Ph.D.

Computer models are used extensively to investigate biological systems. Many of these systems can be described in terms of fields???spatially- and temporally- varying scalar, vector and tensor properties defined over domains. For example, the spatial variation of muscle fibers is a vector field, the spatial and temporal variation in temperature of an organ is a scalar field, and the distribution of stress across muscle tissue is a tensor field. In this thesis I present my research on how to represent fields in a format that allows researchers to store and distribute them independently of models and to investigate and manipulate them intuitively. I also demonstrate how the work can be applied to solving and analysing biomedical models. To represent fields I created a two-layer system. One layer, called the Field Representation Language (FRL), represents fields by storing numeric, analytic and meta data for storage and distribution. The focus of this layer is efficiency rather than usability. The second layer, called the Abstract Field Layer (AFL), provides an abstraction of fields so that they are easier for researchers to work with. This layer also provides common operations for manipulating fields as well as transparent conversion to and from FRL representations. The applications that I used to demonstrate the use of AFL and FRL are (a) a fields visualisation toolkit, (b) integration of models from different scales and solvers, and (c) a solver that uses AFL internally. The layered architecture facilitated the development of tools that use fields. A similar architecture may also prove useful for representations of other modelled entities.

Thesis (Ph.D.) -- McMaster University, 1999. / Includes bibliographical references (p. 112-116). Also available via World Wide Web.

Thesis (M.S.)--University of Missouri-Columbia, 2007. / "August 2007" The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 127-139).

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential. We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation via folding. These results apply to systems with negative parameters, instances not commonly considered in previous studies. We also identify ranges of parameter values that provide sufficient conditions on existence of chaotic and multiple stable orbits of different periods for the planar system. We study a second order exponential difference equation with time varying parameters and obtain sufficient conditions for boundedness of solutions and global convergence to zero. For the autonomous case, we show occurrence of multistable periodic and nonperiodic orbits. For the case where parameters are periodic, we show that the nature of the solutions differs qualitatively depending on whether the period of the parameters is even or odd. The above results are applied to biological models of populations. We investigate a broad class of planar systems that arise in the study of stage-structured single species populations. In biological contexts, these results include conditions on extinction or survival of the species in some balanced form, and possible occurrence of complex and chaotic behavior. Special rational (Beverton-Holt) and exponential (Ricker) cases are considered to explore the role of inter-stage competition, restocking strategies, as well as seasonal fluctuations in the vital rates.

Dans de nombreuses applications telles que la médecine, l'environnement ou les biotechnologies par exemple, la découverte de nouveau processus de régulations de gènes permet une meilleure compréhension des réponses phénotypiques des cellules à des stimuli externes. Pour cela, il est alors d'usage de générer et d'analyser les données transcriptomiques issues d'expériences de types puces à ADN ou plus récemment de RNAseq. Ainsi, pour chaque gène d'un organisme d'étude placé dans différentes conditions expérimentales, un ensemble de niveau d'expression est obtenu. A partir de ces données, les mécanismes de régulation des gènes peuvent être obtenus à travers un ensemble de liens dans des graphes. Dans ces réseaux, les nœuds correspondent aux gènes. A lien entre deux nœuds est identifié si une relation de régulation existent entre les deux gènes correspondant. De tels réseaux sont appelés Réseaux de Régulation de Gènes (RRGs). Malgré la profusion de méthodes d'inférence disponible, leur construction et leur analyse restent encore à ce jour un défi.Dans cette thèse, nous proposons de répondre au problème d'inférence de réseaux par des techniques d'optimisation dans des graphes. A partir d'information de régulation sur l'ensemble des couples de gènes, nous proposons de déterminer la présence d'arêtes dans le RRG final en adoptant une formulation de fonction objectif intégrant des contraintes. Des a priori à la fois biologiques (sur les interactions entre les gènes) et structuraux (sur la connectivité des nœuds) ont été considérés pour restreindre l'espace des solutions possibles. Les différents a priori donnent des fonctions objectifs ayant des propriétés différentes, pour lesquelles des stratégies d'optimisation adaptées (continue et/ou discrète) peuvent être appliquées. Les post-traitement que nous avons développé ont mené à un ensemble de méthodes nommés BRANE, pour "Biologically-Related A priori for Network Enhancement". Pour chacune des méthodes développées (BRANE Cut, BRANE Relax et BRANE Clust), nos contributions sont triples : formulation de la fonction objectif à l'aide d'a priori, développement de la stratégie d'optimisation et validation (numérique et biologique) sur des données de parangonnage issues des challenges DREAM4 et DREAM5, montrant ainsi des améliorations pouvant atteindre 20%.En complément de l'inférence de réseaux, notre travail s'est étendu à des traitements de données sur graphe plus génériques, tels que les problèmes inverses. Nous avons notamment étudié HOGMep, une approche Bayésienne utilisant des stratégies d'approximation Bayésienne variationnelle. Cette méthode a été développée pour résoudre de façon conjointe, des problèmes de restauration et de classification sur des données multi-composantes (signaux et images). Les performances d'HOGMep dans un contexte de déconvolution d'image couleur montrent de bonnes qualités de reconstruction et de segmentation. Une étude préliminaire dans un contexte de classification de données médicales liant génotype et phénotype a également montré des résultats prometteurs pour des adaptions à venir en bioinformatiques. / The discovery of novel gene regulatory processes improves the understanding of cell phenotypicresponses to external stimuli for many biological applications, such as medicine, environmentor biotechnologies. To this purpose, transcriptomic data are generated and analyzed from mi-croarrays or more recently RNAseq experiments. For each gene of a studied organism placed indifferent living conditions, they consist in a sequence of genetic expression levels. From thesedata, gene regulation mechanisms can be recovered by revealing topological links encoded ingeometric graphs. In regulatory graphs, nodes correspond to genes. A link between two nodesis identified if a regulation relationship exists between the two corresponding genes. Such net-works are called Gene Regulatory Networks (GRNs). Their construction as well as their analysisremain challenging despite the large number of available inference methods.In this thesis, we propose to address this network inference problem with recently developedtechniques pertaining to graph optimization. Given all the pairwise gene regulation informa-tion available, we propose to determine the presence of edges in the final GRN by adoptingan energy optimization formulation integrating additional constraints. Either biological (infor-mation about gene interactions) or structural (information about node connectivity) a priorihave been considered to reduce the space of possible solutions. Different priors lead to differentproperties of the global cost function, for which various optimization strategies can be applied.The post-processing network refinements we proposed led to a software suite named BRANE for“Biologically-Related A priori for Network Enhancement”. For each of the proposed methodsBRANE Cut, BRANE Relax and BRANE Clust, our contributions are threefold: a priori-based for-mulation, design of the optimization strategy and validation (numerical and/or biological) onbenchmark datasets.In a ramification of this thesis, we slide from graph inference to more generic data processingsuch as inverse problems. We notably invest in HOGMep, a Bayesian-based approach using aVariation Bayesian Approximation framework for its resolution. This approach allows to jointlyperform reconstruction and clustering/segmentation tasks on multi-component data (for instancesignals or images). Its performance in a color image deconvolution context demonstrates bothquality of reconstruction and segmentation. A preliminary study in a medical data classificationcontext linking genotype and phenotype yields promising results for forthcoming bioinformaticsadaptations.

In models for networks of regulatory interactions in biological molecules, the sigmoid relationship between concentration of regulating bodies and the production rates they control has lead to the use of continuous time 'switching' ordinary differential equations (ODEs), sometimes referred to as Glass networks. These Glass networks are the result of a simplifying assumption that the switching behaviour occurs instantaneously at particular threshold values. Though this assumption produces highly tractable models, it also causes analytic difficulties in certain cases due to the discontinuities of the system, such as non-uniqueness. In this thesis we explore the use of 'ramp' functions as an alternative approximation to the sigmoid, which restores continuity to the ODE and removes the assumption of infinitely fast switching by linearly interpolating the focal point values used in a corresponding Glass network. A general framework for producing a ramp system from a certain Glass network is given. Solutions are explored in two dimensions, and then in higher dimensions under two different restrictions. Periodic behaviour is explored in both cases using mappings between threshold boundaries. Limitations in these methods are explored, and a general proof of the existence of periodic solutions in negative feedback loops is given. / Graduate

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: p. B1-B4. / by Kevin Paul Koch. / M.S.

Systems that require a driving force of some kind are very common in physical and biological settings. Driving forces in a biological context are usually referred to as rhythms, pulses or clocks. Here we are interested in the effect of adding a square wave periodic driving force to a biological model. This is intended to model inputs from biological circuits with all-or-none or switch-like resposes. We study a model of cell division proposed by Novak and Tyson. Our switched input is intended to model the interaction of the mitotic oscillator with an ultradian clock. We thoroughly characterize the behaviour as a function of the durations of the active and inactive phases. We also study a model of vein formation in plant leaves proposed by Mitchison. Pulsed hormonal release greatly accelerates vein formation in this model. / x, 105 leaves : ill. (some col.) ; 29 cm.