The rates of complex multi-enzyme systems, which may contain diffusion processes, can be written in a standard polynomial form. Approximation of this formula leads to the derivation of equations which provide a theoretical basis for the use of log-log plots (for rate-size and rate-substrate relationships), and Arrhenius plots (for rate-temperature relationships) in biology. Sharp discontinuities or "breaks" on such plots can be explained by summations of simple functions and the power to which these must be raised prior to summation. It has been found unnecessary to have large enthalpies (or activation energies) to produce sharp breaks on Arrhenius plots of the rates of complicated biological systems. / Science, Faculty of / Zoology, Department of / Graduate

Guo Bao Zhu. / Thesis (Ph.D.)--Chinese University of Hong Kong. / Includes bibliographical references. / Abstract --- p.1 / Introduction --- p.3 / Chapter Chapter 1. --- Semigroup for Age-Dependent Population Equations with Time Delay / Chapter 1.1 --- Introduction --- p.13 / Chapter 1.2 --- Problem Statement and Linear Theory --- p.14 / Chapter 1.3 --- Spectral Properties of the Infinitesimal Generator --- p.20 / Chapter 1.4 --- A Nonlinear Semigroup of the Logistic Age-Dependent Model with Delay --- p.26 / References --- p.34 / Chapter Chapter 2. --- Global Behaviour of Logistic Model of Age-Dependent Population Growth / Chapter 2.1 --- Introduction --- p.35 / Chapter 2.2 --- Global Behaviour of the Solutions --- p.37 / Chapter 2.3 --- Oscillatory Properties --- p.47 / References --- p.51 / Chapter Chapter 3. --- Semigroups for Age-Size Dependent Population Equations with Spatial Diffusion / Chapter 3. 1 --- Introduction --- p.52 / Chapter 3.2 --- Properties of the Infinitesimal Generator --- p.54 / Chapter 3.3 --- Properties of the Semigroup --- p.59 / Chapter 3.4 --- Dynamics with Age-Size Structures --- p.61 / Chapter 3.5 --- Logistic Model with Diffusion --- p.66 / References --- p.70 / Chapter Chapter 4. --- Semi-Discrete Population Equations with Time Delay / Chapter 4. 1 --- Introduction --- p.72 / Chapter 4.2 --- Linear Semi-Discrete Model with Time Delay --- p.74 / Chapter 4.3 --- Nonlinear Semi-Discrete Model with Time Delay --- p.88 / References --- p.98 / Chapter Chapter 5. --- A Finite Difference Scheme for the Equations of Population Dynamics / Chapter 5.1 --- Introduction --- p.99 / Chapter 5.2 --- The Discrete System --- p.102 / Chapter 5.3 --- The Main Results --- p.107 / Chapter 5.4 --- A Finite Difference Scheme for Logistic Population Model --- p.113 / Chapter 5.5 --- Numerical Simulation --- p.116 / References --- p.119 / Chapter Chapter 6. --- Optimal Birth Control Policies I / Chapter 6. 1 --- Introduction --- p.120 / Chapter 6.2 --- Fixed Horizon and Free Point Problem --- p.120 / Chapter 6.3 --- Time Optimal Control Problem --- p.129 / Chapter 6.4 --- Infinite Horizon Problem --- p.130 / Chapter 6.5 --- Results of the Nonlinear System with Logistic Term --- p.143 / Reference --- p.148 / Chapter Chapter 7. --- Optimal Birth Control Policies II / Chapter 7. 1 --- Free Final Time Problems --- p.149 / Chapter 7.2 --- Systems with Phase Constraints --- p.160 / Chapter 7.3 --- Mini-Max Problems --- p.166 / References --- p.168 / Chapter Chapter 8. --- Perato Optimal Birth Control Policies / Chapter 8.1 --- Introduction --- p.169 / Chapter 8.2 --- The Duboviskii-Mi1yutin Theorem --- p.171 / Chapter 8.3 --- Week Pareto Minimum Principle --- p.172 / Chapter 8.4 --- Problem with Nonsmooth Criteria --- p.175 / References --- p.181 / Chapter Chapter 9. --- Overtaking Optimal Control Problems with Infinite Horizon / Chapter 9. 1 --- Introduction --- p.182 / Chapter 9.2 --- Problem Statement --- p.183 / Chapter 9.3 --- The Turnpike Property --- p.190 / Chapter 9.4 --- Existence of Overtaking Optimal Solutions --- p.196 / References --- p.198 / Chapter Chapter 10. --- Viable Control in Logistic Populatiuon Model / Chapter 10. 1 --- Introduction --- p.199 / Chapter 10. 2 --- Viable Control --- p.200 / Chapter 10.3 --- Minimum Time Problem --- p.205 / References --- p.208 / Author's Publications During the Candidature --- p.209

No description available.

With big science projects like the human genome project, [2], and preliminary attempts to seriously study brain activity, e.g. [9], mathematical biology has come of age, employing formalisms and tools from most branches of mathematics. Recent results, [51] and [53], have extended the relational (or categorical) approach of Rosen [44], to demonstrate that (in a very general class of systems) cellular self-organization/self-replication is implicit in metabolism and repair/stability. This is a powerful philosophical statement and removes the need of teleological argument. However, the result carries a technical limitation to Cartesian closed categories, which excludes many mathematical languages. We review the relevant literature on metabolic-repair pathways, category theory and systems theory, before performing a critique of this work. We find that the restriction to Cartesian closed categories is purely for simplicity, and describe how equivalent arguments may be built for monoidal closed categories. Moreover, any symmetric monoidal category may be "embedded" in a closed one. We discuss how these constructions/techniques provide the formal structure to treat self-organization/self-replication in most contemporary mathematical (modelling) languages. These results signicantly soften the impact on current modelling paradigms while extending the philosophical implications. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

The development of spatial structure and form on vertebrate skin is a complex and poorly understood phenomenon. We consider here a new mechanochemical tissue interaction model for generating vertebrate skin patterns. Tissue interaction, which plays a crucial role in vertebrate skin morphogenesis, is modelled by reacting and diffusing signal morphogens. The model consists of seven coupled partial differential equations, one each for dermal and epidermal cell densities, four for the signal morphogen concentrations and one for describing epithelial mechanics. Because of its complexity, we reduce the full model to a small strain quasi-steady-state model, by making several simplifying assumptions. A steady state analysis demonstrates that our reduced system possesses stable time-independent steady state solutions on one-dimensional spatial domains. A linear analysis combined with a multiple time-scale perturbation procedure and numerical simulations are used to examine the range of patterns that the model can exhibit on both one- and two-dimensions domains. Spatial patterns, such as rolls, squares, rhombi and hexagons, which are remarkably similar to those observed on vertebrate skin, are obtained. Although much of the work on pattern formation is concerned with synchronous spatial patterning, many structures on vertebrate skin are laid down in a sequential fashion. Our tissue interaction model can account for such sequential pattern formation. A linear analysis and a regular perturbation analysis is used to examine propagating epithelial contraction waves coupled to dermal cell invasion waves. The results compare favourably with those obtained from numerical simulations of the model. Furthermore, sequential pattern formation on one-dimensional domains is analysed; first by an asymptotic technique, and then by a new method involving the envelopes of the spatio-temporal propagating solutions. Both methods provide analytical estimates for the speeds of the wave of propagating pattern which are in close agreement with those obtained numerically. Finally, by numerical simulations, we show that our tissue interaction model can account for two-dimensional sequential pattern formation. In particular, we show that complex two-dimensional patterns can be determined by simple quasi-one-dimensional patterns.

Erratum pages inserted onto front end papers. / Bibliography: leaves 226-244. / vi, 244 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis developed mathematical models of commercially exploited fish populations, addressing the question of how to harvest a predator-prey metapopulation. Optimal harvesting strategies are found using dynamic programming and Lagrange multipliers. Rules about harvesting source/sink populations, more/less vulnerable prey subpopulations and more/less efficient predator subpopulations are explored. Strategies for harvesting critical prey subpopulations are suggested. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2000?

Multi-species functional response models are required to model the predation of generalist preda- tors, which consume more than one prey species. In chapter 2, a new model for the multi-species functional response is presented. This model can describe generalist predators that exhibit func- tional responses of Holling type II to some of their prey and of type III to other prey. In chapter 3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and show how Bayesian statistics are particularly well-suited for the fitting of functional response models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi- species functional response model is fitted to field data on two generalist predators: the hen harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous Bayesian model of the multi-species functional response that has been fitted to field data. The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The impact of using Bayesian or frequentist models on the resulting functional response is discussed. In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible reasons are discussed, including poor data quality or a lack of relevance of the available data for informing a behavioural functional response model. I conclude with a comparison of the role that functional responses play in behavioural, population and community ecology and emphasise the need for further research into unifying these different approaches to understanding predation with particular reference to predator movement. In an appendix, I evaluate the possibility of using a functional response for inferring the abun- dances of prey species from performance indicators of generalist predators feeding on these prey. I argue that this approach may be futile in general, because a generalist predator's energy intake does not depend on the density of any single of its prey, so that the possibly unknown densities of all prey need to be taken into account.

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

Carbohydrate Active Enzyme family 6 (CA6) glycosyltransferases (GTs) are type II transmembrane proteins localized in the Golgi apparatus. CA6 GTs have a GT-A fold, a type of structure that resembles the Rossman fold and catalyze the transfer either galactose (Gal) or N-acetylgalactosamine (GalNAc) from the UDP nucleotide sugar to an non-reducing terminal Gal or GalNAc on an acceptor via an a-1,3 linkage. In this reaction, the anomeric configuration of the sugar moiety of the donor is retained in the product. CA6 GTs includes the histo-blood group A and B GTs, a-galactosyltransferase (a3GT), Forssman glycolipid synthase (FS), isogloboside 3 synthase (iGb3) in mammals. a3GT and its products (a-Gal epitode) are present in most mammals but are absent in humans and old world primates because of inactivating mutations. The absence of a3GT and its products results in the production of anti-a-Gal epitope natural antibodies in these species. / Up to date, the catalytic mechanisms of the CA6 GTs are not well understood. Based on previous structural and mutagenesis studies of bovine aB3GT, we investigated active site residues (His315, Asp316, Ser318, His319, and Lys359) that are highly conserved among CA6 GTs. We have also investigated the role of the C-terminal region by progressive C-terminal truncations. Findings from these studies clarify the functional roles of these residues in structure, catalysis, and specificity in these enzymes and have implications for their catalytic mechanisms. GTs are useful tools in synthesis of glycans for various applications in science and medicine. Methods for the large scale production of pure glycans are continuously being developed. We created a limited randomized combinatorial library based on knowledge of structural information and sequence analysis of the enzyme and its mammalian homologues. / Two GalNAc-specific variants were identified from the library and one Glc-specific variant was identified by site-direct mutagenesis. The glycosyltransferase activities of these variants are expected to be improved by further screens of libraries which are designed using the variants as templates. The mammalian CA6 GTs that have been characterized to date are metal-independent and require the divalent cation, Mn2+ for activity. In some recently-discovered bacterial CA6 GTs, the DXD sequence that is present in eukaryotic GTs is replaced by NXN. We cloned and expressed one of these proteins from Bacteroides ovatus, a bacterium that has been linked with inflammatory bowel disease. Functional characterization shows it is a metal-independent monomeric GT that efficiently catalyzes the synthesis of oligosaccharides similar to human blood group A glycan. / Mutational studies indicated that despite the lack of a metal cofactor there are similarities in structure-function relationships between the bacterial and vertebrate family 6 GTs. / by Percy Tumbale. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Modeling a biological systems, is a cyclic process which involves constructing a model from current theory and beliefs and then validating that model against the data. If the data does not match, qualitatively or quantitatively then there may be a problem with either our beliefs or the current theory. At the same time directly finding a model from the existing data would make generalizing results difficult. A considerable difficultly in this process is how to specify the model in the first place. There is a need to be practice which accounts for the growing use of mathematical and statistical methods. However, as a systems becomes more complex, standard mathematical approaches may not be sufficient. In the field of ecology, the standard techniques involve discrete maps, and continuous models such as ODE's. The intent of this work is to present the mathematics necessary to study hybrids of these two models, then consider two case studies. In first case we con sider a coral reef with continuous change, except in the presence of hurricanes. The results of the data are compared quantitatively and qualitatively with simulation results. For the second case we consider a model for rabies with a periodic birth pulse. Here the analysis is qualitative as we demonstrate the existence of a strange attractor by looking at the intersections of the stable and unstable manifold for the saddle point generating the attractor. For both cases studies the introduction of a discrete event into a continuous system is done via a Dirac Distribution or Measure. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection