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1. What is the mean base-pair plane?It is just the average of the two related normal vectors. See the file tech_details.pdf distributed with 3DNA for details.
2. How to project the “exocyclic atoms”?In the same way as base ring atoms. Take a look at the file stacking.pdb after running 'analyze' on a DNA structure, e.g., 355d. In the file, simply ignore the z-coordinate of the base rings atoms, or the extended layer including exocyclic atoms, you get the 'projection' of the atoms onto the mean base pair plane. Again, see tech_details.pdf for details.
The middle frame used in calculating base pair step parameters (Slide, Roll, etc.) is used in 3DNA to reset each dinucleotide in a ‘standard’ orientation (34), which can be transformed into a high quality ‘standardized’ base stacking diagram (Fig. 6). Such diagrams allow for visual inspection of the stacking and hydrogen bonding interactions at the dimer level. A similar image in Figure 3 reveals the twist angle discrepancy in shear‐deformed (base‐mismatched) dinucleotide steps. The stacking interactions are quantified in 3DNA by the shared overlap area, in Å2, of closely associated base rings, i.e. the nine‐membered ring of a purine R (A or G) and the six‐membered ring of a pyrimidine Y (C, T or U), projected in the mean base pair plane. For example, the overlap areas between base rings on the left strands of the dimer steps shown in Figure 6 are 0.63 Å2 (C3···G2), 0 Å2 (G4···C3) and 1.11 Å2 (A5···G4). To account for the stacking interactions (overlap areas) of exocyclic atoms over base rings, e.g. the overlap of the amino N4 atom of residue C3 with the five‐membered pyrrole ring of base G2 in Figure 6, an extended polygon, which includes exocyclic atoms, is used. For cytosine, the extended polygon is defined by the C1′‐O2‐N3‐N4‐C5‐C6‐C1′ atomic sequence. The overlap areas of the bases on the left strand of Figure 6 increase, respectively, to 2.95, 2.66 and 3.94 Å2 when these and other exocyclic atoms are included in the calculations. The sum of the intra‐ and interstrand stacking overlaps is provided for each dinucleotide step in the 3DNA output.
3. As you mentioned “not too far away”, is there a threshold for stacking determination in your algorithm? And what is it?The distance cutoff is 4.5 Å. If the shortest distance of any two-pair between the two sets of atoms is larger than the cutoff, then the stacking area is set to 0.
4. How do you think the relation between stacking areas and stacking energy? Do you know any software out there for direct stacking energy estimations?Note that 3DNA is an analysis tool, based purely on geometry, and it does not perform any energy calculations. The overlap area as calculated from 3DNA is an intuitive measure of base stacking interactions, and can be 'seen' from the standard stacking diagram. See the above quotation from the original 3DNA paper, and Figure 6 (http://nar.oxfordjournals.org/content/31/17/5108/F6.expansion.html).
Created and maintained by Dr. Xiang-Jun Lu [律祥俊], Principal Investigator of the NIH grant R01GM096889
Dr. Lu is currently affiliated with the Bussemaker Laboratory at the Department of Biological Sciences, Columbia University.