# MCQ and LCS-TA

MCQ (Mean of Circular Quantities) has been first presented in the paper “MCQ4Structures to compute similarity of molecule structures” by Zok et al. (Central European Journal of Operations Research, 2014;22(3):457-474. doi: 10.1007/s10100-013-0296-5).

LCS-TA (Longest Continuous Segments in Torsion Angle space) applies a measure first described in the paper “LCS-TA to identify similar fragments in RNA 3D structures” by Wiedemann et al. (BMC Bioinformatics, 2017;18(1):456. doi: 10.1186/s12859-017-1867-6). A full implementation of both methods can be found on github, maintained by Zok and Wiedemann.

Most important features of both methods / measures:

MCQ

- The method applies to a pair of 3D structures and is size independent.
- It can be used for a set of structures in all-against-all or all-against-target mode.
- It translates typical algebraic representation of a 3D structure into the trigonometric one (a set of torsion angles).
- It computes the distance between structures in torsion angle space.
- The distance is measured as mean of local distances between the corresponding angles, and provided in degrees.
- The measure is sequence independent.

LCS-TA

- The method applies to a pair of 3D structures and is size independent.
- It uses MCQ-based measure for structure comparison.
- Within the compared structures, it finds the longest continuous segments which display similarity in torsion angle space.
- Two segments are considered similar if their MCQ is below predefined threshold.
- The method provides segment length and its position in the structure.
- The length of the longest continuous segment is a measure of similarity of two structures.
- The method can be run in sequence dependent or sequence independent mode.

MCQ is maintained by Zok, while LCS-TA is maintained by Wiedemann