Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Functional dna nanostructures for in vitro biosensing in live cells

DNA is a fascinating biomolecule that is well known for its genetic role in living systems. The emerging area of DNA nanotechnology provides an alternative view that exploits unparallel self-assembly ability of DNA molecules for material use of DNA. Although many reports exist on the results of DNA self-assembling systems, still few of them focus on the in vitro study about the function of such DNA nanostructures in live cells. Due to this, there are still a limited research about the in vitro functionality of such designs. To address an aspect of this issue, we have designed, synthesized and characterized two multifunctional fluorescencent nanobiosensors by DNA self-assembling. Each structure was designed and implemented to be introduced in live cells in order to give information on their functioning in real-time. Computational tools were used in order to design a graphic model of two new DNA motifs and also to obtain the specific sequences to all the ssDNA molecules. By thermal self-assembly techniques we have successfully synthesized the structure and corroborate their formation by the PAGE technique. In addition, we have established the conditions to characterize their structural conformation change when they perform their sensor response. The sensing behavior was also accomplished by fluorescence spectroscopy techniques; FRET evaluation and fluorescence microscopy imaging. Providing the evidence about their adequate sensing performance outside and inside the cells detected in real-time. In a preliminary evaluation we have tried to show the in vitro functionality of our structures in different cancer cell lines with the ability to perform local sensing responses. Our findings suggest that DNA sensor nanostructures could serve as a platform to exploit further therapeutic achievements in live cells.