Intra-basepair parameters

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:

Buckle: Indicates the amount of Cusp formation.

Buckle (κ) = −2sin^-1(Z_m . Y₁)

Open angle: Indicates the angle between the two bases on the basepair plane.

Open-angle (σ) = −2sin^-1(Z_m . X₁)

Propeller: Indicates the twisting motion of the two bases about the basepair long axis.

Propeller (π) = cos^-1((X₁ x Z_m) . (X₂ x Z_m))

Stagger: Indicates out-of-plane motion of one base with respect to the other.

Stagger (S_x) = −Y_m x M

Shear: Indicates sliding of one base with respect to the other in basepair plane.

Stagger (S_y) = X_m . M

Stretch: Indicates separation of the two bases relating to the hydrogen-bonding distance.

Stagger (S_z) = Z_m . M

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. (X_m,Y_m,Z_m) defines the mean axis system and M is a vector passing through the pivot points of the two bases of a basepair.

References:

Mukherjee, S., Bansal, M. and Bhattacharyya, D. (2006), J Comput Aided Mol Des, 20, 629.
Olson, W.K., Bansal, M., Burley, S.K., Dickerson, R.E., Gerstein, M., Harvey, S.C., Heinmann, U., Lu, X.J., Neidle, S., Shakked, Z., Sklenar, H., Suzuki, M., Tung, C.S., Westhof, E., Wolberger, C. and Berman, H.M. (2001), J Mol Biol, 313, 229.