Impact of geometry optimization on base-base stacking interaction energies in the canonical A- and B-forms of DNA

Abstract

Base stacking is known to make an important contribution to the stability of DNA and RNA, and accordingly, significant efforts are ongoing to calculate stacking energies using ab initio quantum mechanical methods. To date, impressive improvements have been made in the model chemistries used to perform stacking energy calculations, including extensions that include robust treatments of electron correlation with extended basis sets, as required to treat interactions where dispersion makes a significant contribution. However, those efforts typically use rigid monomer geometries when calculating the interaction energies. To overcome this, in the present work, we describe a novel internal coordinate definition that allows the relative, intermolecular orientation of stacked base monomers to be constrained during geometry optimizations while allowing full optimization of the intramolecular degrees of freedom. Use of the novel reference frame to calculate the impact of full geometry optimization versus constraining the bases to be planar on base monomer stacking energies, combined with density-fitted, spin-component scaling MP2 treatment of electron correlation, shows that full optimization makes the average stacking energy more favorable by -3.4 and -1.5 kcal/mol for the canonical A and B conformations of the 16 5' to 3' base stacked monomers. Thus, treatment of geometry optimization impacts the stacking energies to an extent similar to or greater than the impact of current state of the art increases in the rigor of the model chemistry itself used to treat base stacking. Results also indicate that stacking favors the B-form of DNA, though the average difference versus the A-form decreases from -2.6 to -0.6 kcal/mol when the intramolecular geometry is allowed to fully relax. However, stacking involving cytosine is shown to favor the A-form of DNA, with that contribution generally larger in the fully optimized bases. The present results show the importance of allowing geometry optimization, as well as properly treating the appropriate model chemistry, in studies of nucleic acid base stacking.

Figure 1

Definitions of the vectors and centroid of the A) purine and B) pyrimidine bases used to describe the relative orientation of the stacked bases, including an illustration of stacked monomers. X-axis (red): C4 and N1 for purines or C6 and N3 for pyrimidines; Y-axis (blue): perpendicular axis to the x-axis in the plane of the base; and Z-axis (green): perpendicular vector to the plane of the base originating from the centroid of the reference base. The base centroid is the midpoint connecting C4 and N1 for purines or C6 and N3 for pyrimdines. Based on these definitions, rise_sm corresponds to the length of the green vector, both slide_sm and shift_sm are zero, the twist_sm angle is approximately −30° and both the tilt_sm and the roll_sm are 0°.

Figure 2

DF-SCS-MP2/aug-cc-pVTZ interaction energies (kcal/mol) for canonical A-form and B-form base-stacking conformations. The optimized geometry is the MP2/cc-pVDZ optimization of the intramolecular coordinates. The planar geometry restricts the base monomers to planar geometries, but allows other intramolecular coordinates to optimize.

Figure 3

Difference between the stacking energies of the fully optimized and planar (ΔE = IE_opt − IE_planar, kcal/mol) geometries.

Figure 4

Images of the AT stacked base monomers following full optimization (Optimized) and optimization with the planarity (Planar) of the bases constrained while all other intramolecular degrees of freedom of the individual bases were allowed to relax.

Figure 5

Images of the GC stacked base monomers following full optimization (Optimized) and optimization with the planarity (Planar) of the bases constrained while all other intramolecular degrees of freedom of the individual bases were allowed to relax.

Figure 6

Images of the TT stacked base monomers following full optimization (Optimized) and optimization with the planarity (Planar) of the bases constrained while all other intramolecular degrees of freedom of the individual bases were allowed to relax.

Figure 7

Difference in MP2 interaction energies of the B form versus the A form (B-A) for each possible base stacking conformation. Energies in kcal/mol.