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W. G. Pritchard Lab Seminar: 4:00-5:00 PM, 320 Whitmore Laboratory

	            **Tuesday October 26, 2004**
	
Encoding structures in sequences: plane trees and RNA secondary structure

Christine Heitsch

Department of Mathematics
University of Wisconsin - Madison


Abstract:

We illustrate the interplay between combinatorics and molecular biology 
with results arising from our work on RNA secondary structures.  Unlike 
the canonical double-stranded DNA helix, most RNA molecules are naturally 
single-stranded nucleotide sequences, and the self-bonding or "secondary 
structure" of these sequences is an essential part of their overall 
structure and function. As will be explained, the thermodynamic model 
leads naturally to a combinatorial formulation of the question: how is 
structural information encoded in RNA sequences? In this context, we give 
new combinatorial theorems which yield insight into the folding of RNA 
molecules. We also show that such biological questions can motivate more 
abstract mathematical results by introducing a new operation on plane 
trees which leads to a multipartite graph whose disjoint sets are 
enumerated by the Narayana numbers.

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