Supplementary Material

Supplementary Material Supplementary Text Text S1. Time distributions of the high FRET efficiency at different concentrations of EF-G.GTP From Fig. 1, the model of ribosomal translocation at non-saturating concentration of EF-G.GTP is shown in Fig. S2, where the transition from State I to State C is not shown. Before EF-G.GTP binding, the ribosomal complex can fluctuate spontaneously between the classical non-rotated state (State C) and hybrid state (State H), with the majority being in the hybrid state [S1 S6]. EF-G.GTP can bind to and release from both the pretranslocation states [S7,S8]. In Fig. S2, k 1 is the rate constant of the spontaneous forward ribosomal rotation and k 1 is the rate constant of the spontaneous reverse ribosomal rotation, k 2 k b [EF-G] is the rate of EF-G.GTP binding to the pretranslocation ribosomal complex, with k b representing the binding rate constant and [EF-G] the concentration of EF-G.GTP, and k 2 is the rate of EF-G releasing from the pretranslocation complex. From Fig. S2, the ratio (R 1 ) of the transition of State H to State C to the transition of State H to State H1 can be calculated by using the following scheme k 1 C H From Scheme S1, we easily obtain k b [EF-G] k4 H k 2 1 H1. (Scheme S1) k1 k2 R1 k4 kb [EF-G]. (S1) k1 To be consistent with the smfret data with 1 ms per frame time resolution [S9], we take k 1 =.88 s 1 mentioned in the main text, we have k 4 =.8 gave k b > 1 1 1 μm s (giving high = 1.14 s at EF-G) in the calculation. As 1 s. The available biochemical data [S1], implying that a [EF-G] (.2 μm ), k b [EF-G] >> k 1. Thus, Eq. (S1) can be approximately rewritten as k2 R1 kb [EF-G]. (S2)

From Fig. S2, the ratio (R 2 ) of the transition of State F3 to State C to the transition of State F3 to State H2 can be calculated by using the following scheme F3 k5 H1 k 1 C From Scheme S2, we easily obtain R 2 k b [EF-G] k 2 H2. (Scheme S2) k1 k2 k5. (S3) k5 k [EF-G] A [EF-G] (.2 μm ), we have b k2 k5 k b [EF-G] close to k 2 k b [EF-G]. With k 1 =.88 s 1 and k 5 = 35 s 1, we thus have R 2 2 << b [EF-G].25 k k b [EF-G] k k R 2 1. As it will be shown below, R 1 =.5 2.5 at [EF-G].2 μm. Thus, R 2 is very small. Therefore, to calculate the number of the transition of the high FRET efficiency (.8) to the low efficiency we can neglect the contribution of the transition from State F3 to State C and need only to consider the contribution of the transition from State H to State C. If we take R 1 =.5 at [EF-G] = 1 μm, we have R 1 = 1 (2-fold that at 1 μm EF-G) at [EF-G] =.5 μm and R 1 = 2.5 (5-fold that at 1 μm EF-G) at [EF-G] =.2 μm. Since P E =.5 gives the number of the transition from the hybrid state to the classical non-rotated state at saturating [EF-G] to be 2, we have the number N = 2 + R 1 = 2.5, 3 and 4.5 at [EF-G] = 1,.5 and.2 μm, respectively, which are consistent with the smfret data of 2.3, 2.9 and 4.8, respectively (see Table 1 or Fig. S7C in Kim et al. [S9]). Therefore, the time distribution of the high FRET efficiency can be approximately calculated by f () t R f () t 2 f () t, (S4) high 1 H H where f () t is the time distribution of the transition from State H to State C and H fh () t is the time distribution given in Eq. (6). It is noted here that since a [EF-G] (.2 μm), k b [EF-G] >> k 8 =.2 1 s, we can neglect the effect of the 1 binding of EF-G.GTP on the time distribution fh ( t ). From scheme, H C, k fh () t has the form H 1 1 f () t k exp k t. (S5) 2

At [EF-G] =, fhigh() t fh () t. At [EF-G], fhigh( t ) is calculated by Eqs. (S4), (S5) and (6), with R 1 = 2.5, 1 and.5 for [EF-G] =.2,.5 and 1 μm, respectively. The calculated results are shown in Fig. S3, which are consistent with the smfret data (Fig. S7B in Kim et al. [S9]). It is noted here that the theoretical data (lines) in Fig. S3d are calculated by Eqs. (S4), (S5) and (6) while in Fig. 4c of the main text are calculated by Eq. (6), with a difference of.25 fh ( t ) between the two cases, which gives a slight difference of the theoretical data for f () t between the two cases (see Fig. S4). high References [S1] Blanchard S.C., Kim H.D., Gonzalez Jr. R.L., Puglisi J.D., Chu. S. (24) trna dynamics on the ribosome during translation. Proc. Natl Acad. Sci. USA 11, 12893 12898. [S2] Cornish P.V., Ermolenko D.N., Noller H.F., Ha T. (28) Spontaneous intersubunit rotation in single ribosomes. Mol. Cell 3, 578 588. [S3] Fei J., Kosuri P., MacDougall D.D., Gonzalez Jr. R.L. (28) Coupling of ribosomal L1 stalk and trna dynamics during translation elongation. Mol. Cell 3, 348 359. [S4] Moazed D., Noller H.F. (1989) Intermediate states in the movement of transfer RNA in the ribosome. Nature 342, 142 148. [S5] Valle M., Zavialov A., Sengupta J., Rawat U., Ehrenberg M., Frank J. (23) Locking and unlocking of ribosomal motions. Cell 114, 123 134. [S6] Zavialov A.V., Ehrenberg M. (23) Peptidyl-tRNA regulates the GTPase activity of translation factors. Cell 114, 113 122. [S7] Chen C., Stevens B., Kaur J., Cabral D., Liu H., Wang Y., Zhang H., Rosenblum G., Smilansky Z., Goldman Y.E., Cooperman B. (211) Single-molecule fluorescence measurements of ribosomal translocation dynamics. Mol. Cell 42, 367 377. [S8] Xie P. (213) Translocation dynamics of trna-mrna in the ribosome. Biophys. Chem. 18-181, 22 28. [S9] Kim H-K, Liu F., Fei J., Bustamante C, Gonzalez Jr. R.L., Tinoco Jr. I. (214) A frameshifting stimulatory stem loop destabilizes the hybrid state and impedes ribosomal translocation. Proc. Natl Acad. Sci. U.S.A. 111, 5538 5543. [S1] Savelsbergh A., Katunin V.I., Mohr D., Peske F., Rodnina M.V., Wintermeyer W. (23) An elongation factor G-induced ribosome rearrangement precedes trna-mrna translocation. Mol. Cell 11, 17 23. 3

Text S2. The derivations of time distributions First, we derive Eq. (1) from Scheme 1. As k 6 is very fast, Scheme 1 can be approximately rewritten as k4 k5 kd H H1 POST. (Scheme S1) Denoting by P H, P H1, P POST and P the probabilities for finding the ribosomal complex in State H, State H1, State POST and State, respectively, from Scheme S1 the temporal evolution of these probabilities are described by the following differential equations dph () t kp 4 H () t, (S6) dt dph 1() t kp 4 H() t kp 5 H1() t, (S7) dt dp POST dt () t kp () t kp () t, (S8) 5 H1 d POST dp () t kdppost() t. (S9) dt The initial conditions at t = are imposed as follows: P H () = 1, P H1 () =, P POST () = and P () =. The time distribution of the total high FRET efficiency, f ( t), can be calculated by f () t dp () t dt, i.e., f () t k P () t. (S1) d POST Solving Eqs. (S6) (S8) with the above initial conditions, we can obtain P POST (t). Then from Eq. (S1) we obtain Eq. (1). Similarly, from Schemes (2) (5) we obtain Eqs. (2) (5), respectively. 4

Supplementary Figures Figure S1. The reaction scheme and free-energy landscapes of the translocation proposed by Kim et al. [S9]. The figure is reproduced from Kim et al. [S9]. (A) States C and H denote the classical non-rotated and hybrid states without EF-G, respectively. State G denotes the hybrid state bound with EF-G. State I is an intermediate state, from which the reaction becomes irreversible. State Post denotes the posttranslocation state with deacylated trna dissociated from the E site. (B) Free-energy landscapes along the translocation for the ribosomal complex bound with the mrna lacking the stem loop ( SL ) and bound with the mrna containing the stem loop (FSmRNA). Reversible transitions are highlighted by the red arrows. 5

Figure S2. Model of trna-mrna translocation in the ribosome at non-saturating concentration of EF-G.GTP. In the model, State C, State C and State F1 (inside boxes) have a low L1-tRNA FRET efficiency (.2) in the smfret experiment of Kim et al. [S9], State H, State H, State H1, State H2, State F2, State F3 and State POST have a high L1-tRNA FRET efficiency (.8), while the L1-tRNA FRET efficiency becomes zero at State. 6

1 EF-G 12.2 M EF-G 5 6 5 1 5 1 4.5 M EF-G 3 1 M EF-G 2 5 1 5 1 Figure S3. Results of time distribution of the high FRET efficiency for the mrna containing the downstream secondary structure (with P E =.5) at different concentrations of EF-G.GTP. Black lines represent the theoretical data and the columns are the smfret data taken from Fig. S7B in Kim et al. [S9]. 7

3 1 M EF-G 5 1 Figure S4. Results of the time distribution of the high FRET efficiency for the mrna containing the downstream secondary structure (with P E =.5) at 1 μm EF-G.GTP. The theoretical data of black solid line are calculated by Eqs. (S4), (S5) and (6) while the theoretical data of blue broken line are calculated by Eq. (6). The columns are the smfret data taken from the bottom panel of Fig. S7B in Kim et al. [S9]. 8

(a) (b) 3 5 25 3 6 t last 2 4 t low (c) (d) 3 3 1 2 3 t last 5 1 Figure S5. Effects of uncertainties in the values of rate constants on time distributions at saturating EF-G.GTP. Black, blue and green lines represent the results with k i, k i ki and k i k i (i = 4, 6, 9 and d), respectively, where k i has the value given in the legend of Fig. 1 and k.1k. (a) The time distribution of the last i or total high FRET efficiency for the mrna lacking the downstream secondary structure (with P E = 1). (b) The time distribution of the low FRET efficiency for the mrna containing the downstream secondary structure (with P E =.5). (c) The time distribution of the las FRET efficiency for the mrna containing the downstream secondary structure (with P E =.5). (d) The time distribution of the high FRET efficiency for the mrna containing the downstream secondary structure (with P E =.5). i 9