The RNA folding problem: a variational problem within an adiabatic approximation

Biopolymer folding is an expeditious process taking place within timescales incommensurably shorter than ergodic times. Furthermore, its robustness suggests that the process must depend on a relatively coarse level of resolution of conformation space. To account for these features while focusing on the RNA context, we derive a variational principle formulated within an adiabatic approximation obtained by integrating out fast-relaxing molecular motions. Folding pathways are generated by means of a stochastic process which begets a least effort principle reflecting a stepwise minimization of the conformational entropy cost for each folding event with concurrent maximization of the base pairing. This economy of the process is found to have kinetic consequences if we treat base-pairing contact patterns (BPPs) adiabatically, that is, as quasi-equilibrium states: the probability distribution of overall folding timespans associated to the process resolved at the BPP level is maximized at the brachistochrone or overall least-time pathway for functionally-competent RNAs. In turn, this pathway is shown to yield all the phylogenetically-conserved structural features of the active conformation within biologically-relevant timescales.