How to compute RMSD and RMSF#

Goal#

Measure structural deviation across frames (RMSD) or per-atom positional fluctuation over a trajectory (RMSF).

Minimal example#

from moleculekit.molecule import Molecule
from moleculekit.util import molRMSD

mol = Molecule("3PTB")
ref = mol.copy()

# Select Cα indices for both molecule and reference
ca_idx = mol.atomselect("protein and name CA", indexes=True)

# RMSD of all frames against the reference (returns one value per frame)
rmsd = molRMSD(mol, ref, ca_idx, ca_idx)
print(rmsd)

Parameters that matter#

Parameter

Type

What it does

mol

Molecule

Trajectory to analyse

refmol

Molecule

Reference structure

rmsdsel1

integer np.ndarray

Atom indices in mol

rmsdsel2

integer np.ndarray

Matching atom indices in refmol

Common variations#

import numpy as np
# RMSF per Cα atom over a trajectory
from moleculekit.projections.metricfluctuation import MetricFluctuation

# .project returns squared per-atom displacement (shape (n_frames, n_CA),
# units Ų). RMSF = sqrt(mean over frames of the squared displacement).
sq_disp = MetricFluctuation("protein and name CA").project(mol)
rmsf = np.sqrt(sq_disp.mean(axis=0))   # shape (n_CA,), units Å

# Align before computing RMSD to separate rotation from internal motion
mol.align("protein and name CA", refmol=ref)
rmsd_aligned = molRMSD(mol, ref, ca_idx, ca_idx)

Gotchas#

  • molRMSD() computes raw (non-mass-weighted) RMSD; align the structures first if you want to remove rigid-body motion.

  • RMSF is per-atom and depends on the choice of reference (mean structure); the result is sensitive to conformational heterogeneity.

  • Both mol and refmol must have the same number of selected atoms.

  • MetricFluctuation returns squared per-atom displacement ((n_frames, n_atoms), units Ų) — as its own docstring states (“to get the RMSD you need to compute the square root of the mean of the results this projection returns”). For RMSF take np.sqrt(sq_disp.mean(axis=0)); sq_disp.mean(axis=0) alone is mean-squared-fluctuation, not RMSF.

See also#