For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and attached metal structures. In this thesis, we survey the known types of knots, links, and non-planar graphs in protein structures with and without including such bonds between proteins and metals. Then we present new examples of protein structures containing M\"obius ladders and other non-planar graphs as a result of these bound metal atoms. Finally, we propose hypothetical structures illustrating specific disulfide connectivities that would result in the key ring link, the Whitehead link and the 5_1 knot, the latter two of which have thus far not been identified within protein structures.

Little is known about the molecular components and interactions of the planar cell polarity pathway that regulate neuronal polarity. This study uses a prkl-1 induced backwards locomotion defect as an array to perform a prkl-1 suppressor screen in C. elegans looking for new components of the planar cell polarity pathway involved in the neuronal polarization of VC4 and VC5. The screen discovered twelve new alleles of vang-1, one new allele of fntb-1 and five new mutations in unknown polarity genes. fntb-1 encodes for the worm ortholog of Farnesyltransferase β-subunit and is important for neuronal polarization. Acting cell and non-cell autonomously, fntb-1 regulates the function and localization of prkl-1 through the recognition of a CAAX motif. Therefore, fntb-1 modifies prkl-1 to regulate the neuronal polarity of VC4 and VC5.

During development, cells consume energy, divide, rearrange, and die. Bulk properties such as viscosity and elasticity emerge from cell-scale mechanics and dynamics. Order appears, for example in patterns of hair outgrowth, or in the predominately hexagonal pattern of cell boundaries in the wing of a fruit fly. In the past fifty years, much progress has been made in understanding tissues as living materials. However, the physical mechanisms underlying tissue-scale behaviour are not completely understood. Here we apply theories from statistical physics and fluid dynamics to understand mechanics and order in two-dimensional tissues. We restrict our attention to the mechanics and dynamics of cell boundaries and vertices, and to planar polarity, a type of long-ranged order visible in anisotropic patterns of proteins and hair outgrowth. Our principle tool for understanding mechanics and dynamics is a vertex model where cell shapes are represented using polygons. We analytically derive the ground-state diagram of this vertex model, finding it to be dominated by the geometric requirement that cells be polygons, and the topological requirement that those polygons tile the plane. We present a simplified algorithm for cell division and growth, and furthermore derive a dynamic equation for the vertex model, which we use to demonstrate the emergence of quasistatic behaviour in the limit of slow growth. All our results relating to the vertex model are consistent with and build off past calculations and experiments. To investigate the emergence of planar polarity, we develop quantification methods for cell flow and planar polarity based on confocal microscope images of developing fly wings. We analyze cell flow using a velocity gradient tensor, which is uniquely decomposed into terms corresponding to local compression, shear, and rotations. We argue that a pattern in an inhomogeneously flowing tissue will necessarily be reorganized, motivating a hydrodynamic theory of polarity reorientation. Using such a coarse-grained theory of polarity reorientation, we show that the quantified patterns of shear and rotation in the wing are consistent with the observed polarity reorganization, and conclude that cell flow reorients planar polarity in the wing of the fruit fly. Finally, we present a cell-scale model of planar polarity based on the vertex model, unifying the themes of this thesis.

Coordinated polarity and differentiation of cells in the plane of a tissue layer are essential to the development of multicellular organisms. Arabidopsis thaliana root hairs and trichomes provide model systems to study the pathways that control planar polarity and cell fate specification in plants. A concentration gradient of the plant hormone auxin provides an instructive cue that coordinates polar assembly of signalling complexes at plasma membranes of root epidermal cells; however, knowledge about additional players and cytoskeletal effectors driving cell polarization prior to hair emergence remains limited. On the other hand, epidermal cell fate specification is controlled by a well-characterized gene network of transcription factors that translate positional signals and cell-to-cell communication into tissue-wide patterning. Yet, new components are continuously found to interact with the patterning pathway, shedding light on its connections with diverse developmental processes. This thesis presents the SABRE (SAB) gene as a novel player in planar polarity establishment and root epidermal patterning. SAB is a large protein with sequence similarity to proteins present in all eukaryotes and affects planar polarity as well as orientation of cell divisions and cortical microtubules. Genetic interaction with the microtubule-associated protein gene CLASP further supports involvement of SAB in microtubule arrangement, suggesting a role for this gene in cytoskeletal organisation. Strikingly, SAB also interacts genetically with ACTIN7 (ACT7), and both ACT7 and its modulator ACTIN INTERACTING PROTEIN 1-2 (AIP1-2) contribute to planar polarity of root hair positioning. Cell-file specific expression of AIP1-2 depends on the epidermal-patterning regulator WEREWOLF (WER), revealing a connection between actin organization, planar polarity and cell fate specification. Consistent with this finding, SAB also functions in patterning of the root epidermis by stabilizing cell fate acquisition upstream of the core patterning pathway. These results unveil new roles for SAB in planar polarity and epidermal patterning and suggest that organization of the microtubule and the actin cytoskeleton are important to both planar polarity establishment and cell fate specification. / Samordning av polaritet och differentiering av celler inom ett vävnadslager är avgörande för utvecklingen av multicellulära organismer. Rothår och bladhår hos Arabidopsis thaliana utgör modellsystem för att studera signalvägar som kontrollerar planpolaritet och specifikation av cellers öde hos växter. En koncentrationsgradient av växthormonet auxin ger en instruktiv signal som koordinerar polär hopsättning av signalkomplex vid plasmamembranet i rotepidermisceller; dock är kunskapen om ytterligare aktörer och hur cytoskelettets aktörer påverkar cellpolaritet innan rothår bildas begränsad. Vad gäller differentieringen av epidermala cellers öde kontrolleras dessa genom ett väl karakteriserat nätverk av transkriptionsfaktorer som överför positionssignaler och cell-till-cell kommunikation till vävnadsomfattande mönsterbildning. Fortfarande hittas dock nya komponenter som interagerar med signalvägarna för mönsterbildning, vilket ger nya insikter om dess förbindelser med diverse utvecklingsprocesser. Denna avhandling presenterar genen SABRE (SAB) som en ny aktör i etableringen av planpolaritet och mönsterbildning av rotepidermis. SAB är ett stort protein som har sekvenslikhet med proteiner som finns i alla eukaryoter och det påverkar planpolaritet, orientering av celldelning och kortikala mikrotubler. Genetisk interaktion med genen för det mikrotubuli-associerade proteinet CLASP stärker ytterligare inblandningen av SAB i organiserandet av mikrotubler och antyder att denna gen har en roll i organiserandet av cytoskelettet. Slående är att SAB även interagerar genetiskt med ACTIN7 (ACT7) och att både ACT7 och dess modulator ACTIN-INTERACTING PROTEIN1-2 (AIP1-2) bidrar till planpolaritet vid positionering av rothår. Cellfils-specifikt uttryck av AIP1-2 beror på den epidermala mönsterbildande genen WEREWOLF (WER), vilket påvisar ett samband mellan organisationen av aktin, planpolaritet och specifikationen av cellers öde. SAB fungerar även i mönsterbildning av rotens epidermis och stabiliserar förvärvet av cellöde uppströms av den centrala signalvägen för mönsterbildning. Dessa resultat visar på nya roller för SAB i planpolaritet och mönsterbildning av epidermis och indikerar att organiseringen av mikrotubler och aktin-cytoskelettet är viktiga både för etablerandet av planpolaritet och för specificeringen av cellers öde.

Persistent organic pollutants (POPs) are a threat to the environment and human health because they are ubiquitous, resistant to degradation, can bio-accumulate in organisms and bio-magnify in food chains. They have a detrimental effect on the reproductive, nervous and immunity systems of vertebrates. An international treaty, the Stockholm Convention on POPs, came into force in 2004 and aims to limit and eventually prohibit any use and unintentional production of POPs. South Africa ratified the Convention in 2002. Those compounds currently listed by the Stockholm Convention as POPs include chlorinated pesticides such as dichlorodiphenyltrichlorethane (DDT), chlordane and dieldrin, and industry-related compounds such as polychlorinated biphenyls (PCBs) and hexachlorobenzene. Polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) are also regarded as POPs but - together with some PCBs - they are the unintentional result of anthropogenic activity. This study focussed on the PCDDs, PCDFs and dioxin-like PCBs in the aquatic environment of South Africa particularly because the water resources in this country are under pressure. Despite the fact that South Africa has the sources of these compounds, little is known about the levels of these three groups of compounds. The concentration of twelve dioxin-like PCBs, seven PCDDs and ten PCDFs were determined for 22 sites selected on the grounds of their proximity to possible pollution sources. Analytical determinations included gas chromatography/mass spectrometry and a cell-based bio-assay, the H4IIE-/17C reporter gene assay. Possible sources of the observed pollution were inferred using the following statistical investigative methods: principal component and hierarchical cluster analysis. Seven of the sites had levels higher than the threshold effect concentration of Canada's sediment quality guidelines of 0.85 ngTEQ kg'1 (Toxic Equivalency Quotient). The other sites had lower levels. The highest concentration, 17.8 ng TEQ kg"1, was measured at a site in the southern Gauteng Province. Most of the PCDD/F pollution seemed to have come from combustion sources related to human activity, rather than industrial combustion. Most of the dioxin-like PCB pollution seemed to have been from commercial PCB preparations. Future research would require better characterisation of the sources in order to reduce the formation of these compounds, but also to better understand the exposure and risk scenarios, if humans are to be in close contact with these sources. / Thesis (Ph.D. (Zoology))--North-West University, Potchefstroom Campus, 2008.

Planar cell polarity (PCP) refers to the coordinated orientation, movement, or structure of cells within the plane of a tissue. Zebrafish PCP mutants such as the vangl2 mutant exhibit defects in convergent extension, neural tube morphogenesis, and ciliary positioning. Tmem14a is a putative tetraspanin protein that was identified as an potential interactor of Vangl2 in a membrane yeast-two hybrid screen. GFP-tagged versions of Tmem14a are localized to the trans-Golgi network in zebrafish neuroepithelial cells. Knockdown of Tmem14a activity results in convergent extension defects, an ectopic accumulation of cells in the neural tube, and disorganized cilia. The localization of GFP-tagged Tmem14a to the trans-Golgi network suggested that Tmem14a plays a role in the trafficking of core PCP components to the cell membrane. Indeed, the membrane localization of GFP-Vangl2 was disrupted in Tmem14a morphants. Thus, Tmem14a is an interactor of Vangl2 and a novel regulator of vertebrate planar cell polarity signaling.

This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

Planar cell polarity (PCP) refers to the coordinated orientation, movement, or structure of cells within the plane of a tissue. Zebrafish PCP mutants such as the vangl2 mutant exhibit defects in convergent extension, neural tube morphogenesis, and ciliary positioning. Tmem14a is a putative tetraspanin protein that was identified as an potential interactor of Vangl2 in a membrane yeast-two hybrid screen. GFP-tagged versions of Tmem14a are localized to the trans-Golgi network in zebrafish neuroepithelial cells. Knockdown of Tmem14a activity results in convergent extension defects, an ectopic accumulation of cells in the neural tube, and disorganized cilia. The localization of GFP-tagged Tmem14a to the trans-Golgi network suggested that Tmem14a plays a role in the trafficking of core PCP components to the cell membrane. Indeed, the membrane localization of GFP-Vangl2 was disrupted in Tmem14a morphants. Thus, Tmem14a is an interactor of Vangl2 and a novel regulator of vertebrate planar cell polarity signaling.

The suspension system of a vehicle is conventionally designed such that the spring-damper element is configured in the vertical direction, and the longitudinal connection between the vehicle chassis and wheels is always very stiff compared to the vertical one. This mechanism can isolate vibrations and absorb shocks efficiently in the vertical direction but cannot attenuate the longitudinal impacts caused by road obstacles. In order to overcome such a limitation, a planar suspension system (PSS) is proposed. This novel vehicle suspension system has a longitudinal spring-damper strut between the vehicle chassis and wheel. The dynamic performance, including ride comfort, pitch dynamics, handling characteristics and total dynamic behaviour, of a mid-size passenger vehicle equipped with such planar suspension systems is thoroughly investigated and compared with those of a conventional vehicle. To facilitate this investigation, various number of vehicle models are developed considering the relative longitudinal motions of wheels with respect to the chassis. A 4-DOF quarter-car model is used to conduct a preliminary study of the ride quality, and a pitch plane half-car model is employed to investigate the pitch dynamics in both the frequency and time domain. A 5-DOF yaw plane single-track half-car model along with a pitch plane half-car model is proposed to carry out the handling performance study, and also an 18-DOF full-car model is used to perform total dynamics study. In addition to these mathematical models, virtual full-car models are constructed in Adams/car to validate the proposed mathematical models. For the sake of prediction of the tire-ground interaction force, a radial-spring tire model is modified by adding the tire damping to generate the road excitation forces due to road disturbances in the vertical and longitudinal directions. A dynamic 2D tire friction model based on the LuGre friction theory is modified to simulate the dynamic frictional interaction in the tire-ground contact pitch. The ride quality of a PSS vehicle is evaluated in accordance with the ISO 2631 and compared with that of a conventional vehicle. It is shown that the PSS system exhibits good potential to attenuate the impact and isolate the vibration due to road excitations in both the vertical and longitudinal directions, resulting in improved vehicles’ ride and comfort quality. The relatively soft longitudinal strut can absorb the longitudinal impact and, therefore, can protect the components. The investigation of handling performance including the steady-state handling characteristics, transient and frequency responses in various scenarios demonstrates that the PSS vehicle is directionally stable and generally has comparable handling behaviour to a similar conventional vehicle. The application of PSS in vehicles can enhance the understeer trend, i.e. the understeer becomes more understeer, neutral steer becomes slightly understeer, and oversteer becomes less oversteer. The total dynamic behaviour combining the bounce, pitch, roll and the longitudinal dynamics under various scenarios such as differential brake-in-turn and asymmetric obstacle traversing was thoroughly investigated. Simulation results illustrate that the PSS vehicle has a relatively small roll angle in a turning manoeuvre. In some cases such as passing road potholes, the PSS vehicle has a better directional stability.

The seven-pass transmembrane atypical cadherin, Flamingo (also known as Starry Night) is evolutionally conserved in both structure and function in vertebrates and invertebrates. It plays important roles during the establishment of planar cell polarity (PCP) of epithelial tissues and during the development of axons and dendrites in both peripheral and central neurons. / This thesis looks at the role of Flamingo/Starry Night in axon growth and guidance in the embryonic abdominal peripheral nervous system (PNS) of Drosophila. It describes the expression pattern of Flamingo in the PNS and its environment. A combination of single cell labelling and immunohistochemical techniques was used to define the effect of mutations in flamingo as well as several genes coding for potential Flamingo interaction partners. Rescue- and over-/mis-expression experiments featuring targeted expression of either a wild type version or mutant versions of flamingo provide information on the cellular and molecular mechanisms by which Flamingo regulates sensory axon development. Loss of Flamingo function results in a highly penetrant axon stall phenotype. Both sensory and motor axons frequently halt their advance early along their normal trajectories. Flamingo appears to mediate an axon growth promoting signal upon contact of sensory growth cones with specific early intermediate targets. Expression of Flamingo in sensory neurons is sufficient to rescue the mutant sensory axon phenotype. This rescue is at least partially independent of most of the extracellular region of the Flamingo protein. While Flamingo was previously found to have homophilic adhesion properties in vitro and appears to function by a homophilic mechanism during the neurite development of several types of neurons, this study supports a heterophilic signalling mechanism by which Flamingo fulfils its role in abdominal sensory axon growth promotion.