RNA and protein molecules undergo a dynamic folding process that is important to their function. Computational methods are critical for studying this folding process because it is difficult to observe experimentally. In this work, we introduce new computational techniques to study RNA and protein energy landscapes, including a method to approximate an RNA energy landscape with a coarse graph (map) and new tools for analyzing graph-based approximations of RNA and protein energy landscapes. These analysis techniques can be used to study RNA and protein folding kinetics such as population kinetics, folding rates, and the folding of particular subsequences. In particular, a map-based Master Equation (MME) method can be used to analyze the population kinetics of the maps, while another map analysis tool, map-based Monte Carlo (MMC) simulation, can extract stochastic folding pathways from the map.

To validate the results, I compared our methods with other computational methods and with experimental studies of RNA and protein. I first compared our MMC and MME methods for RNA with other computational methods working on the complete energy landscape and show that the approximate map captures the major features of a much larger (e.g., by orders of magnitude) complete energy landscape. Moreover, I show that the methods scale well to large molecules, e.g., RNA with 200+ nucleotides. Then, I correlate the computational results with experimental findings. I present comparisons with two experimental cases to show how I can predict kinetics-based functional rates of ColE1 RNAII and MS2 phage RNA and their mutants using our MME and MMC tools respectively. I also show that the MME and MMC tools can be applied to map-based approximations of protein energy energy landscapes and present kinetics analysis results for several proteins.