Algorithms for Comparing Molecule Conformations

David Sehnal

Contents

• Motivation

• Algorithm– Outline– Optimal Translation– Quaternions– Optimal Rotation

• Implementation, Results & Applications

Motivation

• Three different conformations of cyclohexane (C6H12):

Motivation (cont.)

Algorithm Outline

• Given sequences

• And

• Find transformation

• So that is minimized.

Optimal translation

• Superimposes centroids

• By expanding the relation for RSMD we obtain:

Optimal rotation

• Assuming both structures are in centroid coordinates we need to minimize

• Expanding previous sum yields

• Which is minimized when is maximized.

Quaternions

• The quaternions are members of a non-commutative division algebra first invented by William Rowan Hamilton.

• Quaternion is a number with and

• The set of unit quaternions is isomorphic to set of rotation matrices in 3D space.

Optimal rotation (cont.)

The algorithm

Implementation

Results

Results (cont.)

Applications

• The implementation will be used in projects of Bioinformatics department in ANF Data

• Advantages– Source code available – Batch-friendly interface– Speed

Thank you for your attention.