• Boltzmann Measure;
  • RNA Folding;
  • Riesz-Markov Representation Theorem


By systematically assigning weights to kinetically-controlled folding pathways we introduce a novel scheme of statistical inference. We provide supporting experimental evidence to show that this approach is suitable to explain the expediency and robustness of RNA folding. The statistical scheme is constructed in four stages, the last of which leads to a suitable representation that allows for direct comparison with experiment: a) An appropriate space of folding histories is defined; b) The space is endowed with a measure and in this way an ensemble is defined; c) The ensemble is systematically simplified by coarse-graining each copy or replica of conformation space. This procedure entails lumping together rapidly-interconverting conformations; d) A base-pair probability matrix (BPPM) is introduced by representing all structures contributing to the ensemble at a given instant. Thus, we take a convenient cross-section of the ensemble by taking a fixed instant in time. The BPPM is contrasted vis-a-vis experimental information on biologically-competent conformations. This last procedure is paramount to verify the theory. Moreover, the essential properties of folding are captured by showing that the statistical weight is concentrated on a very limited domain of closely-related folding pathways whose biological competence has been established experimentally.