The modularity of the Barth-Nieto quintic and its relatives

The moduli space of (1,3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth-Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third \'etale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group \Gamma_1(6). By Tate's conjecture, this should imply that Y, the fibred square of the universal elliptic curve S_1(6), and Verrill's rigid Calabi-Yau Z_{A_3}, which all have the same L-function, are in correspondence over Q. We show that this is indeed the case by giving explicit maps.Comment: 30 pages, Latex2

A new geometric description for Igusa's modular form (azy)5(azy)_5

The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different description for this modular form is provided by resorting to a peculiar geometrical approach.Comment: 10 page

Age-dependent changes in geometry, tissue composition and mechanical properties of fetal to adult cryopreserved human heart valves

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Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

The F-BAR protein pacsin2 inhibits asymmetric VE-cadherin internalization from tensile adherens junctions

Vascular homoeostasis, development and disease critically depend on the regulation of endothelial cell-cell junctions. Here we uncover a new role for the F-BAR protein pacsin2 in the control of VE-cadherin-based endothelial adhesion. Pacsin2 concentrates at focal adherens junctions (FAJs) that are experiencing unbalanced actomyosin-based pulling. FAJs move in response to differences in local cytoskeletal geometry and pacsin2 is recruited consistently to the trailing end of fast-moving FAJs via a mechanism that requires an intact F-BAR domain. Photoconversion, photobleaching, immunofluorescence and super-resolution microscopy reveal polarized dynamics, and organization of junctional proteins between the front of FAJs and their trailing ends. Interestingly, pacsin2 recruitment inhibits internalization of the VE-cadherin complex from FAJ trailing ends and is important for endothelial monolayer integrity. Together, these findings reveal a novel junction protective mechanism during polarized trafficking of VE-cadherin, which supports barrier maintenance within dynamic endothelial tissue

Tissue properties and collagen remodeling in heart valve tissue engineering

Valvular heart disease is a major health problem worldwide causing morbidity and mortality. Heart valve replacement is frequently applied to avoid serious cardiac, pulmonary, or systemic problems. However, the current replacements do not consist of living tissue and, consequently, cannot grow, repair, or remodel in response to changing functional demands. Heart valve tissue engineering (HVTE) seeks to overcome the shortcomings of the existing valve replacements by creating living autologous heart valves. One of the main challenges of HVTE is to control tissue formation, collagen remodeling and consequent tissue mechanical properties during the in vitro culture phase. Additionally, it is important to define benchmarks based on the target native heart valve tissues to compare with the tissue structure and mechanical properties of tissue-engineered (TE) heart valves. The aim of this thesis is to define benchmarks, understand and optimize tissue development and resulting tissue mechanical properties of TE heart valves, with special emphasis on collagen remodeling. In order to provide insights into the evolution and maturation of the extracellular matrix and mechanical properties and to provide benchmarks for TE heart valves, matrix composition, maturation and mechanical properties of native human aortic and pulmonary heart valves were studied. It was observed that the matrix composition and the mechanical properties change with age and that a significant part of the mechanical behaviour of the human native heart valve leaflets is defined by the composition and maturation of the matrix. Tissue (mechanical) properties of TE heart valves should be optimized towards the provided benchmarks during the in vitro culture phase. To this end, possible indicators of in vitro tissue outcome were determined to enable prediction of the properties of the autologous tissues cultured for individual patients. It was found that a-Smooth muscle actin (aSMA) might be such an indicator. In addition, interspecies differences in tissue (mechanical) properties were evaluated to determine whether ovine TE heart valves are representative of human TE heart valves as the ovine model is the prescribed animal model to evaluate heart valve replacements. This study suggested that the culture process of ovine tissue can be controlled, whereas the mechanical properties, and hence functionality, of tissues cultured with human cells are more difficult to predict, indicating once more the importance of early markers to predict tissue outcome. As a further step towards clinical application and to circumvent the use of animal-derived medium components in the culture protocol, fetal bovine serum was replaced by human platelet lysate for the culture of autologous TE heart valve constructs. Although tissue composition and maturation were similar, mechanical properties were much lower for the tissues cultured in platelet lysate, most likely due to an increased production of matrix-degrading enzymes leading to an altered collagen architecture. Thus, collagen architecture, rather than collagen content alone, is dominant in defining the tissue mechanical properties. To stimulate tissue formation and maturation towards the right collagen architecture for in vivo mechanical functionality, mechanical conditioning of the engineered tissue is commonly pursued. Previous studies indicated that intermittent conditioning, in which cyclic and static strain are alternated, is favoured to obtain mature tissues in a short time period. To unravel the underlying mechanism of intermittent conditioning, the effects of cyclic strain and static strain after cyclic strain were examined at gene expression level. This study indicated that a period of static strain is required for collagen synthesis and remodeling, while continuous cyclic strain shifts this balance towards collagen remodeling and maturation. These results imply that the mechanical conditioning protocol should change over time from intermittent conditioning to continuous cyclic strain to improve collagen maturation after its synthesis and, therewith, the mechanical properties of TE heart valves. In summary, the results from this thesis suggest that in addition to collagen content and maturation, collagen organization is particularly important in defining the tissue mechanical properties. Thus, optimization of culture protocols should focus on obtaining the proper collagen architecture for creating mechanically functioning TE heart valves. Autologous culture of TE heart valves using human platelet lysate is not preferred, since it prevents the formation of a load-bearing organized collagen network. Mechanical conditioning protocols should start with intermittent conditioning, followed by continuous cyclic strain to enhance collagen maturation after its synthesis. Considering the interpatient variability in tissue outcome of tissues cultured with similar protocols, it must be noted that further refinement, or even personalization, of culture protocols might be necessary. To this end, markers of tissue outcome, such as aSMA, are necessary to predict and adapt culture protocols and, therewith, individual tissue outcome at an early stage during culture. Although these suggestions require additional (in vivo) study, the results of this thesis provide substantial insight on how to improve in vitro HVTE strategies to control tissue properties and collagen remodeling for optimization of TE heart valves towards their native counterparts