A tilt-pair based method for assigning the projection directions of randomly oriented single-particle molecules.

In this article, we describe an improved method to assign the projection angle for averaged images using tilt-pair images for three-dimensional reconstructions from randomly oriented single-particle molecular images. Our study addressed the so-called 'initial volume problem' in the single-particle reconstruction, which involves estimation of projection angles of the particle images. The projected images of the particles in different tilt observations were mixed and averaged for the characteristic views. After the ranking of these group average images in terms of reliable tilt angle information, mutual tilt angles between images are assigned from the constituent tilt-pair information. Then, multiples of the conical tilt series are made and merged to construct a network graph of the particle images in terms of projection angles, which are optimized for the three-dimensional reconstruction. We developed the method with images of a synthetic object and applied it to a single-particle image data set of the purified deacetylase from archaea. With the introduction of low-angle tilt observations to minimize unfavorable imaging conditions due to tilting, the results demonstrated reasonable reconstruction models without imposing symmetry to the structure. This method also guides its users to discriminate particle images of different conformational state of the molecule.