(Georgia Institute of Technology, 2010-11-18)
Anderson, Johshua; Ash, Andrew
Our task has been to calculate the probability of any two nucleotides pairing in an RNA molecule. When RNA goes into the cytoplasm of a cell, the RNA folds in on itself to a thermodynamically stable state, since unpaired nucleotides are chemically unstable. We predict this behavior by a couple of dynamic programming algorithms using some statistical methods derived from the physics of ideal gasses. In order to find base pair probabilities we must first find the partition function for all continuous substrings in the strand. The partition function is a measure of the possible combinations of foldings weighted by the stability of these foldings. We will also describe finding the minimum free energy structure, currently implemented in gtfold, and its relation to the partition function via something we have come to call "tropicalization." Both the minimum free energy and the partition function problems are solved in a reasonable (O(n³)) amount of time by dynamic programming algorithms.