A measure on the space of RNA folding pathways: towards a new scheme of statistical inference

In this work we define constructively a measure η on the space of sequential folding (SF) pathways for RNA with the aim of making probabilistic inferences on kinetically-controlled folding. This measure will be shown to be adequate for those RNA species known to search for their structure concurrently with their progressive assembling by sequential nucleotide incorporation. We shall validate our approach by showing that the measure is actually concentrated on the SF pathway that has been experimentally confirmed by pulse-chase kinetic probes. The space of SF pathways will be represented as a product of suitably coarse-grained conformation spaces, one for each length of the growing chain. In this context, the measure is induced by a Markovian stochastic process whose specific realizations are precisely the SF pathways. The coarse-graining is necessary to represent only the essential dynamics of SF: We identify rapidly-interconverting structures by regarding the folding dynamics concurrent with chain growth modulo kinetic barriers of order Nα (14⩽α⩽12). Thus, a pathway corresponds to a sequence of clusters of rapidly-equilibrated structures. Within this representation, we show in specific examples that the measure is concentrated solely on the biologically-significant folding pathway whose destination or final structure is functionally-competent, different appreciably from the global free energy minimum.