A study of proteinases of invasive cells using cryoultramicrotomy and immunogold labelling.

Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 1993.This study forms part of an investigation into the possible relevance of the lysosomal proteinases, cathepsins B, H, Land D, in cancer cell invasion. In this study, the main technique adopted was the Tokuyasu "cryo" method, in which the tissues were fixed, frozen and sectioned and labelled using the relevant antibodies, which were detected with protein A gold probes. In order to implement the Tokuyasu technique, it was necessary to rebuild a knife maker, for the production of adequately sharp glass knives, and to modify a sputter-coater into a glow-discharger, for rendering carbon-coated grids hydrophilic, to promote adhesion of hydrated sections. This study was directed towards human tissues and peptide antibodies were investigated as a means of avoiding isolation of proteins from scarce human tissue, and as a means of obtaining antibodies that will target specific regions of proteins of interest. Peptide antibodies were also considered promising for studies of proteinase trafficking and as immunoinhibiting agents, potentially useful in cancer therapy. Various prediction programmes were investigated for their effectiveness in predicting whether a given peptide sequence will elicit antibodies that will react with the native protein. Successful prediction would increase the success rate of peptide antibody production and thus lower the cost. Leucocytes were studied as a model of an invasive cell, since they are more readily available than tumour cells and serve the purpose during the development of methods. In the course of these studies, an optimal protocol for the fixation of PMNs was developed, involving lateral fixation of cut sections, that should be useful for future studies on these cells. Elastase and cathepsins D and G were found on the surface of activated PMNs and could thus play a role in the invasive properties of these cells. Studies on MCF-10A "normal" breast epithelial cells and their ras-transformed Neo-T counterparts revealed that upon transformation, lysosomes shift from a perinuclear position, to a more peripheral position. None of the cathepsins studied was found on the cell surface of either the normal or ras-transfected cells, suggesting that surface distribution of these enzymes may not be a requirement for invasiveness. These studies suggest that immunocytochemical investigation of cells, in the process of invading through a barrier membrane, might be profitable in elucidating the role of proteinases in invasive cancer

Node dynamics on graphs: dynamical heterogeneity in consensus, synchronisation and final value approximation for complex networks

Here we consider a range of Laplacian-based dynamics on graphs such as dynamical invariance and coarse-graining, and node-specific properties such as convergence, observability and consensus-value prediction. Firstly, using the intrinsic relationship between the external equitable partition (EEP) and the spectral properties of the graph Laplacian, we characterise convergence and observability properties of consensus dynamics on networks. In particular, we establish the relationship between the original consensus dynamics and the associated consensus of the quotient graph under varied initial conditions. We show that the EEP with respect to a node can reveal nodes in the graph with increased rate of asymptotic convergence to the consensus value as characterised by the second smallest eigenvalue of the quotient Laplacian. Secondly, we extend this characterisation of the relationship between the EEP and Laplacian based dynamics to study the synchronisation of coupled oscillator dynamics on networks. We show that the existence of a non-trivial EEP describes partial synchronisation dynamics for nodes within cells of the partition. Considering linearised stability analysis, the existence of a nontrivial EEP with respect to an individual node can imply an increased rate of asymptotic convergence to the synchronisation manifold, or a decreased rate of de-synchronisation, analogous to the linear consensus case. We show that high degree 'hub' nodes in large complex networks such as Erdős-Rényi, scale free and entangled graphs are more likely to exhibit such dynamical heterogeneity under both linear consensus and non-linear coupled oscillator dynamics. Finally, we consider a separate but related problem concerning the ability of a node to compute the final value for discrete consensus dynamics given only a finite number of its own state values. We develop an algorithm to compute an approximation to the consensus value by individual nodes that is ϵ close to the true consensus value, and show that in most cases this is possible for substantially less steps than required for true convergence of the system dynamics. Again considering a variety of complex networks we show that, on average, high degree nodes, and nodes belonging to graphs with fast asymptotic convergence, approximate the consensus value employing fewer steps.Open Acces

Fuzzy EOQ Model with Trapezoidal and Triangular Functions Using Partial Backorder

EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR ̃C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the company's problems in estimating the costs for the next term

Functional Analysis of Sam68 during Forebrain and Oligodendrocyte development

During the development of the central nervous sytem (CNS) the maturation of oligodendrocytes occurs through the tightly regulated activity of diverse intrinsic and extrinsic signalling factors. Our group identified the STAR-family protein Sam68 as one of those intrinsic cues involved in oligodendrocyte differentiation. The level of Sam68 increases with ongoing maturation and it regulates the expression of Myelin Basic Protein (MBP). Despite its role in OPC (oligodendrocyte precursor cells) maturation, previous studies already identified Sam68 as a promotor of neural stem cell (NSC) differentiation and as a Tenascin-C- regulated target gene. However, the mechanism(s) how Sam68 regulates NSC and particularly oligodendrocyte development remained incompletely understood. This thesis provides completely new insights into the role of Sam68 during forebrain and particularly, oligodendrocyte development. Furthermore, my results exhibit hnRNPA1 as a new interaction partner of Sam68 in oligodendrocyte development and provide a basic concept for the regulation of MBP-expression through both proteins. Our group already investigated the general expression pattern of the three STAR-family members, Sam68, Slm-1 and Slm-2 and showed a specific expression of all three proteins during forebrain development. The present thesis characterised for the first time the identity of Sam68 expressing cells during forebrain development. Neuroepithelial, radial glia cells and their derivative cell types were exhibited to express Sam68. Furthermore, time-dependent cell culture experiments revealed a significant shift in the expression pattern towards differentiating cells. These findings supported earlier studies of our group indicating a promotive role of Sam68 in cell differentiation. The second part describes a successfully established method for the high efficiency transfection of non-adherent primary rat OPCs. This new transfection protocol enables for the first time the reproducible transfection of non-adherent OPCs with a high viability, a regular maturation pattern and an acceptable transfection efficiency. Regarding the time-consuming and low yield isolation of OPCs, this method represents a big advantage and provides the basis for the main goal of this thesis, which displays the determination of the role of Sam68 during oligodendrocyte development. Although oligodendrocytes count to the best characterised cell types within the CNS, many intracellular signalling pathways regulating their development and differentiation remained elusive. Here, I discovered the respective Sam68 domains which modulates cell growth, MBP-expression and myelin-sheet formation. The complete RNA-binding domain and the NLS-sequence were shown to be relevant for the regulation of MBP-expression as well as for the formation of myelin-sheets. The relevance of the NLS-sequence and the knowledge about Sam68 as a regulator of alternative splicing events led to the assumption that Sam68 may regulate MBP-expression through modulating its splicing. The well-studied splicing regulator hnRNPA1 was already shown to regulate the alternative splicing of myelin-associated glycoprotein in cooperation with the STAR-family member Quaking I. Thus, I assumed a similar interaction of Sam68 and hnRNPA1 in the regulation of MBP expression. Indeed, MBP-level was downregulated after an hnRNPA1 knockdown and this effect was intensified after an additional overexpression of Sam68. These results provide a good basis to unravel the very complex regulation between Sam68 and hnRNPA1 in oligodendrocyte development

Leveraging Relational Structure through Message Passing for Modelling Non-Euclidean Data

Modelling non-Euclidean data is difficult since objects for comparison can be formed of different numbers of constituent parts with different numbers of relations between them, and traditional (Euclidean) methods are non-trivial to apply. Message passing enables such modelling by leveraging the structure of the relations within a (or between) given object(s) in order to represent and compare structure in a vectorized form of fixed dimensions. In this work, we contribute novel message passing techniques that improve state of the art for non-Euclidean modelling in a set of specifically chosen domains. In particular, (1) we introduce an attention-based structure-aware global pooling operator for graph classification and demonstrate its effectiveness on a range of chemical property prediction benchmarks, we also show that our method outperforms state of the art graph classifiers in a graph isomorphism test, and demonstrate the interpretability of our method with respect to the learned attention coefficients. (2) We propose a style similarity measure for Boundary Representations (B-Reps) that leverages the style signals in the second order statistics of the activations in a pre-trained (unsupervised) 3D encoder, and learns their relative importance to an end-user through few-shot learning. Our approach differs from existing data-driven 3D style methods since it may be used in completely unsupervised settings. We show quantitatively that our proposed method with B-Reps is able to capture stronger style signals than alternative methods on meshes and point clouds despite its significantly greater computational efficiency. We also show it is able to generate meaningful style gradients with respect to the input shape. (3) We introduce a novel message passing-based model of computation and demonstrate its effectiveness in expressing the complex dependencies of biological systems necessary to model life-like systems and tracing cell lineage during cancerous tumour growth, and demonstrate the improvement over existing methods in terms of post-analysis

Well-spread sequences and edge-labellings with constant Hamilton-weight

A sequence (a i) of integers is well-spread if the sums a i +a j, for i<j, are all different. For a fixed positive integer r, let W r (N) denote the maximum integer n for which there exists a well-spread sequence 0≤ a 1 <…<a n ≤ N with a i ≡ a j (b mod r) for all i, j. We give a new proof that W r (N)<(N/r) 1/2 +O((N/r) 1/4); our approach improves a bound of Ruzsa [ Acta.Arith. 65(1993), 259--283] by decreasing the implicit constant, essentially from 4 to √ 3. We apply this result to verify a conjecture of Jones et al. from [ Discuss. Math. Graph Theory 23(2003), 287--307]. The application concerns the growth-rate of the maximum label Λ(n) in a `most-efficient' metric, injective edge-labelling of K n with the property that every Hamilton cycle has the same length; we prove that 2n 2-O(n 3/2)<Λ(n)<2n 2 +O(n 61/40)

Proteinases and extracellular matrix degradation in breast cancer.

Thesis (Ph.D.)-University of Natal, Pietermaritzburg , 1996.A variety of proteases have been shown to promote the progression of cancer by virtue of their ability to degrade extracellular proteinaceous barriers, such as basement membrane and interstitial stroma. At the outset of this study available evidence strongly implicated cathepsin D in breast cancer metastasis. It was envisaged that an antibody inhibitory to the activity of this enzyme might retard invasion, and restrain a tumour from spreading. To this end anti-peptide antibodies were generated against a peptide sequence derived from the substrate capturing "flap" of the enzyme. Inhibition of enzyme activity by these antibodies could not be demonstrated, probably due to the lack of a suitably sensitive enzyme assay. However, the rationale of this study and the expertise gained from it could be applied, in the future, to enzymes that have since been found to be more relevant to tumour invasion. A feature of many transformed cells is an anomalous lysosomal enzyme trafficking system, and concomitant hyper-secretion of some enzymes. The distribution of low pH compartments and lysosomal enzyme-containing compartments was investigated in human breast epithelial cells, and their c-Ha-ras- transformed counterparts. Immunofluorescence and immunoelectron microscopy showed that these compartments have a more peripheral cellular distribution with respect to normal cells, and cathepsins B and D were cell surface-associated. Studies were undertaken to reveal the extracellular matrix degrading ability of c-Ha- ras-transformed cells. Transformed cells exhibited increased degradation of fluorescein-labelled extracellular matrix in serum free medium, and increased motility, and degradation and disruption of extracellular matrix in serum-containing medium. In vitro invasion through artificial basement membrane by transformed cells was investigated using scanning electron microscopy, and was further used to preliminarily identify the proteases involved in invasion by specific inhibition. By this means, greatest inhibition of in vitro invasion was obtained using a specific metalloproteinase inhibitor. Overexpression by transformed cells of a metalloproteinase was detected by gelatin zymography. Together these results suggest that the increased invasive capacity of ras-transformed breast epithelial cells may be largely due to increased metalloproteinase activity

Local approaches to global problems in extremal combinatorics

In this thesis we consider five problems in extremal combinatorics all of which which are all amenable to approaches based on local structure. The first part of this thesis looks at rainbow subgraphs at extremal thresholds. We show that as soon as they appear, we can also find rainbow copies of Perfect Matchings, H-factors and Hamilton cycles in large graphs. We then look to random digraphs and consider the D(n, p) model in which each edge is present independently with probability p. We find tail bounds on the size of the largest strongly connected component in the critical window around p = 1/n. Finally, we consider the partition function of the ferromagnetic Potts model on graphs of bounded maximum degree. We show that there exists an open set in C containing an interval [1, w] inside which the partition function has no zeros