According to the IUPAC-IUB convention, the spatial arrangement of one base with respect to each other in a pair can be quantitatively defined with the help of three rotational and three translational intra-basepair parameters - Buckle, Open-angle, Propeller, Stagger, Shear and Stretch [See figure].
Among these six parameters, shear, stretch and open-angle relate directly to the hydrogen bonding pattern and proximity, while buckle, propeller and stagger describe the overall non-planarity of a basepair compared to the ideal coplanar geometry.
Short description of the parameters:
The axis systems (X1,Y1,Z1) and (X2,Y2,Z2) of the bases are determined based on their corresponding hydrogen-boding edges within a specific basepairing pattern. (Xm,Ym,Zm) defines the mean axis system and M is a vector passing through the pivot points of the two bases of a basepair.
Buckle: Indicates the amount of Cusp formation.
Buckle (κ) = −2sin-1(Zm . Y1)
Open angle: Indicates the angle between the two bases on the basepair plane.
Open-angle (σ) = −2sin-1(Zm . X1)
Propeller: Indicates the twisting motion of the two bases about the basepair long axis.
Propeller (π) = cos-1((X1 x Zm) . (X2 x Zm))
Stagger: Indicates out-of-plane motion of one base with respect to the other.
Stagger (Sx) = −Ym x M
Shear: Indicates sliding of one base with respect to the other in basepair plane.
Stagger (Sy) = Xm . M
Stretch: Indicates separation of the two bases relating to the hydrogen-bonding distance.
Stagger (Sz) = Zm . M
- Mukherjee, S., Bansal, M. and Bhattacharyya, D. (2006), J Comput Aided Mol Des, 20, 629.
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