Structural Superposition and Alignment

Structural superposition finds the rigid-body rotation and translation that best overlays one set of atoms onto another by minimizing the root-mean-square deviation. The hard part is rarely the fit itself but the correspondence: deciding which atom in one structure matches which atom in the other. That mapping can come from a sequence alignment or from the 3D geometry directly, and the choice dictates which tool you should reach for.

Superimposer And RMSD

from Bio.PDB import PDBParser, Superimposer

parser = PDBParser(QUIET=True)
ref = parser.get_structure("ref", "1ake.pdb")[0]
mob = parser.get_structure("mob", "4ake.pdb")[0]

# One-to-one correspondence assumed here: matched CA atoms, same order.
ref_atoms = [res["CA"] for res in ref["A"] if "CA" in res]
mob_atoms = [res["CA"] for res in mob["A"] if "CA" in res]
n = min(len(ref_atoms), len(mob_atoms))
ref_atoms, mob_atoms = ref_atoms[:n], mob_atoms[:n]

sup = Superimposer()
sup.set_atoms(ref_atoms, mob_atoms)   # (fixed, moving)
sup.apply(mob.get_atoms())            # mutates moving coordinates in place

rot, tran = sup.rotran                # moving @ rot + tran = fitted
print(f"RMSD = {sup.rms:.3f} A over {n} CA atoms")
print("rotation:\n", rot)
print("translation:", tran)

RMSD = 7.117 A over 214 CA atoms
rotation:
 [[ 0.9962 -0.0808  0.0335]
 [ 0.0790  0.9954  0.0521]
 [-0.0376 -0.0492  0.9981]]
translation: [ 3.214 -1.087  0.556]

TM-align And TM-score

Sequence-based correspondence aligns residues by identity and then superposes the matched atoms, which degrades once identity drops. Structure-based correspondence derives the matching from 3D geometry, so it still works for remote homologs with negligible sequence similarity. TM-align builds such a structure-based alignment directly from geometry, independent of sequence identity (though still sequential, preserving N-to-C residue order), and reports a TM-score normalized by the reference chain length, bounded in (0, 1], where values above 0.5 imply the same fold and below 0.17 indicate no more than random structural similarity.

TMalign 4ake.pdb 1ake.pdb

 **************************************************************************
 * TM-align (Version 20190822): protein structure alignment              *
 **************************************************************************

Name of Chain_1: 4ake.pdb (to be superimposed onto Chain_2)
Name of Chain_2: 1ake.pdb
Length of Chain_1: 214 residues
Length of Chain_2: 214 residues

Aligned length= 196, RMSD=   2.98, Seq_ID=n_identical/n_aligned= 1.000
TM-score= 0.86028 (if normalized by length of Chain_1, i.e., LN=214, d0=5.44)
TM-score= 0.86028 (if normalized by length of Chain_2, i.e., LN=214, d0=5.44)

PyMOL Superposition Commands

from pymol import cmd

cmd.load("1ake.pdb", "ref")
cmd.load("4ake.pdb", "mob")

# align: sequence alignment + iterative outlier rejection. Best when identity is high (>~30%).
r_align = cmd.align("mob", "ref")      # (mobile, target)

# super: sequence-independent, structure-based superposition. Better for low identity.
r_super = cmd.super("mob", "ref")      # (mobile, target)

# cealign: Combinatorial Extension. Best for remote homologs / negligible identity.
r_ce = cmd.cealign("ref", "mob")       # (target, mobile) -> dict

print("align   RMSD =", round(r_align[0], 3), "over", r_align[1], "atoms")
print("super   RMSD =", round(r_super[0], 3), "over", r_super[1], "atoms")
print("cealign RMSD =", round(r_ce["RMSD"], 3), "over", r_ce["alignment_length"], "residues")