PIMS Network Wide Colloquium: Mariel Vázquez

Long DNA and RNA molecules encode the genetic code of viruses and living organisms. We study the changes in DNA topology mediated by essential processes such as DNA packing and transcription of DNA into RNA. These processes are highly regulated, and even small structural changes can lead to catastrophic effects. We use techniques from knot theory and topology, aided by discrete and computational methods, to model these biological processes. Our emphasis is on the geometry and topology of DNA and RNA. In this lecture, I first discuss discrete methods in the study of biopolymers. The rest of the presentation will be devoted to the R-loop grammar, a formal grammar model that allows us to predict the formation and entanglement of DNA:RNA hybrids that arise during transcription. The presentation is accessible to students and suitable for a diverse interdisciplinary audience.