Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Abstract

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported Tightly Bound Ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, based on Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, Monte Carlo Tightly Bound Ion (MCTBI) model, for ion binding properties around an RNA. Due to an enhanced sampling algorithm for ion distribution, the model leads to significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model, which describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model, together with proper RNA conformational sampling and energetics model, may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acids systems.

MCTBI: a web server for predicting metal ion effects in RNA structures

“…The TB region for a given RNA structure and ionic condition is usually a nonuniform thin layer surrounding the RNA surface. The rigorous demarcation of the TB and the DB regions can be found in previous publications (Tan and Chen 2005;He and Chen 2012;Sun and Chen 2016). In the MCTBI model, the TB ions and DB ions are treated as discrete particles (with the correlation effect) and continuum background (without the correlation effect), respectively.…”

“…Below we briefly summarize the main points of the model. Further details can be found in Sun and Chen (2016).…”

“…2. For a given RNA structure with N p nucleotides, the partition function of the whole system can calculated as the sum over all the ion distributions, which can be classified by the number of the TB ions N b (Sun and Chen 2016):…”

“…ΔG non-tb denotes the free energy for the non-TB ions, including the electrostatic interaction energy between the DB ions, between DB ions and other charged particles, and between the charged atoms in RNA. The details about the free energy calculation can be found in the Supplemental Information (SI) and Sun and Chen (2016) 3. The calculation of the total statistical weight W(N b ) for a given number of the TB ions N b involves the sampling of the TB ion distributions.…”

“…Recently, inspired by the demands for the prediction and analysis of the metal ion effects at the atomic resolution for larger RNAs (>100 nt), we developed a new model, the Monte Carlo tightly bound ion (MCTBI) model (Sun and Chen 2016). The main advantages of this new model are the following (see Fig.…”