Gradients and Tissue Patterning, Volume 137 in the Current Topics in Developmental Biology series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics. Each chapter is written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Current Topics in Developmental Biology series Includes the latest information on gradients and tissue patterning

Signalling by morphogens such as the Hedgehog family, Notch, Wingless/Wnt and various growth factors is essential during embryogenesis. The establishment of concentration gradients of these morphogens plays a key role during developmental patterning in all multicellular organisms, assuring that distinct cell/tissue types and organs appear at the right place in the right time during embryogenesis. Regulation of morphogen synthesis, trafficking and diffusion are all known to play a part in setting up these gradients, and a complex web of signaling mechanisms ensures that specific responses occur at the correct threshold concentration in the recipient cells whose fate depends on these morphogens.

Morphogens are signaling molecules that play a key role in animal development. They spread from a restricted source into an adjacent target tissue forming a concentration gradient. The fate of cells in the target tissue is determined by the local concentration of such morphogens. Morphogen transport through the tissue has been studied in experiments which lead to the suggestion of several transport mechanisms. While diffusion in the extracellular space contributes to transport, recent experiments on the morphogen Decapentaplegic (Dpp) in the fruit fly Drosophila provide evidence for the importance of a cellular transport mechanism that was termed "planar transcytosis". In this mechanism, morphogens are transported through cells by repeated rounds of internalization and externalization. Starting from a microscopic theoretical description of these processes, we derive systems of nonlinear transport equations which describe the interplay of transcytosis and passive diffusion. We compare the results of numerical calculations based on this theoretical description of morphogen transport to recent experimental data on the morphogen Dpp in the Drosophila wing disk. Agreement with the experimental data is only achieved if the parameters entering the theoretical description are chosen such that transcytosis contributes strongly to transport. Analyzing the derived transport equations, we find that transcytosis leads to an increased robustness of the created gradients with respect to morphogen over-expression. Indications for this kind of robustness have been found in experiments. Furthermore, we theoretically investigate morphogen gradient formation in disordered systems. Here, an important question is how the position of concentration thresholds can be defined with high precision in the noisy environment present in typical developing tissues. Among other things, we find that the dimensionality of the system in which the gradient is formed plays an important.

This dissertation is concerned with ligands (such as Decapentaplegic or Dpp for short) that are produced along the anterior-posterior border of the Drosophila wing imaginal disc and then transported away toward the disc edge. They bind with cell surface receptors and possibly non-receptors to form concentration gradients of both ligand receptor complexes and ligand non-receptor complexes respectively. Recent articles such as [13], [15], [16], [17], have already focused on systems of diffusion and reversible binding involving ligand, ligand receptor complexes and receptors with and without non-receptors including aggregated source end models ([13] and [17]). We will focus our attention on one of the compartments (posterior or anterior) of the wing imaginal disc in a one dimensional model. We will then extend this model by including non-receptors in the system. Finally, we consider a two dimensional ligand and receptor model by considering the apical-basal extent of the disc as well. It is in this model where we analyze and determine why the wing imaginal disc size changes with environmental temperature changes.

Developmental pattern formation is orchestrated by diffusible signaling molecules, termed morphogens, that form gradients from which cells can determine positionally appropriate fates. Stochasticity in morphogen binding, signal transduction, and gene expression create local cell-to-cell variability in the readout of morphogen gradients. However, little is known about the actual levels of noise in morphogen gradient responses, or the mechanisms that might control it. To investigate this, I quantified the transcriptional activity noise, protein expression noise, and protein half-life of optomotor blind (omb), one of the downstream targets of the morphogen Dpp in the Drosophila larval wing imaginal disc. Using combined fluorescence in situ hybridization (FISH) with intronic probes, immunofluorescence, image segmentation and image analysis, I observed a very high level of transcriptional variability characterized by coefficients of variation (CV) as high as ~110%, in the cells in which omb plays a central role in specifying the location of wing vein primordium L5. However, the half-life of the Omb protein was found to be very long, ~ 6 hours, which would be expected to provide significant temporal filtering of the transcriptional noise. I showed that the reduction in noise from transcript to protein is sufficient to account for the precision of the positional information that patterns vein L5. I also investigated why the positioning of vein L5 is remarkably robust to genetic manipulation that change the shape of the Dpp morphogen gradient. I observed that patters of Dpp signaling and Omb expression are not constant during larval development, but change continuously, and not always in concert with each other. By taking into account the long half-life of Omb it was possible to build a model that explains both these movements and the remarkable robustness of L5 patterning to changes in Dpp gradient shape.

This detailed book presents methods focusing on the visualization of morphogen gradients, the analysis of their biophysical and biological properties, and the theoretical aspects underlying their functions. The study of morphogen gradients combines biophysics, cell and developmental biology, and applied mathematics approaches to understand their formation, their biological functions, and the prediction of their behavior in space and time, and this volume serves as a practical, hands-on guide to the field. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and helpful, Morphogen Gradients: Methods and Protocols is an ideal collection for researchers in this vital area of study.