Complex pattern formation in reaction diffusion systems with spatially-varying parameters

Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer–Meinhardt reaction–diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection

Speed of reaction diffusion in embryogenesis

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis

A simultaneous generalization of independence and disjointness in boolean algebras

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.Comment: Sumbitted to Orde

Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling

In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition—a type cells–cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbours from doing likewise. Lateral inhibition is well documented in flies, worms and vertebrates. In all of these organisms, the transmembrane proteins Notch and Delta (or their homologues) have been identified as mediators of the interaction—Notch as receptor, Delta as its ligand on adjacent cells. However, it is not clear under precisely what conditions the Delta-Notch mechanism of lateral inhibition can generate the observed types of pattern, or indeed whether this mechanism is capable of generating such patterns by itself. Here we construct and analyse a simple and general mathematical model of such contact-mediated lateral inhibition. In accordance with experimental data, the model postulates that receipt of inhibition (i.e. activation of Notch) diminishes the ability to deliver inhibition (i.e. to produce active Delta). This gives rise to a feedback loop that can amplify differences between adjacent cells. We investigate the pattern-forming potential and temporal behavior of this model both analytically and through numerical simulation. Inhomogeneities are self-amplifying and develop without need of any other machinery, provided the feedback is sufficiently strong. For a wide range of initial and boundary conditions, the model generates fine-grained patterns similar to those observed in living systems

Commercialization of the land remote sensing system: An examination of mechanisms and issues

In September 1982 the Secretary of Commerce was authorized (by Title II of H.R. 5890 of the 97th Congress) to plan and provide for the management and operation of the civil land remote sensing satellite systems, to provide for user fees, and to plan for the transfer of the ownership and operation of future civil operational land remote sensing satellite systems to the private sector. As part of the planning for transfer, a number of approaches were to be compared including wholly private ownership and operation of the system by an entity competitively selected, mixed government/private ownership and operation, and a legislatively-chartered privately-owned corporation. The results of an analysis and comparison of a limited number of financial and organizational approaches for either transfer of the ownership and operation of the civil operational land remote sensing program to the private sector or government retention are presented

Progress Towards Modeling the Ablation Response of NuSil-Coated PICA

The Mars Science Laboratory (MSL) Entry, Descent and Landing Instrumentation (MEDLI) collected in-flight data largely used by the ablation community to verify and validate physics-based models for the response of the Phenolic Impregnated Carbon Ablator (PICA) material [1-4]. MEDLI data were recently used to guide the development of NASAs high-fidelity material response models for PICA, implemented in the Porous material Analysis Toolbox based on OpenFOAM (PATO) software [5-6]. A follow-up instrumentation suite, MEDLI2, is planned for the upcoming Mars 2020 mission [7] after the large scientific impact of MEDLI. Recent analyses performed as part of MEDLI2 development draw the attention to significant effects of a protective coating to the aerothermal response of PICA. NuSil, a silicone-based overcoat sprayed onto the MSL heatshield as contamination control, is currently neglected in PICA ablation models. To mitigate the spread of phenolic dust from PICA, NuSil was applied to the entire MSL heatshield, including the MEDLI plugs. NuSil is a space grade designation of the siloxane copolymer, primarily used to protect against atomic oxygen erosion in the Low Earth Orbit environment. Ground testing of PICA-NuSil (PICA-N) models all exhibited surface temperature jumps of the order of 200 K due to oxide scale formation and subsequent NuSil burn-off. It is therefore critical to include a model for the aerothermal response of the coating in ongoing code development and validation efforts

Deletion of Tsc2 in nociceptors reduces target innervation, ion channel expression, and sensitivity to heat

AbstractThe mechanistic target of rapamycin complex 1 (mTORC1) is known to regulate cellular growth pathways, and its genetic activation is sufficient to enhance regenerative axon growth following injury to the central or peripheral nervous systems. However, excess mTORC1 activation may promote innervation defects, and mTORC1 activity mediates injury-induced hypersensitivity, reducing enthusiasm for the pathway as a therapeutic target. While mTORC1 activity is required for full expression of some pain modalities, the effects of pathway activation on nociceptor phenotypes and sensory behaviors are currently unknown. To address this, we genetically activated mTORC1 in mouse peripheral sensory neurons by conditional deletion of its negative regulator Tuberous Sclerosis Complex 2 (Tsc2). Consistent with the well-known role of mTORC1 in regulating cell size, soma size and axon diameter of C-nociceptors were increased in Tsc2-deleted mice. Glabrous skin and spinal cord innervation by C-fiber neurons were also disrupted. Transcriptional profiling of nociceptors enriched by fluorescence-associated cell sorting (FACS) revealed downregulation of multiple classes of ion channels as well as reduced expression of markers for peptidergic nociceptors in Tsc2-deleted mice. In addition to these changes in innervation and gene expression, Tsc2-deleted mice exhibited reduced noxious heat sensitivity and decreased injury-induced cold hypersensitivity, but normal baseline sensitivity to cold and mechanical stimuli. Together, these data show that excess mTORC1 activity in sensory neurons produces changes in gene expression, neuron morphology and sensory behavior.</jats:p

Improving Group Work: Voices of Students

Group work is increasingly being used in a variety of college courses. A number of strengths have driven the increase in the use of this form of collaborative learning. Still, a number of problems potentially limit the use of group projects. In this study, we report on research in which we examined how students recommended changing group projects. Results are categorized into student-centered themes and faculty-centered themes. Implications are provided

A model of primitive streak initiation in the chick embryo

Initiation of the primitive streak in avian embryos provides a well-studied example of a pattern-forming event that displays a striking capacity for regulation. The mechanisms underlying the regulative properties are, however, poorly understood and are not easily accounted for by traditional models of pattern formation, such as reaction–diffusion models. In this paper, we propose a new activator–inhibitor model for streak initiation. We show that the model is consistent with experimental observations, both in its pattern-forming properties and in its ability to form these patterns on the correct time-scales for biologically realistic parameter values. A key component of the model is a travelling wave of inhibition. We present a mathematical analysis of the speed of such waves in both diffusive and juxtacrine relay systems. We use the streak initiation model to make testable predictions. By varying parameters of the model, two very different types of patterning can be obtained, suggesting that our model may be applicable to other processes in addition to streak initiation