A vector equilibrium problem for the two-matrix model in the quartic/quadratic case

We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and (q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) = x^2/2 and W(y) = y^4/4 + ty^2. From an asymptotic analysis of the coefficients in the recurrence relation satisfied by these polynomials, we obtain the limiting distribution of the zeros of the polynomials p_{n,n} as n tends to infinity. The limiting zero distribution is characterized as the first measure of the minimizer in a vector equilibrium problem involving three measures which for the case t=0 reduces to the vector equilibrium problem that was given recently by two of us. A novel feature is that for t < 0 an external field is active on the third measure which introduces a new type of critical behavior for a certain negative value of t. We also prove a general result about the interlacing of zeros of biorthogonal polynomials.Comment: 60 pages, 9 figure

Blood flow drives lumen formation by inverse membrane blebbing during angiogenesis in vivo

How vascular tubes build, maintain and adapt continuously perfused lumens to meet local metabolic needs remains poorly understood. Recent studies showed that blood flow itself plays a critical role in the remodelling of vascular networks, and suggested it is also required for the lumenization of new vascular connections. However, it is still unknown how haemodynamic forces contribute to the formation of new vascular lumens during blood vessel morphogenesis. Here we report that blood flow drives lumen expansion during sprouting angiogenesis in vivo by inducing spherical deformations of the apical membrane of endothelial cells, in a process that we have termed inverse blebbing. We show that endothelial cells react to these membrane intrusions by local and transient recruitment and contraction of actomyosin, and that this mechanism is required for single, unidirectional lumen expansion in angiogenic sprouts. Our work identifies inverse membrane blebbing as a cellular response to high external pressure. We show that in the case of blood vessels such membrane dynamics can drive local cell shape changes required for global tissue morphogenesis, shedding light on a pressure-driven mechanism of lumen formation in vertebrates

Artery-vein specification in the zebrafish trunk is pre-patterned by heterogeneous Notch activity and balanced by flow-mediated fine tuning

How developing vascular networks acquire the right balance of arteries, veins and lymphatic vessels to efficiently supply and drain tissues is poorly understood. In zebrafish embryos, the robust and regular 50:50 global balance of intersegmental veins and arteries that form along the trunk, prompts the intriguing question how the organism keeps "count". Previous studies suggest that the ultimate fate of an intersegmental vessel (ISV) is determined by the identity of the approaching secondary sprout emerging from the posterior cardinal vein (PCV). Here, we show that the formation of a balanced trunk vasculature involves an early heterogeneity in endothelial cell (EC) behavior and Notch signaling activity in the seemingly identical primary ISVs that is independent of secondary sprouting and flow. We show that Notch signaling mediates the local patterning of ISVs, and an adaptive flow-mediated mechanism subsequently fine-tunes the global balance of arteries and veins along the trunk. We propose that this dual mechanism provides the adaptability required to establish a balanced network of arteries, veins and lymphatic vessels

Zebrafish prox1b Mutants Develop a Lymphatic Vasculature, and prox1b Does Not Specifically Mark Lymphatic Endothelial Cells

Background: The expression of the Prospero homeodomain transcription factor (Prox1) in a subset of cardinal venous cells specifies the lymphatic lineage in mice. Prox1 is also indispensible for the maintenance of lymphatic cell fate, and is therefore considered a master control gene for lymphangiogenesis in mammals. In zebrafish, there are two prox1 paralogues, the previously described prox1 (also known as prox1a) and the newly identified prox1b. Principal Findings: To investigate the role of the prox1b gene in zebrafish lymphangiogenesis, we knocked-down prox1b and found that depletion of prox1b mRNA did not cause lymphatic defects. We also generated two different prox1b mutant alleles, and maternal-zygotic homozygous mutant embryos were viable and did not show any lymphatic defects. Furthermore, the expression of prox1b was not restricted to lymphatic vessels during zebrafish development. Conclusion: We conclude that Prox1b activity is not essential for embryonic lymphatic development in zebrafish

Single-cell profiling and zebrafish avatars reveal LGALS1 as immunomodulating target in glioblastoma

Glioblastoma (GBM) remains the most malignant primary brain tumor, with a median survival rarely exceeding 2 years. Tumor heterogeneity and an immunosuppressive microenvironment are key factors contributing to the poor response rates of current therapeutic approaches. GBM-associated macrophages (GAMs) often exhibit immunosuppressive features that promote tumor progression. However, their dynamic interactions with GBM tumor cells remain poorly understood. Here, we used patient-derived GBM stem cell cultures and combined single-cell RNA sequencing of GAM-GBM co-cultures and real-time in vivo monitoring of GAM-GBM interactions in orthotopic zebrafish xenograft models to provide insight into the cellular, molecular, and spatial heterogeneity. Our analyses revealed substantial heterogeneity across GBM patients in GBM-induced GAM polarization and the ability to attract and activate GAMs—features that correlated with patient survival. Differential gene expression analysis, immunohistochemistry on original tumor samples, and knock-out experiments in zebrafish subsequently identified LGALS1 as a primary regulator of immunosuppression. Overall, our work highlights that GAM-GBM interactions can be studied in a clinically relevant way using co-cultures and avatar models, while offering new opportunities to identify promising immune-modulating targets

Coordinating cell behaviour during blood vessel formation

The correct development of blood vessels is crucial for all aspects of tissue growth and physiology in vertebrates. The formation of an elaborate hierarchically branched network of endothelial tubes, through either angiogenesis or vasculogenesis, relies on a series of coordinated morphogenic events, but how individual endothelial cells adopt specific phenotypes and how they coordinate their behaviour during vascular patterning is unclear. Recent progress in our understanding of blood vessel formation has been driven by advanced imaging techniques and detailed analyses that have used a combination of powerful in vitro, in vivo and in silico model systems. Here, we summarise these models and discuss their advantages and disadvantages. We then review the different stages of blood vessel development, highlighting the cellular mechanisms and molecular players involved at each step and focusing on cell specification and coordination within the network