SummaryDrosophila ovarian germline stem cells (GSCs) are maintained by Dpp signaling and the Pumilio (Pum) and Nanos (Nos) translational repressors. Upon division, Dpp signaling is extinguished, and Nos is downregulated in one daughter cell, causing it to switch to a differentiating cystoblast (CB). However, downstream effectors of Pum-Nos remain unknown, and how CBs lose their responsiveness to Dpp is unclear. Here, we identify Brain Tumor (Brat) as a potent differentiation factor and target of Pum-Nos regulation. Brat is excluded from GSCs by Pum-Nos but functions with Pum in CBs to translationally repress distinct targets, including the Mad and dMyc mRNAs. Regulation of both targets simultaneously lowers cellular responsiveness to Dpp signaling, forcing the cell to become refractory to the self-renewal signal. Mathematical modeling elucidates bistability of cell fate in the Brat-mediated system, revealing how autoregulation of GSC number can arise from Brat coupling extracellular Dpp regulation to intracellular interpretation.

ERK signaling regulates the expression of target genes, but it is unclear how ERK activity dynamics are interpreted. Here, we investigate this question using simultaneous, live, single-cell imaging of two ERK activity reporters and expression of Fra-1, a target gene controlling epithelial cell identity. We find that Fra-1 is expressed in proportion to the amplitude and duration of ERK activity. In contrast to previous "persistence detector" and "selective filter" models in which Fra-1 expression only occurs when ERK activity persists beyond a threshold duration, our observations demonstrate that the network regulating Fra-1 expression integrates total ERK activity and responds to it linearly. However, exploration of a generalized mathematical model of the Fra-1 coherent feedforward loop demonstrates that it can perform either linear integration or persistence detection, depending on the basal mRNA production rate and protein production delays. Our data indicate that significant basal expression and short delays cause Fra-1 to respond linearly to integrated ERK activity.

Background:In individual cells, EGF stimulation results in sporadic pulses of ERK activity. Results: ERK pulses are disrupted upon stimulation by alternate receptors or inhibition of EGFR. Conclusion: ERK activity pulses are generated at the level of EGFR. Significance: The dynamics of ERK activity, which control cellular proliferation and gene expression, are inconsistent with models that rely on downstream feedback.

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Discovery in developmental biology is often driven by intuition that relies on the integration of multiple types of data such as fluorescent images, phenotypes, and the outcomes of biochemical assays. Mathematical modeling helps elucidate the biological mechanisms at play as the networks become increasingly large and complex. However, the available data is frequently under-utilized due to incompatibility with quantitative model tuning techniques. This is the case for stem cell regulation mechanisms explored in the Drosophila germarium through fluorescent immunohistochemistry. To enable better integration of biological data with modeling in this and similar situations, we have developed a general parameter estimation process to quantitatively optimize models with qualitative data. The process employs a modified version of the Optimal Scaling method from social and behavioral sciences, and multi-objective optimization to evaluate the trade-off between fitting different datasets (e.g. wild type vs. mutant). Using only published imaging data in the germarium, we first evaluated support for a published intracellular regulatory network by considering alternative connections of the same regulatory players. Simply screening networks against wild type data identified hundreds of feasible alternatives. Of these, five parsimonious variants were found and compared by multi-objective analysis including mutant data and dynamic constraints. With these data, the current model is supported over the alternatives, but support for a biochemically observed feedback element is weak (i.e. these data do not measure the feedback effect well). When also comparing new hypothetical models, the available data do not discriminate. To begin addressing the limitations in data, we performed a model-based experiment design and provide recommendations for experiments to refine model parameters and discriminate increasingly complex hypotheses.