Appendix A: $Q$

In MultiSeq, Q has been generalized to measure the fraction of similar contact distances between all the aligned residues in two homologous proteins or RNA molecules. This term computes the fraction of $C^{\alpha}$-$C^{\alpha}$ (or $P$-$P$) pair distances that are the same or similar between two aligned structures. ``Evaluationg protein structure-prediction schemes using energy landscape theory'' by Eastwood, M.P., C. Hardin, Z. Luthey-Schulten, and P.G. Wolynes in IBM J . Res. Dev. 45: 475-497. 2001.

$$Q=\frac{2}{ (N-1)(N-2)} \sum _{i<j-1}\exp \left[ -\frac{\left( r_{ij}-r^{N}_{ij} \right)^{2}}{2\sigma ^{2}_{ij}}\right]$$

$r_{ij}$ is the distance between a pair of $C^{\alpha}$ (or P) atoms.
 
$r_{ij}^N$ is the $C^{\alpha}$-$C^{\alpha}$ distance between residues $i$ and $j$ in the native state of a protein or RNA.
 
$\sigma ^{2}_{ij}=\left\vert i-j\right\vert ^{0.15}$ is the standard deviation, determining the width of the Gaussian function.
 
$N$ is the number of residues of the protein being considered.