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Rapid communication reply to comment on: “Fast determination of the optimal rotational matrix for macromolecular superpositions”
Author(s) -
Liu Pu,
Agrafiotis Dimitris K.,
Theobald Douglas L.
Publication year - 2010
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21606
Subject(s) - matrix (chemical analysis) , macromolecule , mathematics , computer science , statistical physics , physics , chemistry , chromatography , biochemistry
The rotational matrix that optimally superpositions two molecular structures can be obtained by solving a symmetric 4 3 4 matrix constructed from the structural coordinates. This is traditionally accomplished by a computationally expensive inversion or decomposition of this matrix. In our recent communication, a simple and robust algorithm was proposed to rapidly determine the optimal rotation by using instead a Newton-Raphson quaternion-based method and an adjoint matrix. After determination of the 4 3 4 matrix, our method is more than an order of magnitude more efficient than traditional inversion/decomposition methods. Kneller correctly points out that, for relatively large molecular systems, the time to construct the 4 3 4 matrix can outweigh the diagonalization of this matrix. In particular, he determined that the crossover point is about 100 atoms (e.g., 112 atoms from Kneller’s empirical equation 7). The time in constructing the matrix scales linearly with the system size, while the time for solving this matrix is constant. Thus, the former will unavoidably dominate the latter when the system is large. Our method is nevertheless useful in many, perhaps most, common applications. First, structural biologists conventionally superposition proteins using only the alpha carbons (one per residue), which significantly reduces the number of atoms in the computation by roughly an order of magnitude. Furthermore, many practical superposition analyses use only a single domain, an important factor as a large fraction of domains are less than 100 residues (see Fig. 1). In fact, from Kneller’s equation 7, our algorithm nearly halves the time to calculate the rotational matrix for proteins with 150 atoms. Second, as mentioned in the first paragraph of our original article, many high-throughput Figure 1. Frequency distribution as a function of the number of residues for all protein domains with less than 40% identity in SCOP domain database (as of May 15, 2010). The unique mode of the distribution is roughly 83 residues. The majority of domains are less than 150 residues. Correspondence to: P. Liu; e-mail: pliu24@its.jnj.com