Trajectories of the ribosome as a Brownian nanomachine

Abstract

A Brownian machine, a tiny device buffeted by the random motions of molecules in the environment, is capable of exploiting these thermal motions for many of the conformational changes in its work cycle. Such machines are now thought to be ubiquitous, with the ribosome, a molecular machine responsible for protein synthesis, increasingly regarded as prototypical. Here we present a new analytical approach capable of determining the free-energy landscape and the continuous trajectories of molecular machines from a large number of snapshots obtained by cryogenic electron microscopy. We demonstrate this approach in the context of experimental cryogenic electron microscope images of a large ensemble of nontranslating ribosomes purified from yeast cells. The free-energy landscape is seen to contain a closed path of low energy, along which the ribosome exhibits conformational changes known to be associated with the elongation cycle. Our approach allows model-free quantitative analysis of the degrees of freedom and the energy landscape underlying continuous conformational changes in nanomachines, including those important for biological function.

Keywords: cryo-electron microscopy; elongation cycle; manifold embedding; nanomachines; translation.

Fig. 1.

Flowchart representation of the approach used to determine the free-energy landscape, work-cycle trajectory, and associated continuous conformational changes from experimental snapshots of nanomachines in unknown orientational and conformational states.

Fig. 2.

(A) Representative cryo-EM snapshots, and (B) 2D view of a typical conformational manifold. The manifold is derived from a measure of similarity among ∼1,500 cryo-EM snapshots of ribosome particles viewed within a tight orientational aperture. The axes ${\psi }_1,{\psi }_2$ represent the first two eigenvectors obtained by the diffusion map algorithm with a kernel able to deal with defocus variations.

Fig. 3.

(A) Three views of a cryo-EM map of the 80S ribosome from yeast (32), with arrows indicating four key conformational changes associated with the elongation work cycle of the ribosome. (B) The energy landscape traversed by the ribosome. The color bar shows the energy scale. The energy range has been truncated at 2 kcal/mol to show details of the triangular trough. The error in energy determination along the closed triangle is 0.05 kcal/mol. The roughly triangular minimum free-energy trajectory is divided into 50 states. The arrows indicate the structural changes between 7 selected states, each identified by its place in the sequence of 50 states.

Fig. 4.

Example of conformational changes along the trajectory: ratchet-like motion. (A) Unrotated ribosome, map 14 in Fig. 3B. (B) Maximally rotated ribosome, map 36. (C) Superposition of the two maps. The full set of frames showing continuous conformational changes is shown in three common viewing directions in Movies S2–S4.