Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

Abstract

RNA molecules cannot fold in the absence of counterions. 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 for 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 predict accurately 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 rRNA, 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.

Contributions and competition of Mg2+and K+in folding and stabilization of the Twister Ribozyme

“…In combination with the results above, with K + the increased direct interactions in the helical regions indicate that the monovalent ion contributes to stabilization of the helical regions. This is consistent with a report indicating that the stability of G-C base pairs is enhanced by binding of monovalent ions at the N7 position through polarization (Šponer et al 2000) with the nucleobases indicates that the assumption in the course-grained model that omit direct Mg 2+ -base interactions is reasonable (Nguyen et al 2019). Finally, the course-grained model is quite impressive in its ability to model the impact of ions on the thermodynamics of folding from fully unfolded states through the native states, a capability that is still a challenge for all-atom models.…”

“…Notably, in the presence of limited amounts of divalent ions, the monovalent ions may assume a supporting role in stabilizing the native, folded state of Twister by facilitating short NBPO pair interactions. Given Twisters ability to self-cleave at low Mg 2+ concentrations further studies are required to address if these observations may be applied to other RNAs.Many of the present results are consistent with those reported by Thirumalai and coworkers on alternate RNAs based on course-grained simulations in conjunction with both explicit ions(Denesyuk and Thirumalai 2015;Hori et al 2019) and explicit divalent with a RISM monovalent ion model(Denesyuk et al 2018;Nguyen et al 2019). This includes the occurrence of RNA-Mg 2+ interactions in unfolded states with the number of interactions increasing upon going to the folded state and increases in Mg 2+ concentration increasing the extent of such interactions.The importance of specific Mg 2+ -RNA interactions is also observed.…”

“…Thus, the folding of the RNA leads to more direct ion-RNA interactions with both Mg 2+ and K + though the pool for those additional ions differs, with the increased charge neutralization being associated with increased condensation of the monovalent K + in both the presence and absence of divalent Mg 2+ . Recently, it was reported that one inner-shell coordination with divalent ion releases two monovalent ions from the ionic atmosphere, a process that is entropically favorable (Nguyen et al 2019). In the present study, based on ion counting data, upon going from the 0 mM to 100 mM MgCl2 systems the average number of K + ions released from the local ion atmosphere based on ions in direct contact with the RNA is close to 2.0 (…”

“…Computational investigations of simultaneous mono-and divalent ion interactions with polynucleotides have observed limited success and have largely been performed on folded states or lack comprehensive spatial sampling of ions around the RNA (Yoo and Aksimentiev 2012;Ucisik et al 2016;Fischer et al 2018;Xi et al 2018). A significant step forward are studies using coarse-grained models from the Thirumalai group that have had success in prediction of ion condensation, the specificity of Mg 2+ -RNA interactions and to understand RNA folding in monoand divalent ion mixtures using both fully explicit ion representations and treatment of the monovalent ions using the reference interaction site model (RISM) (Denesyuk and Thirumalai 2013;Denesyuk and Thirumalai 2015;Denesyuk et al 2018;Hori et al 2019;Nguyen et al 2019).…”

“…The reaction coordinate (RC) was defined as the distance between centers of masses of two parts of the Twister ribozyme ( Figure S1) such that with increasing distance the major tertiary interactions would be broken motivated by experimental studies on Twister (Panja et al 2017). This yielded free energy profiles for different MgCl2 concentrations from the native states though partially unfolded states that lacked tertiary structure but maintained the secondary structural features; recent RNA folding studies have similarly shown secondary, helical structures to form prior to the formation of tertiary structures (Nguyen et al 2019).…”