Amplitude spectrum distance: measuring the global shape divergence of protein fragments

In structural bioinformatics, there is an increasing interest in identifying and understanding the evolution of local protein structures regarded as key structural or functional protein building blocks. A central need is then to compare these, possibly short, fragments by measuring efficiently and accurately their (dis)similarity. Progress towards this goal has given rise to scores enabling to assess the strong similarity of fragments. Yet, there is still a lack of more progressive scores, with meaningful intermediate values, for the comparison, retrieval or clustering of distantly related fragments.

We introduce here the Amplitude Spectrum Distance (ASD), a novel way of comparing protein fragments based on the discrete Fourier transform of their C(α) distance matrix. Defined as the distance between their amplitude spectra, ASD can be computed efficiently and provides a parameter-free measure of the global shape dissimilarity of two fragments. ASD inherits from nice theoretical properties, making it tolerant to shifts, insertions, deletions, circular permutations or sequence reversals while satisfying the triangle inequality. The practical interest of ASD with respect to RMSD, RMSDd, BC and TM scores is illustrated through zinc finger retrieval experiments and concrete structure examples. The benefits of ASD are also illustrated by two additional clustering experiments: domain linkers fragments and complementarity-determining regions of antibodies.

Taking advantage of the Fourier transform to compare fragments at a global shape level, ASD is an objective and progressive measure taking into account the whole fragments. Its practical computation time and its properties make ASD particularly relevant for applications requiring meaningful measures on distantly related protein fragments, such as similar fragments retrieval asking for high recalls as shown in the experiments, or for any application taking also advantage of triangle inequality, such as fragments clustering. ASD program and source code are freely available at: http://www.irisa.fr/dyliss/public/ASD/.