3D Shape Reconstruction of Loop Objects in X-Ray Protein Crystallography

Knowledge of the shape of crystals can benefit data collection in X-ray crystallography. A preliminary step is the determination of the loop object, i.e., the shape of the loop holding the crystal. Based on the standard set-up of experimental X-ray stations for protein crystallography, the paper reviews a reconstruction method merely requiring 2D object contours and presents a dedicated novel algorithm. Properties of the object surface (e.g., texture) and depth information do not have to be considered. The complexity of the reconstruction task is significantly reduced by slicing the 3D object into parallel 2D cross-sections. The shape of each cross-section is determined using support lines forming polygons. The slicing technique allows the reconstruction of concave surfaces perpendicular to the direction of projection. In spite of the low computational complexity, the reconstruction method is resilient to noisy object projections caused by imperfections in the image-processing system extracting the contours. The algorithm developed here has been successfully applied to the reconstruction of shapes of loop objects in X-ray crystallography.