Analyzing DNA Structures¶

MDNA provides tools for computing rigid base parameters, linking numbers, and groove widths from DNA structures and MD trajectories.

Loading a Trajectory¶

import mdna

# From files
dna = mdna.load(filename='trajectory.xtc', top='topology.pdb')

# Or from an existing MDTraj trajectory
import mdtraj as md
traj = md.load('trajectory.xtc', top='topology.pdb')
dna = mdna.load(traj=traj, chainids=[0, 1])

dna.describe()

Rigid Base Parameters¶

The rigid base formalism describes DNA geometry through 12 parameters split into two groups:

Base Pair Parameters (intra-base pair)¶

Describe the relative position/orientation of two bases within a pair:

Parameter	Type	Unit
Shear	Translation	nm
Stretch	Translation	nm
Stagger	Translation	nm
Buckle	Rotation	degrees
Propeller	Rotation	degrees
Opening	Rotation	degrees

Base Pair Step Parameters (inter-base pair)¶

Describe the relative position/orientation between consecutive base pair steps:

Parameter	Type	Unit
Shift	Translation	nm
Slide	Translation	nm
Rise	Translation	nm
Tilt	Rotation	degrees
Roll	Rotation	degrees
Twist	Rotation	degrees

Computing Parameters¶

# Get all 12 parameters
params, names = dna.get_parameters()
print(names)   # List of parameter names
print(params.shape)  # (n_frames, n_bp, 12)

# Get only step parameters
step_params, step_names = dna.get_parameters(step=True)

# Get only base pair parameters
bp_params, bp_names = dna.get_parameters(base=True)

# Get a single parameter by name
twist = dna.get_parameter('twist')
roll = dna.get_parameter('roll')

Plotting Parameters¶

The NucleicFrames object provides built-in plotting:

rigid = dna.get_rigid_object()
rigid.plot_parameters()

Custom Visualization¶

import matplotlib.pyplot as plt

params, names = dna.get_parameters(step=True)

fig, axes = plt.subplots(2, 3, figsize=(12, 6))
for i, (ax, name) in enumerate(zip(axes.flat, names)):
    data = params[:, :, i]
    ax.plot(data.mean(axis=0))
    ax.fill_between(
        range(data.shape[1]),
        data.mean(axis=0) - data.std(axis=0),
        data.mean(axis=0) + data.std(axis=0),
        alpha=0.3
    )
    ax.set_title(name)
plt.tight_layout()

Rigid Base Parameters from a Trajectory¶

For standalone analysis without creating a Nucleic object:

import mdtraj as md

traj = md.load('dna.pdb')
rigid = mdna.compute_rigid_parameters(traj, chainids=[0, 1])

This returns a NucleicFrames object with the same interface as dna.get_rigid_object().

Base Reference Frames¶

Access the individual base reference frames (useful for custom geometry analysis):

base_frames = dna.get_base_frames()
# Returns dict: {residue_topology: frames (n_frames, 4, 3)}

The frame rows are: origin, \(\hat{b}_L\) (long axis), \(\hat{b}_D\) (short axis), \(\hat{b}_N\) (normal).

Linking Number¶

For circular DNA, compute the linking number and its decomposition into writhe and twist:

dna = mdna.make(n_bp=200, circular=True, dLk=2)
Lk, Wr, Tw = dna.get_linking_number()
print(f'Lk = {Lk:.2f}, Wr = {Wr:.2f}, Tw = {Tw:.2f}')

The linking number is computed using Gauss's linking integral via the PyLk library.

Groove Width Analysis¶

The GrooveAnalysis class computes major and minor groove widths by fitting cubic splines through phosphorus atom positions:

import mdtraj as md

traj = md.load('dna_trajectory.xtc', top='dna.pdb')
grooves = mdna.GrooveAnalysis(traj)

# Plot groove widths
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=(6, 3))
grooves.plot_groove_widths(ax=ax)

Torsion Angle Analysis¶

The TorsionAnalysis class computes backbone torsion angles:

torsions = mdna.TorsionAnalysis(traj)

Summary¶

Analysis	Function / Method	Returns
All rigid base parameters	`nucleic.get_parameters()`	`(params, names)`
Single parameter	`nucleic.get_parameter('twist')`	`np.ndarray`
NucleicFrames object	`nucleic.get_rigid_object()`	`NucleicFrames`
Standalone rigid params	`mdna.compute_rigid_parameters(traj)`	`NucleicFrames`
Base frames	`nucleic.get_base_frames()`	`dict`
Linking number	`nucleic.get_linking_number()`	`[Lk, Wr, Tw]`
Groove widths	`mdna.GrooveAnalysis(traj)`	`GrooveAnalysis`
Torsion angles	`mdna.TorsionAnalysis(traj)`	`TorsionAnalysis`