Global stabilization of the chemostat with delayed and sampled measurements and control

International audienceThe classical model of the chemostat with one substrate, one species and a Haldane type growth rate function is considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of asymptotically stabilizing an equilibrium point of this system in the case where the measured concentrations are delayed and piecewise constant with a piecewise constant control is addressed

A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v

Hybrid Control of a Bioreactor with Quantized Measurements: Extended Version

We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number ("quantized"), with control of the dilution rate. The model is a differential system with two variables, and the output is the biomass growth. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic

Towards the implementation of distributed systems in synthetic biology

The design and construction of engineered biological systems has made great strides over the last few decades and a growing part of this is the application of mathematical and computational techniques to problems in synthetic biology. The use of distributed systems, in which an overall function is divided across multiple populations of cells, has the potential to increase the complexity of the systems we can build and overcome metabolic limitations. However, constructing biological distributed systems comes with its own set of challenges. In this thesis I present new tools for the design and control of distributed systems in synthetic biology. The first part of this thesis focuses on biological computers. I develop novel design algorithms for distributed digital and analogue computers composed of spatial patterns of communicating bacterial colonies. I prove mathematically that we can program arbitrary digital functions and develop an algorithm for the automated design of optimal spatial circuits. Furthermore, I show that bacterial neural networks can be built using our system and develop efficient design tools to do so. I verify these results using computational simulations. This work shows that we can build distributed biological computers using communicating bacterial colonies and different design tools can be used to program digital and analogue functions. The second part of this thesis utilises a technique from artificial intelligence, reinforcement learning, in first the control and then the understanding of biological systems. First, I show the potential utility of reinforcement learning to control and optimise interacting communities of microbes that produce a biomolecule. Second, I apply reinforcement learning to the design of optimal characterisation experiments within synthetic biology. This work shows that methods utilising reinforcement learning show promise for complex distributed bioprocessing in industry and the design of optimal experiments throughout biology

Nonlinear predictors for systems with bounded trajectories and delayed measurements

Novel nonlinear predictors are studied for nonlinear systems with delayed measurements without assuming globally Lipschitz conditions or a known predictor map but requiring instead bounded state trajectories. The delay is constant and known. These nonlinear predictors consists of a series of dynamic filters that generate estimates of the state vector (and its maximum magnitude) at different delayed time instants which differ from one another by a small fraction of the overall delay

Modeling microbial regulation of pesticide turnover in soils

Pesticides are widely used for pest control in agriculture. Besides their intended use, their long-term fate in real systems is not well understood. They may persist in soils, thereby altering ecosystem functioning and ultimately affecting human health. Pesticide fate is assessed through dissipation experiments in the laboratory or the field. While field experiments provide a close representation of real systems, they are often costly and can be influenced by many unknown or uncontrollable variables. Laboratory experiments, on the other hand, are cheaper and have good control over the governing variables, but due to simplification, extrapolation of the results to real systems can be limited. Mechanistic models are a powerful tool to connect lab and field data and help us to improve our process understanding. Therefore, I used mechanistic, process-based models to assess key microbial regulations of pesticide degradation. I tested my model hypotheses with two pesticide classes: i) chlorophenoxy herbicides (MCPA (2-methyl-4-chlorophenoxyacetic acid) and 2,4-D (2,4-Dichlorophenoxyacetic acid)), and ii) triazines (atrazine (AT)), in an ideal scenario, where bacterial degraders and pesticides are co-localized. This thesis explores some potential controls of pesticide degradation in soils: i) regulated gene expression, ii) mass-transfer process across the bacterial cell membranes, iii) bioenergetic constraints, and iv) environmental factors (soil temperature and moisture). The models presented in this thesis show that including microbial regulations improves predictions of pesticide degradation, compared to conventional models based on Monod kinetics. The gene-centric models achieved a better representation of microbial dynamics and enable us to explore the relationship between functional genes and process rates, and the models that used transition state theory to account for bioenergetic constraints improved the description of degradation at low concentrations. However, the lack of informative data for the validation of model processes hampered model development. Therefore, in the fourth part of this thesis, I used atrazine with its rather complex degradation pathway to apply a prospective optimal design method to find the optimal experimental designs to enable us identifying the degradation pathway present in a given environment. The optimal designs found suggest to prioritize determining metabolites and biomass of specific degraders, which are not typically measured in environmental fate studies. These data will lead to more robust model formulations for risk assessment and decision-making. With this thesis, I revealed important regulations of pesticide degradation in soils that help to improve process understanding and model predictions. I provided simple model formulations, for example the Hill function for gene expression and transition state theory for bioenergetic growth constraints, which can easily be integrated into biogeochemical models. My thesis covers initial but essential steps towards a predictive pesticide degradation model usable for risk assessment and decision-making. I also discuss implication for further research, in particular how mechanistic process-based modeling could be combined with new technologies like omics and machine learning.Pestizide sind weit verbreitet in der landwirtschaftlichen Schädlingsbekämpfung. Anders als ihre Wirkungsweise, ist ihr Langzeitverbleib in der Umwelt nicht gut verstanden. Sie gelangen in den Boden und können sich dort anreichen und die Bodenfunktionen beeinträchtigen und letzendlich auch die menschliche Gesundheit gefährden. Die Ausbreitung von Pestiziden wird anhand von Abbauversuchen in Labor- und Feldexperimenten ermittelt. Feldexperimente bieten ein relativ genaues Abbild natürlicher Systeme, sind jedoch meist teuer und können durch unbekannte oder nicht kontrollierbare Faktoren stark beeinflusst werden. Laborexperimente sind in dieser Hinsicht kostengünstiger und bieten eine gute Kontrolle der einwirkenden Faktoren. Allerdings lassen sich die Ergebnisse nur begrenzt auf natürliche Systeme übertragen. Mechanistische Modelle sind ein mächtiges Werkzeug, um Labor- und Felddaten zusammenzuführen und helfen uns dabei, die mikrobiellen Regulationsmechanismen des Pestizidabbaus im Boden besser zu verstehen. Aus diesem Grund habe ich mechanistische, prozess basierte Modelle eingesetzt. Ich habe meine Modellhypothesen bei zwei Pestizidgruppen getestet: i) Chlorphenoxyherbiziden (MCPA (2-Methyl-4-chlorphenoxyessigsäure) und 2,4-D (2,4-Dichlorphenoxyessigsäure)) und ii) Triazinen (Atrazin (AT)), in einem Idealszenario, wo bakterielle Abbauer und Pestizid kolokalisiert auftreten. Meine Doktorarbeit konzentriert sich auf einige der potenziellen Kontrollmechanismen des Pestizidabbaus im Boden: i) regulierte Genexpression, ii) Massetransferprozesse durch die Zellmembran, iii) bioenergetische Limitierungen und iv) Umweltfaktoren (Bodentemperatur und Bodenfeuchte). Die in dieser Doktorarbeit vorgestellten Modelle zeigen, dass die Berücksichtigung mikrobieller Regulationen Vorhersagen des Pestizidabbaus verbessert, gegenüber herkömmlichen, auf Monod-Kinetik-basierenden Modellen. Die gen-basierten Modelle erreichten eine bessere Repräsentation der mikrobiellen Dynamik und geben uns die Möglichkeit, den Zusammenhang zwischen funktionellen Genen und Prozessraten herzustellen, wohingegen Modelle, die die Abbaugeschwindigkeit auf Grundlage der Theorie des Übergangszustandes limitieren, eine genauere Konzentrationen liefern. Der Mangel an Messdaten zur Validierung behinderte allerdings die Modellentwicklung. Daher benutzte ich ich im vierten Teil dieser Arbeit, am Beispiel von Atrazin, mit seinem eher komplexen Abbauweg, eine Methode des prospective optimal design, um das bestmögliche Experimentaldesign zu finden, mit dem wir den in einer bestimmten Umgebung vorherrschenden Abbauweg identifizieren können. Die gefundenen optimalen Designs weisen auf die Erfordenis hin, die Messung von Hauptmetaboliten und Biomasse von spezifischen Abbauern zu priorisieren, welche in Abbauversuchen typischerweise nicht gemessen werden. Die Informationen aus diesen Daten werden zu besseren Modellformulierungen führen, die sich für Risikoabschätzung und Entscheidungsfindung nutzen lassen. Mit dieser Doktorarbeit konnte ich für den Pestizidabbau im Boden wichtige Regulationsmechanismen aufdecken, und so, unser Verständnis und Vorhersagen solcher Prozesse verbessern. Ich stelle einfache Modellformulierungen bereit, beispielsweise die Hill-Funktion für Genexpression und eine Implementierung der Theorie des Übergangszustands, welche sich einfach in biogeochemische Modelle integrieren lassen. Meine Arbeit liefert grundlegende und entscheidende Schritte zur Entwicklung eines Vorhersagemodells für den Pestizidabbau und dessen Einsatz in Risikoabschätzung und Entscheidungsfindung. Darüber hinaus gebe ich einen Ausblick auf weiterführende Forschungsansätze, insbesondere wie sich mechanistische, prozess-basierte Modellansätze mit neuen Technologien wie omics und Machine Learning verbinden lassen könnten

Global stabilisation of continuous bioreactors: tools for analysis and design of feeding laws

[EN] This work revisits the dynamic behaviour of stirred continuous reactors in which a single bioreaction with unknown kinetics occurs. Conditions on the feeding strategy to avoid washing out the biomass and falling in batch operation are obtained. These conditions derive in a closed positively invariant region including the desired operating point. It is stated that no closed orbits may exist in this region and, furthermore, that no fixed point exists but on one of its borders. Therefore, global stability is achieved by finding a feeding law that fulfils the aforementioned invariant conditions and gives a single equilibrium for a first-order dynamics. These results are useful to determine the stability properties of different control laws and, more importantly, to design new ones. The main advantages of the proposed approach are its simplicity and that, differing from previous results, input saturation does not affect stability results. The potentiality of the developed tools is illustrated by means of classical and novel feeding laws. (C) 2017 Elsevier Ltd. All rights reserved.Financed by I216-2016 (UNLP), PICT2014-2394 (ANPCyT) and PIP112-2015-01-00837 (CONICET), Argentina; and by DPI2014-55276-C5-1-R MINECO/AEI/FEDER, UE. The material in this paper was not presented at any conference.De Battista, H.; Jamilis, M.; Garelli, F.; Picó, J. (2018). Global stabilisation of continuous bioreactors: tools for analysis and design of feeding laws. Automatica. 89:340-348. https://doi.org/10.1016/j.automatica.2017.12.041S3403488

Control of ATP homeostasis during the respiro-fermentative transition in yeast

Respiring Saccharomyces cerevisiae cells respond to a sudden increase in glucose concentration by a pronounced drop of their adenine nucleotide content. Transient accumulation of the purine salvage pathway intermediate inosine accounts for the apparent loss of adenine nucleotides.Inosine formation in response to perturbations of cellular energy balance depends on the presence of a fermentable carbon source. Under respiratory conditions, AMP accumulates instead and no inosine is formed.Conversion of AXPs into inosine is facilitated by AMP deaminase, Amd1, and IMP-specific 5'-nucleotidase, Isn1. Inosine recycling into the AXP pool is facilitated by the purine nucleoside phosphorylase, Pnp1, and joint action of the phosphoribosyltransferases, Hpt1 and Xpt1.Impaired inosine formation results in altered metabolite pool dynamics in response to glucose addition, but does not change glycolytic flux. However, mutants blocked in inosine formation exhibit delayed growth acceleration after glucose addition