High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.

RCD+: Fast loop modeling server

Modeling loops is a critical and challenging step in protein modeling and prediction. We have developed a quick online service (http://rcd.chaconlab.org) for ab initio loop modeling combining a coarse-grained conformational search with a full-atom refinement. Our original Random Coordinate Descent (RCD) loop closure algorithm has been greatly improved to enrich the sampling distribution towards near-native conformations. These improvements include a new workflow optimization, MPI-parallelization and fast backbone angle sampling based on neighbor-dependent Ramachandran probability distributions. The server starts by efficiently searching the vast conformational space from only the loop sequence information and the environment atomic coordinates. The generated closed loop models are subsequently ranked using a fast distance-orientation dependent energy filter. Top ranked loops are refined with the Rosetta energy function to obtain accurate all-atom predictions that can be interactively inspected in an user-friendly web interface. Using standard benchmarks, the average root mean squared deviation (RMSD) is 0.8 and 1.4 Å for 8 and 12 residues loops, respectively, in the challenging modeling scenario in where the side chains of the loop environment are fully remodeled. These results are not only very competitive compared to those obtained with public state of the art methods, but also they are obtained ∼10-fold faster.

Random Coordinate Descent with Spinor-matrices and Geometric Filters for Efficient Loop Closure

Protein loop closure constitutes a critical step in loop and protein modeling whereby geometrically feasible loops must be found between two given anchor residues. Here, a new analytic/iterative algorithm denoted random coordinate descent (RCD) to perform protein loop closure is described. The algorithm solves loop closure through minimization as in cyclic coordinate descent but selects bonds for optimization randomly, updates loop conformations by spinor-matrices, performs loop closure in both chain directions, and uses a set of geometric filters to yield efficient conformational sampling. Geometric filters allow one to detect clashes and constrain dihedral angles on the fly. The RCD algorithm is at least comparable to state of the art loop closure algorithms due to an excellent balance between efficiency and intrinsic sampling capability. Furthermore, its efficiency allows one to improve conformational sampling by increasing the sampling number without much penalty. Overall, RCD turns out to be accurate, fast, robust, and applicable over a wide range of loop lengths. Because of the versatility of RCD, it is a solid alternative for integration with current loop modeling strategies.