Continuous changes in structure mapped by manifold embedding of single-particle data in cryo-EM

Abstract

Cryo-electron microscopy, when combined with single-particle reconstruction, is a powerful method for studying macromolecular structure. Recent developments in detector technology have pushed the resolution into a range comparable to that of X-ray crystallography. However, cryo-EM is able to separate and thus recover the structure of each of several discrete structures present in the sample. For the more general case involving continuous structural changes, a novel technique employing manifold embedding has been recently demonstrated. Potentially, the entire work-cycle of a molecular machine may be observed as it passes through a continuum of states, and its free-energy landscape may be mapped out. This technique will be outlined and discussed in the context of its application to a large single-particle dataset of yeast ribosomes.

Keywords: Classification; Heterogeneity; Machine learning; Molecular machines; Protein synthesis; Ribosome.

Fig. 1

Example for the classification of molecule images (the 43S translation pre-initiation complex) using Relion. Initially 650,000 particles were classified into 10 classes. Of these, only one class of 180,000 was found to contain intact particles recognizable as 40S subunits. Another step of classification, this time into 9 classes, yielded three high-quality maps (enlarged, at the bottom), of which only one (on the right) displays all expected components of the eukaryotic pre-initiation complex. (Adapted from[20]).

Fig. 2

Schematic diagram of the translation elongation cycle in bacteria. In each clockwise round, a new amino acid is added to the nascent polypeptide as specified by the genetic code on the mRNA. In principle, in a sample of ribosomes purified from cell extract, all states of the ribosome during the elongation cycle should be present, but the purification often eliminates the bound ligands: tRNA, mRNA, EF-G, and the aa-tRNA•EF-Tu•GTPbn ternary complex. (In addition, states associated with initiation, termination, and recycling should also be present in such a sample, but they occur with less frequency). (Reproduced with permission from [50]).

Fig. 3

Analysis of data falling into a single projection direction by manifold embedding. This particular projection direction shows the side view of the 80S ribosome (surface representation in upper left). The changes picked out by the first eigenvector, ψ₁, can be recognized as the result of intersubunit rotation (see lower 5 panels which, from right to left, show an increasing redistribution of mass consistent with the increasing rotation of the small subunit with respect to the large subunit). In other words, through manifold embedding, the projection data were sorted according to changes in angle between the two subunits. The other eigenvectors, ψ₂ through ψ₅, depict more subtle changes in conformation.

Fig. 4

Conformational variability and energy landscape of the ribosome. (a) Three views of a cryo-EM map of the 80S ribosome from yeast, with arrows and symbols indicating four prominent conformational changes associated with the elongation work cycle of the ribosome (see key on the bottom right). The three views are orthogonal to one another. “Solvent” refers to the solvent view with respect to the small subunit, also called “front view” of the 80S ribosome. (b) The energy landscape constructed by the manifold embedding technique of Dashti et al. (2014), showing the preferred path followed by the ribosome. Horizontal and vertical axes are the first two eigenvectors ψ₁ and ψ₂, respectively. The color bar shows the energy scale. The energy range has been truncated at 2 kcal/mol to show details of the roughly triangular, closed minimum free-energy trajectory. The error in energy determination along the trajectory is 0.05 kcal/mol. The trajectory has been divided into 50 states. The pointers indicate 7 selected minima, each identified by its position along the sequence of the 50 states. Arrows along circle between successive minima indicate combinations of observed conformational changes explained on the left. (Reproduced from [28] with permission)