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The decision to stop growing and mature into an adult is a critical point in development that determines adult body size, impacting multiple aspects of an adult’s biology. In many animals, growth cessation is a consequence of hormone release that appears to be tied to the attainment of a particular body size or condition. Nevertheless, the size-sensing mechanism animals use to initiate hormone synthesis is poorly understood. Here, we develop a simple mathematical model of growth cessation inDrosophila melanogaster, which is ostensibly triggered by the attainment of a critical weight (CW) early in the last instar. Attainment of CW is correlated with the synthesis of the steroid hormone ecdysone, which causes a larva to stop growing, pupate, and metamorphose into the adult form. Our model suggests that, contrary to expectation, the size-sensing mechanism that initiates metamorphosis occurs before the larva reaches CW; that is, the critical-weight phenomenon is a downstream consequence of an earlier size-dependent developmental decision, not a decision point itself. Further, this size-sensing mechanism does not require a direct assessment of body size but emerges from the interactions between body size, ecdysone, and nutritional signaling. Because many aspects of our model are evolutionarily conserved among all animals, the model may provide a general framework for understanding how animals commit to maturing from their juvenile to adult form. 

It has long been known that FGF signaling contributes to mesoderm formation, a germ layer found in triploblasts that is composed of highly migratory cells that give rise to muscles and to the skeletal structures of vertebrates. FGF signaling activates several pathways in the developing mesoderm, including transient activation of the Erk pathway, which triggers mesodermal fate specification through the induction of the gene brachyury and activates morphogenetic programs that allow mesodermal cells to position themselves in the embryo. In this review, we discuss what is known about the generation and interpretation of transient Erk signaling in mesodermal tissues across species. We focus specifically on mechanisms that translate the level and duration of Erk signaling into cell fate and cell movement instructions and discuss strategies for further interrogating the role that Erk signaling dynamics play in mesodermal gastrulation and morphogenesis. 

Markers for the endoderm and mesoderm germ layers are commonly expressed together in the early embryo, potentially reflecting cells’ ability to explore potential fates before fully committing. It remains unclear when commitment to a single-germ layer is reached and how it is impacted by external signals. Here, we address this important question in Drosophila , a convenient model system in which mesodermal and endodermal fates are associated with distinct cellular movements during gastrulation. Systematically applying endoderm-inducing extracellular signal-regulated kinase (ERK) signals to the ventral medial embryo—which normally only receives a mesoderm-inducing cue—reveals a critical time window during which mesodermal cell movements and gene expression are suppressed by proendoderm signaling. We identify the ERK target gene huckebein ( hkb ) as the main cause of the ventral furrow suppression and use computational modeling to show that Hkb repression of the mesoderm-associated gene snail is sufficient to account for a broad range of transcriptional and morphogenetic effects. Our approach, pairing precise signaling perturbations with observation of transcriptional dynamics and cell movements, provides a general framework for dissecting the complexities of combinatorial tissue patterning. 

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila , a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches. 

Optogenetic approaches are transforming quantitative studies of cell-signaling systems. A recently developed photoswitchable mitogen-activated protein kinase kinase 1 (MEK1) enzyme (psMEK) short-circuits the highly conserved Extracellular Signal-Regulated Kinase (ERK)-signaling cascade at the most proximal step of effector kinase activation. However, since this optogenetic tool relies on phosphorylation-mimicking substitutions in the activation loop of MEK, its catalytic activity is predicted to be substantially lower than that of wild-type MEK that has been phosphorylated at these residues. Here, we present evidence that psMEK indeed has suboptimal functionality in vivo and propose a strategy to circumvent this limitation by harnessing gain-of-function, destabilizing mutations in MEK. Specifically, we demonstrate that combining phosphomimetic mutations with additional mutations in MEK, chosen for their activating potential, restores maximal kinase activity in vitro. We establish that this modification can be tuned by the choice of the destabilizing mutation and does not interfere with reversible activation of psMEK in vivo in both Drosophila and zebrafish. To illustrate the types of perturbations enabled by optimized psMEK, we use it to deliver pulses of ERK activation during zebrafish embryogenesis, revealing rheostat-like responses of an ERK-dependent morphogenetic event.