Cell, Volume 153. Supplemental Information. The Ribosome as an Optimal Decoder: A Lesson in Molecular Recognition. Yonatan Savir and Tsvi Tlusty

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1 ell, Volume 153 Supplemental Information The Ribosome as an Optimal Decoder: A Lesson in Molecular Recognition Yonatan Savir and Tsvi Tlusty

2 1 Extended Experimental Procedures Michaelis-Menten Kinetics Michaelis-Menten (MM) kinetics are a special case of equations (1) and () in the MS. The MM scheme consists of two basic steps: A reversible step of binding and unbinding with rates k on and k off, respectively, which is followed by an irreversible catalysis step that occurs with rate k cat. The rate, per substrate per enzyme, of the overall reaction is k R k off k k cat on cat k k k k off on on cat (S1) In this case, the barriers b 1 and b are merged into one barrier, such that s is the initial state (set to be the zero energy) and s 3 is the intermediate complex state, kon e ( s3 ), k e ( b3 s3) and kcat e. Hence, in the case of two competing reactions the correct rate is, R off 1 b3 e e (S) and the incorrect one is, R 1 ' b3 e e (S3) e consider a general performance measure F which is a function of the correct and wrong decoding rates, ( ) ( ). The derivatives with respect to the various parameters are (using Eq. (S) and Eq. (S3))

3 (S4.1) (S4.) (S4.3) (S4.4) F F R e R F F R e ' R 3 b3 ' F F F R e R e R R ' F F F R e R e b R R b3 b3 (S4) iologically relevant measures F obey,, and therefore and As a result, δ and δ are expected to increase towards their respective biophysical limits. The two derivatives, and, cannot vanish simultaneously unless δ = δ. If vanishes and δ > δ (in the case of the ribosome, δ 0), is always negative. In the case that k on is the same for the competing reactions, which is the case for the ribosome, δ =0 and Eq. (S) and (S3) are reduced to Eq. (1) and () in the MS. Optimal Decoding The Max-Min Solution The normalized decoding fitness is obtained by normalizing F = R d R by the difference between the maximal and minimal values of F per given d, such that the normalized 0 F 1, is given by e ( R d R) d e 1 d e ( R d R) e d 1 / 1/ e d / e 1 F e ( R d R) d 1 1 d e / 1/ e d / e 1 d 1 e ( R d R) d 1 e d d 1 (S5) Note that, e R ( u) 1 e R ( u), e R ( u) 1 e R ( u) and as a result, F( u, d) F( u,1/ d) (S6) The derivative with respect to d when d 1 is

4 3 e R R 0 F ( d 1) d R R d(e d) / (e 1) e ( de ) / 3 e d e d 1 (S7) / Foru 0, R e R 0 and thus in this regime F(d 1) F(d=0) = e / R. For u 0, R e R 0 and as a result F(d 1) F(d ) = 1 e R. Using the symmetry of the F (Eq. (S6)) we get, 1 e R u 0 u / 1 e min( F) 1 1 e R 1 u 0 u / 1 e (S8) In terms of b 3, e b / b3 e e min( F) e 1 b / b3 e e (S9) The Max-Min solution is obtained by maximizing (S9). The barrier b 3 that provides the Max-Min solution for decoding is b * 3 (S10) The value of u at which R reaches half of its maximal value at u = δ/ while which R reaches half of its maximal value at u = -δ/. Thus the width of the Max-Min peak scales like δ (Fig. in the MS). Note that the Max-Min solution (Eq. (S10)) also maximizes the net rate, R R.

5 Table S1. Kinetic Parameters of the Decoding Reaction, Related to Figures 1, 3, and 4 k 1 k -1 k k - k 3 [µm -1 s -1 ] [s -1 ] [s -1 ] [s -1 ] [s -1 ] Δ p [k T] UU δ [k T] UUU U UU GU U UUA UUG Error ±0 ±10 Standard deviation of all measured values was ~ 15%. ±0.045 ±1.45 ±.05 These data (Gromadski et al., 004a, 006) were used to produce Figures 3 and 4. Table S. The Effect of Streptomycin on the Kinetic Parameters, Related to Figure 4 UUU (+Str) U (+Str) k ± ± 0 k ± 5 80 ± 5 k 40 ± ± 0 k - < ± 0 k 3. ± ± 0.6 p 0.66 ± ± 0.1 Δ -5.4 ± ± 0.3 δ 6.6 ± 0.38 These data (Gromadski et al., 004b) were used to produce Figure 4.

6 Table S3. The Effect of rpsd and rpsl Mutations on the Kinetic Parameters, Related to Figure 4 T rpsd (ram) rpsl (res) ognate (UU) Near-ognate (U) ognate (UU) Near-ognate (U) ognate (UU) Near-ognate (U) k k k Δ δ These data (Zaher et al., 010) were used to produce Figures 4 and S1. Table S4. Kinetic Parameters of the Decoding Reaction Measured Using FRET, Related to Figure 4 ognate (UUU) Near-ognate (UU) k k Δ δ 6.06 These data (Lee et al., 007, [5 mm Mg + ]) were used to produce Figure 4. k - is obtained by observing transition out of the codon-recognition state (s 3 in Figure 1 in the MS). e note that the authors (Lee et al., 007) hypothesized that this rate includes another, irreversible, exit pathway from the codonrecognition state.