On the multiple simultaneous superposition of molecular structures by rigid body transformations

Area of Science:

• Structural biology
• Computational chemistry
• Bioinformatics

Background:

• Superimposing multiple 3D coordinate sets is crucial for structural biology and comparative analysis.
• Existing methods may struggle with large datasets, initial orientations, or detecting enantiomorphism.

Purpose of the Study:

• To develop an optimized method for superimposing 'n' coordinate sets using rigid body transformations.
• To minimize the sum of pairwise residuals for accurate structural alignment.
• To address challenges like enantiomorphism and multiple minima in structural superposition.

Main Methods:

• Rigid body transformations are applied to 'n' coordinate sets.
• Minimization of the sum of all pairwise residuals is performed.
• The workload scales linearly with 'n' and is independent of structure size and initial orientation.

Main Results:

• The method achieves efficient superposition with approximately linear workload scaling.
• Enantiomorphism is detected, with options to adjust chirality.
• Successfully identified four distinct minima in a case with multiple minima.

Conclusions:

• The presented method offers an efficient and robust solution for optimal superposition of multiple 3D coordinate sets.
• It provides a rational approach to handling enantiomorphism and multiple minima in structural alignment.
• The method's source code is available for studying domain disposition in multidomain structures.