Predicting ion-nucleic acid interactions by energy landscape-guided sampling

Abstract

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Figure 1

The computer time as a function of the sequence length for an RNA duplex in 0.02M NaCl and 0.005M MgCl₂ mixed solution. The original TBI: square; the previously improved TBI: triangle; the current new TBI model: circle.

Figure 2

The distribution of the number of modes (NOM) Ω(N_b, ΔG_M) for the BWYV pseudoknot in the different [Mg²⁺] ion solutions with a fixed 0.054 [Na⁺] background. The numbers (8, 10 · · ·) in the figure denote the N_b values. Not all the N_b results are shown in the figure.

Figure 3

(a) The reduced (1D) electrostatic energy landscape ΔG(N_b) for the BWYV pseudoknot in the different ion solutions with the fixed [Na⁺]=0.054M and varying [Mg²⁺] (in M) (labeled on the curves). (b)The partition functions as a function of N_b for the different solutions. The filled squares and the labels denote the locations of the free energy minima and the corresponding $N_b^{\ast }$.

Figure 4

The electrostatic free energy ΔG (upper panels) and the Mg²⁺ and Na⁺ (or K⁺) binding fractions per nucleotide (lower panel) for various RNA tertiary structures: (a) BWYV pseudoknot fragment, (b) 58-nt rRNA fragment, (c) Yeast tRNA^Phe. (d) 40-bp RNA duplex. The corresponding experimental data are from Refs.^,– respectively. In the lower panels, the black symbols are the experimental data and solid lines are the predicted results.