Constant pH Molecular Dynamics Simulations of Nucleic Acids in Explicit Solvent

Abstract

The nucleosides of adenine and cytosine have pKa values of 3.50 and 4.08, respectively, and are assumed to be unprotonated under physiological conditions. However, evidence from recent NMR and X-Ray crystallography studies has revealed the prevalence of protonated adenine and cytosine in RNA macromolecules. Such nucleotides with elevated pKa values may play a role in stabilizing RNA structure and participate in the mechanism of ribozyme catalysis. With the work presented here, we establish the framework and demonstrate the first constant pH MD simulations (CPHMD) for nucleic acids in explicit solvent in which the protonation state is coupled to the dynamical evolution of the RNA system via λ-dynamics. We adopt the new functional form λ(Nexp) for λ that was recently developed for Multi-Site λ-Dynamics (MSλD) and demonstrate good sampling characteristics in which rapid and frequent transitions between the protonated and unprotonated states at pH = pKa are achieved. Our calculated pKa values of simple nucleotides are in a good agreement with experimentally measured values, with a mean absolute error of 0.24 pKa units. This work demonstrates that CPHMD can be used as a powerful tool to investigate pH-dependent biological properties of RNA macromolecules.

Figure 1

Protonation site of (a) adenosine and (b) cytidine and their respective pKa values.

Figure 2

Transitions between the protonated and unprotonated state of adenosine in λ phase space at pH = pKa for a 1 ns trajectory with varying k_bias values of (a) 20, (b) 30 and (c) 40.

Figure 3

Effect of increasing k_bias on the transition rate and fraction physical ligand (FPL) for (a) adenosine and (b) cytosine. Sampling characteristics were obtained from 5 independent MD runs of 1 ns each.

Figure 4

RDF of water molecules for (a) N1(ADE)-O(TIP3P) distances and (b) N1(ADE)-H(TIP3P) distances within a sphere of 10 Å from the N1 atom of adenosine in both protonated and unprotonated states.

Figure 5

Unsigned deviation for the free energy of deprotonation of adenosine as a function of (a) total simulation time from all N trajectories and (b) individual simulation time of each of the N trajectories.

Figure 6

Sample titration curves for model nucleoside compounds, (a) adenosine and (b) cytidine.

Figure 7

(a) Titration curves for CYT-ADE and (b) time series of distance between N3 CYT and N1 ADE atoms at pH 3 for all 3 sets of pKa calculation.