Elucidate Rna Hairpin Folding Mechanisms

Simulating biologically relevant timescales at atomic resolution is a challenging task since typical atomistic simulations are at least two orders of magnitude shorter. Markov State Model (MSMs) provide one means of overcoming this gap without sacrificing atomic resolution by extracting long time dynamics from short simulations. MSMs coarse grain space by dividing conformational space into long-lived, or metastable states. This is equivalent to coarse graining time by integrating out fast motions within metastable states. Therefore, MSMs are inherently multi-resolution. Here we introduce a new algorithm Super-level-set Hierarchical Clustering (SHC), to our knowledge, the first algorithm capable of constructing MSMs at multi-resolutions. The key insight of this algorithm is to generate a set of super levels covering different density regions of the phase space, then cluster each super level separately, and finally recombine this information into a single MSM. SHC is able to produce MSMs at different resolutions using different super level sets. To demonstrate the power of this algorithm we apply it to a small RNA hairpin, and generate MSMs at four different resolutions. These MSMs are successfully validated by their ability to reproduce the orignial simulation data. Fuerthmore, long time folding dynamics can be extracted from these models. The results show that there are no metastable on-pathway intermediate states, while the folded state serves as a hub by directly connecting to multiple unfolded/misfolded states separated by large free energy barriers.