Connecting energy landscapes with experimental rates for aminoacyl-tRNA accommodation in the ribosome

Abstract

Using explicit-solvent simulations of the 70S ribosome, the barrier-crossing attempt frequency was calculated for aminoacyl-tRNA elbow-accommodation. In seven individual trajectories (200-300 ns, each, for an aggregate time of 2.1 μs), the relaxation time of tRNA structural fluctuations was determined to be ∼10 ns, and the barrier-crossing attempt frequency of tRNA accommodation is ∼1-10 μs(-1). These calculations provide a quantitative relationship between the free-energy barrier and experimentally measured rates of accommodation, which demonstrate that the free-energy barrier of elbow-accommodation is less than 15 k(B)T, in vitro and in vivo.

Figure 1

Structural representation of the aa-tRNA (yellow), p-tRNA (red), mRNA (green), and the associated amino-acids (grey, purple), in the partially-bound A/T conformation (left) and fully-bound A/A conformation (right). Elbow-accommodation is measured by R_Elbow: the distance between the O3’ atoms of U8 on p-tRNA and U47 on aa-tRNA (blue spheres).

Figure 2

A) Time traces of R_elbow from 7 explicit-solvent simulations. B) Mean-squared displacement $\langle \mathrm{\Delta }{R}_{\mathit{\text{elbow}}}^2(\tau )\rangle$ as a function of time delay τ. D_Elbow waṣestimated by the slope between 10 and 20 ns. Inset shows $\langle \mathrm{\Delta }{R}_{\mathit{\text{elbow}}}^2(\tau )\rangle$ for τ=0–30 ns. C) 300 ns trajectory, displayed at 1 ns intervals. Inset shows subset at 5 ps intervals. D) Dispersion and relaxations were calculates from the residuals of linear fit (slopes in Table 1), ΔR_elbow. E) Autocorrelation function of ΔR_elbow fitted to sum of 2 exponentials (SI). D_Elbow was calculated from the average decay time <τ>. F) Accommodation rate k_a and attempt frequency C_a, for D_Elbow=1.1µs²/s, versus the free-energy barrier height. Range of experimentally-determined rates shaded in blue.