GPU implementation of reverse coordinate conversion for proteins

We describe the first parallel algorithm to obtain Cartesian coordinates of a molecular structure from internal coordinates. This algorithm is important for problems such as protein engineering and fitting protein structures to experimental data. Proteins contain thousands to millions of atoms. Their positions can be represented using one of two methods: Cartesian or internal coordinates (bond lengths, angles, etc.). In molecular dynamics and modeling of proteins in different conformational states, it is often necessary to transform one coordinate system to another. In addition, since protein structures change over time, any computation must be done over successive time frames, increasing the computational load. To lessen this computational load we have applied different parallel techniques to the coordinate conversion problem. Converting Cartesian coordinates to internal ones is easily parallelized, and we have previously reported a GPU implementation. On the other hand, the reverse computation has inherent linear dependency because bond lengths and angles are relative to neighboring atoms. Existing implementations walk over a protein structure in a sequential fashion. This paper presents the first parallel implementation of internal to Cartesian coordinates, in which substructures of the protein backbone are converted into their own local Cartesian coordinate spaces, and then combined using a reduction technique to find global Cartesian coordinates. We observe one order of magnitude speedup using parallel processing on a GPU.