Coarse-grained dynamic RNA titration simulations

Abstract

Electrostatic interactions play a pivotal role in many biomolecular processes. The molecular organization and function in biological systems are largely determined by these interactions. Owing to the highly negative charge of RNA, the effect is expected to be more pronounced in this system. Moreover, RNA base pairing is dependent on the charge of the base, giving rise to alternative secondary and tertiary structures. The equilibrium between uncharged and charged bases is regulated by the solution pH, which is therefore a key environmental condition influencing the molecule's structure and behaviour. By means of constant-pH Monte Carlo simulations based on a fast proton titration scheme, coupled with the coarse-grained model HiRE-RNA, molecular dynamic simulations of RNA molecules at constant pH enable us to explore the RNA conformational plasticity at different pH values as well as to compute electrostatic properties as local pK _a values for each nucleotide.

Keywords: RNA; coarse-grained model; pH; titration.

Figure 1.

Structures of neutral and protonated adenine (top) and cytosine (bottom) together with the pK_a values for isolated bases (left). For values of pH less than pK_a, the bases are protonated, while for values above they are in their neutral state. The three most common base pairs formed by these protonated bases are shown on the right (images of pairs from http://www.saha.ac.in/biop/www/db/local/BP/rnabasepair.html [16]). (Online version in colour.)

Figure 2.

Two alternative pairings for bases A and G: the canonical WC base pair between G (red) and A (orange) and the non-canonical base pair between the Hoogsteen edge of G and the protonated WC edge of A⁺ (blue). Two separate sets of variables, indicated here by the coloured dashed lines and arcs, are used in the potential as references for the position of the base pairing energy minimum. For the neutral base A, the orange set is present and the blue set is absent, while for the charged base A⁺ the opposite occurs. (Online version in colour.)

Figure 3.

Base pairing of the three systems extracted from the experimental structures. Solid lines represent canonical pairs, dashed lines represent non-canonical pairs. The green lines for the stem-loop branch-point helix (17RA) highlight that two alternative pairs are proposed by the experiment. (Online version in colour.)

Figure 4.

Comparison of the computed pK_a values from the FPTS_static and CGMD/FPTS with the experimental values. Horizontal error bars correspond to experimental uncertainties, while vertical error bars indicate computational uncertainties. The shaded area shows the values for which the experimental value is only known to be below a certain pK_a. Dashed lines represent linear regressions of the simulation data. The values of the slope of the regression (s) and of the Pearson correlation coefficient (rc) and the p-value of the correlation (pv) are reported for each kind of simulation. For 17RA alone we do not compute the correlation because there are only two points for which experimental values are known precisely. We do, however, include all systems in the overall correlation (bottom right plot). (Online version in colour.)

Figure 5.

Titration curves for the weakly paired adenine A6 of 17RA (left) and for the strongly Watson–Crick paired base A17 (right). The effective pK_a is read off the intersection between the fitting curve and the 〈z〉 = 0.5 axes (dashed line). The spread of the points at 〈z〉 = 0.5 gives the error in our estimates. (Online version in colour.)

Figure 6.

Fraction of folded structures as a function of pH exhibiting the expected sigmoidal behaviour. (Online version in colour.)