We investigate reaction-diffusion models for populations whose members undergo two specific processes: dispersal and settling. Systems of this type occur throughout biological science, in contexts ranging from ecology to cell biology.Here we consider three distinct applications, namely: / • animal translocation, / • the invasion of a domain by precursor and differentiated cells, and / • the development of tissue-engineered cartilage. / Mathematical modelling of these systems provides an understanding of the population-level patterns that emerge from the behaviour of individuals. / A multi-species reaction-diffusion model is developed and analysed for each of the three applications. We present numerical results, which are illuminated through analytical results derived for simplified or limiting cases. For these special cases, results are obtained using analytical techniques including perturbation analysis, travelling wave analysis and phase plane methods. These analytic results provide a more complete understanding of system behaviour than numerical results alone. Emphasis is placed on connecting modelling results with experimental observations. / The first application considered is animal translocations. Translocations are widely used to reintroduce threatened species to areas where they have disappeared. A variety of different dispersal and settling mechanisms are considered, and results compared. The model is applied to a case study of a double translocation of the Maud Island frog, Leiopelma pakeka. Results suggest that settling occurs at a constant rate, with repulsion playing a significantrole in dispersal. This research demonstrates that mathematical modelling of translocations is useful in suggesting design and monitoring strategies for future translocations, and as an aid in understanding observed behaviour. / The second application we investigate is the invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric (intestinal) nervous system, but is presented in general terms and is of broader applicability. Regions of the parameter space are characterised according to existence, shape and speed of travelling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, these results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells. / As a third application, we propose a model for the development of cartilage around a single chondrocyte. The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components. Our observations could explain differences observed experimentally between various scaffold media. Modelling results are also used to predict the minimum chondrocyte seeding density required to produce functional cartilage. / In summary, we develop reaction-diffusion models for dispersing and settling populations for three biological applications. Numerical and analytical results provide an understanding of population-level behaviour. This thesis demonstrates that mathematical modelling of biological systems can further understanding of biological systems and help to answer questions posed by experimental research.

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A model of an artificial ecosystem has been formulated for use as a tool to investigate the dynamics of autonomous biosystems. The model is part of a composite model of an EcoCyborg which consists of an ecosystem and its control system, both of which are contained inside a cylindrical space station. The objectives of this project were to design a model of the ecosystem, and to develop a method for its creation and implementation within the overall framework of the EcoCyborg Project. / The modeling approach that has been adopted for the ecosystem model is individual-based and object-oriented. This enables the inclusion of a description of the abiotic environment, as well as of the organisms that inhabit it. A total of 1000 species representing a range of taxonomic groups may be modeled. Individuals in each species are described by their behaviours and phenotypic traits. / The ecosystem model will be linked with the other components of the EcoCyborg model in a multi-process simulation under OS/2 Warp. The behaviour of the system will be studied to elucidate preliminary guidelines for the design, maintenance and control of complex systems.

In this thesis, a philosophy and lexicon for the engineering of biosystems are established. The focus is on a specific class of biosystems ( ecocyborgs) created by combining ecosystems and technological Components. This work is part of the EcoCyborg Project, a highly interdisciplinary research program which concerns the development of a general theory for biosystems engineering, with an emphasis on system autonomy as a design goal. In the short term, the objective is to develop computational models and simulations for use in the study of ecocyborgs as representative instances of substantially autonomous biosystems. Accordingly, in this thesis an explicit conceptual basis is established for the EcoCyborg Project, as well as for biosystems engineering in general. / First, in the body of the thesis, a biosystem is defined as a coherent assemblage of entities that is alive to some degree as a whole. The sole criterion for life is considered to be comportment that is somewhat autopoietic , whereby local interactions among the components combine to Continually renew the overall system. Next, concepts related to autonomy, or the formulation and pursuit of proprietary goals, are elaborated. The degree of autonomy of a system is seen to depend on its consciousness, or ability to reason using a model of itself. Hence, a substantially autonomous system requires an ensemble of information storage and processing devices (mind) of the type and sophistication (intelligence ) appropriate for this. The approach that is taken here to the creation of ecocyborgs with such minds is described, and a specific mental architecture is delineated, comprising functionally semidifferentiated, intermediate-scale components arranged according to a semihierarchical control organization. Finally, the characterization of such systems is scrutinized as an epistemic process in which knowledge is generated by an observer, but in which only a limited degree of objectivity is possible. A paradigm appropriate to the engineering of ecocyborgs is defined as an illustration, and associated archetypal concepts and descriptive procedures (such as measures) are given that are useful in this context. Such tools are required by significantly autonomous ecocyborgs because they must characterize themselves. They are also necessary to observers with scientific and engineering agendas.

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published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

Understanding of a global biological network structure by studying its simple local properties through the well-developed field of graph theory is of interest. In particular, in this research an observed biological network was explored through a simulation study. However, one difficulty in such exploration lies on the fitting of graphical models on biological network data. An Exponential Random Graph Model (ERGM) was considered to determine estimations of the several network attributes of complex biological network data. We also compared the estimates of observed network to our random simulated network for both Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMCMLE) and Maximum Pseudo Likelihood Estimation (MPLE) methods under ERGM. The motivation behind this was to determine how different the observed network could be from a randomly simulated network if the physical numbers of attributes were approximately same. Cut-off points of some common attributes of interest for different order of nodes were determined through simulations. We implemented our method to a known regulatory network database of E. coli. / Department of Mathematical Sciences

Thesis (MSc (Biochemistry))--University of Stellenbosch, 2009. / A Python package called PySUNDIALS has been developed which provides an interface to the suite of nonlinear di erential/algebraic equation solvers (SUNDIALS) using ctypes as a foreign function interface (FFI). SUNDIALS is a C implementation of a set of modern algorithms for integrating and solving various forms of the initial value problem (IVP). Additionally, arbitrary root nding capabilities, time dependent sensitivity analysis, and the solution of di erential and algebraic systems are available in the various modules provided by SUNDIALS. A signi cant focus of the project was to ensure the python package conforms to Python language standards and syntactic expectations. Multiple examples of the SUNDIALS modules (CVODE, CVODES, IDA and KINSOL) are presented comparing PySUNDIALS to C SUNDIALS (for veri cation of correctness), and comparing PySUNDIALS to various other comparable software packages. The examples presented also provide benchmark comparisons for speed, and code length. Speci c uses of the features of the SUNDIALS package are illustrated, including the modelling of discontinuous events using root nding, time dependent sensitivity analysis of oscillatory systems, and the modelling of equilibrium blocks using a complete set of implicit di erential and algebraic equations. PySUNDIALS is available as open source software for download. It is being integrated into the systems biology software PySCeS as an optional solver set, on an ongoing basis. A brief discussion of potential methods of optimization and the continuation of the project to wrap the parallel processing modules of SUNDIALS is presented.

The key to understanding any system, including physiologic and pathologic systems, is to obtain a truly comprehensive view of the system. The purpose of this dissertation was to develop foundational analytical and modeling tools, which would enable such a comprehensive view to be obtained of any physiological or pathological system by combining experimental, clinical, and theoretical viewpoints. Specifically, we focus on the development of analytical and modeling techniques capable of predicting and prioritizing the mechanisms, emergent dynamics, and underlying principles necessary in order to obtain a comprehensive system understanding. Since physiologic systems are inherently complex systems, our approach was to translate the philosophy of complex systems into a set of applied and quantitative methods, which focused on the relationships within the system that result in the system's emergent properties and behavior. The result was a set of developed techniques, referred to as relational modeling and analysis that utilize relationships as either a placeholder or bridging structure from which unknown aspects of the system can be effectively explored. These techniques were subsequently tested via the construction and analysis of models of five very different systems: synaptic neurotransmitter spillover, secondary spinal cord injury, physiological and pathological axonal transport, and amyotrophic lateral sclerosis and to analyze neurophysiological data of in vivo cat spinal motoneurons. Our relationship-based methodologies provide an equivalent means by which the different perspectives can be compared, contrasted, and aggregated into a truly comprehensive viewpoint that can drive research forward.