Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. More importantly, we derive a number of consequences from the model that are independent of parameter values. First, that the ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties invariant across perfusion systems. This conclusion is robust even in the presence of multi-stability, which is explained in our model by the negative feedback loop on cell growth due to toxic byproduct accumulation. Moreover, a complex landscape of steady states in continuous cell culture emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced. Thus, in order to actually reflect the expected behavior in perfusion, performance benchmarks of cell-lines and culture media should be carried out in a chemostat

Facing the complexity of grape quality management and delivering an highthroughput device: VinePAT

The physiological response of plants to external perturbation is complex and occurs at different levels of their metabolism. This is a multivariate and multi-scale phenomena, therefore high-throughput methodologies are required to extract relevant information. The nonexistence of a device with such characteristics constitutes a barrier to the interpretation of the consequences of external inputs. Spectroscopy is a multivariate methodology with greatest interest for metabolic studies in biological systems. In fact, this technique provides detailed information on the molecular structure and reaction mechanisms. Moreover due to its non-destructive character, this methodology is currently used to characterize proteins, peptides, lipids, membranes, carbohydrates in pharmaceuticals and food products as well as plants and animal tissues. VinePAT is a vineyard management system based in the Process Analytical Technologies (PAT) methodologies to provide winemakers with state-of-the-art metabolic images of vineyards for precision winemaking by using UV-VIS-SWNIR spectroscopy techniques. The system hardware is based on miniaturized fiber-optics spectrometer adapted for grape and leaves measurements and suited for outdoor data acquisition. Combining these georeferenced outdoor measurements collected at the vineyard with state-of-the-art spectroscopy signal processing, the winemaker will be able to observe vine metabolism by using a non-destructive 'in-vivo' methodology, as well as, the global-picture of the vineyard for implementing precision winemaking technologies based on process analytical technology. Here we demonstrate the potential of the VinePAT technology for grape-growers by presenting: i) spectroscopy equipment in action; ii) the variance imaging and zone diagnostics; iii) metabolic imaging with especial incidence in key metabolites for grape maturation; iv) how to use multivariate control charts; and v) the full potential of the technology deployed by process analytical technology.info:eu-repo/semantics/publishedVersio

A Multi-Species Analysis Defines Anaplerotic Enzymes and Amides as Metabolic Markers for Ammonium Nutrition

Nitrate and ammonium are the main nitrogen sources in agricultural soils. In the last decade, ammonium (NH4+), a double-sided metabolite, has attracted considerable attention by researchers. Its ubiquitous presence in plant metabolism and its metabolic energy economy for being assimilated contrast with its toxicity when present in high amounts in the external medium. Plant species can adopt different strategies to maintain NH4+ homeostasis, as the maximization of its compartmentalization and assimilation in organic compounds, primarily as amino acids and proteins. In the present study, we report an integrative metabolic response to ammonium nutrition of seven plant species, belonging to four different families: Gramineae (ryegrass, wheat, Brachypodium distachyon), Leguminosae (clover), Solanaceae (tomato), and Brassicaceae (oilseed rape, Arabidopsis thaliana). We use principal component analysis (PCA) and correlations among metabolic and biochemical data from 40 experimental conditions to understand the whole-plant response. The nature of main amino acids is analyzed among species, under the hypothesis that those Asn-accumulating species will show a better response to ammonium nutrition. Given the provision of carbon (C) skeletons is crucial for promotion of the nitrogen assimilation, the role of different anaplerotic enzymes is discussed in relation to ammonium nutrition at a whole-plant level. Among these enzymes, isocitrate dehydrogenase (ICDH) shows to be a good candidate to increase nitrogen assimilation in plants. Overall, metabolic adaptation of different carbon anaplerotic activities is linked with the preference to synthesize Asn or Gln in their organs. Lastly, glutamate dehydrogenase (GDH) reveals as an important enzyme to surpass C limitation during ammonium assimilation in roots, with a disparate collaboration of glutamine synthetase (GS).The design of the study, analysis, and interpretation of data and writing of the manuscript was supported by the Basque Government [IT932-16] or GIC15/179, the Spanish Ministry of Economy and Competitiveness [AGL2015-64582-C3-2-R] and [BIO2017-84035-R]. IVM held a postdoctoral grant from the Basque Government (conv. 2018) and MDLP held a PhD grant by COLCIENCIAS (conv. 672)

Metabolic Games

Metabolic networks have been used to successfully predict phenotypes based on optimization principles. However, a general framework that would extend to situations not governed by simple optimization, such as multispecies communities, is still lacking. Concepts from evolutionary game theory have been proposed to amend the situation. Alternative metabolic states can be seen as strategies in a “metabolic game,” and phenotypes can be predicted based on the equilibria of this game. In this survey, we review the literature on applying game theory to the study of metabolism, present the general idea of a metabolic game, and discuss open questions and future challenges

Biological Networks

Networks of coordinated interactions among biological entities govern a myriad of biological functions that span a wide range of both length and time scales—from ecosystems to individual cells and from years to milliseconds. For these networks, the concept “the whole is greater than the sum of its parts” applies as a norm rather than an exception. Meanwhile, continued advances in molecular biology and high-throughput technology have enabled a broad and systematic interrogation of whole-cell networks, allowing the investigation of biological processes and functions at unprecedented breadth and resolution—even down to the single-cell level. The explosion of biological data, especially molecular-level intracellular data, necessitates new paradigms for unraveling the complexity of biological networks and for understanding how biological functions emerge from such networks. These paradigms introduce new challenges related to the analysis of networks in which quantitative approaches such as machine learning and mathematical modeling play an indispensable role. The Special Issue on “Biological Networks” showcases advances in the development and application of in silico network modeling and analysis of biological systems

A novel approach to dynamic flux balance analysis that accounts for the dynamic transfer of information by internal metabolites

Understanding the dynamics of information feedback amongst components of complex biological systems is crucial to the success of engineering desirable metabolic phenotypes. Flux Balance Analysis (FBA) is a structural metabolic modelling procedure that allows for local topological constraints to be related to steady-state global behaviors of metabolic systems. A vast majority of biological systems of interest, such as microbial communities, however do not exist under steady-state conditions. Therefore, extending FBA methods to the dynamical setting has been a major challenge to metabolic modelling. In dynamic FBA (dFBA), the representation of feedback dynamics is made possible by combining the methods of FBA with those of Ordinary Differential Equations (ODE). Although numerous dFBA models have been constructed to date, very little effort has gone into the theoretical analysis of how static FBA models and dynamic ODE models should be combined in dFBA. To develop a better understanding of the mathematical structure of dFBA, we investigate the properties of FBA. In order to predict time-derivatives of population growth, every dFBA model must make the assumption that the underlying metabolic network modeled via FBA optimizes a phenotypic function of growth rate. We show however, that under certain circumstances, this requirement introduces a rigid correspondence between growth rate, and a related quantity, the growth yield. The consequence of this is that the dFBA models become rigid in its predictions, effectively becoming a near-static representation of metabolism. In this thesis, we show that this tight correspondence between yield and rate may be broken by combining two inversely related approaches to formulating the FBA problem

Network Analysis and Modeling in Systems Biology

This thesis is dedicated to the study and comprehension of biological networks at the molecular level. The objectives were to analyse their topology, integrate it in a genotype-phenotype analysis, develop richer mathematical descriptions for them, study their community structure and compare different methodologies for estimating their internal fluxes. The work presented in this document moves around three main axes. The first one is the biological. Which organisms were studied in this thesis? They range from the simplest biological agents, the viruses, in this case the Potyvirus genus to prokariotes such as Escherichia coli and complex eukariotes (Arabidopsis thaliana, Nicotiana benthamiana). The second axis refers to which biological networks were studied. Those are protein-protein interaction (PPIN) and metabolic networks (MN). The final axis relates to the mathematical and modelling tools used to generate knowledge from those networks. These tools can be classify in three main branches: graph theory, constraint-based modelling and multivariate statistics. The document is structured in six parts. The first part states the justification for the thesis, exposes a general thesis roadmap and enumerates its main contributions. In the second part important literature is reviewed, summarized and integrated. From the birth and development of Systems Biology to one of its most popular branches: biological network analysis. Particular focus is put on PPIN and MN and their structure, representations and features. Finally a general overview of the mathematical tools used is presented. The third, fourth and fifth parts represent the central work of this thesis. They deal respectively with genotypephenotype interaction and classical network analysis, constraint-based modelling methods comparison and modelling metabolic networks and community structure. Finally, in the sixth part the main conclusions of the thesis are summarized and enumerated. This thesis highlights the vital importance of studying biological entities as systems and how powerful and promising this integrated analysis is. Particularly, network analysis becomes a fundamental avenue of research to gain insight into those biological systems and to extract, integrate and display this new information. It generates knowledge from just data.Esta tesis está dedicada al estudio y comprensión de redes biológicas a nivel molecular. Los objetivos fueron analizar su topología, integrar esta en un análisis de genotipo-fenotipo, desarrollar descripciones matemáticas más completas para ellas, estudiar su estructura de comunidades y comparar diferentes metodologías para estimar sus flujos internos. El trabajo presentado en este documento gira entorno a tres ejes principales. El primero es el biológico. ¿Qué organismos han sido estudiados en esta tesis? Estos van desde los agentes biológicos mas simples, los virus, en este caso el género Potyvirus, hasta procariotas como Escherichia coli y eucariotas complejos (Arabidopsis thaliana, Nicotiana benthamiana). El segundo eje hace referencia a las redes biológicas estudiadas, que fueron redes de interacción de proteínas (PPIN) y redes metabólicas (MN). El eje final es el de las herramientas matemáticas y de modelización empleadas para interrogar esas redes. Estas herramientas pueden clasificarse en tres grandes grupos: teoría de grafos, modelización basada en restricciones y estadística multivariante. Este documento está estructurado en seis partes. La primera expone la justificación para la tesis, muestra un mapa visual de la misma y enumera sus contribuciones principales. En la segunda parte, la bibliografía relevante es revisada y resumida. Desde el nacimiento y desarrollo de la Biología de Sistemas hasta una de sus ramas más populares: el análisis de redes biomoleculares. Especial interés es puesto en PPIN y MN: su estructura, representación y características. Finalmente, un resumen general de las herramientas matemáticas usadas es presentado. Los capítulos tercero, cuarto y quinto representan el cuerpo central de esta tesis. Estos tratan respectivamente sobre la interacción de genotipo-fenotipo y análisis topolólogico clásico de redes, modelos basados en restricciones y modelización de redes metabólicas y su estructura de comunidades. Finalmente, en la sexta parte las principales conclusiones de la tesis son resumidas y expuestas. Esta tesis pone énfasis en la vital importancia de estudiar los fenómenos biológicos como sistemas y en la potencia y prometedor futuro de este análisis integrativo. En concreto el análisis de redes supone un camino de investigación fundamental para obtener conocimiento sobre estos sistemas biológicos y para extraer y mostrar información sobre los mismos. Este análisis genera conocimiento partiendo únicamente desde datos.Aquesta tesi està dedicada a l'estudi i comprensió de xarxes biològiques a nivell molecular. Els objectius van ser analitzar la seva topologia, integrar aquesta en una anàlisi de genotip-fenotip, desenvolupar descripcions matemàtiques més completes per a elles, estudiar la seva estructura de comunitats o modularitat i comparar diferents metodologies per estimar els fluxos interns. El treball presentat en aquest document gira entorn de tres eixos principals. El primer és el biològic. ¿Què organismes han estat estudiats en aquesta tesi? Aquests van des dels agents biològics mes simples, els virus, en aquest cas el gènere Potyvirus, fins procariotes com Escherichia coli i eucariotes complexos (Arabidopsis thaliana, Nicotiana benthamiana). El segon eix fa referència a les xarxes biològiques estudiades, que van ser les xarxes d'interacció de proteïnes (PPIN) i les xarxes metabòliques (MN). L'eix final és el de les eines matemàtiques i de modelització emprades per interrogar aquestes xarxes. Aquestes eines poden classificarse en tres grans grups: teoria de grafs, modelització basada en restriccions i estadística multivariant. Aquest document està estructurat en sis parts. La primera exposa la justificació per a la tesi, mostra un mapa visual de la mateixa i enumera les seves contribucions principals. A la segona part, la bibliografia rellevant és revisada i resumida. Des del naixement i desenvolupament de la Biologia de Sistemes fins a una de les seves branques més populars: l'anàlisi de xarxes moleculars. Especial interès és posat en PPIN i MN: la seva estructura, representació i característiques. Finalment, un resum general de les eines matemàtiques utilitzades és presentat. Els capítols tercer, quart i cinquè representen el cos central d'aquesta tesi. Aquests tracten respectivament sobre la interacció de genotip-fenotip i anàlisi topolólogico clàssic de xarxes, models basats en restriccions i modelització de xarxes metabòliques i la seva estructura de comunitats. Finalment, en la sisena part les principals conclusions de la tesi són resumides i exposades. Aquesta tesi posa èmfasi en la vital importància d'estudiar els fenòmens biològics com sistemes i en la potència i prometedor futur d'aquesta anàlisi integratiu. En concret l'anàlisi de xarxes suposa un camí d'investigació fonamental per obtenir coneixement sobre aquests sistemes biològics i per extreure i mostrar informació sobre els mateixos. Aquest anàlisi genera coneixement partint únicament des de dades.Bosque Chacón, G. (2017). Network Analysis and Modeling in Systems Biology [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/79082TESI

Robust Nonlinear Model Predictive Control of Biosystems described by Dynamic Metabolic Flux Models

The accuracy of the model used for prediction in Nonlinear Model Predictive Controller (NMPC) is one of the main factors affecting the closed loop performance. Since it is impossible to formulate a perfect model for a real process, there are always differences between the responses predicted by the model and the responses observed from the process. Hence, robustness to model error is an essential property that the controller must have to be adopted in industrial applications. Propagating the uncertainty in the model onto the variables used by the controller is one the key challenges for efficient implementation of a robust controller. Uncertainty propagation approaches such as Monte Carlo simulations and the Polynomial Chaos Expansions (PCE) has been found to suffer from exponentially increasing computational effort with the number of uncertain parameters. Accordingly, the main goal of this thesis is to develop a novel formulation of NMPC based on an uncertainty propagation approach that is more computationally efficient as compared to previously reported approaches. The proposed robust controller in this thesis is specifically targeted to biosystems that are modeled by Dynamic Metabolic Flux models. These models that are becoming increasingly popular for modelling bioprocesses are based on the premise that microorganisms have learned through natural evolution to optimally allocate their resources (nutrients) to maximize a biological objective such as growth or ATP production. Accordingly, these flux models are formulated by LP (Linear Programming) optimizations with constraints that are solved at each time interval and then can be used in conjunction with mass balances to predict the dynamic evolution of different metabolites. The uncertainty in these models is associated to inaccuracies of model parameters involved in the constraints. Thus, although the problem can be solved for particular model parameters by an LP, in the presence of uncertainty the problem becomes nonlinear since different active sets of constraints may become active for parameters’ values within their possible range of variation. Accordingly, the solution space of this nonlinear system can be divided into a set of polyhedrons where each point corresponds to a particular set of parameters within their range of uncertainty. The solution space is often referred in the thesis as the RHS (Right Hand Side) space since it is defined by the variations in the RHS of the constraints with respect to the uncertain parameters. To identify these polyhedrons a dividing procedure has been developed. Since all the polyhedrons can be proven to be convex cones based on a standard simplex form of LP, this dividing method is referred to as the Convex Cone Method (CCM). The regions found by the CCM method are then compared to regions calculated with 100 Percent Rule where the latter has been often used to find a region of existence of a particular tableau in the Simplex method. From this comparison it is found that the CCM can both identify all the possible tableaus with a given region of uncertain parameters and it can also be used the probability for occurrence of each one of the tableaus. These two facts make the CCM an attractive basis for uncertainty propagation in an LP problem instead of the 100 Percent Rule. After identifying the possible tableaus for a given region of model parameters, a novel method is developed for propagating uncertainty onto the controlled variables to be referred to as Tableau Based Tree (TBT) method. The TBT method is based on the concept of propagating uncertainty into the prediction horizon of the controlled by using a tree structure which branches correspond to different tableaus identified by the CCM approach. It is then shown that the conservativeness of the NMPC controller can be significantly reduced based on this tree structure as compared to a Monte Carlo approach for uncertainty propagation. After propagating the uncertainty onto the relevant variables, the control actions for each branch of the tree structure can be obtained by a simple linear calculation. An EMPC (Economic Model Predictive Controller) is adopted in this work as a special realization of an NMPC algorithm where the controller pursues the maximization of an economic objective function. A simple theoretical comparison with a Monte Carlo uncertainty propagation approach shows that the TBT method have a potential to save considerable computational effort as compared to Monte Carlo simulation and PCEs. Finally, the TBT-based robust EMPC is applied in a case study dealing with a fed-batch reactor which is described by dynamic metabolic flux model (DMFM)