Figure 1.
Short length-scale diffusion on a rough landscape (bottom) may be averaged, yielding an effective diffusion
, which is obtained from simulation. Effective diffusion leads to barrier crossing attempts, where the probability of crossing is governed by the height of the long length-scale barrier (
).
Figure 2.
Explicit-solvent simulation of an E. coli ribosome (water molecules and ions not shown), colored by region: 23S/5S rRNA (gray), 16S rRNA (cyan), proteins (light blue), P/P tRNA (red) and A/A tRNA (yellow). During translocation, tRNA molecules adopt hybrid configurations (middle). Rotation of the 30S body () and head (
) is associated with tRNA movement between binding sites. Here, we initiated the simulation in the pre-translocation configuration and characterized the structural fluctuations about the classical tRNA configuration and unrotated subunit configuration.
Figure 3.
Reaction coordinates for 30S rotation and tRNA movement.
A) rmsf, by residue, for the 23S (left) and 16S (right) rRNA. rmsf measures (See Text S1) were used to define the core residues (shown with side chains) of the: B) 23S rRNA (gray) and C) 16S body (cyan) and 16S head (blue). Core residue groups were used to define the planes of rotation for D) body rotation (, positive in the counter-clockwise direction) and E) head swivel (
). The vectors that define the rotation planes are depicted by orange arrows. The angle between the vectors is
. In (D) and (E), the classical and rotated configurations are shown in cyan and white. tRNA position is measured by
, as defined previously [49], [50] and is shown for F) the classical A/A-P/P tRNA configuration.
Figure 4.
Estimating diffusion coefficients for subunit rotation and tRNA movement.
A) Rotation coordinates and
as functions of time for a simulation about the pre-translocation (A/A-P/P) configuration (every 1 ns shown). B) Effective diffusion coefficients
and
were obtained from the displacement squared in the angles
.
is linear for
30 ns, which is characteristic of diffusive dynamics. Linear fits are depicted with gray dashed lines. C)
over the course of the simulation. D) Displacement squared of
is linear for
10 ns, allowing the tRNA effective diffusion coefficient
to be measured.
Figure 5.
Rates, free-energy barriers and crossing attempt frequencies.
Using ,
, and
, the rates of barrier crossing were calculated as functions of the barrier heights for A) body rotation, B) head swivel, and C) tRNA displacements. From the rates, the barrier-crossing attempt frequencies
,
, and
were derived (D–F). With these values, the energy landscape may be quantified for any kinetic scheme that can be decomposed into body rotation, head swivel and tRNA displacement. Dashed lines mark 5 and
(range of rates measured for translocation [59]–[64]), providing an upper-limit range for the barrier height associated with each substep of translocation.