Calculation of Ion-Dependent RNA Folding Free Energy using Coarse-Grained Simulation

Abstract

Magnesium ions (Mg2+) are fundamentally important in RNA biology, playing indispensable roles in RNA structure, folding and function. In order to develop a model that treats monovalent ions implicitly while retaining explicit divalent cations we developed a theory based on liquid state integral equation theory that captures both inner shell and outer shell bindings of Mg to phosphate groups. Coupling this approach with our thermodynamically consistent RNA model reproduces Mg2+-RNA free energies for several RNA molecules, ranging from a small pseudoknot to the aptamer domain of adenine riboswitch. The model not only works for the RNA folded state, but also can be used to give accurate Mg2+-RNA thermodynamics for intermediate and unfolded states. In addition, we provide here one of the first attempts to elucidate the full three dimensional distribution of Mg2+ ions around RNA. Comparing Mg2+ with Ca2+ , it is revealed that magnesium binds using inner shell and outer shell equally well while calcium prefers to bind directly with phosphate groups due to the ease of dehydration of the lower charge density cation. Our model provides a comprehensive treatment of Mg2+-RNA interaction in terms of both energetic and structural features, allowing us to study ion-dependent RNA folding.