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Cryo-Electron Microscopy (cryo-EM) of macromolecular complexes is a fundamental structural biology technique which is expanding at a very fast pace. Key to its success in elucidating the three-dimensional structure of a macromolecular complex, especially of small and non-symmetric ones, is the ability to start from a low resolution map, which is subsequently refined with the actual images collected at the microscope. There are several methods to produce this first structure. Among them, Random Conical Tilt (RCT) plays a prominent role due to its unbiased nature (it can create an initial model based on experimental measurements). In this article, we revise the fundamental mathematical expressions supporting RCT, providing new expressions handling all key geometrical parameters without the need of intermediate operations, leading to improved automation and overall reliability, essential for the success of cryo-EM when analyzing new complexes. We show that the here proposed RCT workflow based on the new formulation performs very well in practical cases, requiring very few image pairs (as low as 13 image pairs in one of our examples) to obtain relevant 3D maps.

Activation of C3, deposition of C3b on the target surface, and subsequent amplification by formation of a C3-cleaving enzyme (C3-convertase; C3bBb) triggers the effector functions of complement that result in inflammation and cell lysis. Concurrently, surface-bound C3b is proteolyzed to iC3b by factor I and appropriate cofactors. iC3b then interacts with the complement receptors (CR) of the Ig superfamily, CR2 (CD21), CR3 (CD11b/CD18), and CR4 (CD11c/CD18) on leukocytes, down-modulating inflammation, enhancing B cell-mediated immunity, and targeting pathogens for clearance by phagocytosis. Using EM and small-angle X-ray scattering, we now present a medium-resolution structure of iC3b (24 Å). iC3b displays a unique conformation with structural features distinct from any other C3 fragment. The macroglobulin ring in iC3b is similar to that in C3b, whereas the TED (thioester-containing domain) domain and the remnants of the CUB (complement protein subcomponents C1r/C1s, urchin embryonic growth factor and bone morphogenetic protein 1) domain have moved to locations more similar to where they were in native C3. A consequence of this large conformational change is the disruption of the factor B binding site, which renders iC3b unable to assemble a C3-convertase. This structural model also justifies the decreased interaction between iC3b and complement regulators and the recognition of iC3b by the CR of the Ig superfamily, CR2, CR3, and CR4. These data further illustrate the extraordinary conformational versatility of C3 to accommodate a great diversity of functional activities.

Disruption of the thioester in native C3 yields a C3 molecule that functionally resembles C3b. It has been proposed that this C3 molecule (iC3) plays a key role in initiation of the alternative pathway of the C system. However, its presence in plasma has never been demonstrated. We investigated the presence of iC3 in plasma, using mAb that recognize iC3 as well as C3 activation products but not native C3. One of these mAb, anti-C3-5, which binds iC3 via its C3a moiety, was used together with polyclonal 125I-anti-C3c to develop a RIA for iC3. Plasma incubated with methylamine yielded a strong response in this RIA, whereas neither fresh plasma nor serum in which the C system had been activated by incubation with aggregated IgG, did show this strong response. The specificity of this RIA was further demonstrated by additional experiments including experiments with purified preparations of the various forms of C3. Mean level of iC3 in freshly obtained plasma samples from 10 normal donors was 27 nmol/liter, which is 0.49% of total C3. Analysis by SDS-PAGE of C3 species that had been immunoprecipitated by mAb antiC3-5, revealed that some iC3 consisted of C3 molecules with an intact alpha-chain whereas another part consisted of iC3 molecules with an alpha-chain that had been cleaved by factor I. Thus, this study shows that fresh human plasma contains a C3 species with the conformation of "C3b-like C3" (iC3).