Nearest neighbor rules for RNA helix folding thermodynamics: improved end effects

Abstract

Nearest neighbor parameters for estimating the folding stability of RNA secondary structures are in widespread use. For helices, current parameters penalize terminal AU base pairs relative to terminal GC base pairs. We curated an expanded database of helix stabilities determined by optical melting experiments. Analysis of the updated database shows that terminal penalties depend on the sequence identity of the adjacent penultimate base pair. New nearest neighbor parameters that include this additional sequence dependence accurately predict the measured values of 271 helices in an updated database with a correlation coefficient of 0.982. This refined understanding of helix ends facilitates fitting terms for base pair stacks with GU pairs. Prior parameter sets treated 5'GGUC3' paired to 3'CUGG5' separately from other 5'GU3'/3'UG5' stacks. The improved understanding of helix end stability, however, makes the separate treatment unnecessary. Introduction of the additional terms was tested with three optical melting experiments. The average absolute difference between measured and predicted free energy changes at 37°C for these three duplexes containing terminal adjacent AU and GU pairs improved from 1.38 to 0.27 kcal/mol. This confirms the need for the additional sequence dependence in the model.

Figure 1.

GU pair stacking and hydrogen bonding for three contexts of tandem GU pairs. Three distinct patterns of hydrogen bonding (shown in green) are observed in these three examples of cis Watson–Crick/Watson–Crick pairs by the Leontis and Westhof nomenclature (152). (A) X-ray crystal structure (1.4 Å resolution, R_free = 20.7%) with terminal stacking GU pairs in 5′UGCUCCUAGUACGUAAGGACCGGAGUG, PDB ID# 1MSY (153). Nucleotides in bold in the sequence are shown. The nucleotides with gold carbon atoms are in the forefront and these constitute the terminal base pair, while nucleotides with gray carbon atoms are in the back. The crystal packing has the terminal GU pairs of two molecules stacking on each other. Here, the GU pair, although cis Watson–Crick/Watson–Crick has a single hydrogen bond. (B) NMR structure with internal UG pairs in (5′GAGUGCUC)₂, PDB ID# 1EKA (137). 28 unique NOE measurements define the orientation for these nucleotides. (C) NMR structure with internal GU pairs in (5′GGCGUGCC)₂. PDB ID# 1EKD (137). 26 unique NOE measurements define the orientation for these nucleotides.

Figure 2.

Correlation between predicted and measured ΔG°₃₇ for duplexes with only WCF pairs. ΔG°₃₇ values predicted from updated nearest neighbor parameters for duplexes composed solely of WCF base pairs (Table 1A) are plotted against values determined from optical melting experiments.

Figure 3.

Correlation between predicted and observed ΔG°₃₇ for duplexes with WCF and GU pairs. ΔG°₃₇ values predicted from parameters in Table 1 plotted against values determined from optical melting experiments.

Figure 4.

Example calculations of helical ΔG°₃₇. Panel (A) shows the stability calculation for (5′UGUCGAUA)₂, which is shown in Table 2 to have an experimentally determined ΔG°₃₇ of –6.10 kcal/mol. This sequence is self-complementary and therefore the symmetry penalty is added. Panel (B) shows the stability calculation for 5′UAGGUCAG paired to 5′CUGGUCUA. This demonstrates the difference in treatment for the (GGUC)₂ motif. For both sequences, calculations are provided for the current parameters derived here and the previous parameters (24,25). The total stability is the sum of the stability increments.