From: The difficulty of protein structure alignment under the RMSD
Input: | sequences P = (p_{1},…,p_{ n }), Q = (q_{1},…,q_{ m }) and $\ell \in \mathbb{I}$. |
Without loss of generality assume m ≥ n. | |
Output: | (i) subsets P^{′} ⊆ P, Q^{′} ⊆ Q, |P^{′}| = |Q^{′}|, and |
(ii) mapping f:P^{ ′ }↦Q^{′}, fulfilling the following conditions: | |
(A) |P^{′}| = ℓ, | |
(B) d = RMSD(P^{′},f(p^{′})) is minimized. | |
1. | For each translation t ∈ {I/ℓ| - ℓ c_{ max } ≤ I ≤ ℓ c_{ max }}^{3}, |
For each 3 × 3 matrix M, where ∀e ∈ M, e ∈ {I/ℓ^{2}|-, | |
$\phantom{\rule{2em}{0ex}}\{4{\ell}^{3}{c}_{\mathit{\text{max}}}^{2}\le I\le 4{\ell}^{3}{c}_{\mathit{\text{max}}}^{2}\}$ | |
Compute rotation matrix R from M. | |
$Q\leftarrow \mathit{RQ}-t$. | |
Apply an algorithm for the case where the superposition | |
is known to P and $Q$ (as discussed in the ‘Complexity Of | |
The LCP And MAD When The Optimal Superposition Is | |
Known’ section), and denote the solution MAD(P, $Q$). | |
2. | Output the MAD(P, $Q$) of the smallest RMSD as the solution. |