Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Anisotropically oriented electrospun matrices with an imprinted periodic micropattern: a new scaffold for engineered muscle constructs

Engineered muscle constructs provide a promising perspective on the regeneration or substitution of irreversibly damaged skeletal muscle. However, the highly ordered structure of native muscle tissue necessitates special consideration during scaffold development. Multiple approaches to the design of anisotropically structured substrates with grooved micropatterns or parallel-aligned fibres have previously been undertaken. In this study we report the guidance effect of a scaffold that combines both approaches, oriented fibres and a grooved topography. By electrospinning onto a topographically structured collector, matrices of parallel-oriented poly(ε-caprolactone) fibres with an imprinted wavy topography of 90 µm periodicity were produced. Matrices of randomly oriented fibres or parallel-oriented fibres without micropatterns served as controls. As previously shown, un-patterned, parallel-oriented substrates induced myotube orientation that is parallel to fibre direction. Interestingly, pattern addition induced an orientation of myotubes at an angle of 24° (statistical median) relative to fibre orientation. Myotube length was significantly increased on aligned micropatterned substrates in comparison to that on aligned substrates without pattern (436 ± 245 µm versus 365 ± 212 µm; p < 0.05). We report an innovative, yet simple, design to produce micropatterned electrospun scaffolds that induce an unexpected myotube orientation and an increase in myotube length.

Engineered fibrin matrices for functional display of cell membrane-bound growth factor-like activities: study of angiogenic signaling by ephrin-B2

With the rapid increase in approaches to pro- or anti-angiogenic therapy, new and effective methodologies for administration of cell-bound growth factors will be required. We sought to develop the natural hydrogel matrix fibrin as platform for extensive interactions and continuous signaling by the vascular morphogen ephrin-B2 that normally resides in the plasma membrane and requires multivalent presentation for ligation and activation of Eph receptors on apposing endothelial cell surfaces. Using fibrin and protein engineering technology to induce multivalent ligand presentation, a recombinant mutant ephrin-B2 receptor binding domain was covalently coupled to fibrin networks at variably high densities. The ability of fibrin-bound ephrin-B2 to act as ligand for endothelial cells was preserved, as demonstrated by a concomitant, dose-dependent increase of endothelial cell binding to engineered ephrin-B2-fibrin substrates in vitro. The therapeutic relevance of ephrin-B2-fibrin implant matrices was demonstrated by a local angiogenic response in the chick embryo chorioallontoic membrane evoked by the local and prolonged presentation of matrix-bound ephrin-B2 to tissue adjacing the implant. This new knowledge on biomimetic fibrin vehicles for precise local delivery of membrane-bound growth factor signals may help to elucidate specific biological growth factor function, and serve as starting point for development of new treatment strategies.