Robust detection and verification of linear relationships to generate metabolic networks using estimates of technical errors

<p>Abstract</p> <p>Background</p> <p>The size and magnitude of the metabolome, the ratio between individual metabolites and the response of metabolic networks is controlled by multiple cellular factors. A tight control over metabolite ratios will be reflected by a linear relationship of pairs of metabolite due to the flexibility of metabolic pathways. Hence, unbiased detection and validation of linear metabolic variance can be interpreted in terms of biological control. For robust analyses, criteria for rejecting or accepting linearities need to be developed despite technical measurement errors. The entirety of all pair wise linear metabolic relationships then yields insights into the network of cellular regulation.</p> <p>Results</p> <p>The Bayesian law was applied for detecting linearities that are validated by explaining the residues by the degree of technical measurement errors. Test statistics were developed and the algorithm was tested on simulated data using 3–150 samples and 0–100% technical error. Under the null hypothesis of the existence of a linear relationship, type I errors remained below 5% for data sets consisting of more than four samples, whereas the type II error rate quickly raised with increasing technical errors. Conversely, a filter was developed to balance the error rates in the opposite direction. A minimum of 20 biological replicates is recommended if technical errors remain below 20% relative standard deviation and if thresholds for false error rates are acceptable at less than 5%. The algorithm was proven to be robust against outliers, unlike Pearson's correlations.</p> <p>Conclusion</p> <p>The algorithm facilitates finding linear relationships in complex datasets, which is radically different from estimating linearity parameters from given linear relationships. Without filter, it provides high sensitivity and fair specificity. If the filter is activated, high specificity but only fair sensitivity is yielded. Total error rates are more favorable with deactivated filters, and hence, metabolomic networks should be generated without the filter. In addition, Bayesian likelihoods facilitate the detection of multiple linear dependencies between two variables. This property of the algorithm enables its use as a discovery tool and to generate novel hypotheses of the existence of otherwise hidden biological factors.</p

Tissue Proteomes: Quantitative Mass Spectrometry of Murine Liver and Ovarian Endometrioma

A human genome contains more than 20 000 protein-encoding genes. A human proteome, instead, has been estimated to be much more complex and dynamic. The most powerful tool to study proteins today is mass spectrometry (MS). MS based proteomics is based on the measurement of the masses of charged peptide ions in a gas-phase. The peptide amino acid sequence can be deduced, and matching proteins can be found, using software to correlate MS-data with sequence database information. Quantitative proteomics allow the estimation of the absolute or relative abundance of a certain protein in a sample. The label-free quantification methods use the intrinsic MS-peptide signals in the calculation of the quantitative values enabling the comparison of peptide signals from numerous patient samples. In this work, a quantitative MS methodology was established to study aromatase overexpressing (AROM+) male mouse liver and ovarian endometriosis tissue samples. The workflow of label-free quantitative proteomics was optimized in terms of sensitivity and robustness, allowing the quantification of 1500 proteins with a low coefficient of variance in both sample types. Additionally, five statistical methods were evaluated for the use with label-free quantitative proteomics data. The proteome data was integrated with other omics datasets, such as mRNA microarray and metabolite data sets. As a result, an altered lipid metabolism in liver was discovered in male AROM+ mice. The results suggest a reduced beta oxidation of long chain phospholipids in the liver and increased levels of pro-inflammatory fatty acids in the circulation in these mice. Conversely, in the endometriosis tissues, a set of proteins highly specific for ovarian endometrioma were discovered, many of which were under the regulation of the growth factor TGF-β1. This finding supports subsequent biomarker verification in a larger number of endometriosis patient samples.Siirretty Doriast

Mathematical Analysis and Modeling of Signaling Networks

Mathematical models are in focus of modern systems biology and increasingly important to understand and manipulate complex biological systems. At the same time, new and improved techniques in metabolomics and proteomics enhance the ability to measure cellular states and molecular concentrations. In consequence, this leads to important biological insights and novel potential drug targets. Model development in systems biology can be described as an iterative process of model refinement to match the observed properties. The resulting research cycle is based on a well-defined initial model and requires careful model revision in each step. {As an initial step, a stoichiometry-based mathematical model of the muscarinic acetylcholine receptor subtype 2 (M2 receptor)-induced signaling in Chinese hamster ovary (CHO) cells was derived. To validate the obtained initial model based on spatially accessible, not neces-sarily time-resolved data, the novel constrained flux sampling (CFS) is proposed in this work. The thus verified static model was then translated into a dynamical system based on ordinary differential equations (ODEs) by incorporating time-dependent experimental data. To learn from the errors of systems biological models, the dynamic elastic-net (DEN), a novel approach based on optimal control theory, is proposed in this thesis. Next, the Bayesian dy-namic elastic-net (BDEN), a systematic, fully algorithmic method based on the Markov chain Monte Carlo method was derived, which allows to detect hidden influences as well as missed reactions in ODE-based models. The BDEN allows for further validation of the developed M2 receptor-induced signaling pathway and thus provides evidence for the completeness of the obtained dynamical system. This thesis introduces the first comprehensive model of the M2 receptor-induced signaling in CHO cells. Furthermore, this work presents several novel algorithms to validate and correct static and dynamic models of biological systems in a semi-automatic manner. These novel algorithms are expected to simplify the development of further mathematical models in systems biology.Mathematische Modellierung und Analyse von Signalnetzwerken Mathematische Modelle stehen im Zentrum der modernen Systembiologie und werden immer wichtiger, um komplexe biologische Systeme verstehen und manipulieren zu können. Gleichzeitig erweitern neue und verbesserte Verfahren der Metabolomik und Proteomik die Möglichkeiten, Zellzustände und Molekülkonzentrationen zu bestimmen. Dies ermöglicht die Gewinnung neuer und wichtiger biologischer Erkenntnisse und die Identifizierung neuer potentieller Ansatzpunkte für medizinische Wirkstoffe. Die Modellentwicklung in der Systembiologie kann als ein iterativer Prozess der permanenten Modellverbesserung beschrieben werden, der das Ziel hat, die beobachteten Eigenschaften korrekt wiederzugeben. Der resultierende Modellierungskreislauf basiert auf einem klar bestimmten Anfangsmodell und erfordert das sorgfältige Anpassen des Modells in jedem einzelnen Modellierungsschritt. In einem ersten Schritt wurde ein auf stöchiometrischen Daten basierendes mathematisches Modell für die durch den muskarinischen Acetylcholinrezeptor des Subtyps 2 (M2-Rezeptor) induzierte Signalübertragung in CHO-Zellen aufgestellt. Zur Validierung des ursprünglichen Modells auf der Grundlage von räumlich erfassbaren, nicht notwendigerweise zeitaufgelösten Daten wird in dieser Arbeit das neu entwickelte Constrained Flux Sampling (CFS) vorgestellt. Das auf diese Weise verifizierte statische Modell wurde dann unter Einbeziehung zeitabhängiger experimenteller Messdaten in ein dynamisches Modell basierend auf gewöhnlichen Differentialgleichungen (DGL) umgewandelt. Um aus den mathematischen Unsicherheiten systembiologischer Modelle zu lernen, wird in dieser Arbeit das Dynamic Elastic-Net (DEN) eingeführt, ein neuer Ansatz basierend auf der Theorie der optimalen Steuerungen. Als nächster Schritt wurde das Bayesian Dynamic Elastic-Net (BDEN) entwickelt, eine systematische, vollständig algorithmische Methode basierend auf dem Markov-Chain-Monte-Carlo-Verfahren, die es erlaubt, sowohl verborgene Einflussfaktoren als auch übersehene Reaktionen in DGL-basierten Modellen aufzuspüren. Das BDEN ermöglicht die weitere Validierung des durch den M2-Rezeptor induzierten Signalwegs und liefert so den Beweis für die Vollständigkeit des modellierten dynamischen Systems. In dieser Arbeit wird das erste vollständige Modell für den durch den M2-Rezeptor induzierten Signalweg in CHO-Zellen eingeführt. Des Weiteren werden in dieser Arbeit verschiedene neue Algorithmen zur halbautomatischen Validierung und Korrektur statischer und dynamischer Modelle biologischer Systeme vorgestellt. Es wird erwartet, dass diese neuen Algorithmen die Entwicklung weiterer mathematischer Modelle in der Systembiologie stark vereinfachen

Development of exploratory data analysis methods for chemical, spatial and temporal analysis of surface water quality data: the Ontario Provincial Water Quality Monitoring Network

Surface water quality (SWQ) databases have been widely compiled to provide information characterizing environmental conditions. But SWQ databases appear to be under-utilized, given the large investment in their creation. One reason is that database spatial, temporal, and compositional dimension vary through time, reflecting changing priorities through time and contrasts between different agencies, making coherent analysis challenging. This thesis explores the Ontario Provincial Water Quality Monitoring Network (PWQMN) to derive higher order hydrochemical properties, to render SWQ data in “network space” permitting catchment-wide visualization, and in undertaking temporal trend analysis. Rivers play a critical role in the terrestrial carbon cycle, but the level and role of dissolved carbon dioxide is poorly understood because it is difficult to measure or estimate. A stepwise algorithm was developed to extract an exceptionally large and accurate PCO2 data set from the PWQMN. The results showed ubiquitous supersaturation and decrease downstream, implying high rates of organic matter import into surface waters. The spatial pattern of surface water monitoring shows a close relationship to a novel upstream ordering system that was exploited to develop a “network space” transformation of rivers and SWQ data. Mapping of chloride, carbon dioxide, oxygen and total phosphorus data in network space showed spatial coherence, clear urban impact, and systematic inter-catchment differences. A complementary mixing algorithm allowed budgeting for high-resolution data sets, but was less successful for general mapping where its value was in auditing the data for point sources or poor monitoring. Rendering of SWQ data in time using network space was very effective, but risky due to bias and possible errors in the data. Overall, PCO2 levels peaked in the mid-1990s, then fell dramatically to variable, but non-treading levels. These changes were associated with significant transitions in monitoring policy and priorities, so were investigated as possible artifacts. Inter-catchment and epochal differences in PCO2 (and its determinants: alkalinity and pH) were unexpected. This may arise from regional acid rain control programs, but may be a result of contrasting field protocols in different agencies

Basic Research Needs for Geosciences: Facilitating 21st Century Energy Systems

Executive Summary Serious challenges must be faced in this century as the world seeks to meet global energy needs and at the same time reduce emissions of greenhouse gases to the atmosphere. Even with a growing energy supply from alternative sources, fossil carbon resources will remain in heavy use and will generate large volumes of carbon dioxide (CO2). To reduce the atmospheric impact of this fossil energy use, it is necessary to capture and sequester a substantial fraction of the produced CO2. Subsurface geologic formations offer a potential location for long-term storage of the requisite large volumes of CO2. Nuclear energy resources could also reduce use of carbon-based fuels and CO2 generation, especially if nuclear energy capacity is greatly increased. Nuclear power generation results in spent nuclear fuel and other radioactive materials that also must be sequestered underground. Hence, regardless of technology choices, there will be major increases in the demand to store materials underground in large quantities, for long times, and with increasing efficiency and safety margins. Rock formations are composed of complex natural materials and were not designed by nature as storage vaults. If new energy technologies are to be developed in a timely fashion while ensuring public safety, fundamental improvements are needed in our understanding of how these rock formations will perform as storage systems. This report describes the scientific challenges associated with geologic sequestration of large volumes of carbon dioxide for hundreds of years, and also addresses the geoscientific aspects of safely storing nuclear waste materials for thousands to hundreds of thousands of years. The fundamental crosscutting challenge is to understand the properties and processes associated with complex and heterogeneous subsurface mineral assemblages comprising porous rock formations, and the equally complex fluids that may reside within and flow through those formations. The relevant physical and chemical interactions occur on spatial scales that range from those of atoms, molecules, and mineral surfaces, up to tens of kilometers, and time scales that range from picoseconds to millennia and longer. To predict with confidence the transport and fate of either CO2 or the various components of stored nuclear materials, we need to learn to better describe fundamental atomic, molecular, and biological processes, and to translate those microscale descriptions into macroscopic properties of materials and fluids. We also need fundamental advances in the ability to simulate multiscale systems as they are perturbed during sequestration activities and for very long times afterward, and to monitor those systems in real time with increasing spatial and temporal resolution. The ultimate objective is to predict accurately the performance of the subsurface fluid-rock storage systems, and to verify enough of the predicted performance with direct observations to build confidence that the systems will meet their design targets as well as environmental protection goals. The report summarizes the results and conclusions of a Workshop on Basic Research Needs for Geosciences held in February 2007. Five panels met, resulting in four Panel Reports, three Grand Challenges, six Priority Research Directions, and three Crosscutting Research Issues. The Grand Challenges differ from the Priority Research Directions in that the former describe broader, long-term objectives while the latter are more focused

Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed