Low-resolution real-space envelopes: improvements to the condensing protocol approach and a new method to fix the sign of such envelopes

The condensing-protocol strategy for obtaining low-resolution real-space envelopes of macromolecules from native Fourier intensities alone was recently reported [Subbiah (1991). Science, 252, 128-133]. The present work introduces three improvements to the original methodology. In terms of the j index, which was defined as the crude ratio of correctly placed scatterers to those incorrectly placed, these changes collectively contribute to j values that range from 8 to 28 and in one case even infinity. This compares with the previously reported values of 1.9 and 2.6. Nevertheless, under different conditions, both the original and the current improved condensing protocol can preferentially converge on the solvent or the matter region. Since such control is not absolute there still remains a certain amount of ambiguity in deciding whether the congealed gas represents bulk solvent or bulk matter. To overcome this ambiguity, a simple method based on the systematic placement of point scatterers on a grid lattice within and without the envelope is presented. This `sign-fixing' method is shown to work with both perfect envelopes as well as the cruder envelopes produced by the improved condensing protocol. The new methodology is illustrated using four macromolecular examples.