insights that can guide biomedical research and develop potential strategies for prevention and cure. In the present study we developed a comprehensive model of the sphingolipid biosynthesis in the yeast Saccharomyces cerevisiae. Sphingolipids are one of the four major lipid categories, along with (glycero)phospholipids, sterols and fatty acids synthesized in the yeast S. cerevisiae. The importance of sphingolipids present in any higher eukaryote has been demonstrated in many recent studies. For this study, S. cerevisiae has been chosen as a model organism due to its high homology of cellular processes with mammalian cells. The developed model will be an essential part towards the construction of a detailed kinetic model of the whole lipidome of the cell. We first constructed a stoichiometric model that contains all the currently known reactions for the biosynthesis of ceramides and complex sphingolipids in the yeast. Additionally, we have accounted for all five reported hydroxylation states, along with the reactions synthesizing the necessary precursor metabolites from other lipid pathways (i.e. palmitate-CoA from fatty acid synthesis and phosphatidylinositol from the phospholipids metabolism). We next developed a kinetic model and we used a large number of lipidomic measurements of wild type yeast to consistently calibrate our model. Curation of the kinetic information of the model came from the comprehensive mining of references for operation of the enzymes as well as ranges of kinetic parameters from online databases. These datasets created the pool for a sampling technique that accounts for the uncertainty in the parameters of the model. This lead to a robust dynamic model, containing mass balances for all the components of the biochemical network as well as terms that accounted for the dillution of these molecules in the cell due to growth. We performed a thorough kinetic analysis of the system by examining the impact of different assumptions in enzyme operation on the levels of ceramides and complex sphingolipids (e.g. substrate competition, (un)competitive inhibition). By applying the principles of Metabolic Control Analysis (MCA) we were able to quantify the effect of enzyme activities on the lipid profiles and we identified enzymes of the biochemical reaction network as efficient targets for metabolic engineering towards a desired state. We also applied a reverse engineering method and we were able to identify enzyme perturbations responsible for an observed altered state compared to the wild type cellular lipidomic profile. Such an approach could lead to the identification of genetic mutations by imploring the information containd within metabolomic measurements. Although we demonstrate the application of the method in models of lipid metabolism it is possible to be applied to biochemical systems of various parts of metabolism and sizes creating a modular platform for kinetic analysis of cellular operations.

2014

Modeling of uncertainties in biochemical reactions

Vassily Hatzimanikatis, Ljubisa Miskovic

Wiley-Blackwell2010

Kinetic reconstruction and analysis of sphingolipid metabolism

Vassily Hatzimanikatis, Howard Riezman, Georgios Savoglidis

2014