A trajectory-based algorithm to determine and refine Euler angles of projections in three-dimensional microscopy. Improvements and tests

An improvement of the trajectory matching algorithm is presented, which is based on the use of the derivative of trajectories and of the projection of experimental sinogram lines in the factor space determined by sinogram lines of projections of a model. The algorithm performance is illustrated by use of different phantom structures, to show the effect of symmetry on trajectory matching. A GroEL complex has also been reconstructed from both cryo-negatively stained and unstained frozen-hydrated samples. The refinement of this structure has been carried out by the trajectory matching algorithm as well as by conventional cross-correlation methods. Slight differences among the two results are discussed. The improved trajectory matching algorithm, based on χ2 distances, runs much faster than correlation analysis and looks satisfactory as for the quality of the reconstructed structures.