Automated multi-model reconstruction from single-particle electron microscopy data

Abstract

Biological macromolecules can adopt multiple conformational and compositional states due to structural flexibility and alternative subunit assemblies. This structural heterogeneity poses a major challenge in the study of macromolecular structure using single-particle electron microscopy. We propose a fully automated, unsupervised method for the three-dimensional reconstruction of multiple structural models from heterogeneous data. As a starting reference, our method employs an initial structure that does not account for any heterogeneity. Then, a multi-stage clustering is used to create multiple models representative of the heterogeneity within the sample. The multi-stage clustering combines an existing approach based on Multivariate Statistical Analysis to perform clustering within individual Euler angles, and a newly developed approach to sort out class averages from individual Euler angles into homogeneous groups. Structural models are computed from individual clusters. The whole data classification is further refined using an iterative multi-model projection-matching approach. We tested our method on one synthetic and three distinct experimental datasets. The tests include the cases where a macromolecular complex exhibits structural flexibility and cases where a molecule is found in ligand-bound and unbound states. We propose the use of our approach as an efficient way to reconstruct distinct multiple models from heterogeneous data.

Figure 1

(a) Method flowchart. For illustrative purposes a two-model reconstruction process is shown, though the method is generally applicable for more than two models. Grey boxes refer to new approaches introduced in this work. The input is a starting model and a set of boxed images. On the left side, the images are clustered into two groups to generate the two initial models. In the “Angular assignment” step, Euler angles are assigned to the experimental images by aligning them against the model projections. In the “Intra-angular clustering” step, we apply clustering within each Euler angle based on Multivariate Statistical Analysis (MSA) to separate all images of a specific projection direction into two homogeneous groups. This results in two subclass-average images for each Euler angle. In the “Global clustering” step, subclass-averages are grouped into two global clusters where subclass-averages from the same Euler angle are assigned to different clusters. Two initial 3D models are reconstructed from the two global clusters of subclass-averages in the “Backprojection reconstruction” step. These two initial models are improved in the iterative two-model refinement procedure, the right part of the figure. In this process, first, all experimental images are reclassified to the most similar projections of the two models. Then, new models are computed and the two-model refinement procedure is repeated. (b) More detailed algorithmic presentation of the “Global clustering” stage from (a). First, similarities between all subclass-averages are computed. Next, subclass-averages are clustered into two groups by applying the Spectral Clustering method. In the last step, two clusters are iteratively optimized by improving the score based on the normalized cut criterion.

Figure 2

Results from the reconstructions of 70S with and without EF-G. (a) shows the two reconstructions resulting from the implementation of our method, pink in the structure to the left indicates the assumed EF-G, other colors indicate the 30S and 50S subunits. (b) shows the difference map created by subtracting the structure of 70S alone from the structure assumed to contain EF-G, the difference is indicated in pink. It is clear from the difference map that not only have we captured the presence or absence of EF-G, but also a ratchet movement between the two subunits (Gao et al., 2003).

Figure 3

(a) Structure of unliganded eIF3 (EMDB entry EMD-1170) used as an initial model in our two-model reconstruction process. (b-c) Results of two-model reconstruction from a mixed set of 6,736 images of eIF3 and 19,027 images of eIF3-IRES. (d) Structure from (c) colored according to the density map difference between (c) and (b). (e-f) Results of two-model reconstruction from 19,027 images of eIF3-IRES. (g) Structure from (f) colored according to the density map difference between (f) and (e). (h) Example of five visually most distinctive subclass averages (columns) partitioned into two groups (rows). The clustering procedure clearly separated subclass averages with IRES structure (white arrows) from unliganded eIF3 (second row). Notice that the IRES is not well defined in the subclass-averages due to its high flexibility (Siridechadilok et al., 2005).

Figure 4

Human RNA polymerase II. (a) Reconstruction from the entire dataset. (b)-(c) Our result of the two-model reconstruction. Most of the structural changes happen in the stalk, clamp and jaw regions. (d) Structure from (b) colored according to the density map difference between (b) and (c). (e)-(f) Two previously published models that correspond to the closed and open forms (Kostek et al., 2006). The resolution of these two structures is not available. (g) Structure from (e) colored according to the density map difference between (e) and (f).