![Page 1: Algorithms for Comparing Molecule Conformations David Sehnal](https://reader036.vdocument.in/reader036/viewer/2022062315/5697bf751a28abf838c803ee/html5/thumbnails/1.jpg)
Algorithms for Comparing Molecule Conformations
David Sehnal
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Contents
• Motivation
• Algorithm– Outline– Optimal Translation– Quaternions– Optimal Rotation
• Implementation, Results & Applications
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Motivation
• Three different conformations of cyclohexane (C6H12):
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Motivation (cont.)
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Algorithm Outline
• Given sequences
• And
• Find transformation
• So that is minimized.
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Optimal translation
• Superimposes centroids
• By expanding the relation for RSMD we obtain:
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Optimal rotation
• Assuming both structures are in centroid coordinates we need to minimize
• Expanding previous sum yields
• Which is minimized when is maximized.
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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.
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Optimal rotation (cont.)
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The algorithm
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Implementation
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Results
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Results (cont.)
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Applications
• The implementation will be used in projects of Bioinformatics department in ANF Data
• Advantages– Source code available – Batch-friendly interface– Speed
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Thank you for your attention.