Well-posedness and asymptotic behavior of a multidimensional model of morphogen transport

Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions for both stationary and evolution problems. Moreover we show that the solution converges exponentially to the equilibrium in $C^1\times C^0$ topology. We prove all results for arbitrary dimension of the domain. Our results improve significantly previously known results for the same model in the case of one dimensional domain

CELL DEATH DIFFERENTIATION IN BLACK HEADED RAMS SPERMATOZOA, USING FLUORESCENT LABELED ANNEXIN V

Double staining kit of Annexin V Cy3.18/6-CFDA was used to investigate the changes in phospholipide asymmetry after treating sperm cells with dexamethasone. The % of spermatozoa with registered translocation of PS in treated with dexamethazone groups at the 10-th min and in control no treated varied from 2.74%±0.65 to 2.30%±0.89. After the 5 hour of incubation these % increased to 39.83±3.33 for the treated group and 23.44±1.12 for the control. It was concluded that Annexin V binding assay is more sensitive in the detection of deterioration in membrane function than other conventional methods such as motility analysis and supravital techniques

Methods in Molecular Biology

Developmental processes are inherently dynamic and understanding them requires quantitative measurements of gene and protein expression levels in space and time. While live imaging is a powerful approach for obtaining such data, it is still a challenge to apply it over long periods of time to large tissues, such as the embryonic spinal cord in mouse and chick. Nevertheless, dynamics of gene expression and signaling activity patterns in this organ can be studied by collecting tissue sections at different developmental stages. In combination with immunohistochemistry, this allows for measuring the levels of multiple developmental regulators in a quantitative manner with high spatiotemporal resolution. The mean protein expression levels over time, as well as embryo-to-embryo variability can be analyzed. A key aspect of the approach is the ability to compare protein levels across different samples. This requires a number of considerations in sample preparation, imaging and data analysis. Here we present a protocol for obtaining time course data of dorsoventral expression patterns from mouse and chick neural tube in the first 3 days of neural tube development. The described workflow starts from embryo dissection and ends with a processed dataset. Software scripts for data analysis are included. The protocol is adaptable and instructions that allow the user to modify different steps are provided. Thus, the procedure can be altered for analysis of time-lapse images and applied to systems other than the neural tube

ОПРЕДЕЛЯНЕ А ЕКСПРЕСИЯТА НА ФОСФАТИДИЛСЕРИН ПРИ СПЕРМАТОЗОИДИ В РАННА АПОПТОЗА ЧРЕЗ ФЛУОРЕСЦЕНТНО БИЛЯЗАН АНЕКСИН V

Double staining kit of Annexin V Cy3.18/6-CFDA was used to investigate the changes in phospholipide asymmetry after treating sperm cells with dexamethasone. The % of spermatozoa with registered translocation of PS in treated with dexamethazone groups at the 10-th min and in control no treated varied from 2.74%±0.65 to 2.30%±0.89. After the 5 hour of incubation these % increased to 39.83±3.33 for the treated group and 23.44±1.12 for the control. It was concluded that Annexin V binding assay is more sensitive in the detection of deterioration in membrane function than other conventional methods such as motility analysis and supravital techniques.Приложен е кит за двойно оцветяване с Анексин V Cy3.18 и 6-CFDA, даващ възможност за диференциране на апоптични от мъртви клетки. Процентът сперматозоиди с регистрирана експресия на ФС при свежи нетретирани сперматозоиди – контролна проба и експериментални, третирани с дексаметазон на 10-тата минута, варира от 2.30%±0.89 до 2.74%±0.65. След съхранение, на 5-я час този процент нараства до 23.44±1.12 за контролата и до 39.83±3.33 за опитната група. С настоящето изследване се доказва, че Анексин V теста е по-чувствителен за определяне промените в ПМ, в сравнение с конвенционалните методи на изследване за подвижност и преживяемост на сперматозоидите

Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms.

In the vertebrate neural tube, the morphogen Sonic Hedgehog (Shh) establishes a characteristic pattern of gene expression. Here we quantify the Shh gradient in the developing mouse neural tube and show that while the amplitude of the gradient increases over time, the activity of the pathway transcriptional effectors, Gli proteins, initially increases but later decreases. Computational analysis of the pathway suggests three mechanisms that could contribute to this adaptation: transcriptional upregulation of the inhibitory receptor Ptch1, transcriptional downregulation of Gli and the differential stability of active and inactive Gli isoforms. Consistent with this, Gli2 protein expression is downregulated during neural tube patterning and adaptation continues when the pathway is stimulated downstream of Ptch1. Moreover, the Shh-induced upregulation of Gli2 transcription prevents Gli activity levels from adapting in a different cell type, NIH3T3 fibroblasts, despite the upregulation of Ptch1. Multiple mechanisms therefore contribute to the intracellular dynamics of Shh signalling, resulting in different signalling dynamics in different cell types

Incorporating chemical signalling factors into cell-based models of growing epithelial tissues

In this paper we present a comprehensive computational framework within which the effects of chemical signalling factors on growing epithelial tissues can be studied. The method incorporates a vertex-based cell model, in conjunction with a solver for the governing chemical equations. The vertex model provides a natural mesh for the finite element method (FEM), with node movements determined by force laws. The arbitrary Lagrangian–Eulerian formulation is adopted to account for domain movement between iterations. The effects of cell proliferation and junctional rearrangements on the mesh are also examined. By implementing refinements of the mesh we show that the finite element (FE) approximation converges towards an accurate numerical solution. The potential utility of the system is demonstrated in the context of Decapentaplegic (Dpp), a morphogen which plays a crucial role in development of the Drosophila imaginal wing disc. Despite the presence of a Dpp gradient, growth is uniform across the wing disc. We make the growth rate of cells dependent on Dpp concentration and show that the number of proliferation events increases in regions of high concentration. This allows hypotheses regarding mechanisms of growth control to be rigorously tested. The method we describe may be adapted to a range of potential application areas, and to other cell-based models with designated node movements, to accurately probe the role of morphogens in epithelial tissues

ОПРЕДЕЛЯНЕ А ЕКСПРЕСИЯТА НА ФОСФАТИДИЛСЕРИН ПРИ СПЕРМАТОЗОИДИ В РАННА АПОПТОЗА ЧРЕЗ ФЛУОРЕСЦЕНТНО БИЛЯЗАН АНЕКСИН V

Double staining kit of Annexin V Cy3.18/6-CFDA was used to investigate the changes in phospholipide asymmetry after treating sperm cells with dexamethasone. The % of spermatozoa with registered translocation of PS in treated with dexamethazone groups at the 10-th min and in control no treated varied from 2.74%±0.65 to 2.30%±0.89. After the 5 hour of incubation these % increased to 39.83±3.33 for the treated group and 23.44±1.12 for the control. It was concluded that Annexin V binding assay is more sensitive in the detection of deterioration in membrane function than other conventional methods such as motility analysis and supravital techniques.Приложен е кит за двойно оцветяване с Анексин V Cy3.18 и 6-CFDA, даващ възможност за диференциране на апоптични от мъртви клетки. Процентът сперматозоиди с регистрирана експресия на ФС при свежи нетретирани сперматозоиди – контролна проба и експериментални, третирани с дексаметазон на 10-тата минута, варира от 2.30%±0.89 до 2.74%±0.65. След съхранение, на 5-я час този процент нараства до 23.44±1.12 за контролата и до 39.83±3.33 за опитната група. С настоящето изследване се доказва, че Анексин V теста е по-чувствителен за определяне промените в ПМ, в сравнение с конвенционалните методи на изследване за подвижност и преживяемост на сперматозоидите

Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc

Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior–posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial “overshoot” of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio