Topological Theory in Bioconstructivism

In the essay “Landscapes of Change: Boccioni’s Stati d’animo as a General Theory of Models,” in Assemblage 19, 1992, Sanford Kwinter proposed a number of theoretical models which could be applied to computer-generated forms in Bioconstructivism. These included topological theory, epigenesis, the epigenetic landscape, morphogenesis, catastrophe and catastrophe theory. Topological theory entails transformational events or deformations in nature which introduce discontinuities into the evolution of a system. Epigenesis entails the generation of smooth landscapes, in waves or the surface of the earth, for example, formed by complex underlying topological interactions. The epigenetic landscape is the smooth forms of relief which are the products of the underlying complex networks of interactions. Morphogenesis describes the structural changes occurring during the development of an organism, wherein forms are seen as discontinuities in a system, as moments of structural instability rather than stability. A catastrophe is a morphogenesis, a jump in a system resulting in a discontinuity. Catastrophe theory is a topological theory describing the discontinuities in the evolution of a system in nature. A project which applies these models, and which helps to establish a theoretical basis for Bioconstructivism by applying topological models, is a design for a theater by Amy Lewis in a Graduate Architecture Design Studio directed by Associate Professor Andrew Thurlow at Roger Williams University, in Spring 2011. In the project, moments of structural stability are juxtaposed with moments of structural instability, to represent the contradiction inherent in self-generation or immanence. The singularity of the surfaces of the forms in the epigenetic landscape contradicts the complex network of interactions of topological forces from which they result. Actions in the environment on unstable, unstructured forms, and undifferentiated structures, result in stable, structured forms, and differentiated structures

The morphogenesis of intention and structural stability of motifs.

This article is based on the Agent-action-Objective (AaO) axiom and assumes that intention can be discovered and made evident. But this requirement can be satisfied only under the condition that a particular individual can be identified with his style of writing. This implies that the nature of writing becomes approachable. Getting a style under control presupposes the A-component, which is discussed with a focus on string rotation and the establishment of lawful relations that include intention in laws that are governing the patterning of strings. It is demonstrated that angular articulations are characterising dynamical string movements. However, independent of their textually embedded magnitudes, they cannot survive. As the result of the text production of two Swedish students, convoluted structures have come into existence and reflect transformations on the meaning of topological invariants. Thus, spaces have been realised, which have been shown to restrict string rotations. Over the given environments, it is demonstrated that uniqueness is achieved in the comprehension of a particular task. In the formation of motifs, the morphogenesis of intention and its structural stability have provided the basis for a 3D writing style control, while the growth curves of motifs have been shown to evolve in complex landscapes

Turing Patterns and Biological Explanation

Turing patterns are a class of minimal mathematical models that have been used to discover and conceptualize certain abstract features of early biological development. This paper examines a range of these minimal models in order to articulate and elaborate a philosophical analysis of their epistemic uses. It is argued that minimal mathematical models aid in structuring the epistemic practices of biology by providing precise descriptions of the quantitative relations between various features of the complex systems, generating novel predictions that can be compared with experimental data, promoting theory exploration, and acting as constitutive parts of empirically adequate explanations of naturally occurring phenomena, such as biological pattern formation. Focusing on the roles that minimal model explanations play in science motivates the adoption of a broader diachronic view of scientific explanation

The E3 ubiquitin ligase IDOL regulates synaptic ApoER2 levels and is important for plasticity and learning.

Neuronal ApoE receptors are linked to learning and memory, but the pathways governing their abundance, and the mechanisms by which they affect the function of neural circuits are incompletely understood. Here we demonstrate that the E3 ubiquitin ligase IDOL determines synaptic ApoER2 protein levels in response to neuronal activation and regulates dendritic spine morphogenesis and plasticity. IDOL-dependent changes in ApoER2 abundance modulate dendritic filopodia initiation and synapse maturation. Loss of IDOL in neurons results in constitutive overexpression of ApoER2 and is associated with impaired activity-dependent structural remodeling of spines and defective LTP in primary neuron cultures and hippocampal slices. IDOL-deficient mice show profound impairment in experience-dependent reorganization of synaptic circuits in the barrel cortex, as well as diminished spatial and associative learning. These results identify control of lipoprotein receptor abundance by IDOL as a post-transcriptional mechanism underlying the structural and functional plasticity of synapses and neural circuits

The influence of receptor-mediated interactions on reaction-diffusion mechanisms of cellular self-organisation

Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction

Stable States of Biological Organisms

A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole. The organism is modeled by a five-dimensional dynamical system. The organism homeostasis is described by the evolution equations for five interacting components: healthy cells, ill cells, innate immune cells, specific immune cells, and pathogens. The stability analysis demonstrates that, in a wide domain of the parameter space, the system exhibits robust structural stability. There always exist four stable stationary solutions characterizing four qualitatively differing states of the organism: alive state, boundary state, critical state, and dead state.Comment: Latex file, 12 pages, 4 figure

Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and Lambda-Transitions

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e. ``spontaneous breaking'' of the topology) of the original object on a secular time scale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems.Comment: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in Ap

PAKing up to the endothelium

Angiogenesis recapitulates the growth of blood vessels that progressively expand and remodel into a highly organized and stereotyped vascular network. During adulthood, endothelial cells that formed the vascular wall retain their plasticity and can be engaged in neo-vascularization in response to physiological stimuli, such as hypoxia, wound healing and tissue repair, ovarian cycle and pregnancy. In addition, numerous human diseases and pathological conditions are characterized by an excessive, uncontrolled and aberrant angiogenesis. The signalling pathways involving the small Rho GTPase, Rac and its downstream effector the p21-activated serine/threonine kinase (PAK) had recently emerged as pleiotropic modulators in these processes. Indeed, Rac and PAK were found to modulate endothelial cell biology, such as sprouting, migration, polarity, proliferation, lumen formation, and maturation. Elucidating the Rac/PAK molecular circuitry will provide essential information for the development of new therapeutic agents designed to normalize the blood vasculature in human diseases.Comment: Cell Signal (2009) epub ahead of prin