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Quantification of host-parasite interactions : sheep and their nematodesPrada Jimenez de Cisneros, Joaquin M. January 2014 (has links)
The objective of this dissertation is to use modelling and statistical approaches to expand our knowledge of the immune responses against gastrointestinal nematode infections, to assess the impact of nematode infection, and to use our improved knowledge to examine novel means of selective breeding in farm animals (sheep) as a control strategy. To expand the knowledge of the host immune response against infection, Chapter 2 of this dissertation focuses on immunoglobulin A (IgA), an antibody that binds nematode molecules, and its transfer through the body from the abomasal mucus (i.e. site of infection, where it is produced) to the blood plasma, where it is typically measured. These findings have been published in Parasitology (Prada Jimenez de Cisneros et al., 2014a). The implications of low levels of infection in adult milking ewes, which are more resistant than lambs, were also studied. A relationship is generated between infection levels using parasitological data and production data. There were however limitations in the dataset, which are discussed at the end of Chapter 3. Parasite resistance in adults sheep at low levels of infection was also studied, especially since the most common parasitological marker of disease is the faecal egg count (i.e. number of nematode eggs in the animals faeces) which is subject to substantial measurement error, among other limitations. Chapter 4 analyses a dataset of adult animals with low infection levels using a zero inflated binomial model (ZINB) and extends the model by including other evidence of parasite resistance to discriminate between exposed and unexposed animals. To examine selective breeding, an individual-based data-driven immunogenetically explicit mathematical model was developed. One application of this model is to compare the efficacy of two selective breeding schemes, each based on a different marker for disease, namely faecal egg counts and plasma IgA. This work has been published in Journal of the Royal Society Interface (Prada Jimenez de Cisneros et al., 2014b). The model can be extended to create a distribution for the variation in larval intake that best fits the field data. This allows the partitioning of the variation in adult worm burden into different components. The purpose is to quantify the contribution of the immune response and larval intake to determine which of the two accounts for more of the variation in the level of infection. The model can be also extended to explore selection schemes in the two components of the immune response (i.e. namely the IgA mediated and IgE mediated immune response) and estimate animal size at the end of the grazing season.
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Dynamical systems and games theoryCarvalho, Maria Suzana Balparda de January 1983 (has links)
This thesis consists of two parts, which deal with different topics in dynamical systems. Part I (DYNAMICS FROM GAMES) is the main scope of the work. There we study a family of flows which are often applied in studies of some game dynamics in animal competition and evolutionary biochemistry. These flows are the solutions, on simplexes, of cubic differential equations determined by "pay-off" matrices. The main result in this part is a proof for a classification of stable flows in this family, in dimension 2, first conjectured by Zeeman in 1979 (stability under small perturbations in the pay-off matrix). We add necessary and sufficient conditions for stability, which decide the exact class for each stable flow in the family. We also give as preliminary properties some simple expressions to calculate eigenvalues at fixed points and prove that hyperbolicity of these is necessary for stability, in all dimensions. In order to complete Zeeman's classification we had to adapt, in dimension 2, some techniques of structural stability for flows not satisfying the usually required transversality condition. We discuss some aspects and difficulties present when one attempts to study cases in dimension i3. One important three-dimensional example, involving a Hopf bifurcation, is discussed in detail. In the final chapter, we present some three-dimensional cases to which a discussion of stability is feasible. Part II (LIAPUNOVF UNCTIONSF OR DIFFEOMORPHISMSh) as as its purpose the construction of Liapunov functions for diffeomorphisms. A local construction is presented in neighbourhood of compact isolated invariant sets. A globalization is obtained for Axiom A diffeos with no cycles.
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The fluid mechanics of embryonic nodal ciliaSmith, Andrew January 2013 (has links)
Symmetry breaking of the left-right body axis is a crucial step in development for many vertebrate species. In many this is initiated with a directional cilia-driven fluid flow in the organising structure. This work focuses on the mouse and the zebrafish organising structures, the node and Kupffer's vesicle, wherein cilia perform a tilted rotation producing an asymmetric flow. Using singularities of Stokes flow, slender body theory and the boundary integral equation, a computational model of flow in the mouse node for a range of cilia configurations simulating developmental stages is developed and run on the University of Birmingham's cluster, BlueBEAR. The results show the emergence of a directional flow as the cilia tilt increases. To model the Kupffer's vesicle the regularised boundary integral equation is used with a mesh representation of the entire domain to investigate potential cilia mechanisms that produce the observed flow as there is not a consensus. The results show that a combination of the experimental observations could be a sufficient mechanism. This model is expanded using observations of cilia with two rotation frequencies which are incorporated by allowing such cilia to ‘wobble’. This wobble accentuates the asymmetric flow in wildtype embryos and diminishes it in mutant embryos. All of these results agree well with experiment suggesting that vertebrates develop a combination of rotation mechanisms in their organising structures before an appropriate symmetry breaking flow is established.
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Representing spatial interactions in simple ecological modelsMorris, Andrew John January 1997 (has links)
The real world is a spatial world, and all living organisms live in a spatial environment. For mathematical biologists striving to understand the dynamical behaviour and evolution of interacting populations, this obvious fact has not been an easy one to accommodate. Space was considered a disposable complication to systems for which basic questions remained unanswered and early studies ignored it. But as understanding of non-spatial systems developed attention turned to methods of incorporating the effects of spatial structure. The essential problem is how to usefully manage the vast amounts of information that are implicit in a fully heterogeneous spatial environment. Various solutions have been proposed but there is no single best approach which covers all circumstances. High dimensional systems range from partial differential equations which model continuous population densities in space to the more recent individual-based systems which are simulated with the aid of computers. This thesis develops a relatively new type of model with which to explore the middle ground between spatially naive models and these fully complex systems. The key observation is to note the existence of correlations in real systems which may naturally arise as a consequence of their dynamical interaction amongst neighbouring individuals in a local spatial environment. Reflecting this fact - but ignoring other large scale spatial structure - the new models are developed as differential equations (pair models) which are based on these correlations. Effort is directed at a first-principles derivation from explicit assumptions with well stated approximations so the origin of the models is properly understood. The first step is consideration of simple direct neighbour correlations. This is then extended to cover larger local correlations and the implications of local spatial geometry. Some success is achieved in establishing the necessary framework and notation for future development. However, complexity quickly multiplies and on occasion conjectures necessarily replace rigorous derivations. Nevertheless, useful models result. Examples are taken from a range of simple and abstract ecological models, based on game theory, predator-prey systems and epidemiology. The motivation is always the illustration of possibilities rather than in depth investigation. Throughout the thesis, a dual interpretation of the models un-folds. Sometimes it can be helpful to view them as approximations to more complex spatial models. On the other hand, they stand as alternative descriptions of space in their own right. This second interpretation is found to be valuable and emphasis is placed upon it in the examples. For the game theory and predator-prey examples, the behaviour of the new models is not radically different from their non-spatial equivalents. Nevertheless, quantitative behavioural consequences of the spatial structure are discerned. Results of interest are obtained in the case of infection systems, where more realistic behaviour an improvement on non-spatial models is observed. Cautiously optimistic conclusions are reached that this, middle road of spatial modelling has an important contribution to make to the field.
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Cell scale modelling and numerical simulation of transmembrane potential in neurons and gliaGeorge, Stuart January 2015 (has links)
No description available.
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Optimising plant and soil managementHeppell, James January 2014 (has links)
This thesis is an accumulation of work regarding the role of phosphorus (P) and water in soils in relation to crop growth and food production. We use a multiscale modelling approach to initially capture the interactions of soil and water on a single cylindrical root and further expand to a growing root structure. Moreover, we have a multi-physics problem involving fluid dynamics of water uptake in plants, and reactive solute transport in the soil for plant P uptake. We use detailed climate data and the super computer at the University of Southampton (Iridis 4) to parameterise our models. These facilities allow us to analyse the root structure as well as P and water in the soil in great detail. The collaboration of mathematics, biology and operational research makes it possible to complete this project. The analytical models recently developed within our group have shown to agree remarkably well with full 3D simulation models. These analytical models help provide the structure for the models used within this thesis and will for the first time enable us to start using optimisation techniques to find the optimal conditions for increasing plant P uptake efficiency. By using mathematical models to predict plant P and water uptake within the soil, we have addressed a number of questions surrounding the optimal plant root structure for P accumulation, and the survival of crops in a low P environment. In addition, we were able to predict the behaviour of water in the soil over the course of a full year. And finally, utilising all the above, we have outlined the optimal fertiliser and soil management strategy.
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Observation and prediction of biocide release with fluorescence techniques and mathematical modellingGoodes, L. R. January 2013 (has links)
Antifouling coatings are crucial for protection of vessels’ hulls against marine biofouling. A range of technologies is available, although biocidal coatings - containing toxic or deterrent compounds – still represent a majority of the market. A long-term goal is the development of less environmentally harmful and persistent compounds; one of many potential avenues is that of synthetic analogues of natural products from marine organisms. The development of coatings using natural products has been hampered by poor performance in the field without sufficient work on their leach rates and behaviour. Furthermore, little work has been carried out on the leach rate of traditional organic biocides as used in modern coatings. Prediction of biocide diffusion is crucial to estimation of antifouling efficacy. However, diffusion in glassy polymers is a complex and oft-neglected topic; the chemically and physically changeable environment of the ocean and swelling of the polymer in such a ternary system also increase the complexity of models. A test matrix of antifouling paint coatings was composed, including polymethylmethacrylate (pMMA), an erodible rosin-based commercial binder and a novel trityl methacrylate/butylacrylate copolymer (pTrMA/BA) as binders. Copper (I) oxide and usnic acid, a natural product biocide of interest, were incorporated into the binders and the coatings were subjected to 10 months of natural immersion and 6 months of accelerated rotor immersion tests (17 knots, 25 °C). A novel application of fluorescence microscopy was developed, allowing quantification of the usnic acid content within the test coatings from both immersion schemes. This fluorescence technique and optical microscopy techniques were applied to these coatings before and after immersion, allowing quantification of the organic biocide and pigment distribution. Existing literature models for diffusion in glassy systems were adapted with a novel method for taking into account the presence of seawater as a diluent, to obtain effective diffusion coefficients for usnic acid. These have been integrated into mathematical models of diffusion to predict biocide lifetime. These data were compared with experimental data for biocide leaching from the long term immersions. The biocide leached completely from the p(TrMA/BA) binder during rotor testing, compared to 35% from the pMMA binder. For pontoon immersions, 61% of the additive was lost from the pMMA coating, and 53% from the rosin-based binder. An accelerated loss of usnic acid occurred in the surface of the rosin-based binder, due to rosin depletion. In all samples, release of the biocide was inhibited beyond the cuprous oxide front, which was congruent with the leached layer in samples where cuprous oxide release occurred. The erodible binder was the only one which demonstrated synchronous depletion of both additives, and it demonstrated a good resistance to fouling in immersion trials. Results of the mathematical modelling of the biocide diffusion were in good agreement with the observed data in the case of pMMA, highlighting in particular the importance of water uptake with respect to biocide diffusion. However, there was poor agreement in the case of p(TrMA/BA), for which the model under-predicted the release rate by about three orders of magnitude.
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Advances in Monte Carlo techniques with application to lattice protein aggregationXu, Yuanwei January 2016 (has links)
Motivated by an intricate mechanism to transport folded proteins across biological membranes, known as the Twin-arginine translocation (Tat) pathway, we construct lattice protein models in an attempt to study the aggregation of the membrane protein TatA, which plays an integral role during active Tat translocation. We develop force field that characterizes intra- and inter-residue interactions, as well as how each residue interacts with its environment. Although written with the Tat process in mind, this thesis is mainly devoted to developing efficient Monte Carlo schemes for biomolecular simulations, which are often challenged and impeded by complex energy landscapes. To tackle the local trap problem that is typical in Metropolis sampling, the idea of dynamic weighting is incorporated into the parallel tempering (PT) algorithm. Our results show that, when applied to the lattice-protein model, the modified PT algorithm is capable of locating the low energy state much more quickly, but does not produce reliable estimates for equilibrium expectations. A modern method for free energy calculation, called the multistate Bennett acceptance ratio (MBAR) estimator, is reviewed from a statistical perspective, reminiscent of the underlying statistical theory which the method is based upon. Instead of adopting the common practice of using MBAR as a post-simulation analysis tool, we propose a new approach that integrates MBAR into simulation, allowing the simulation to benefit from the statistical optimality of the MBAR estimator. We show that the MBAR-enhanced Monte Carlo improves simulation efficiency of the lattice-protein aggregation model and, since it can also be applied to continuous models, provides a promising alternative to the study of more realistic systems. The new method is then applied to our model of TatA, where the protein features both a transmembrane and an amphipathic helix. The effect of individual helices on dimerization was studied and problem with the move set was identified. In this thesis, we used pull move and translation move as our Monte Carlo trial moves. Implementation details of pull moves, which are often omitted by many researchers who use them for sampling configuration space, are given in Chapter 1. We show that, for our double-helix TatA model, pull moves are no longer efficient moves and therefore, for future study of more realistic systems, we point to several methods which all attempt to design efficient trial moves. Aggregation of more than two polymer chains was also considered in this thesis.
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Modelling the phenological effects of environmental drivers on mosquito abundance : implications for West Nile virus transmission potential in the UKEwing, David January 2017 (has links)
Mosquito-borne diseases cause substantial mortality and morbidity worldwide. These impacts are widely predicted to increase as temperatures warm, since mosquito biology and disease ecology are strongly linked to temperature. However, direct evidence linking environmental change to changes in mosquito-borne disease is rare, and the ecological mechanisms that may underpin such changes are poorly understood. Environmental drivers, can have non-linear, opposing impacts on the demographic rates of different mosquito life cycle stages and on disease transmission processes. As such, model frameworks that explicitly incorporate the effects of temperature are required to predict seasonal mosquito abundance and the intensity and persistence of disease transmission under environmental fluctuations. Chapter 2 develops a variable-delay delay differential equation (DDE) model to estimate seasonal abundance of each life stage of the West Nile virus (WNV) vector mosquito species, Cx. pipiens, given temperature and photoperiod conditions experienced. The model highlights that the timing and intensity of warm periods can be more influential in shaping abundance patterns than average temperatures. Chapter 3 presents an extensive body of fieldwork, which led to a high temporal resolution seasonal abundance dataset of each life stage of Cx. pipiens. Chapter 4 challenges assumptions of the DDE model from Chapter 2 in light of the seasonal abundance data collected in Chapter 3. The importance of using appropriate, high temporal resolution input temperature datasets is displayed. Chapter 5 extends the DDE model from Chapter 4 to explicitly model WNV transmission cycles between vectors and avian hosts. The disease model predicts that the current climate in the South of England is too cold to facilitate WNV outbreaks. However, given projected warming in the UK in coming decades it is predicted that WNV infection rates in mosquitoes will be consistent with the lower range of values observed during WNV outbreaks 2080 if virus introduction coincides with warm periods. The risk of these outbreaks is predicted to increase sharply with increases in human greenhouse gas emissions.
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Mathematical modelling of tissue metabolism and growthCatt, Christopher Joseph January 2010 (has links)
The work presented in this thesis is concerned with modelling the growth of tissue constructs, with particular focus on the effects the local micro environment has on the cell cycle and metabolism. We consider two cases; multicellular tumour spheroids and orthopaedic tissue constructs. This thesis is divided into two parts. In the first part we will present a multispecies model of an avascular tumour that studies how a cell’s metabolism affects the cell cycle, spheroid growth and the mechanical forces that arise during growth. The second part consists of a study of the growth of an engineered cartilaginous tissue layer. Experimental observations will be compared to a model of the distribution of cells and extracellular matrix. The efficiency of cancer treatments such as radiotherapy and chemotherapy are sensitive to the local environment of a cell. Therefore an essential task in tumour biology is to understand the microenvironment within a tumour. Many mathematical models study the effects of nutrients and waste products, usually assuming growth is limited by the diffusion of a single nutrient. We will look in detail at the metabolic pathways from which cells obtain energy (ATP). A multispecies model is presented that considers the transition from aerobic to anaerobic respi- ration and includes relevant chemical and ionic buffering reactions and transport mechanisms. Results show that potential ATP production affects the cell cycle and consequently the rate of growth. This model is simplified using mathematical analysis and is integrated with a morphoelastic model to study the development of mechanical forces. The model shows that mechanical effects are particularly important during necrosis, where large tensile forces are shown to develop. A review of the equations governing nutrient conservation is given, by developing alternative macroscopic equations based on the microscopic features of a tumour using homogenization techniques. The second part of this thesis studies the growth of cartilaginous tissue. Bio-materials are being engineered in an attempt to replace dysfunctional tissue in the human body using cells extracted from living organisms. We model the growth of a cartilaginous tissue construct that has been grown from expanded chondrocytes seeded onto collagen coated filters. A model is developed to explain the distribution of cells and the concentration and distribution of collagen and GAGs. This is achieved by studying the local environment of the cells. Model predictions are compared to a range of experimental data and show most of the growth takes place in the upper region of the construct.
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