Mathematical modeling of Notch dynamics in Drosophila neural development.

Notch signalling is a well-conserved signalling pathway that regulates cell fate through cell-cell communication. A typical feature of Notch signalling is 'lateral inhibition', whereby two neighbouring cells of equivalent state of differentiation acquire different cell fates. Recently, mathematical and computational approaches have addressed the Notch dynamics in Drosophila neural development. Typical examples of lateral inhibition are observed in the specification of neural stem cells in the embryo and sensory organ precursors in the thorax. In eye disc development, Notch signalling cooperates with other signalling pathways to define the evenly spaced positioning of the photoreceptor cells. The interplay between Notch and epidermal growth factor receptor signalling regulates the timing of neural stem cell differentiation in the optic lobe. In this review, we summarize the theoretical studies that have been conducted to elucidate the Notch dynamics in these systems and discuss the advantages of combining mathematical models with biological experiments.

Intracellular trafficking of Notch orchestrates temporal dynamics of Notch activity in the fly brain.

While Delta non-autonomously activates Notch in neighboring cells, it autonomously inactivates Notch through cis-inhibition, the molecular mechanism and biological roles of which remain elusive. The wave of differentiation in the Drosophila brain, the 'proneural wave', is an excellent model for studying Notch signaling in vivo. Here, we show that strong nonlinearity in cis-inhibition reproduces the second peak of Notch activity behind the proneural wave in silico. Based on this, we demonstrate that Delta expression induces a quick degradation of Notch in late endosomes and the formation of the twin peaks of Notch activity in vivo. Indeed, the amount of Notch is upregulated and the twin peaks are fused forming a single peak when the function of Delta or late endosomes is compromised. Additionally, we show that the second Notch peak behind the wavefront controls neurogenesis. Thus, intracellular trafficking of Notch orchestrates the temporal dynamics of Notch activity and the temporal patterning of neurogenesis.

A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices.

In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically converted into a spatially continuous model; this renders both models point-wisely equivalent. Moreover, by the convolution with suitable kernels, we mollify the shift operator and approximate the spatially discretized models using the nonlocal evolution equations, rendering suitable for the application in both experimental and mathematical analyses. We also demonstrate that this approximation is supported by the singular limit analysis, and that the information of the lattice and cells is expressed in the shift and nonlocal operators. The continuous models designed using our method can successfully replicate the patterns corresponding to those of the original spatially discretized models obtained from the numerical simulations. Furthermore, from the observations of the isotropy of the Delta-Notch signaling system in a developing real fly brain, we propose a radially symmetric kernel for averaging the cell shape using our continuation method. We also apply our method for cell division and proliferation to spatially discretized models of the differentiation wave and describe the discrete models on the sphere surface. Finally, we demonstrate an application of our method in the linear stability analysis of the planar cell polarity model.

Role for phagocytosis in the prevention of neoplastic transformation in Drosophila.

Immunity is considered to be involved in the prevention of cancer. Although both humoral and cellular immune reactions may participate, underlying mechanisms have yet to be clarified. The present study was conducted to clarify this issue using a Drosophila model, in which neoplastic transformation was induced through the simultaneous inhibition of cell-cycle checkpoints and apoptosis. We first determined the location of hemocytes, blood cells of Drosophila playing a role of immune cells, in neoplasia-induced and normal larvae, but there was no significant difference between the two groups. When gene expression pattern in larval hemocytes was determined, the expression of immunity-related genes including those necessary for phagocytosis was reduced in the neoplasia model. We then asked the involvement of phagocytosis in the prevention of neoplasia examining animals where the expression of engulfment receptors instead of apoptosis was retarded. We found that the inhibition of engulfment receptor expression augmented the occurrence of neoplasia induced by a defect in cell-cycle checkpoints. This suggested a role for phagocytosis in the prevention of neoplastic transformation in Drosophila.

Dscam1 establishes the columnar units through lineage-dependent repulsion between sister neurons in the fly brain.

The brain is organized morphologically and functionally into a columnar structure. According to the radial unit hypothesis, neurons from the same lineage form a radial unit that contributes to column formation. However, the molecular mechanisms that link neuronal lineage and column formation remain elusive. Here, we show that neurons from the same lineage project to different columns under control of Down syndrome cell adhesion molecule (Dscam) in the fly brain. Dscam1 is temporally expressed in newly born neuroblasts and is inherited by their daughter neurons. The transient transcription of Dscam1 in neuroblasts enables the expression of the same Dscam1 splice isoform within cells of the same lineage, causing lineage-dependent repulsion. In the absence of Dscam1 function, neurons from the same lineage project to the same column. When the splice diversity of Dscam1 is reduced, column formation is significantly compromised. Thus, Dscam1 controls column formation through lineage-dependent repulsion.

Regulation of Proneural Wave Propagation Through a Combination of Notch-Mediated Lateral Inhibition and EGF-Mediated Reaction Diffusion.

Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt-and-pepper pattern formation during various biological processes. In many cases, Notch signaling acts together with other signaling systems. However, it is not clear what happens when Notch signaling is combined with other signaling systems. Mathematical modeling and the use of a simple biological model system will be essential to address this uncertainty. A wave of differentiation in the Drosophila visual center, the "proneural wave," accompanies the activity of the Notch and EGF signaling pathways. Although all of the Notch signaling components required for lateral inhibition are involved in the proneural wave, no salt-and-pepper pattern is found during the progression of the proneural wave. Instead, Notch is activated along the wave front and regulates proneural wave progression. How does Notch signaling control wave propagation without forming a salt-and-pepper pattern? A mathematical model of the proneural wave, based on biological evidence, has demonstrated that Notch-mediated lateral inhibition is implemented within the proneural wave and that the diffusible action of EGF cancels salt-and-pepper pattern formation. The results from numerical simulation have been confirmed by genetic experiments in vivo and suggest that the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a novel function of Notch signaling that regulates propagation of the proneural wave. Similar mechanisms may play important roles in diverse biological processes found in animal development and cancer pathogenesis.

Temporal patterning of neurogenesis and neural wiring in the fly visual system.

During neural development, a wide variety of neurons are produced in a highly coordinated manner and form complex and highly coordinated neural circuits. Temporal patterning of neuron type specification plays very important roles in orchestrating the production and wiring of neurons. The fly visual system, which is composed of the retina and the optic lobe of the brain, is an outstanding model system to study temporal patterning and wiring of the nervous system. All of the components of the fly visual system are topographically connected, and each ommatidial unit in the retina corresponds to a columnar unit in the optic lobe. In the retina, the wave of differentiation follows the morphogenetic furrow, which progresses in a posterior-to-anterior direction. At the same time, differentiation of the optic lobe also accompanies the wave of differentiation or temporally coordinated neurogenesis. Thus, temporal patterning plays important roles in establishing topographic connections throughout the fly visual system. In this article, we review how neuronal differentiation and connectivity are orchestrated in the fly visual system by temporal patterning mechanisms.

Netrin Signaling Defines the Regional Border in the Drosophila Visual Center.

The brain consists of distinct domains defined by sharp borders. So far, the mechanisms of compartmentalization of developing tissues include cell adhesion, cell repulsion, and cortical tension. These mechanisms are tightly related to molecular machineries at the cell membrane. However, we and others demonstrated that Slit, a chemorepellent, is required to establish the borders in the fly brain. Here, we demonstrate that Netrin, a classic guidance molecule, is also involved in the compartmental subdivision in the fly brain. In Netrin mutants, many cells are intermingled with cells from the adjacent ganglia penetrating the ganglion borders, resulting in disorganized compartmental subdivisions. How do these guidance molecules regulate the compartmentalization? Our mathematical model demonstrates that a simple combination of known guidance properties of Slit and Netrin is sufficient to explain their roles in boundary formation. Our results suggest that Netrin indeed regulates boundary formation in combination with Slit in vivo.

JAK/STAT guarantees robust neural stem cell differentiation by shutting off biological noise.

Organismal development is precisely regulated by a sequence of gene functions even in the presence of biological noise. However, it is difficult to evaluate the effect of noise in vivo, and the mechanisms by which noise is filtered during development are largely unknown. To identify the noise-canceling mechanism, we used the fly visual system, in which the timing of differentiation of neural stem cells is spatio-temporally ordered. Our mathematical model predicts that JAK/STAT signaling contributes to noise canceling to guarantee the robust progression of the differentiation wave in silico. We further demonstrate that the suppression of JAK/STAT signaling causes stochastic and ectopic neural stem cell differentiation in vivo, suggesting an evolutionarily conserved function of JAK/STAT to regulate the robustness of stem cell differentiation.

Adaptation to dietary conditions by trehalose metabolism in Drosophila.

Trehalose is a non-reducing disaccharide that serves as the main sugar component of haemolymph in insects. Trehalose hydrolysis enzyme, called trehalase, is highly conserved from bacteria to humans. However, our understanding of the physiological role of trehalase remains incomplete. Here, we analyze the phenotypes of several Trehalase (Treh) loss-of-function alleles in a comparative manner in Drosophila. The previously reported mutant phenotype of Treh affecting neuroepithelial stem cell maintenance and differentiation in the optic lobe is caused by second-site alleles in addition to Treh. We further report that the survival rate of Treh null mutants is significantly influenced by dietary conditions. Treh mutant larvae are lethal not only on a low-sugar diet but also under low-protein diet conditions. A reduction in adaptation ability under poor food conditions in Treh mutants is mainly caused by the overaccumulation of trehalose rather than the loss of Treh, because the additional loss of Tps1 mitigates the lethal effect of Treh mutants. These results demonstrate that proper trehalose metabolism plays a critical role in adaptation under various environmental conditions.

Notch-mediated lateral inhibition regulates proneural wave propagation when combined with EGF-mediated reaction diffusion.

Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or "proneural wave" accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation.

A Combination of CRISPR/Cas9 and Standardized RNAi as a Versatile Platform for the Characterization of Gene Function.

Traditional loss-of-function studies in Drosophila suffer from a number of shortcomings, including off-target effects in the case of RNA interference (RNAi) or the stochastic nature of mosaic clonal analysis. Here, we describe minimal in vivo GFP interference (miGFPi) as a versatile strategy to characterize gene function and to conduct highly stringent, cell type-specific loss-of-function experiments in Drosophila miGFPi combines CRISPR/Cas9-mediated tagging of genes at their endogenous locus with an immunotag and an exogenous 21 nucleotide RNAi effector sequence with the use of a single reagent, highly validated RNAi line targeting this sequence. We demonstrate the utility and time effectiveness of this method by characterizing the function of the Polymerase I (Pol I)-associated transcription factor Tif-1a, and the previously uncharacterized gene MESR4, in the Drosophila female germline stem cell lineage. In addition, we show that miGFPi serves as a powerful technique to functionally characterize individual isoforms of a gene. We exemplify this aspect of miGFPi by studying isoform-specific loss-of-function phenotypes of the longitudinals lacking (lola) gene in neural stem cells. Altogether, the miGFPi strategy constitutes a generalized loss-of-function approach that is amenable to the study of the function of all genes in the genome in a stringent and highly time effective manner.

Wnt Signaling Specifies Anteroposterior Progenitor Zone Identity in the Drosophila Visual Center.

UNLABELLED: During brain development, various types of neuronal populations are produced from different progenitor pools to produce neuronal diversity that is sufficient to establish functional neuronal circuits. However, the molecular mechanisms that specify the identity of each progenitor pool remain obscure. Here, we show that Wnt signaling is essential for the specification of the identity of posterior progenitor pools in the Drosophila visual center. In the medulla, the largest component of the visual center, different types of neurons are produced from two progenitor pools: the outer proliferation center (OPC) and glial precursor cells (GPCs; also known as tips of the OPC). We found that OPC-type neurons are produced from the GPCs at the expense of GPC-type neurons when Wnt signaling is suppressed in the GPCs. In contrast, GPC-type neurons are ectopically induced when Wnt signaling is ectopically activated in the OPC. These results suggest that Wnt signaling is necessary and sufficient for the specification of the progenitor pool identity. We also found that Homothorax (Hth), which is temporally expressed in the OPC, is ectopically induced in the GPCs by suppression of Wnt signaling and that ectopic induction of Hth phenocopies the suppression of Wnt signaling in the GPCs. Thus, Wnt signaling is involved in regionalization of the fly visual center through the specification of the progenitor pool located posterior to the medulla by suppressing Hth expression. SIGNIFICANCE STATEMENT: Brain consists of considerably diverse neurons of different origins. In mammalian brain, excitatory and inhibitory neurons derive from the dorsal and ventral telencephalon, respectively. Multiple progenitor pools also contribute to the neuronal diversity in fly brain. However, it has been unclear how differences between these progenitor pools are established. Here, we show that Wnt signaling, an evolutionarily conserved signaling, is involved in the process that establishes the differences between these progenitor pools. Because ß-catenin signaling, which is under the control of Wnt ligands, specifies progenitor pool identity in the developing mammalian thalamus, Wnt signaling-mediated specification of progenitor pool identity may be conserved in insect and mammalian brains.

Temporal regulation of the generation of neuronal diversity in Drosophila.

For the construction of complex neural networks, the generation of neurons and glia must be tightly regulated both spatially and temporally. One of the major issues in neural development is the generation of a large variety of neurons and glia over time from a relatively small number of neural stem cells. In Drosophila, neural stem cells, called neuroblasts (NBs), have been used as a useful model system to uncover the molecular and cellular machinery involved in the establishment of neural diversity. NBs divide asymmetrically and produce another self-renewing progenitor cell and a differentiating cell. NBs are subdivided into several types based on their location in the central nervous system. Each type of NB has specific features related to the timing of cell generation, cell cycle progression, temporal patterning for neuronal specification, and termination mechanism. In this review, we focus on the molecular mechanisms that regulate the proliferation of NBs and generate a large variety of neuronal and glia subtypes during development.

A regulatory transcriptional loop controls proliferation and differentiation in Drosophila neural stem cells.

Neurogenesis is initiated by a set of basic Helix-Loop-Helix (bHLH) transcription factors that specify neural progenitors and allow them to generate neurons in multiple rounds of asymmetric cell division. The Drosophila Daughterless (Da) protein and its mammalian counterparts (E12/E47) act as heterodimerization factors for proneural genes and are therefore critically required for neurogenesis. Here, we demonstrate that Da can also be an inhibitor of the neural progenitor fate whose absence leads to stem cell overproliferation and tumor formation. We explain this paradox by demonstrating that Da induces the differentiation factor Prospero (Pros) whose asymmetric segregation is essential for differentiation in one of the two daughter cells. Da co-operates with the bHLH transcription factor Asense, whereas the other proneural genes are dispensible. After mitosis, Pros terminates Asense expression in one of the two daughter cells. In da mutants, pros is not expressed, leading to the formation of lethal transplantable brain tumors. Our results define a transcriptional feedback loop that regulates the balance between self-renewal and differentiation in Drosophila optic lobe neuroblasts. They indicate that initiation of a neural differentiation program in stem cells is essential to prevent tumorigenesis.

Fat/Hippo pathway regulates the progress of neural differentiation signaling in the Drosophila optic lobe.

A large number of neural and glial cell species differentiate from neuronal precursor cells during nervous system development. Two types of Drosophila optic lobe neurons, lamina and medulla neurons, are derived from the neuroepithelial (NE) cells of the outer optic anlagen. During larval development, epidermal growth factor receptor (EGFR)/Ras signaling sweeps the NE field from the medial edge and drives medulla neuroblast (NB) formation. This signal drives the transient expression of a proneural gene, lethal of scute, and we refer to its signal array as the "proneural wave," as it is the marker of the EGFR/Ras signaling front. In this study, we show that the atypical cadherin Fat and the downstream Hippo pathways regulate the transduction of EGFR/Ras signaling along the NE field and, thus, ensure the progress of NB differentiation. Fat/Hippo pathway mutation also disrupts the pattern formation of the medulla structure, which is associated with the regulation of neurogenesis. A candidate for the Fat ligand, Dachsous is expressed in the posterior optic lobe, and its mutation was observed to cause a similar phenotype as fat mutation, although in a regionally restricted manner. We also show that Dachsous functions as the ligand in this pathway and genetically interacts with Fat in the optic lobe. These findings provide new insights into the function of the Fat/Hippo pathway, which regulates the ordered progression of neurogenesis in the complex nervous system.

Coordinated sequential action of EGFR and Notch signaling pathways regulates proneural wave progression in the Drosophila optic lobe.

During neurogenesis in the medulla of the Drosophila optic lobe, neuroepithelial cells are programmed to differentiate into neuroblasts at the medial edge of the developing optic lobe. The wave of differentiation progresses synchronously in a row of cells from medial to the lateral regions of the optic lobe, sweeping across the entire neuroepithelial sheet; it is preceded by the transient expression of the proneural gene lethal of scute [l(1)sc] and is thus called the proneural wave. We found that the epidermal growth factor receptor (EGFR) signaling pathway promotes proneural wave progression. EGFR signaling is activated in neuroepithelial cells and induces l(1)sc expression. EGFR activation is regulated by transient expression of Rhomboid (Rho), which is required for the maturation of the EGF ligand Spitz. Rho expression is also regulated by the EGFR signal. The transient and spatially restricted expression of Rho generates sequential activation of EGFR signaling and assures the directional progression of the differentiation wave. This study also provides new insights into the role of Notch signaling. Expression of the Notch ligand Delta is induced by EGFR, and Notch signaling prolongs the proneural state. Notch signaling activity is downregulated by its own feedback mechanism that permits cells at proneural states to subsequently develop into neuroblasts. Thus, coordinated sequential action of the EGFR and Notch signaling pathways causes the proneural wave to progress and induce neuroblast formation in a precisely ordered manner.

Recognition of pre- and postsynaptic neurons via nephrin/NEPH1 homologs is a basis for the formation of the Drosophila retinotopic map.

Topographic maps, which maintain the spatial order of neurons in the order of their axonal connections, are found in many parts of the nervous system. Here, we focus on the communication between retinal axons and their postsynaptic partners, lamina neurons, in the first ganglion of the Drosophila visual system, as a model for the formation of topographic maps. Post-mitotic lamina precursor cells differentiate upon receiving Hedgehog signals delivered through newly arriving retinal axons and, before maturing to extend neurites, extend short processes toward retinal axons to create the lamina column. The lamina column provides the cellular basis for establishing stereotypic synapses between retinal axons and lamina neurons. In this study, we identified two cell-adhesion molecules: Hibris, which is expressed in post-mitotic lamina precursor cells; and Roughest, which is expressed on retinal axons. Both proteins belong to the nephrin/NEPH1 family. We provide evidence that recognition between post-mitotic lamina precursor cells and retinal axons is mediated by interactions between Hibris and Roughest. These findings revealed mechanisms by which axons of presynaptic neurons deliver signals to induce the development of postsynaptic partners at the target area. Postsynaptic partners then recognize the presynaptic axons to make ensembles, thus establishing a topographic map along the anterior/posterior axis.

Drosophila optic lobe neuroblasts triggered by a wave of proneural gene expression that is negatively regulated by JAK/STAT.

Neural stem cells called neuroblasts (NBs) generate a variety of neuronal and glial cells in the central nervous system of the Drosophila embryo. These NBs, few in number, are selected from a field of neuroepithelial (NE) cells. In the optic lobe of the third instar larva, all NE cells of the outer optic anlage (OOA) develop into either NBs that generate the medulla neurons or lamina neuron precursors of the adult visual system. The number of lamina and medulla neurons must be precisely regulated because photoreceptor neurons project their axons directly to corresponding lamina or medulla neurons. Here, we show that expression of the proneural protein Lethal of scute [L(1)sc] signals the transition of NE cells to NBs in the OOA. L(1)sc expression is transient, progressing in a synchronized and ordered ;proneural wave' that sweeps toward more lateral NEs. l(1)sc expression is sufficient to induce NBs and is necessary for timely onset of NB differentiation. Thus, proneural wave precedes and induces transition of NE cells to NBs. Unpaired (Upd), the ligand for the JAK/STAT signaling pathway, is expressed in the most lateral NE cells. JAK/STAT signaling negatively regulates proneural wave progression and controls the number of NBs in the optic lobe. Our findings suggest that NBs might be balanced with the number of lamina neurons by JAK/STAT regulation of proneural wave progression, thereby providing the developmental basis for the formation of a precise topographic map in the visual center.