Rigid Base Parameters¶
This page explains the rigid base formalism used by MDNA for describing DNA geometry.
Overview¶
The rigid base model treats each nucleobase as a rigid body with a well-defined reference frame. DNA geometry is then described by the relative positions and orientations of these frames, yielding 12 parameters per base pair step.
Reference Frames¶
Each base has a local coordinate system (reference frame) defined by the Tsukuba convention:
- Origin (\(\mathbf{b}_R\)): The base reference point, computed from the glycosidic nitrogen and C1' sugar atom
- Long axis (\(\hat{b}_L\)): Points roughly along the base pair hydrogen bonds
- Short axis (\(\hat{b}_D\)): Perpendicular to the long axis, in the base plane
- Normal (\(\hat{b}_N\)): Perpendicular to the base plane (right-hand rule)
The mid-step frame (average of two consecutive base pair frames) serves as the reference for computing step parameters.
Base Pair Parameters¶
These describe the relative geometry of two bases within a Watson-Crick pair:
| Parameter | Description | Axis | Unit |
|---|---|---|---|
| Shear | Lateral displacement | Along \(\hat{b}_L\) | nm |
| Stretch | Separation along H-bond direction | Along \(\hat{b}_D\) | nm |
| Stagger | Vertical offset | Along \(\hat{b}_N\) | nm |
| Buckle | Rotation opening the base pair like a book | Around \(\hat{b}_L\) | degrees |
| Propeller | Rotation of bases in opposite directions | Around \(\hat{b}_D\) | degrees |
| Opening | Rotation that opens the Watson-Crick edge | Around \(\hat{b}_N\) | degrees |
Base Pair Step Parameters¶
These describe the relative geometry between consecutive base pair steps:
| Parameter | Description | Axis | Unit |
|---|---|---|---|
| Shift | Lateral displacement of one step relative to the next | Along \(\hat{b}_L\) | nm |
| Slide | Displacement along the short axis | Along \(\hat{b}_D\) | nm |
| Rise | Vertical separation between steps | Along \(\hat{b}_N\) | nm |
| Tilt | Rotation around the long axis | Around \(\hat{b}_L\) | degrees |
| Roll | Rotation around the short axis (bending) | Around \(\hat{b}_D\) | degrees |
| Twist | Rotation around the helical axis | Around \(\hat{b}_N\) | degrees |
Computation Method¶
MDNA computes these parameters through the following steps:
- Base identification: Extract nucleobase heavy atoms from the MDTraj trajectory
- Frame fitting: Fit each base to a canonical reference frame using the
ReferenceBaseclass - Mid-pair frames: Average the two base frames within each pair
- Euler decomposition: Compute the rotation matrix and displacement between consecutive mid-pair frames
- Parameter extraction: Decompose the rotation into Euler angles (Tilt, Roll, Twist) and project the displacement onto the local axes (Shift, Slide, Rise)
The rotation decomposition uses the RigidBody.extract_omega_values() method, which handles edge cases near \(\pm\pi\) rotation angles.
Typical Values for B-DNA¶
| Parameter | Typical Range |
|---|---|
| Shift | -0.5 to 0.5 nm |
| Slide | -0.5 to 0.5 nm |
| Rise | 0.31 to 0.37 nm |
| Tilt | -10° to 10° |
| Roll | -10° to 10° |
| Twist | 30° to 40° (mean ~36°) |
| Shear | -0.5 to 0.5 nm |
| Stretch | -0.3 to 0.3 nm |
| Stagger | -0.5 to 0.5 nm |
| Buckle | -20° to 20° |
| Propeller | -25° to -5° |
| Opening | -5° to 5° |
References¶
- Olson, W. K., et al. (2001). A standard reference frame for the description of nucleic acid base-pair geometry. J. Mol. Biol., 313(1), 229–237.
- Lu, X. J., & Olson, W. K. (2003). 3DNA: a software package for the analysis, rebuilding and visualization of three-dimensional nucleic acid structures. Nucleic Acids Res., 31(17), 5108–5121.