Modeling Wnt/β-catenin target gene expression in APC and Wnt gradients under wild type and mutant conditions

The Wnt/β-catenin pathway is involved in the regulation of a multitude of physiological processes by controlling the differential expression of target genes. In certain tissues such as the adult liver, the Wnt/β-catenin pathway can attain different levels of activity due to gradients of Wnt ligands and/or intracellular pathway components like APC. How graded pathway activity is converted into regionally distinct patterns of Wnt/β-catenin target gene expression is largely unknown. Here, we apply a mathematical modeling approach to investigate the impact of different regulatory mechanisms on target gene expression within Wnt or APC concentration gradients. We develop a minimal model of Wnt/beta-catenin signal transduction and combine it with various mechanisms of target gene regulation. In particular, the effects of activation, inhibition, and an incoherent feedforward loop (iFFL) are compared. To specify activation kinetics, we analyze experimental data that quantify the response of β-catenin/TCF reporter constructs to different Wnt concentrations, and demonstrate that the induction of these constructs occurs in a cooperative manner with Hill coefficients between 2 and 5. In summary, our study shows that the combination of specific gene regulatory mechanisms with a time-independent gradient of Wnt or APC is sufficient to generate distinct target gene expression patterns as have been experimentally observed in liver. We find that cooperative gene activation in combination with a TCF feedback can establish sharp borders of target gene expression in Wnt or APC gradients. In contrast, the iFFL renders gene expression independent of gradients of the upstream signaling components. Our subsequent analysis of carcinogenic pathway mutations reveals that their impact on gene expression is determined by the gene regulatory mechanism and the APC concentration of the cell in which the mutation occurs

Local stress anomaly in the Bavarian Molasse Basin

Background: The characterization of fault zones in the Bavarian Molasse Basin plays a major role for further geothermal reservoir development. Hence, their identification, geological origin, and hydraulic characterization are discussed extensively. Methods: Stress indicators and fractures are interpreted from image and caliper logs of three highly deviated wells at the Sauerlach site. We transform the identified stress field into the borehole coordinate system and compare the observed orientation to the modeled stress field which assumes a homogeneous borehole surrounding. Results: High breakout occurrence, cross-cutting fractures, and a fracture orientation from N-S to NNE-SSW are observed in Sauerlach Th1. In Sauerlach Th2 and Th3, fractures strike primarily ENE-WSW and N-S to NNE-SSW. Drilling-enhanced natural fractures and drilling-induced tensile fractures are observed in all three wells and indicate the orientation of tensile stress at the borehole wall. In Sauerlach Th2 and Th3, stress transformation indicates a S$_{H}$-dir. ~ N 10°E in a strike-slip stress regime. The modeled stress orientations match the observed orientations within the well Sauerlach Th1 if either S$_{H}$-dir. is N 320°E in a strike-slip regime or S$_{H}$-dir. is N 10°E in a normal faulting regime. Conclusion: This approach improves the detection of the local stress field especially for non-vertical wells, which has, in combination with the facture pattern, a major impact on the hydraulic system of the geothermal reservoir

Fermat's principle of least time in the presence of uniformly moving boundaries and media

The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: a) the material half-space is moving parallel to the interface; b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtained refraction formula is provided, and in the latter case, an intriguing backward refraction of light is noticed and thoroughly discussed. The results confirm the validity of Fermat's principle when the optical media and the boundaries between them are moving at relativistic speeds.Comment: 11 pages, 6 figures, RevTeX 4, comments welcome; V2: revised, Fig. 7 added; V3: several typos corrected, accepted for publication in European Journal of Physics (online at: http://stacks.iop.org/EJP/28/933

Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio

Effects of interphase boundary anisotropy on the three-phase growth dynamics in the β(In) – In 2 Bi – γ(Sn) ternary-eutectic system

International audienceWe present an experimental investigation on the effects of the interphase energy anisotropy on the formation of three-phase growth microstructures during directional solidification (DS) of the β(In)-In2Bi-γ(Sn) ternary-eutectic system. Standard DS and rotating directional solidification (RDS) experiments were performed using thin alloy samples with real-time observation. We identified two main types of eutectic grains (EGs): (i) quasi-isotropic EGs within which the solidification dynamics do not exhibit any substantial anisotropy effect, and (ii) anisotropic EGs, within which RDS microstructures exhibit an alternation of locked and unlocked microstructures. EBSD analyses revealed (i) a strong tendency to an alignment of the In2Bi and γ(Sn) crystals (both hexagonal) with respect to the thin-sample walls, and (ii) the existence of special crystal orientation relationships (ORs) between the three solid phases in both quasi-isotropic and anisotropic EGs. We initiate a discussion on the dominating locking effect of the In2Bi-β(In) interphase boundary during quasi steady-state solidification, and the existence of strong crystal selection mechanisms during early nucleation and growth stages

A Model for Prejudiced Learning in Noisy Environments

Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a deterministic learning rule obeying the axioms is constructed, and shown to be equivalent to the logistic map. The system's performance is analysed in an environment in which it is subject to external randomness, weighing learning defectiveness against stability gained. The corresponding random dynamical system with inhomogeneous, additive noise is studied, and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations. The overall results allow for the interpretation that prejudice in uncertain environments entails a considerable portion of stubbornness as a secondary phenomenon.Comment: 21 pages, 11 figures; reduced graphics to slash size, full version on Author's homepage. Minor revisions in text and references, identical to version to be published in Applied Mathematics and Computatio

Two-photon diffraction and quantum lithography

We report a proof-of-principle experimental demonstration of quantum lithography. Utilizing the entangled nature of a two-photon state, the experimental results have bettered the classical diffraction limit by a factor of two. This is a quantum mechanical two-photon phenomenon but not a violation of the uncertainty principle.Comment: 5 pages, 5 figures Submitted to Physical Review Letter

Remote Nanoimaging on Mars - Results of the Atomic Force Microscope Onboard NASA's Phoenix Mission

Extended abstract of a paper presented at Microscopy and Microanalysis 2011 in Nashville, Tennessee, USA, August 7-August 11, 201