Director Strings as Combinators

A simple calculus (the Director String Calculus-DSC) for expressing abstractions is introduced, which captures the essence of the “long reach” combinators introduced by Turner. We present abstraction rules that preserve the applicative structure of the original lambda term, and that cannot increase the number of subterms in the translation. A translated lambda term can be reduced according to the evaluation rules of DSC. If this terminates with a DSC normal form, this can be translated into a lambda term using rules presented below. We call this process of abstracting a lambda term, reducing to normal form in the space of DSC terms, and translating back to a lambda term an implementation. We show that our implementation of the lambda calculus is correct: For lambda terms with a normal form that contains no lambdas (ground terms), the implementation is shown to yield a lambda calculus normal form. For lambda terms whose normal forms represent functions, it is shown that the implementation yields lambda terms that are beta-convertible in zero or more steps to the normal form of the original lambda term. In this sense, our implementation involves weak reduction according to Hindley et al. [9]

The autophagic tumor stroma model of cancer: Role of oxidative stress and ketone production in fueling tumor cell metabolism

A loss of stromal caveolin-1 (Cav-1) in the tumor fibroblast compartment is associated with early tumor recurrence, lymphnode metastasis and tamoxifen-resistance, resulting in poor clinical outcome in breast cancer patients. Here, we have used Cav-1 (−/−) null mice as a pre-clinical model for this “lethal tumor micro-environment”. Metabolic profiling of Cav-1 (−/−) mammary fat pads revealed the upregulation of numerous metabolites (nearly 100), indicative of a major catabolic phenotype. Our results are consistent with the induction of oxidative stress, mitochondrial dysfunction and autophagy/mitophagy. The two most prominent metabolites that emerged from this analysis were ADMA (asymmetric dimethyl arginine) and BHB (beta-hydroxybutyrate; a ketone body), which are markers of oxidative stress and mitochondrial dysfunction, respectively. Transcriptional profiling of Cav-1 (−/−) stromal cells and human tumor stroma from breast cancer patients directly supported an association with oxidative stress, mitochondrial dysfunction and autophagy/mitophagy, as well as ADMA and ketone production. MicroRNA profiling of Cav-1 (−/−) stromal cells revealed the upregulation of two key cancer-related miR's, namely miR-31 and miR-34c. Consistent with our metabolic findings, these miR's are associated with oxidative stress (miR-34c) or activation of the hypoxic response/HIF1α (miR-31), which is sufficient to drive authophagy/mitophagy. Thus, via an unbiased comprehensive analysis of a lethal tumor micro-environment, we have identified a number of candidate biomarkers (ADMA, ketones and miR-31/34c) that could be used to identify high-risk cancer patients at diagnosis, for treatment stratification and/or for evaluating therapeutic efficacy during anti-cancer therapy. We propose that the levels of these key biomarkers (ADMA, ketones/BHB, miR-31 and miR-34c) could be (1) assayed using serum or plasma from cancer patients or (2) performed directly on excised tumor tissue. Importantly, induction of oxidative stress and autophagy/mitophagy in the tumor stromal compartment provides a means by which epithelial cancer cells can directly “feed off” of stromal-derived essential nutrients, chemical building blocks (amino acids, nucleotides) and energy-rich metabolites (glutamine, pyruvate, ketones/BHB), driving tumor progression and metastasis. Essentially, aggressive cancer cells are “eating” the cancer-associated fibroblasts via autophagy/mitophagy in the tumor micro-environment. Lastly, we discuss that this “autophagic tumor stroma model of cancer metabolism” provides a viable solution to the “autophagy paradox” in cancer etiology and chemotherapy

Generation of diverse biological forms through combinatorial interactions between tissue polarity and growth

A major problem in biology is to understand how complex tissue shapes may arise through growth. In many cases this process involves preferential growth along particular orientations raising the question of how these orientations are specified. One view is that orientations are specified through stresses in the tissue (axiality-based system). Another possibility is that orientations can be specified independently of stresses through molecular signalling (polarity-based system). The axiality-based system has recently been explored through computational modelling. Here we develop and apply a polarity-based system which we call the Growing Polarised Tissue (GPT) framework. Tissue is treated as a continuous material within which regionally expressed factors under genetic control may interact and propagate. Polarity is established by signals that propagate through the tissue and is anchored in regions termed tissue polarity organisers that are also under genetic control. Rates of growth parallel or perpendicular to the local polarity may then be specified through a regulatory network. The resulting growth depends on how specified growth patterns interact within the constraints of mechanically connected tissue. This constraint leads to the emergence of features such as curvature that were not directly specified by the regulatory networks. Resultant growth feeds back to influence spatial arrangements and local orientations of tissue, allowing complex shapes to emerge from simple rules. Moreover, asymmetries may emerge through interactions between polarity fields. We illustrate the value of the GPT-framework for understanding morphogenesis by applying it to a growing Snapdragon flower and indicate how the underlying hypotheses may be tested by computational simulation. We propose that combinatorial intractions between orientations and rates of growth, which are a key feature of polarity-based systems, have been exploited during evolution to generate a range of observed biological shapes

Modeling Plant Tissue Growth and Cell Division

Morphogenesis is the creation of form, a complex process requiring the integration of genetics, mechanics, and geometry. Patterning processes driven by molecular regulatory and signaling networks interact with growth to create organ shape, often in unintuitive ways. Computer simulation modeling is becoming an increasingly important tool to aid our understanding of these complex interactions. In this chapter we introduce computational approaches for studying these processes on spatial, multicellular domains. For some problems, such as the exploration of many patterning processes, simulation can be done on static (non-growing) templates. These can range from abstract idealized cells, such as rectangular or hex grids, to more realistic shapes such as Voronoi regions, or even shapes extracted from bio-imaging data. More dynamic processes like phyllotaxis involve the interaction of growth and patterning, and require the simulation of growing domains. In the simplest case growth can be modeled descriptively, provided as an input to the model. Growth is specified globally, and must be designed carefully to avoid conflicts (growing cells must fit together). We present several methods for this that can be applied to shoots, roots, leaves, and other plant organs. However when shape is an emergent property of the model, different cells or areas of the tissue need to specify their growth locally, and physically-based methods (mechanics) are required to resolve conflicts. Among these are mass-spring, finite element, and Hamiltonian-based approaches