Appendix 3—figure 1. Measuring binding affinity by competition.

(A) Competitive binding reaction scheme. R*: labeled RNA ligand; R_comp: unlabeled competitor RNA; ${\displaystyle K_{\text{D}}^{\text{*}}}$: protein affinity for R*; ${\displaystyle K_{\text{D,comp}}}$: protein affinity for R_comp. (B) Mixing scheme for a competition measurement. (C) Competition between the U1C point mutant of the Puf4 consensus (R_comp = CGUAUAUUA) and the labeled consensus RNA (R*= ³²P-AUGUGUAUAUUAGU). The data were fit to the following equation (Lin and Riggs, 1972; Weeks and Crothers, 1992):

$$\begin{gathered} {\displaystyle \mathrm{F}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}=\mathrm{A}\times \frac{1}{2[{\mathrm{R}}^{\ast }{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}[K_{\mathrm{D}}^{\ast }+\frac{K_{\mathrm{D}}^{\ast }}{K_{\mathrm{D},\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}}[{\mathrm{R}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}+[\mathrm{P}{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}+[{\mathrm{R}}^{\ast }{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}- \\ \sqrt{{\left(K_{\mathrm{D}}^{\ast }+\frac{K_{\mathrm{D}}^{\ast }}{K_{\mathrm{D},\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}}[{\mathrm{R}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}+[\mathrm{P}{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}+[{\mathrm{R}}^{\ast }{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\right)}^2-4[{\mathrm{R}}^{\ast }{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}[\mathrm{P}{]}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}]}+\mathrm{O}} \end{gathered}$$ (9)

A indicates the maximum amplitude, constrained to the fit amplitude of the R* binding curve that is measured in parallel by a direct binding experiment (A = 0.89 for Puf4 binding to R*). O is the y axis offset (background). [R*]_total was constrained to the lower limit of the labeled RNA concentration. ${\displaystyle K_{\text{D}}^{\text{*}}}$ was constrained to Puf4 affinity for the labeled RNA, as determined by direct measurement in the same experiment (0.105 nM, after accounting for active protein fraction of 75%). [P]_total was 0.45 nM, after accounting for active protein fraction. The fit ${\displaystyle K_{\text{D,comp}}}$ value was 204 nM. Incubation times of 10, 30, and 110 min gave consistent ${\displaystyle K_{\text{D,comp}}}$ values (190–210 nM), as did lowering the protein concentration by three-fold (180 nM). Equation 9 is applicable only for ${\displaystyle K_{\text{D,comp}}>>K_{\text{D}}^{\text{*}}}$. For other cases see Wang, 1995.