Detecting asymmetry in the presence of symmetry with maximum likelihood three-dimensional reconstructions of viruses from electron microscope images

Various modes of transmission electron microscopy can provide unique structural information on nanometre-scale biological machines such as viruses and ribosomes. A maximum-likelihood statistical reconstruction algorithm using information from two such modalities, single-particle cryo-electron microscopy and computed electron tomography, is described for the problem where the machine is nearly symmetrical, but the localised regions of asymmetry are important for the functioning of the machine. The algorithm is demonstrated on experimental bacteriophage Lambda procapsid data. Key features of the algorithm are the use of probability density functions (pdfs) derived from normalised correlation rather than Gaussian pdfs and the solution of a constrained classification problem in which 11 out of 12 sites of asymmetry belong to one class while the 12th site belongs to a second class.