Seminar January 18

The Geometry-Topology Seminar returns for the Spring term at 3:30PM on Tuesday, January 18 with two speakers.

Steve Simon, from NYU will speak on

Title: Two Generalizations of the Ham Sandwich Theorem

Abstract: The Ham Sandwich Theorem states that for any n finite Borel measures on R^n, there exists a hyperplane which bisects each of the measures. This talk will present two generalizations of this theorem. In one direction, we ask for the number of mutually orthogonal hyperplanes which bisect a collection of numbers. This number will be related to the number of linearly independent vector fields on a sphere. The talk will also provide group-theoretic generalizations of the Ham Sandwich Theorem for fundamental regions corresponding to finite subgroups of spheres of dimension 0, 1, and 3.

Mateo Castronovo, from Temple will speak on

Title: The Effect of Confinement on Molecular Mechanism Inside Bio-Nanosensors

Abstract: The explosive increase of research in biology has spurred the need for new techniques and devices that can surmount experimental roadblocks. Current in-vitro techniques cannot accurately identify small differences in concentration in samples containing few molecules in a single or a few cells. Nanotechnology overcomes these limitations with the possibility of fabricating nano-sensors that measure protein amounts down to a hundred molecules.

The pairing of two complementary strands of DNA, also called DNA hybridization, allows the formation of a stable helical structure. In turn, the pairing mechanism provides DNA molecules with a self-assembly functionality. The latter offers tremendous potential in nanotechnology toward developing programmable nano-sensors. For instance, in our work we fabricate prototypical nanosensors by locally, and chemically attaching short sequences of DNA to a surface. The latter form a confined patch of monolayer (i.e. a DNA brush) at the solid-liquid interface that can be selectively, and reversibly modified by hybridizing the DNA in the brush with a DNA-linked probe-molecule, which is able to recognize a target-molecule in solution. Little is known, however, about the effect of confinement on the mechanism of recognition between molecules inside such systems. In our experimental work we have studied the mechanism by which a restriction enzyme, i.e. a protein that binds DNA and cuts it in a specific site, works inside a DNA brush. We address the effect of confinement by varying the DNA surface density. We unequivocally show that confinement has a quantifiable effect on the reaction. Namely, enzymes do not access to the DNA directly from the solution, but 2D-diffuse inside the DNA brush exclusively from the side. Moreover, if the DNA surface density is sufficiently high, the enzyme becomes completely unable to access the substrate and, therefore, to cut the DNA molecules.

Our findings demonstrate that DNA-enzyme reaction mechanisms can be significantly altered when occurring in nanoscale materials, and may have broad implications on the design of innovative nanotechnology approaches to biomolecular detection.

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