Magnesium-aided folding of group I ribozymes with a minimal loss of entropy

The aim of this work is to quantify, rationalize and incorporate the effect of Mg(II) ions on the kinetic barriers of entropic origin associated to RNA folding events in vitro. This study encompasses the scaffolding effect of Mg(II) upon the formation of the pseudoknot structural motif which is believed to be crucial for shaping the catalytic core of group I ribozymes. Our results are contrasted with recent experimental probes on folding kinetics. The first set of objectives is accomplished by determining the participation of Mg(II) in the reduction of the conformational entropy cost during folding. First, the dominant contribution to conformational entropy loss associated to loop closure is obtained. The derivation hinges upon the notion that loop closure entails the formation of an inner and outer solvent domain and backbone phosphate groups orient themselves concurrently towards the best dielectric environment. At this point, the role of Mg(II) ions can be assessed by taking into account that Mg(II) coordinates with two adjacent backbone phosphates in unpaired regions. Thus, for a small loop of even length, the energy decrease due to coordination reduces the conformational entropy loss due to phosphate orientation by one half. In the case of pseudoknot formation, the orientational effect prevents the coplanarity of the loops comprising the pseudoknot and allows us to determine the kinetic barrier associated to its formation in the presence of magnesium. Incorporating these facts to kinetically controlled Monte Carlo simulations, we find that the predicted folding pathway for group I introns leads to the phylogenetically inferred secondary structures and allows us to elucidate the magnesium-dependent rate-limiting step in the formation of the P3-P7 pseudoknotted region of the catalytic core.