SUMMARY Background How morphogen gradients form has long been a subject of controversy. The strongest support for the view that morphogens do not simply spread by free diffusion has come from a variety of studies of the Decapentaplegic (Dpp) gradient of the Drosophila larval wing disc. Results In the present study, we initially show how the failure, in such studies, to consider the coupling of transport to receptor-mediated uptake and degradation has led to estimates of transport rates that are orders of magnitude too low, lending unwarranted support to a variety of hypothetical mechanisms, such as “planar transcytosis” and “restricted extracellular diffusion”. Using several independent dynamic methods, we obtain data that are inconsistent with such models, and that show directly that Dpp transport occurs by simple, rapid diffusion in the extracellular space. We discuss the implications of these findings for other morphogen systems in which complex transport mechanisms have been proposed. Conclusions We believe that these findings resolve a major, longstanding question about morphogen gradient formation, and provide a solid framework for interpreting experimental observations of morphogen gradient dynamics.
A large, diverse, and growing number of strategies have been proposed to explain how morphogen gradients achieve robustness and precision. We argue that, to be useful, the evaluation of such strategies must take into account the constraints imposed by competing objectives and performance tradeoffs. This point is illustrated through a mathematical and computational analysis of the strategy of self-enhanced morphogen clearance. The results suggest that the usefulness of this strategy comes less from its ability to increase robustness to morphogen source fluctuations per se, than from its ability to overcome specific kinds of noise, and to increase the fraction of a morphogen gradient within which robust threshold positions may be established. This work also provides new insights into the longstanding question of why morphogen gradients show a maximum range in vivo.I n recent years, much research on morphogen gradients has shifted from purely mechanistic questions-how gradients form and how morphogens signal-to strategic ones-how gradients perform well in the face of various kinds of constraints and perturbations. Forty years ago, Francis Crick was among the first to call attention to constraints that morphogens face, noting that the time required to spread a signal by random transport through a tissue varies with the square of distance (Crick 1970). Using order-of-magnitude calculations, he argued that observed biological maxima for morphogen-mediated patterning were just about where they should be if morphogen signals spread by aqueous diffusion.Although the idea that diffusion time is what limits the sizes of morphogen gradients remains untested, Crick's work established a precedent of seeking explanations for developmental processes in terms of constraints imposed by the physical world. In the area of biological pattern formation, continued interest in how real-world limits constrain mechanisms has led many current investigators to focus on matters of robustness, the engineering term that describes the relative insensitivity of a system's behavior to perturbations it may be expected to encounter. With respect to morphogen gradients, most work has focused on parametric robustness, i.e., insensitivity to parameter values (e.g., the dosage of genes, [Eldar et al. 2002;Eldar et al. 2003;Eldar et al. 2004;Bollenbach et al. 2005;Shimmi et al. 2005;White et al. 2007]). Some investigators have also focused on the "precision" of morphogen gradients, which may be understood as robustness to the causes and effects of natural variation among individuals in a population (Houchmandzadeh et al. 2002;Gregor et al. 2007;Tostevin et al. 2007;Bollenbach et al. 2008;Emberly 2008).Remarkably, after hardly a decade of intensive study of such questions, we find ourselves awash in a sea of diverse and intriguing mechanisms for conferring one or another type of robustness on morphogen-mediated patterning. Mechanisms that operate at the level of gradient formation include self-enhanced morphogen degradation (Eldar et al. 2003), facilit...
Studies of developing and self-renewing tissues have shown that differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit amplifying; TA) cell stages, which ultimately give rise to terminally differentiated (TD) cells. In several cases, self-renewal and differentiation of stem and progenitor cells within such lineages have been shown to be under feedback regulation. Together, the existence of multiple cell stages within a lineage and complex feedback regulation are thought to confer upon a tissue the ability to autoregulate development and regeneration, in terms of both cell number (total tissue volume) and cell identity (the proportions of different cell types, especially TD cells, within the tissue). In this paper, we model neurogenesis in the olfactory epithelium (OE) of the mouse, a system in which the lineage stages and mediators of feedback regulation that govern the generation of terminally differentiated olfactory receptor neurons (ORNs) have been the subject of much experimental work. Here we report on the existence and uniqueness of steady states in this system, as well as local and global stability of these steady states. In particular, we identify parameter conditions for the stability of the system when negative feedback loops are represented either as Hill functions, or in more general terms. Our results suggest that two factors – autoregulation of the proliferation of transit amplifying (TA) progenitor cells, and a low death rate of TD cells – enhance the stability of this system.
Cdc42 plays a central role in establishing polarity in yeast and animals, yet how polarization of Cdc42 is achieved in response to spatial cues is poorly understood. Using live-cell imaging, we found distinct dynamics of Cdc42 polarization in haploid budding yeast in correlation with two temporal steps of the G1 phase. The position at which the Cdc42-GTP cluster develops changes rapidly around the division site during the first step but becomes stabilized in the second step, suggesting that an axis of polarized growth is determined in mid G1. Cdc42 polarization in the first step and its proper positioning depend on Rsr1 and its GTPase-activating protein (GAP) Bud2. Interestingly, Rga1, a Cdc42 GAP, exhibits transient localization to a site near the bud neck and to the division site during cytokinesis and G1, and this temporal change of Rga1 distribution is necessary for determination of a proper growth site. Mathematical modeling suggests that a proper axis of Cdc42 polarization in haploid cells might be established through a biphasic mechanism involving sequential positive feedback and transient negative feedback.
In developing and self-renewing tissues, terminally differentiated (TD) cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit-amplifying) cell stages, which ultimately give rise to TD cells. As the tissue reaches a tightly controlled steady-state size, cells at different lineage stages assume distinct spatial locations within the tissue. Although tissue stratification appears to be genetically specified, the underlying mechanisms that direct tissue lamination are not yet completely understood. Herein, we use modeling and simulations to explore several potential mechanisms that can be utilized to create stratification during developmental or regenerative growth in general systems and in the model system, the olfactory epithelium of mouse. Our results show that tissue stratification can be generated and maintained through controlling spatial distribution of diffusive signaling molecules that regulate the proliferation of each cell type within the lineage. The ability of feedback molecules to stratify a tissue is dependent on a low TD death rate: high death rates decrease tissue lamination. Regulation of the cell cycle lengths of stem cells by feedback signals can lead to transient accumulation of stem cells near the base and apex of tissue.
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