Large-scale dynamic models of metabolic networks

The development and application of methods quantifying the metabolic fluxes such as Flux Balance Analysis (FBA) has been one of the driving forces behind the successful growth of metabolic engineering. However, applications of FBA have been limited by the fact that FBA does not take into account kinetic properties of the network and therefore it cannot be used to identify rate-limiting steps and comprehend time course evolutions of the system. Dynamic mathematical descriptions of the metabolism offer a large advantage compared to constraint-based stoichiometric models, but unfortunately their development comes with inevitable difficulties due to: (i) structural uncertainties, such as incomplete knowledge about stoichiometry or about kinetic laws of the enzymes, and (ii) quantitative/parametric uncertainties such as lack of knowledge concerning kinetic parameters. Recent developments and vast resources of curated genome scale metabolic networks address to a great extent the issues around stoichiometric uncertainty. However, the knowledge about kinetic rate laws and in particular their parameters is to these days still limited. In this contribution, starting from large-scale stoichiometric models we use the ORACLE (Optimization and Risk Analysis of Complex Living Entities) framework that integrates available information in a set of stable log-linear kinetic models sharing the same steady state. These models are used to compute kinetic parameters of the enzymatic mechanisms in the metabolic network, e.g. the maximal velocities, Vmax, and Michaelis constants, Km. Using these kinetic parameters, we systematically develop populations of stable dynamic models having the same steady-state as the log-linear ones. The estimated parameters are comparable to the experimental information as seen in BRENDA and other databases. These non-linear estimations about the stable state can be therefore used to analyze properties of the system upon large perturbations and investigate time course evolutions in and around this steady state. We demonstrate the capabilities of the proposed approach by building a dynamic E. coli core model that includes ca. 200 metabolites and more than 400 reactions. We discuss the strengths and limitations of this approach and possible avenues for development.

Mapping and Analysis of the Complexity of Lipid Metabolism for Applications in Health and Sustainability

Vassily Hatzimanikatis, Sofia Tsouka

Metabolism is a network of biotransformations that sustain life in cells. Over the past decades, metabolism has been studied in multiple contexts, ranging from medicine to industrial manufacturing. In particular, lipid metabolism has been linked to various physiopathologies, and its study could lead to new diagnostics and treatments. Metabolic networks are extremely complex and a systems approach is essential in deciphering the different levels of cellular organization and regulation that an organism possesses. Genome-scale metabolic models (GEMs) encompass all the available information for an organism, though their large size and complexity introduce a lot of uncertainty in the accuracy of predictions. GEM reductions are usually done in an ad hoc manner to produce context-specific models, and cannot serve multiple studies. The study of regulatory mechanisms requires the development of kinetic models that can accurately capture dynamic responses to perturbations. To this end, constraint-based models can be enhanced through the integration of kinetic information. Constructing consistent large-scale kinetic models is a challenging endeavor, since detailed knowledge about regulatory mechanisms and kinetic parameter values is scarce.Examining the mechanisms of enzymatic and metabolic restructuring in states of mutation could increase our fundamental understanding of how diseases evolve, and facilitate phenotype mapping. Metabolic Control Analysis (MCA) has been a well-established tool for the prediction and evaluation of genetic modification strategies. However, it fails to account for the physiological limitations of an organism and can often lead to unrealistic predictions.In this thesis, we developed computational models, tools, and methodologies to facilitate the study of lipids and their regulatory mechanisms. Firstly, we constructed and curated a metabolic model that focuses on lipid metabolism, through the integration of detailed lipid pathways into a GEM of S. cerevisiae. This model was then systematically reduced around these pathways to provide a more manageable model size for complex studies. We show that this model is as consistent and inclusive as other yeast GEMs, and can be used as a scaffold for integrating lipidomics data to improve predictions in studies of lipid-related biological functions. Secondly, we used this model as a basis to build a large-scale kinetic model. Enzymes in the lipid metabolism are typically promiscuous and multifunctional, giving rise to enzymatic coupling. To accurately capture these properties, we assigned suitable kinetic rate expressions to the reactions in the network. We generated populations of kinetic parameter sets through a sampling-based workflow and we demonstrate how the consideration of enzymatic coupling is essential for factual predictions. Thirdly, we developed a constraint-based formulation that utilizes MCA-based control coefficients for the consistent derivation of metabolic engineering strategies. We show how the parametrization and introduction of biological constraints enhances this formulation in comparison to the classical MCA approach, and we highlight its ability to generate alternative optimal strategies. Fourthly, we defined and introduced additional mathematical objectives and constraints to this formulation to enable the mapping of enzymes that are responsible for different phenotypes. Concluding, we discuss the contribution and potential applications of this thesis.

EPFL2020

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiology constraints

Anirikh Chakrabarti, Vassily Hatzimanikatis, Ljubisa Miskovic, Keng Cher Soh

Mathematical modeling is an essential tool for a comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information about enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works consider only the mass action kinetics for the reactions in the metabolic networks. In this work, we applied the ORACLE framework and constructed a large-scale, mechanistic kinetic model of optimally grown E. coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of the metabolic fluxes and metabolite concentrations. Our results further suggest that the enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of the cellular metabolism.

2013

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.