The iterative helical real space reconstruction method: Surmounting the problems posed by real polymers

Many important biological macromolecules exist as helical polymers. Examples are actin, tubulin, myosin, RecA, Rad51, flagellin, pili, and filamentous bacteriophage. The first application of three-dimensional reconstruction from electron microscopic images was to a helical polymer, and a number of laboratories today are using helical tubes of integral membrane proteins for solving the structure of these proteins in the electron microscope at near atomic resolution. We have developed a method to analyze and reconstruct electron microscopic images of macromolecular helical polymers, the iterative helical real space reconstruction (IHRSR) algorithm. We can show that when there is disorder or heterogeneity, when the specimens diffract weakly, or when Bessel functions overlap, we can do far better with our method than can be done using traditional Fourier–Bessel approaches. In many cases, structures that were not even amenable to analysis can be solved at fairly high resolution using our method. The problems inherent in the traditional approach are discussed, and examples are presented illustrating how the IHRSR approach surmounts these problems.