Regulation of ROCK1 via Notch1 during breast cancer cell migration into dense matrices

Background The behaviour of tumour cells depends on factors such as genetics and the tumour microenvironment. The latter plays a crucial role in normal mammary gland development and also in breast cancer initiation and progression. Breast cancer tissues tend to be highly desmoplastic and dense matrix as a pre-existing condition poses one of the highest risk factors for cancer development. However, matrix influence on tumour cell gene expression and behaviour such as cell migration is not fully elucidated. Results We generated high-density (HD) matrices that mimicked tumour collagen content of 20 mg/cm3 that were ~14-fold stiffer than low-density (LD) matrix of 1 mg/cm3. Live-cell imaging showed breast cancer cells utilizing cytoplasmic streaming and cell body contractility for migration within HD matrix. Cell migration was blocked in the presence of both the ROCK inhibitor, Y-27632, and the MMP inhibitor, GM6001, but not by the drugs individually. This suggests roles for ROCK1 and MMP in cell migration are complicated by compensatory mechanisms. ROCK1 expression and protein activity, were significantly upregulated in HD matrix but these were blocked by treatment with a histone deacetylase (HDAC) inhibitor, MS-275. In HD matrix, the inhibition of ROCK1 by MS-275 was indirect and relied upon protein synthesis and Notch1. Inhibition of Notch1 using pooled siRNA or DAPT abrogated the inhibition of ROCK1 by MS-275. Conclusion Increased matrix density elevates ROCK1 activity, which aids in cell migration via cell contractility. The upregulation of ROCK1 is epigenetically regulated in an indirect manner involving the repression of Notch1. This is demonstrated from inhibition of HDACs by MS-275, which caused an upregulation of Notch1 levels leading to blockade of ROCK1 expression.

The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula

Regulation of canonical Wnt signalling pathway during cementum regeneration

This project highlights the important role of cell signalling pathway during tooth regeneration. Biomaterials can be designed to activate relevant cell signals for the purpose of dental repair and tooth regeneration. Based on the results in the present project, strategies directly targeting cell signalling pathway may provide new approaches for periodontal regenerative tissue engineering.

Activation of the canonical Wnt signaling pathway induces cementum regeneration

Canonical Wnt signaling is important in tooth development but it is unclear whether it can induce cementogenesis and promote the regeneration of periodontal tissues lost due to disease. Therefore, the aim of this study is to investigate the influence of canonical Wnt signaling enhancers on human periodontal ligament cell (hPDLCs) cementogenic differentiation in vitro and cementum repair in a rat periodontal defect model. Canonical Wnt signaling was induced by (i) local injection of lithium chloride; (ii) local injection of sclerostin antibody; and (iii) local injection of a lentiviral construct overexpressing β-catenin. The results showed that the local activation of canonical Wnt signaling resulted in significant new cellular cementum deposition and the formation of well-organized periodontal ligament fibers, which was absent in the control group. In vitro experiments using hPDLCs showed that the Wnt signaling pathway activators significantly increased mineralization, alkaline phosphatase (ALP) activity, and gene and protein expression of the bone and cementum markers osteocalcin (OCN), osteopontin (OPN), cementum protein 1 (CEMP1), and cementum attachment protein (CAP). Our results show that the activation of the canonical Wnt signaling pathway can induce in vivo cementum regeneration and in vitro cementogenic differentiation of hPDLCs.

Estimating link-dependent origin-destination matrices from sample trajectories and traffic counts

In transport networks, Origin-Destination matrices (ODM) are classically estimated from road traffic counts whereas recent technologies grant also access to sample car trajectories. One example is the deployment in cities of Bluetooth scanners that measure the trajectories of Bluetooth equipped cars. Exploiting such sample trajectory information, the classical ODM estimation problem is here extended into a link-dependent ODM (LODM) one. This much larger size estimation problem is formulated here in a variational form as an inverse problem. We develop a convex optimization resolution algorithm that incorporates network constraints. We study the result of the proposed algorithm on simulated network traffic.

Estimating link-dependent origin-destination matrices from sample trajectories and traffic counts

Origin-Destination matrices (ODM) estimation can benefits of the availability of sample trajectories which can be measured thanks to recent technologies. This paper focus on the case of transport networks where traffic counts are measured by magnetic loops and sample trajectories available. An example of such network is the city of Brisbane, where Bluetooth detectors are now operating. This additional data source is used to extend the classical ODM estimation to a link-specific ODM (LODM) one using a convex optimisation resolution that incorporates networks constraints as well. The proposed algorithm is assessed on a simulated network.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

The connection between Mueller and Jones matrices of polarization optics

A necessary and sufficient condition for the 4 × 4 Mueller matrix to be derivable from the 2 × 2 Jones matrix is obtained. This condition allows one to determine if a given Mueller matrix describes a totally polarized system or a partially polarized (depolarizing) system. The result of Barakat is analysed in the light of this condition. A recently reported experimentally measured Mueller matrix is examined using this condition and is shown to represent a partially polarized system.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Characterization of Mycobacterium leprae RecA intein, a LAGLIDADG homing endonuclease, reveals a unique mode of DNA-binding, helical distortion and cleavage, compared to a canonical LAGLIDADG homing endonuclease

Mycobacterium leprae, which has undergone reductive evolution leaving behind a minimal set of essential genes, has retained intervening sequences in four of its genes implicating a vital role for them in the survival of the leprosy bacillus. A single in-frame intervening sequence has been found embedded within its recA gene. Comparison of M. leprae recA intervening sequence with the known intervening sequences indicated that it has the consensus amino acid sequence necessary for being a LAGLIDADG-type homing endonuclease. In light of massive gene decay and function loss in the leprosy bacillus, we sought to investigate whether its recA intervening sequence encodes a catalytically active homing endonuclease. Here we show that the purified M. leprae RecA intein (PI-MleI) binds to cognate DNA and displays endonuclease activity in the presence of alternative divalent cations, Mg2+ or Mn2+. A combination of approaches including four complementary footprinting assays such as DNase I, Cu/phenanthroline, methylation protection and KMnO4, enhancement of 2-aminopurine fluorescence and mapping of the cleavage site revealed that PI-MleI binds to cognate DNA flanking its insertion site, induces helical distortion at the cleavage site and generates two staggered double-strand breaks. Taken together, these results implicate that PI-MleI possess a modular structure with separate domains for DNA target recognition and cleavage, each with distinct sequence preferences. From a biological standpoint, it is tempting to speculate that our findings have implications for understanding the evolution of LAGLIDADG family of homing endonucleases

FreeS: A fast algorithm to discover frequent free subtrees using a novel canonical form

Web data can often be represented in free tree form; however, free tree mining methods seldom exist. In this paper, a computationally fast algorithm FreeS is presented to discover all frequently occurring free subtrees in a database of labelled free trees. FreeS is designed using an optimal canonical form, BOCF that can uniquely represent free trees even during the presence of isomorphism. To avoid enumeration of false positive candidates, it utilises the enumeration approach based on a tree-structure guided scheme. This paper presents lemmas that introduce conditions to conform the generation of free tree candidates during enumeration. Empirical study using both real and synthetic datasets shows that FreeS is scalable and significantly outperforms (i.e. few orders of magnitude faster than) the state-of-the-art frequent free tree mining algorithms, HybridTreeMiner and FreeTreeMiner.

Theological Exegesis in the Canonical Context : Brevard S. Childs' Methodology of Biblical Theology

Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.