In-Time Parallelization Of Atmospheric Chemical Kinetics

This work investigates the potential of an in-time parallelization of atmospheric chemical ki- netics. Its numerical calculation is one time-consuming step within the numerical prediction of the air quality. The widely used parallelization strategies only allow a limited potential level of parallelism. A higher level of parallelism within the codes will be necessary to enable benefits from future exa-scale computing architectures. In air quality prediction codes, chem- ical kinetics is typically considered to react in isolated boxes over short splitting intervals. This allows their trivial parallelization in space, which however is limited by the number of grid entities. This work pursues a parallelization beyond this trivial potential and investigates a parallelization across time using the so called “parareal algorithm”. The latter is an iterative prediction-correction scheme, whose efficiency strongly depends on the choice of the predictor. For that purpose, different options are being investigate and compared: Time-stepping schemes with fixed step size, adaptive time-stepping schemes and repro-models, functional representations, that map a given state to a later state in time. Only the choice of repromodels leads to a speed-up through parallelism, compared to the sequential reference for the scenarios considered here

Sum Over Histories Representation of Chemical Kinetics: an Interpretive and Predictive Method for Modeling Chemical Kinetics Using Time-Dependent Pathways

Chemical kinetics can be viewed as an intricate network of inter-related chemical reactions that work cooperatively to convert reagent species into product species. The network is in general time dependent reacting the non-steady state nature of the chemistry. When it comes to interpreting and predicting chemical kinetics, the history of chemical moieties can play vital roles. In order to study the histories of chemical substances using time-dependent chemical network, this thesis focuses on developing a Sum Over Histories Representation (SOHR for short) of chemical kinetics.The description of time-dependent chemistry of a reaction network is provided by chemical pathways defined at a molecular level. Using this methodology, the quantitative time evolution of the kinetics is described by enumerating the most important pathways followed by a chemical moiety such as a tagged atom. An explicit formula for the pathway probabilities is derived which takes the form of an integral over a time-ordered product. This expression has a simple and computationally efficient Monte Carlo representation which permits the method to be applied to a wide range of problems.In SOHR, the history of the chemical moiety can be described by time-dependent pathways. Unlike the static flux methods for path analysis, SOHR includes the explicit time-dependence of pathway probabilities. Using SOHR, the sensitivity of an observable with respect to a kinetic parameter such as a rate coefficient is then analyzed in terms of how that parameter affects the chemical pathway probabilities. This thesis demonstrates that large sensitivities are often associated with rate limiting steps along important chemical pathways or by reactions that control the branching of reactive flux, though they vary with time.In addition to interpreting chemical kinetics, this thesis studies the practical approach to modeling chemical kinetics without solving conventional mass-action ODEs. An iterative framework was introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of elementary rate coefficients. To avoid the pitfall of integrating over the histories of long paths, we proposed a sector-by-sector strategy that shortens the candidate path without losing numerical accuracy. This method was successfully applied to the model Lotka-Volterra system and to a realistic H2 combustion system.This thesis culminates with a discussion of the interpretative and predictive applicability ofSOHR

Trace Metal Bioremediation: Assessment of Model Components from Laboratory and Field Studies to Identify Critical Variables

The objective of this project was to gain an insight into the modeling support needed for the understanding, design, and operation of trace metal/radionuclide bioremediation. To achieve this objective, a workshop was convened to discuss the elements such a model should contain. A ''protomodel'' was developed, based on the recommendations of the workshop, and was used to perform sensitivity analysis as well as some preliminary simulations in support for bioremediation test experiments at UMTRA sites. To simulate the numerous biogeochemical processes that will occur during the bioremediation of uranium contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled, steady state mass balance equations, accounting for advection, diffusion, dispersion, and a kinetic formulation of the transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and uranium. This set of equations is solved numerically, using a finite element scheme. The redox conditions of the domain are characterized by estimating the pE, based on the concentrations of the dominant terminal electron acceptor and its corresponding reduced specie. This pE and the concentrations of relevant species are passed to a modified version of MINTEQA2, which calculates the speciation and solubilities of the species of interest. Kinetics of abiotic reactions are described as being proportional to the difference between the actual and equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. Results indicated that for the usually high nitrate contents found ate many DOE sites, overall bioremediation of trace metals was highly sensitive to the formulation of the denitrification process. Simulations were performed to illustrate the effect of biostimulation on the transport and precipitation of uranium in the subsurface, at conditions equivalent to UMTRA sites. These simulations predicted that uranium would precipitate in bands that are located relatively close to the acetate injection well. The simulations also showed the importance of properly determining U(IV) oxidative dissolution rates, in order to assess the stability of precipitates once oxygenated water reenters the aquifer after bioremediation is discontinued. The objective of this project was to provide guidance to NABIR's Systems Integration Element, on the development of models to simulate the bioremediation of trace metals and radionuclides. Such models necessarily need to integrate hydrological, geochemical, and microbiological processes. In order to gain a better understanding of the key processes that such a model should contain, it was deemed desirable to convene a workshop with experts from these different fields. The goal was to obtain a preliminary consensus on the required level of detail for the formulations of these different chemical, physical, and microbiological processes. The workshop was held on December 18, 1998

On Signal Transduction in Human Embryonic Stem Cells: Towards a Systems View

Human embryonic stem cells (hESC) have been a major cell source for research in regenerative medicine due to the demonstration of properties of self-renewal and efficient lineage specific differentiation, both on additions of external cues. Self-renewal provides the potential to extract large quantities of naïve cells that can then be differentiated to clinically relevant mature lineages. While there exists significant proof-of-concept to transform stem cells to the desired lineage, generating fully functional cell types is still an unmet challenge. A major reason for this is our limited understanding of the complexity of the transformation process. The overarching goal of this PhD research was to provide strategies to bring mathematical modeling into the realm of stem cell research, particularly to analyze the complex regulatory network of signaling events controlling cell fate. This work focused on the signaling pathways that in concert control the balance of self-renewal and endoderm differentiation of hESCs. We proposed a framework for developing mechanistic understanding from disparate signaling pathways using combinations of data-driven and equation based models. As a first step, we analyzed growth factor mediated PI3K/AKT pathway that must remain highly active to inhibit differentiation in self-renewal state. Using an integrated approach of mechanistic modeling, systems analysis and experimental validation we identified the role of a regulatory process (negative feedback) in maintaining signal amplitudes and controlling the propagation of parameter uncertainty down the pathway in the self-renewal state. To analyze endoderm differentiation, biclustering with bootstrapping formulation was used to identify co-regulated transcription factor patterns under a combinatorial modulation of endoderm inducing signaling pathways. In the final step, a detailed mechanistic analysis was done to characterize the dynamic features of TGF-β/SMAD pathway for inducing endoderm. Utilizing a dynamic Bayesian network formulism, AKT mediated crosstalk connections were inferred from the detailed time series data. Modeling of competing AKT-SMAD interactions followed by parametric ensemble analysis enabled identification of plausible hypotheses that could explain experimental observations. Using our integrated approach, we can now begin to rationally optimize for desirable fate of hESCs with reduced variability and accelerate the path towards therapeutic applications of hESCs

Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment

This paper presents a concise state-of-the-art review along with an exhaustive comparative investigation on surrogate models for critical comparative assessment of uncertainty in natural frequencies of composite plates on the basis of computational efficiency and accuracy. Both individual and combined variations of input parameters have been considered to account for the effect of low and high dimensional input parameter spaces in the surrogate based uncertainty quantification algorithms including the rate of convergence. Probabilistic characterization of the first three stochastic natural frequencies is carried out by using a finite element model that includes the effects of transverse shear deformation based on Mindlin’s theory in conjunction with a layer-wise random variable approach. The results obtained by different metamodels have been compared with the results of traditional Monte Carlo simulation (MCS) method for high fidelity uncertainty quantification. The crucial issue regarding influence of sampling techniques on the performance of metamodel based uncertainty quantification has been addressed as an integral part of this article

Experimental and Chemical Kinetic Modelling Study on the Combustion of Alternative Fuels in Fundamental Systems and Practical Engines

In this work, experimental data of ignition delay times of n-butanol, gasoline, toluene reference fuel (TRF), a gasoline/n-butanol blend and a TRF/n-butanol blend were obtained using the Leeds University Rapid Compression Machine (RCM) while autoignition (knock) onsets and knock intensities of gasoline, TRF, gasoline/n-butanol and TRF/n-butanol blends were measured using the Leeds University Optical Engine (LUPOE). The work showed that within the RCM, the 3-component TRF surrogate captures the trend of gasoline data well across the temperature range. However, based on results obtained in the engine, it appears that the chosen TRF may not be an excellent representation of gasoline under engine conditions as the knock boundary of TRF as well as the measured knock onsets are significantly lower than those of gasoline. The ignition delay times measured in the RCM for the blend, lay between those of gasoline and n-butanol under stoichiometric conditions across the temperature range studied and at lower temperatures, n-butanol acts as an octane enhancer over and above what might be expected from a simple linear blending law. In the engine, the measured knock onsets for the blend were higher than those of gasoline at the more retarded spark timing of 6 CA bTDC but the effect disappears at higher spark advances. Future studies exploring the blending effect of n-butanol across a range of blending ratios is required since it is difficult to conclude on the overall effect of n-butanol blending on gasoline based on the single blend that has been considered in this study. The chemical kinetic modelling of the fuels investigated has also been evaluated by comparing results from simulations employing the relevant reaction mechanisms with the experimental data sourced from either the open literature or measured in-house. Local as well as global uncertainty/sensitivity methods accounting for the impact of uncertainties in the input parameters, were also employed within the framework of ignition delay time modelling in an RCM and species concentration prediction in a JSR, for analysis of the chemical kinetic modelling of DME, n-butanol, TRF and TRF/n-butanol oxidation in order to advance the understanding of the key reactions rates that are crucial for the accurate prediction of the combustion of alternative fuels in internal combustion engines. The results showed that uncertainties in predicting key target quantities for the various fuels studied are currently large but driven by few reactions. Further studies of the key reaction channels identified in this work at the P-T conditions of relevance to combustion applications could help to improve current mechanisms. Moreover, the chemical kinetic modelling of the autoignition and species concentration of TRF, TRF/n-butanol and n-butanol fuels was carried out using the adopted TRF/n-butanol mechanism as input in the engine simulations of a recently developed commercial engine software known as LOGEengine. Similar to the results obtained in the RCM modelling work, the knock onsets predicted for TRF and TRF/n-butanol blend under engine conditions were consistently higher than the measured data. Overall, the work demonstrated that accurate representation of the low temperature chemistry in current chemical kinetic models of alternative fuels is very crucial for the accurate description of the chemical processes and autoignition of the end gas in the engine

A scaling analysis of ozone photochemistry: I Model development

International audienceA scaling analysis has been used to capture the integrated behaviour of several photochemical mechanisms for a wide range of precursor concentrations and a variety of environmental conditions. The Buckingham Pi method of dimensional analysis was used to express the relevant variables in terms of dimensionless groups. These grouping show maximum ozone, initial NOx and initial VOC concentrations are made non-dimensional by the average NO2 photolysis rate (jav) and the rate constant for the NO-O3 titration reaction (kNO); temperature by the NO-O3 activation energy (ENO) and Boltzmann constant (k) and total irradiation time by the cumulative jav?t photolysis rate (?3). The analysis shows dimensionless maximum ozone concentration can be described by a product of powers of dimensionless initial NOx concentration, dimensionless temperature, and a similarity curve directly dependent on the ratio of initial VOC to NOx concentration and implicitly dependent on the cumulative NO2 photolysis rate. When Weibull transformed, the similarity relationship shows a scaling break with dimensionless model output clustering onto two straight line segments, parameterized using four variables: two describing the slopes of the line segments and two giving the location of their intersection. A fifth parameter is used to normalize the model output. The scaling analysis, similarity curve and parameterization appear to be independent of the details of the chemical mechanism, hold for a variety of VOC species and mixtures and a wide range of temperatures and actinic fluxes

Quantitative Analysis of Robustness in Systems Biology:Combining Global and Local Approaches

To characterize the behavior and robustness of cellular circuits is a major challenge for Systems Biology. Many of the published methods that address this question quantify the local robustness of the models. In this thesis, I tried to underpin the inappropriateness of such local measures and proposed an alternative solution: a glocal measure for robustness that combines both global and local aspects. It comprises a broad exploration of the parameter space and a further refinement based on different local measures. The method is general and such glocal analysis could be applied to many problems. Along with the theoretical and formal aspects of this new analysis method, I developed sampling algorithms that efficiently investigate the generally high-dimensional parameter space of models. To show the usefulness of my method, I applied it on different models of cyclic systems such as the circadian clock and the mitotic cycle. I first considered two models of the cyanobacterial circadian clock and compared their robustness properties. Also in the context of circadian rhythms, I studied the effect of additional feedback loops on the robustness properties in relation with entrainment. Models of the mitotic cycle are also used to assess the effect of an additional positive feedback loop on circuit robustness to parameter changes and molecular noise. Finally, I established some principles for the design of a synthetic circuit based on robustness. The thesis carries on with a discussion that emphasizes the advantages of the glocal method for robustness analysis: in all works, correlations between parameter values and local robustness can be found. Such results facilitate our understanding of the biochemical systems and can be a guide for new experiments to discriminate models or give directions for altering the robustness of the systems. I conclude by discussing potential applications for my method and possible improvements

Novel approaches for dynamic modelling of E. coli and their application in Metabolic Engineering

PhD thesis in BioengineeringOne of the trends of modern societies is the replacement of chemical processes by biochemical ones, with new compounds being synthesized by engineered microorganisms, while some waste products are also being degraded by biotechnological means. Biotechnology holds the promise of creating a more profitable and environmental friendly industry, with a reduced number of waste products, when contrasted with the traditional chemical industry. However, in an era in which genomes are sequenced at a faster pace than ever before, and with the advent omic measurements, this information is not directly translated into the targeted design of new microorganisms, or biological processes. These experimental data in isolation do not explain how the different cell constituents interact. Reductionist approaches that dominated science in the last century study cellular entities in isolation as separate chunks, without taking into consideration interactions with other molecules. This leads to an incomplete view of biological processes, which compromises the development of new knowledge. To overcome these hurdles, a formal systems approach to Biology has been surging in the last thirty years. Systems biology can be defined as the conjugation of different fields (such as Mathematics, Computer Science, Biology), to describe formally and non-ambiguously the behavior of the different cellular systems and their interactions, using to models and simulations. Metabolic Engineering takes advantage of these formal specifications, using mathematically based methods to derive strategies to optimize the microbial metabolism, in order to achieve a desired goal, such as the increase of the production of a relevant industrial compound. In this work, we develop a mechanistic dynamic model based on ordinary differential equations, comprised by elementary mass action descriptions of each reaction, from an existing model of Escherichia coli in the literature. We also explore different calibration processes for these reaction descriptions. We also contribute to the field of strain design by utilizing evolutionary algorithms with a new representation scheme that allows to search for enzyme modulations, in continuous or discrete scales, as well as reaction knockouts, in existing dynamic metabolic models, aiming at the maximization of product yields. In the bioprocess optimization field, we extended the Dynamic Flux Balance Analysis formulation to incorporate the possibility to simulate fed-batch bioprocesses. This formulation is also enhanced with methods that possess the capacity to design feed profiles to attain a specific goal, such as maximizing the bioprocess yield or productivity. All the developed methods involved some form of sensitivity and identifiability analysis, to identify how model outputs are affected by their parameters. All the work was constructed under a modular software framework (developed during this thesis), that permits the interaction of distinct algorithms and languages, being a flexible tool to utilize in a cluster environment. The framework is available as an open-source software package, and has appeal to systems biologists describing biological processes with ordinary differential equations.Uma das tendências na nossa sociedade actual é a substituição de processos químicos por processos bioquímicos, e a síntese de novos compostos por microrganismos, bem como a degradação de resíduos por meios biotecnológicos. A Biotecnologia tem, assim, a promessa de criar uma indústria mais rentavél e mais amiga do ambiente, com um número reduzido de resíduos, contrastando com a indústria química. No entanto, numa era em que os genomas são sequenciados a um ritmo nunca visto, assim como as medições de dados ómicos, esta informação não é diretamente traduzida no desenho de estirpes microbianas ou processos biológicos. Estes dados experimentais em isolamento não explicam como os diferentes componentes celulares interagem. As abordagens reducionistas que dominaram a ciência no século passado, estudam os constituintes celulares em isolamento, como pedaços isolados, sem tomar em consideração as interacções com outras moléculas, o que traduz uma visão incompleta do mundo, que compromete o desenvolvimento de novo conhecimento. Para superar estes obstáculos, uma nova abordagem à Biologia tem emergido nos últimos trinta anos. A Biologia de Sistemas pode ser definida como a conjugação de diferentes áreas (como a Matemática, Ciência da Computação, Biologia), para descrever formalmente e de forma não ambígua o comportamento dos diferentes sistemas celulares e as suas interações utilizando a modelação. A Engenharia Metabólica tira partido destas especificações formais, utilizando métodos matemáticos para derivar estratégias tendo em vista a optimização do metabolismo de microrganismos, de forma a atingir um objetivo definido como por exemplo o aumento da produção de um composto relevante a nível industrial. Neste trabalho, desenvolvemos um modelo dinâmico mecanístico baseado em equações diferenciais ordinárias, composto por descrições ação de massas elementares para cada reacção, partindo de um modelo já existente da Escherichia coli na literatura. Utilizamos também algoritmos evolucionários com um novo esquema de representação que permite pesquisar por modulações enzimáticas, numa escala contínua ou discreta, assim como eliminar reações em modelos metabólicos existentes de forma a maximizar o rendimento ou a produtividade. Todos os métodos desenvolvidos envolveram alguma forma de análise de sensibilidade ou identifiabilidade, de forma a verificar como as saídas do modelo são afetados pelos parâmetros. Todo o trabalho foi construído de acordo com uma plataforma de software modular (desenvolvida durante esta tese) que permite a interação de algoritmos e linguagens distintos, sendo uma ferramenta flexível para utilizar em ambientes de cluster. A plataforma encontra-se disponível como um pacote de software de código aberto e tem utilidade para biólogos de sistemas que pretendam descrever processos com equações diferencias ordinárias