A mechanism for early branching in lung morphogenesis

The lung is a highly branched fluid-filled structure, that develops by repeated dichotomous branching of a single bud off the foregut, of epithelium invaginating into mesenchyme. Incorporating the known stress response of developing lung tissues, we model the developing embryonic lung in fluid mechanical terms. We suggest that the repeated branching of the early embryonic lung can be understood as the natural physical consequence of the interactions of two or more plastic substances with surface tension between them. The model makes qualitative and quantitative predictions, as well as suggesting an explanation for such observed phenomena as the asymmetric second branching of the embryonic bronchi.     

Turing bifurcations with a temporally varying diffusion coefficient

This paper is concerned with the possibility of Turing bifurcations in a reaction-diffusion system in which the diffusion coefficient of one species varies periodically in time. This problem was introduced and investigated numerically by Timm and Okubo (J. Math. Biol. 30, 307, 1992) in the context of predator-prey interactions in plankton populations. Here, I consider the simple case in which the temporal variation in diffusivity has a square-tooth form, alternating between two constant values, with a period that is long compared with the time scale of the kinetics. The analysis is valid for any set of reaction kinetics. I derive explicit expressions for the Floquet multipliers that determine the stability of the steady state, and thereby obtain the conditions for diffusion driven instability to occur. These conditions imply that, depending on the kinetics, the homogeneous equilibrium may be either more or less stable than when the diffusion coefficient is a constant equal to the mean of the variable diffusivity. I go on to consider the form of the solution when diffusion driven instability does occur, and I use perturbation theory to determine the effect of a small temporal variation in the diffusion coefficient on the spatial wavelength of the pattern that results from diffusion driven instability.     

Independent roles of Drosophila Moesin in imaginal disc morphogenesis and hedgehog signalling

The three ERM proteins (Ezrin, Radixin and Moesin) form a conserved family required in many developmental processes involving regulation of the cytoskeleton. In general, the molecular function of ERM proteins is to link specific membrane proteins to the actin cytoskeleton. In Drosophila, loss of moesin (moe) activity causes incorrect localisation of maternal determinants during oogenesis, failures in rhabdomere differentiation in the eye and alterations of epithelial integrity in the wing imaginal disc. Some aspects of Drosophila Moe are related to the activity of the small GTPase RhoA, because the reduction of RhoA activity corrects many phenotypes of moe mutant embryos and imaginal discs. We have analysed the phenotype of moesin loss-of-function alleles in the wing disc and adult wing, and studied the effects of reduced Moesin activity on signalling mediated by the Notch, Decapentaplegic, Wingless and Hedgehog pathways. We found that reductions in Moesin levels in the wing disc cause the formation of wing-tissue vesicles and large thickenings of the vein L3, corresponding to breakdowns of epithelial continuity in the wing base and modifications of Hedgehog signalling in the wing blade, respectively. We did not observe any effect on signalling pathways other than Hedgehog, indicating that the moe defects in epithelial integrity have not generalised effects on cell signalling. The effects of moe mutants on Hedgehog signalling depend on the correct gene-dose of rhoA, suggesting that the requirements for Moesin in disc morphogenesis and Hh signalling in the wing disc are mediated by its regulation of RhoA activity. The mechanism linking Moesin activity with RhoA function and Hedgehog signalling remains to be elucidated.     

Modelling in vitro lung branching morphogenesis during development

It has been shown experimentally that lung epithelial explants have an ability to undergo branching morphogenesis without mesenchyme. However, the mechanisms of this phenomenon remain to be elucidated. In the present study, we construct a mathematical model that can reproduce the dynamics of in vitro branching morphogenesis. We show that the system is essentially governed by three variables--c(0) which is the initial fibroblast growth factor (FGF) concentration, D which is the diffusion coefficient of FGF, and beta which describes the mechanical strength of the cytoskeleton. It is confirmed by numerical simulations that this model can reproduce the experimentally obtained patterns qualitatively. Finally, we experimentally verify two predictions from the model: effects of very high FGF concentration and effects of small mechanical contributions of the cytoskeleton. The theoretical predictions match well with the experimental results.     

Multiple roles of the gene zinc finger homeodomain-2 in the development of the Drosophila wing

The gene zfh2 and its human homolog Atbf1 encode huge molecules with several homeo- and zinc finger domains. It has been reported that they play important roles in neural differentiation and promotion of apoptosis in several tissues of both humans and flies. In the Drosophila wing imaginal disc, Zfh2 is expressed in a dynamic pattern and previous results suggest that it is involved is proximal–distal patterning. In this report we go further in the analysis of the function of this gene in wing development, performing ectopic expression experiments and studying its effects in genes involved in wing development. Our results suggest that Zfh2 plays an important role controlling the expression of several wing genes and in the specification of those cellular properties that define the differences in cell proliferation between proximal and distal domains of the wing disc.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

Formation and deformation of patterns through diffusion

Simulating various patterns exhibited on biological forms with mathematical models has become an important supplement to theoretical biology. Models based on a certain mechanism are intended to provide explanations to the formation of a basic pattern. However, in real phenomena, among a basic pattern there always exist some difference between any two individuals. Such differences are consequences of environmental factors posed during the developmental processes. These factors, such as temperature, affect the diffusion rates of corresponding morphogenes which, in turn, alter a basic pattern to certain extent. We provide, in this paper, a quantitative characterization of this effect for a class of reaction-diffusion models.Mathematically, we study the emergence of stationary patterns and their dependence on diffusion rates for this class of models (RD-equations) with no-flux boundary conditions. The results are generalized to systems with homogeneous Dirichlet boundary conditions when the kinetic terms are odd functions. Through an analysis of the phase dynamics, we show that the deformation of stationary patterns, as the diffusion rates change, is governed by the variation of certain plane curves in the phase space. A constructive proof is given which shows explicitly how to obtain such curves.Applications of this study are illustrated with three model examples. We use these models to explain the biological implications of the mathematical features we investigated. Results from computer simulations are presented and compared with physical patterns.     

The mechanism of sudden stripe formation during dorso-ventral patterning in <Emphasis Type="Italic">Drosophila</Emphasis>

The front and back (ventral and dorsal part respectively) of arthropods and chordates are defined by a highly conserved mechanism during early embryonic development [De Robertis and Kuroda in Annu. Rev. Cell Dev. Biol. 20, 285–308 (2004)]. An important feature is the sudden formation of a narrow midline peak of signaling. Mathematical models have helped to improve our understanding of the underlying mechanism [Eldar et al. in Nature 419(6904), 304–308 (2002); Mizutani in Dev. Cell 8(6), 915–924 (2005); Shimmi et al. in Cell 120(6), 873–886, (2005)]. In particular, the most recent model shows that diffusion and receptor-dependent degradation of the morphogen together with protease-mediated cleavage of a carrier protein for the morphogen are sufficient for the sudden generation of a sharp midline peak [Mizutani in Dev. Cell 8(6), 915–924 (2005)]. How these processes give rise to the observed pattern and how sensitive the model is to changes in parameter values has, however, not been resolved by this numerical study. By analysing the model in detail, we find that the sudden formation of a signaling peak is the consequence of the inversion of the gradient of the morphogen-carrier complex in the dorsal domain. As a consequence ligand is suddenly transported into rather than out of the midline, and a midline peak forms. We further show that a two-component carrier complex, consisting of Sog and Tsg, is required for abrupt peak formation. We derive quantitative conditions for the time and concentration at which the peak forms. We identify the receptor concentration, the ligand production and degradation rates, and the carrier production, diffusion, and cleavage rates as parameters to which the model is sensitive. Numerical studies confirm our analysis.      

mRNA diffusion explains protein gradients in Drosophila early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of Drosophila. In this model, we consider that bicoid mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11-14 of the developing embryo of Drosophila. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of bicoid mRNA is in the range , in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of bicoid mRNA in Drosophila [Spirov et al. (2009). Development 136, 605-614].     

Live imaging of endogenous RNA reveals a diffusion and entrapment mechanism for nanos mRNA localization in Drosophila

BACKGROUND: Localization of nanos mRNA to the posterior pole of the Drosophila embryo directs local synthesis of Nanos protein that is essential for patterning of the anterior-posterior body axis and germ cell function. While nanos RNA is synthesized by the ovarian nurse cells and appears at the posterior pole of the ooctye late in oogenesis, the mechanism by which this RNA is translocated to and anchored at the oocyte posterior is unknown. RESULTS: By labeling endogenous nanos RNA with GFP, we have been able to follow the dynamic pathway of nanos localization in living oocytes. We demonstrate that nanos localization initiates immediately upon nurse cell dumping, whereby diffusion, enhanced by microtubule-dependent cytoplasmic movements, translocates nanos RNA from the nurse cells to the ooctye posterior. At the posterior, nanos is trapped by association, in particles, with the posteriorly localized germ plasm. Actin-dependent anchoring of nanos RNA complexed to the germ plasm at the posterior maintains localization in the face of rapid cytoplasmic movements. CONCLUSIONS: These results reveal a diffusion-based, late-acting posterior localization mechanism for long-range transport of nanos mRNA. This mechanism differs from directed transport-based localization mechanisms in its reliance on bulk movement of RNA.     

Gawky is a component of cytoplasmic mRNA processing bodies required for early Drosophila development

In mammalian cells, the GW182 protein localizes to cytoplasmic bodies implicated in the regulation of messenger RNA (mRNA) stability, translation, and the RNA interference pathway. Many of these functions have also been assigned to analogous yeast cytoplasmic mRNA processing bodies. We have characterized the single Drosophila melanogaster homologue of the human GW182 protein family, which we have named Gawky (GW). Drosophila GW localizes to punctate, cytoplasmic foci in an RNA-dependent manner. Drosophila GW bodies (GWBs) appear to function analogously to human GWBs, as human GW182 colocalizes with GW when expressed in Drosophila cells. The RNA-induced silencing complex component Argonaute2 and orthologues of LSm4 and Xrn1 (Pacman) associated with 5'-3' mRNA degradation localize to some GWBs. Reducing GW activity by mutation or antibody injection during syncytial embryo development leads to abnormal nuclear divisions, demonstrating an early requirement for GWB-mediated cytoplasmic mRNA regulation. This suggests that gw represents a previously unknown member of a small group of genes that need to be expressed zygotically during early embryo development.     

Characterization of early steps in muscle morphogenesis in a Drosophila primary culture system

Myogenesis in Drosophila embryos requires fusion between Founder cells (FCs) and Fusion Competent myoblasts (FCMs) to form multinucleate myotubes. Myoblast fusion is well characterized in embryos, and many factors required for this process have been identified; however, a number of questions pertaining to the mechanisms of fusion remain and are challenging to answer in the embryo. We have developed a modified primary cell culture protocol to address these questions in vitro. Using this system, we determined the optimal time for examining fusion in culture and confirmed that known fusion proteins are expressed and localized as in embryos. Importantly, we disrupted the actin and microtubule networks with the drugs latrunculin B and nocodazole, respectively, confirming that actin is required for myoblast fusion and showing for the first time that microtubules are also required for this process in Drosophila. Finally, we show that myotubes in culture adopt and maintain specific muscle identities.     

Analysis of morphogenetic movements in the development of the notum anlage of Drosophila melanogaster

Summary A comparison of the morphogenetic maps of the notum anlage of Drosophila melanogaster derived from the gynandromorph data and mosaics induced by somatic crossing-over during the first instar larval stage revealed that practically no major morphogenetic movements occur in the development of the anlage between the blastoderm and first instar larval stages and the adult stage. By comparing the morphogenetic map derived from gynandromorphs and the fate map derived from data on the transplantation of fragments of the mature wing imaginal disc, it was observed that no major morphogenetic movements occur in the notum anlage between the stages of the allocation of the disc and the mature disc. The results are consistent with the observations of other authors concerning the larval development of eye-antenna, wing and leg discs.     

Different requirements for l(1)giant in two embryonic domains of Drosophila melanogaster

L(1)giant is a zygotic lethal mutation which affects the embryonic development of both the labial/thoracic segments and a subset of posterior abdominal segments. Using antibodies specific for proteins encoded by several Drosophila genes to identify the compartmental origin of the defects, we show that the requirement of giant activity is different in these two embryonic domains. Anteriorly, the posterior compartment of the labial segment is missing at the blastoderm stage. Posteriorly, cells are specifically deleted by cell death within the anterior compartments of abdominal segments 5–7 during germ band elongation. In mature embryos, posterior compartment structures of the peripheral nervous system of A5–7 are fused. In addition to a different pattern of defect in the two parts of the embryo, the kind of action appears different. Anteriorly, giant resembles a gap mutation in that a particular region is missing from the blastoderm fate map, whereas in the abdominal domain, giant affects the development of anterior compartment-specific structures.