High Level Theory
Magnesium plays a special role in folding of large globular RNAs (1, 2). These RNAs are closely associated with magnesium ions, many of which can be visualized by X-ray diffraction. For example, 118 magnesium ions associate with the 23S rRNA in the large ribosomal subunit of Haloarcula marismortui (PDB entry 1JJ2, described in 3, 4). Although magnesium’s most common first-shell ligand is water, the oxyanions of RNA phosphates (i.e., the non-bridging phosphate oxygens) have significant affinity for magnesium. Ninety-eight of the magnesium ions associated with the LSU of H. marismortui contain phosphate oxyanions within their first coordination shells (characterized by Mg2+-OP distances < 2.4 Å). Other RNAs show the same trend. Seventy-one magnesium ions associate with the P4-P6 domain of the tetrahymena Group 1 intron (PDB 1HR2, described in 5, 6). Twenty-six of these contain phosphate oxyanions within their first coordination shell.
Our work here focuses on multidentate chelation of magnesium by RNA, where multiple phosphate oxyanions enter the first coordination shell of a magnesium ion. These complexes are rigid with well-defined geometry because the first coordination shell of magnesium is a well-packed octahedron (7, 8). Tight ligand packing and crowding is a hallmark of magnesium complexes, leading to highly restrained geometry, and strong ligand-ligand interactions. Multidentate chelation of magnesium by RNA is also associated with non-canonical conformation states (1, 4, 9).
The most frequent multidentate chelation mode of magnesium by large RNAs is the coordination of a common cation by oxyanions of two adjacent nucleotides (1, 9) (Figure 1A, also see the supplementary information). One observes these “clamps” of adjacent phosphates on a magnesium ion twenty-five times in the H. marisortui large ribosomal subunit (3), twice in the P4-P6 domain of the tetrahymena Group 1 intron (5, 6), once in a self-splicing group II intron from Oceanobacillus iheyensis (PDB entry 3IGI, described in 10), and once in the L1 ligase (PDB entry 2OIU, described in 11). The folding and function of each of these RNAs is magnesium-dependent. The 10-membered ring systems (Mg2+-O-P-P-O5’-C5’-C4’-C3’-O3’-P-O-P-Mg2+, Figure 1A) that characterize these clamps appear to be elemental units of RNA folding and assembly. Tri- and tetradentate RNA-magnesium complexes nearly always contain at least one of these 10-membered ring systems (1). One magnesium ion is clamped twice, by both the mRNA and the rRNA, in the assembled Thermus thermophilus ribosome (PDB entry 2J01, described in 12).
The forces and energetics of cation association with nucleic acids and other ligands can be characterized by application of high level theory (13-16) using density functional theory methods (17-19). Here we provide a quantum mechanical (QM) description of first shell RNA-magnesium interactions, demonstrating unique features that appear to explain folding of large RNAs. The results here show that magnesium can induce specific conformational and electronic states of RNA that are inaccessible with other biological cations. The stability of complexes is dependent on cation type, position, and coordination, and has significant polarization, charge-transfer and exchange components. One must treat these systems quantum mechanically because continuum theories such as NLPB or GBSA are not applicable when cations are effectively part of the macromolecule (20). In cases where immobilized cations are responsible for specific structural integrity, they must be considered explicitly, not in a continuum framework.
Here we dissect the conformations and energetics of RNA and DNA clamps of magnesium, calcium, or sodium, in an aqueous environment. A magnesium-RNA clamp (Figure 1A) extracted from within the H. marismortui large ribosomal subunit (PDB entry 1JJ2) was used to build a template clamp containing phosphates attached to both the O3’ and O5’ atoms of a ribose. The 5’ and 3’ phosphates were capped with methyl groups in lieu of the remainder of the RNA polymer.
Magnesium, from the time of life’s origins, has been closely associated with some of the central players in biological systems - phosphates and phosphate esters (21). Here we show that magnesium shares a special geometric and energetic relationship with the phosphates of RNA. Adjacent RNA phosphates form clamps selectively with magnesium ions (Figure 1). The ionic radius of Mg2+ is small (0.65 Å), the charge density is high, the coodination geometry is octahedral (the AOCN, Average Observed Coordination Number, is 5.98), the preferred ligands are charged or neutral oxygens, and the hydration enthalpy is large (-458 kcal/mol) (7, 8, 22, 23). In comparison with group I ions, calcium, or polyamines, magnesium has a much greater affinity for phosphate oxygens, and binds to them with well-defined geometry. Unlike other cations, magnesium can bring phosphate oxygens in its first shell into close proximity.
Here we demonstrate that neither sodium nor calcium can replicate the structures or energetics of RNA-magnesium clamps. RNA forms more stable clamps with magnesium than with calcium or sodium. Clamps with sodium in particular are unstable, and spontaneously open. Magnesium is closer than the other cations to oxyanion ligands, and so magnesium clamps are stabilized not only by electrostatic interactions but also by charge transfer and polarization. Those interactions are quite substantial at short range. These effects are less pronounced for calcium due to its larger size and for sodium due to its smaller charge. The clamps are specific to RNA in that ribose clamps are more stable than deoxyribose clamps. The nature of the extra stability of RNA clamps is twofold: a) a slightly attenuated energetic penalty of the ring closure, and b) elevated electrostatic interactions between the RNA and cations. Thus, we can now explain, at least in part, the origin of the special role of magnesium in folding of large RNAs.
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