Folding RNA in mixtures of monovalent and divalent cations: Theory and simulations

Abstract

RNA molecules cannot fold in the absence of counter ions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the Reference Interaction Site Model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial in an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to accurately predict the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the ribosomal RNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.\n\nSignificance StatementRNA molecules require ions to fold. The problem of how ions of differing sizes and valences drive the folding of RNA molecules is unsolved. Here, we take a major step in its solution by creating a method, based on the theory of polyatomic liquids, to calculate the potential between divalent ions and the phosphate groups. The resulting model, accounting for inner and outer sphere coordination of Mg2+ and Ca2+ to phosphates, when used in coarse-grained molecular simulations predicts folding free energies for a number of RNA molecules in the presence of both divalent and monovalent ions that are in excellent agreement with experiments. The work sets the stage for probing sequence and ion effects on DNA and synthetic polyelectrolytes.