The protein SmpB binds to a special species of tRNA, tmRNA, to eliminate the incomplete

Chapter 0, Problem 3-14

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The protein SmpB binds to a special species of tRNA, tmRNA, to eliminate the incomplete proteins made from truncated mRNAs in bacteria. If the binding of SmpB to tmRNA is plotted as fraction tmRNA bound versus SmpB concentration, one obtains a symmetrical S-shaped curve as shown in Figure Q33. This curve is a visual display of a very useful relationship between Kd and concentration, which has broad applicability. The general expression for fraction of ligand bound is derived from the equation for Kd (Kd = [Pr][L]/[PrL]) by substituting ([L]TOT [L]) for [PrL] and rearranging. Because the total concentration of ligand ([L]TOT) is equal to the free ligand ([L]) plus bound ligand ([PrL]), fraction bound = [PrL]/[L]TOT = [Pr]/([Pr] + Kd) For SmpB and tmRNA, the fraction bound = [SmpB tmRNA]/[tmRNA]TOT = [SmpB]/([SmpB] + Kd). Using this relationship, calculate the fraction of tmRNA bound for SmpB concentrations equal to 104Kd, 103Kd, 102Kd, 101Kd, Kd, 101Kd, 102Kd, 103Kd, and 104Kd.