**Examples for using MPSA**

MPSA can iteratively refine an initial 3D model generated from 2D images with random orientations into a converged 3D model. The key for this refinement procedure is the orientation and center determination (2D alignment) of the 2D images using common line method. After 2D alignment, we synthesize a 3D density model from the inverse Fourier transform of a 3D Fourier volume filled with 2D FFT slices of the 2D images according to the central section theorem. The most important parameter of the 2D alignment is the data range in Fourier space (resolution range) that will be used for calculating correlation (phase residual) of the common lines between a raw image and 2D references. In general, the upper range should not go beyond the data point where incorrect FFT starts to occur (i.e. the point corresponding to the model's resolution). At the beginning, the 2D references generated from previous (or initial) 3D model do not contain much high-resolution information, so only the low-resolution information will be used for 2D alignment. After the 3D model converged, the data range for 2D alignment can be increased accordingly. The following examples illustrate what resolution range of 2D image data we used for 2D orientation and center alignment, and what resolution of 3D model we can obtain. |