An action principle for biopolymer foldingin vitro: A new perspective on the design of expeditiously-folded RNA molecules

Abstract

The exploration of conformation space performed by a biopolymer becomes rapidly biased towards a confined region and takes place under a stringent schedule incompatible with the thermodynamic limit. The theoretical underpinnings of such properties have been missing to a considerable extent. By introducing anaction principle in the space of folding pathways, we show how folding is guided expeditiously within realistic time frames. The variational principle is constructed in three stages: (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) This measure induces a Lagrangian which, in turn, defines the underlying action principle. The theory is specialized to account for the expeditious folding of an RNA species resolved to the level of secondary structure. Thus, using the Lagrangian, a time-dependent Base-Pair Probability Matrix (BPPM) is generated. This representational tool is introduced to display all RNA structures contributing to the cross section of the ensemble of pathways at each instant in time. The BPPM is contrastedvis-a-vis experimental information on biologically-competent RNA conformations. The results reveal that the statistical weight is concentrated on a very limited domain of folding pathways which yield the biologically-relevant destination structure within realistic timescales. To conclude, we assess in a preliminary fashion the potential of the action principle as a tool to aid the design of RNA species capable of folding within experimental timeframes.