Control Theory Concepts for Modeling Uncertainty in Enzyme Kinetics of Biochemical Networks

Analysis of the dynamic and steady-state properties of biochemical networks hinges on information about the parameters of enzyme kinetics. The lack of experimental data characterizing enzyme activities and kinetics along with the associated uncertainties impede the development of kinetic models, and researchers commonly use Monte Carlo sampling to explore the parameter space. However, the sampling of parameter spaces is a computationally expensive task for larger biochemical networks. To address this issue, we exploit the fact that reaction rates of biochemical reactions and network responses can be expressed as a function of displacements from the thermodynamic equilibrium of elementary reaction steps and concentrations of free enzymes and their intermediary complexes. For a set of kinetic mechanisms ubiquitously found in biochemistry, we express kinetic responses of enzymes to changes in network metabolite concentrations through these quantities both analytically and schematically. The tailor-made sampling of these quantities allows for characterizing the missing kinetic parameters and accelerating the efforts towards building genome-scale kinetic metabolic models

Model-Driven Understanding of Palmitoylation Dynamics: Regulated Acylation of the Endoplasmic Reticulum Chaperone Calnexin

Cellular functions are largely regulated by reversible post-translational modifications of proteins which act as switches. Amongst these, S-palmitoylation is unique in that it confers hydrophobicity. Due to technical difficulties, the understanding of this modification has lagged behind. To investigate principles underlying dynamics and regulation of palmitoylation, we have here studied a key cellular protein, the ER chaperone calnexin, which requires dual palmitoylation for function. Apprehending the complex inter-conversion between single-, double- and non- palmitoylated species required combining experimental determination of kinetic parameters with extensive mathematical modelling. We found that calnexin, due to the presence of two cooperative sites, becomes stably acylated, which not only confers function but also a remarkable increase in stability. Unexpectedly, stochastic simulations revealed that palmitoylation does not occur soon after synthesis, but many hours later. This prediction guided us to find that phosphorylation actively delays calnexin palmitoylation in resting cells. Altogether this study reveals that cells synthesize 5 times more calnexin than needed under resting condition, most of which is degraded. This unused pool can be mobilized by preventing phosphorylation or increasing the activity of the palmitoyltransferase DHHC

Efficient cleavage of aryl ether C–O linkages by Rh–Ni and Ru–Ni nanoscale catalysts operating in water

Bimetallic Ru–Ni and Rh–Ni nanocatalysts coated with a phase transfer agent efficiently cleave aryl ether C–O linkages in water in the presence of hydrogen. For dimeric substrates with weaker C–O linkages, i.e. α-O-4 and β-O-4 bonds, low loadings of the precious metal (Rh or Ru) in the nanocatalysts quantitatively afford monomers, whereas for the stronger 4-O-5 linkage higher amounts of the precious metal are required to achieve complete conversion. Under the optimized, relatively mild operating conditions, the C–O bonds in a range of substituted ether compounds are efficiently cleaved, and mechanistic insights into the reaction pathways are provided. This work paves the way to sustainable approaches for the hydrogenolysis of C–O bonds

Automatic control and optimization algorithms with application to anaerobic digesters

The process of anaerobic digestion is a commonly used method of wastewater treatment. One of the major issues that arise is the maximization of the biogas production rate for energy utilization purposes. In maximum biogas production conditions, the process becomes marginally stable, many times leading to washout of the biomass. The problem can be even more complicated under the effect of potential disturbances in the feed (organic overload, presence of inhibitor).For the reasons mentioned above, a two state model of the biomass and the limiting substrate was developed for control purposes. The model also included the rate of decay of the biomass. The model parameters were estimated through data collected from an experimental setup of a lab-scale anaerobic digestion system. Specifically, a CSTR-type 3 liter reactor was used loaded with anaerobic mixed culture bacteria from a wastewater treatment plant, to simulate the process of anaerobic digestion. The synthetic feed, mainly consisting of glucose, was periodically pumped into the reactor through a peristaltic pump.For monitoring of the process, a LabView monitoring environment was developed. The biogas production rate was measured in discrete time intervals using a standard volume device which was recording the time needed for the known volume to be filled with biogas. On these intervals, the fraction of the methane in the biogas was also measured using an infrared ion detector.For stabilizing the system of the anaerobic reactor, a proportional with respect to the measured methane production rate output feedback control law was developed. The proposed control law stabilizes the process in a very large region around the optimal steady state without driving the system towards washout of the biomass. This ability of the controller was tested both with simulation and experimentally. Both simulation and experimental studies proved that the output feedback control law manages to stabilize the system to the optimal steady state under pulse disturbances on the organic load (pulse up and pulse down disturbances).Also a nonlinear observer theory was developed based on the exact error linearization method for the calculation of the observer gains. The observer was used for estimating the unknown states and parameters that cannot be measured and detection of the potential presence and magnitude of a disturbance. These disturbances were step disturbances on the organic load of same magnitude, as in pulse tests of the controller. The nonlinear observer was tested in an extensive simulation study and some early experimental results.Η διεργασία της αναερόβιας χώνευσης είναι μία ευρέως διαδεδομένη μέθοδος για την κατεργασία υγρών αποβλήτων. Ένα από τα σημαντικότερα προβλήματα που παρουσιάζονται είναι η μεγιστοποίηση του ρυθμού παραγωγής του βιοαερίου, για χρήση του στον τομέα της παραγωγής ενέργειας. Στις συνθήκες στις οποίες μεγιστοποιείται η παραγωγή του βιοαερίου, η διεργασία γίνεται οριακά ευσταθής, οδηγώντας πολλές φορές στην έκπλυση της βιομάζας. Το πρόβλημα μπορεί να γίνει ακόμα πιο περίπλοκο, με την επίδραση πιθανών διαταραχών, οι οποίες εισέρχονται κατά κύριο λόγο με την τροφοδοσία (υπερφόρτιση της συγκέντρωσης των οργανικών στην είσοδο του συστήματος, παρουσία παρεμποδιστικής προς την ανάπτυξη της βιομάζας ουσίας).Για τους λόγους που αναφέρθηκαν παραπάνω, εξήχθη ένα απλοποιημένο μοντέλο δύο καταστάσεων, της βιομάζας και του περιοριστικού υποστρώματος, για χρήση του για τους σκοπούς της ρύθμισης της διεργασίας. Το μοντέλο περιελάμβανε και όρο για το θάνατο της μικροβιακής βιομάζας. Οι παράμετροι του μοντέλου εκτιμήθηκαν μέσω συλλογής δεδομένων από μία πειραματική διάταξη ενός εργαστηριακής κλίμακας συστήματος αναερόβιας χώνευσης. Πιο συγκεκριμένα, χρησιμοποιήθηκε ένας αντιδραστήρας 3 λίτρων τύπου CSTR, ο οποίος φορτώθηκε με αναερόβια μεικτή καλλιέργεια βακτηρίων, προερχόμενη από τη μονάδα επεξεργασίας υγρών λυμάτων της Πάτρας, για να προσομοιωθεί η διεργασία της αναερόβιας χώνευσης. Η συνθετική τροφοδοσία, η οποία αποτελούνταν κατά κύριο λόγο από γλυκόζη, τροφοδοτούνταν στο σύστημα μέσω μιας περισταλτικής αντλίας.Για την παρακολούθηση της διεργασίας κατασκευάσθηκε ένα περιβάλλον παρακολούθησης σε LabView. Η μέτρηση του ρυθμού παραγωγής του βιοαερίου γινόταν σε διακριτούς χρόνους, χρησιμοποιώντας μία συσκευή, η οποία κατέγραφε το χρόνο που χρειαζόταν για την πλήρωση ενός συγκεκριμένου βαθμονομημένου όγκου με βιοαέριο. Σε αυτά τα διαστήματα παρεχόταν, επίσης, η μέτρηση της σύστασης του βιοαερίου σε μεθάνιο, χρησιμοποιώντας ένα ανιχνευτή υπέρυθρης ακτινοβολίας.Για τη σταθεροποίηση του συστήματος του αναερόβιου χωνευτήρα, αναπτύχθηκε ένας αναλογικός, ως προς τη μέτρηση του βιοαερίου, νόμος ανάδρασης εξόδου. Ο προτεινόμενος νόμος ανάδρασης σταθεροποιεί τη διεργασία σε μία μεγάλη περιοχή γύρω από τη βέλτιστη μόνιμη κατάσταση, χωρίς να οδηγεί στην έκπλυση της βιομάζας. Αυτή η ικανότητα του ρυθμιστή, δοκιμάσθηκε τόσο σε επίπεδο προσομοιώσεων όσο και σε πειραματικό επίπεδο. Τόσο οι προσομοιώσεις όσο και τα πειραματικά αποτελέσματα αποδεικνύουν ότι ο νόμος ανάδρασης εξόδου καταφέρνει να σταθεροποιήσει το σύστημα υπό παλμικές μεταβολές στη συγκέντρωση του οργανικού φορτίου στην είσοδο του συστήματος (παλμική αύξηση και παλμική μείωση).Αναπτύχθηκε, επίσης, θεωρία σχεδιασμού μη γραμμικών παρατηρητών, η οποία βασίζεται στη μέθοδο της ακριβούς γραμμικοποίησης του σφάλματος για τον υπολογισμό των ενισχύσεων των παρατηρητών. Ένας τέτοιος παρατηρητής χρησιμοποιείται για την εκτίμηση των άγνωστων καταστάσεων και παραμέτρων που δεν μπορούν να μετρηθούν, καθώς και για την ανίχνευση πιθανών διαταραχών και υπολογισμό του μεγέθους τους. Οι διαταραχές αυτές ήταν βηματικές διαταραχές στη συγκέντρωση του οργανικού φορτίου στην είσοδο του αναερόβιου χωνευτήρα, ίδιου εύρους όπως οι παλμοί στα αποτελέσματα του νόμου ανάδρασης, που είχαν μελετηθεί νωρίτερα. Οι ιδιότητες του μη γραμμικού παρατηρητή δοκιμάσθηκαν με μία εκτενή μελέτη προσομοιώσεων αλλά και σε πρώιμα πειραματικά αποτελέσματα από τον βιοχημικό αντιδραστήρα

A comprehensive reconstruction of the fatty acid biosynthesis in Saccharomyces cerevisiae

The role of lipids in eukaryotic cells is of high importance. They are one of the main components of cell membranes, act as storage of high potential energy as well as being a scaffold of signaling proteins or participate in signaling themselves. 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, Huttington diseases and cancer, all originate from alterations in some stage of lipid biosynthesis. Therefore, advancement of knowledge in the field of lipid metabolism will provide novel insights for further biomedical research and potential strategies for drug development. Fatty acids are the backbone of the lipid metabolism. Being lipids themselves they also participate in the biosynthesis of the majority of the lipid classes. Thus, the study of their synthesis and biotransformation in a cell constitutes the basic step towards a systematic investigation of the phenomena attributed to lipids. In the current study we reconstructed a comprehensive representation of the biosynthesis of fatty acids in a model eukaryote such as Saccharomyces cerevisiae. The model accounts for approximately 300 reactions and 230 metabolites, taking part in 3 compartments of the cell, describing the steps of synthesis, elongation and β-oxidation of fatty acids. We make use of other systems approaches in order to identify the input fluxes to the model and we explore the diverse capabilities of the network with respect to flux profiles and distribution of fatty acids

Identification of the enzymes that determine the robustness of lipid profiles in yeast

Lipids play a very important role in cell structure and function, as well as in the physiopathology of many diseases. Maintenance of the lipid profiles should be tightly regulated as it is very important for preserving membrane permeability, cell integrity and several other functions. Large-scale kinetic models of metabolic networks are essential in order to accurately capture and predict such behaviors of cellular systems when subject to perturbations. We have thus developed a detailed model of the lipid metabolism for the yeast S. cerevisiae, in order to identify how the stoichiometric and kinetic coupling determines lipid homeostasis and its regulation. The model encompasses 308 reactions (of which 230 are enzymatic reactions, 32 are transport reactions and 29 are elementary reactions that contribute to biomass formation) and 212 unique metabolites, and includes the following subsystems: glycolysis, fatty acid biosynthesis and elongation, biosynthesis of phospholipids, sphingolipids, cardiolipin and sterols, triacylglycerides decomposition and the mevalonate pathway. We curated this model using thermodynamic data as well as lipidomic measurements and we used the Optimization and Risk Analysis of Complex Living Entities (ORACLE) framework to generate populations of parametrized kinetic models that are consistent with the given physiology, while satisfying the stoichiometric and thermodynamic constraints. We computed and analyzed the distributions of these models’ flux and concentration control coefficients (FCCs and CCCs, respectively), which quantify the magnitude to which a change in a system parameter (i.e. enzyme activities) will affect and control fluxes through reactions and metabolic concentrations at a representative steady state. We used these coefficients to reverse engineer changes in enzyme activities that will lead to desired phenotypes as well as to identify mutations based on lipidomic measurements

Kinetic modeling of the yeast sphingolipid metabolism identifies prevalent mutant strains through integration of lipidomic data profiles

Sphingolipids are abundant components of eukaryotic cells. Their localization in the plasma membrane allows for the cell to carry out multiple important functions for its viability. One of the most important roles of the sphingolipids is their ability to form, along with other lipid compounds, complex structures which attribute to the membrane of the cell its functional role to selectively allow transport of molecules, participate in signaling, react under heat stress and regulate growth. In yeast multiple complex sphingolipids have been identified based on the localization of the head group on the long chain base. Recent evidence points to the fact that alterations in the sphingolipids levels cause numerous diseases such as infections, diabetes, Alzheimer’s disease and various types of cancer. In the present study we developed a mathematical model of the sphingolipid biosynthesis in Saccharomyces cerevisiae. The model accounts for all the different complex sphingolipids formed, according to the various hydroxylation states, as reported in recent studies. Biochemical and kinetic information integrated in the model are implemented from the literature. The resulting kinetic model is able to generate dynamic and steady state phase profiles of the all the species of the network. These results are in agreement with experiments performed; where radioactively labeled palmitate and inositol are used to quantify the metabolic steps in the backbone sphingolipid synthesis and the incorporation of the head group respectively. Finally, a systematic framework of identifying and ranking quantitatively, possible gene mutations from altered complex sphingolipid species profiles was developed. The proposed method was able to identify the genes targeted for regulation by incorporating the variation of the lipidomic profile of the network with respect to the steady state conditions

Integrating omics data into metabolic models of lipids: a platform for the identification of gene mutations from lipidomics data

Kinetic models of metabolic networks are mapping the biochemical reactions taking part in a cell to a mathematical representation. They are the blueprints of the biochemical network, connecting enzymatic activities and metabolic compounds. Kinetic models have been used in systems biology to produce estimates of response of an organism to stress and to reveal potentially efficient targets for cellular engineering. Lipids are major constituents of the cell membrane. 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, all originate from alterations in some stage of lipid biosynthesis. Therefore, advancement of knowledge in the field of lipid metabolism will provide novel insights for further biomedical research and potential strategies for drug development. In the current study we combine lipidomics data and metabolic models of lipid metabolism in yeast Saccharomyces cerevisiae. We use the models as platform for the application of sensitivity analysis and metabolic control analysis, which involves direct and inverse sensitivity analysis. In direct sensitivity analysis we quantify how the changes in enzymatic activities, either by gene deletion or RNAi, are mapped through the metabolic pathway model into variations in lipid profiles. This analysis allows us to identify the effects of the perturbations in enzyme activities (inhibition or overexpression) on the distribution of the lipids synthesized as the end products of the network. We further extend the analysis by casting the inverse problem. With the inverse sensitivity analysis framework, we consider as input an altered lipidomic profile and we are able to identify, the responsible perturbations in enzyme activities that account for such a change. The results of the analysis have been confirmed based on lipidomics analysis of mutant yeast cells. 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 identification of mutations

Ionic polymers and use thereof in processing of biomass

The invention provides ionic polymers (IP) consisting of anions and a polymeric backbone containing cations. The invention also provides the ionic polymers incorporated in membranes or attached to solid supports and use of the ionic polymers in processing of biomass

Kinetic reconstruction and analysis of sphingolipid metabolism

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