Author Correction: Polyelectrolyte interactions enable rapid association and dissociation in high-affinity disordered protein complexes

Correction to: Nature Communications https://doi.org/10.1038/s41467-020-18859-x, published online 12 November 2020

The original Article contained errors in text in the Methods section, and in Equations (2), (4), (6), (11), and (15). All calculations were performed with the correct equations, so none of the reported results or conclusions are affected.

In the section “Single-molecule fluorescence spectroscopy” of the Methods section, the second sentence incorrectly read ‘After passing through a 100-mm pinhole, …’. The correct version states ‘100-μm pinhole’ instead of ‘100-mm pinhole’.

Equation (2) incorrectly read

$$\theta ({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}})=\frac{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }+{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}})+\sqrt{{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }+{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}})}^{2}-4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}}}}{2{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}}}$$

The correct form of Equation (2) is

$$\theta ({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}})=\frac{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }+{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}})-\sqrt{{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }+{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}})}^{2}-4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}}}}{2{c}_{{{{\rm{P}}}}\ast }^{{{{\rm{tot}}}}}}$$

Equation (4) incorrectly read

$${\theta }_{{{{\rm{coupled}}}}}({c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}})=\frac{{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}^{\ast }+{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}^{\ast }-2{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}-{K}_{{{{\rm{D}}}}}^{\ast }{K}_{{{{\rm{D}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }\sqrt{{(-{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}+{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}})}^{2}+4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}}}{2[{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}({K}_{{{{\rm{D}}}}}^{\ast }-{K}_{{{{\rm{D}}}}})+{K}_{{{{\rm{D}}}}}^{\ast }(-{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}}-{K}_{{{{\rm{D}}}}}+{K}_{{{{\rm{D}}}}}^{\ast })]}$$

The correct form of Equation (4) is

$${\theta }_{{{{\rm{coupled}}}}}({c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}})=\frac{{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}^{\ast }-{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}^{\ast }-2{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}-{K}_{{{{\rm{D}}}}}^{\ast }{K}_{{{{\rm{D}}}}}+{K}_{{{{\rm{D}}}}}^{\ast }\sqrt{{(-{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}+{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}})}^{2}+4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{K}_{{{{\rm{D}}}}}}}{2[{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}({K}_{{{{\rm{D}}}}}^{\ast }-{K}_{{{{\rm{D}}}}})+{K}_{{{{\rm{D}}}}}^{\ast }(-{c}_{{{{\rm{P}}}}}^{{{{\rm{tot}}}}}-{K}_{{{{\rm{D}}}}}+{K}_{{{{\rm{D}}}}}^{\ast })]}$$

Equation (6) incorrectly read

$$\theta ({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}})=\frac{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{{{{\rm{PHH}}}}}+{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}})+\sqrt{{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{{{{\rm{PHH}}}}}+{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}})}^{2}-4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}}}}{2{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}}}$$

The correct form of Equation (6) is

$$\theta ({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}})=\frac{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{{{{\rm{PHH}}}}}+{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}})-\sqrt{{({c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}+{K}_{{{{\rm{D}}}}}^{{{{\rm{PHH}}}}}+{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}})}^{2}-4{c}_{{{{\rm{H}}}}}^{{{{\rm{tot}}}}}{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}}}}{2{c}_{{{{{\rm{P}}}}}^{\ast }}^{{{{\rm{tot}}}}}}$$

Equation (11) incorrectly read

$$\langle E\rangle (t)=(1-{p}_{{{{\rm{same}}}}}(t)){\langle E\rangle }_{{{{\rm{eq}}}}}+{p}_{{{{\rm{same}}}}}(t)({\langle E\rangle }_{{{{\rm{eq}}}}}-\langle E\rangle (0)){e}^{-{k}_{{{{\rm{ex}}}}}t}$$

The correct form of Equation (11) is

$$\langle E\rangle (t)=(1-{p}_{{{{\rm{same}}}}}(t)){\langle E\rangle }_{{{{\rm{eq}}}}}+{p}_{{{{\rm{same}}}}}(t)[{\langle E\rangle }_{{{{\rm{eq}}}}}+(\langle E\rangle (0)-{\langle E\rangle }_{{{{\rm{eq}}}}}){e}^{-{k}_{{{{\rm{ex}}}}}t}]$$

Equation (15) incorrectly read

$${\tau }_{{{{\rm{high}}}}}^{{{{\rm{P}}}}}=\frac{2{c}_{{{{\rm{H}}}}}({k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}+{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})+{c}_{{{{\rm{PH}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}}(2{k}_{{{{\rm{off}}}}}+{k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}+2{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})}{{k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}(2{k}_{{{{\rm{off}}}}}+{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})({c}_{{{{\rm{H}}}}}{k}_{{{{\rm{on}}}}}+{c}_{{{{\rm{PH}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})}$$

The correct form of Equation (15) is

$${\tau }_{{{{\rm{high}}}}}^{{{{\rm{P}}}}}=\frac{2{c}_{{{{\rm{H}}}}}{k}_{{{{\rm{on}}}}}({k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}+{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})+{c}_{{{{\rm{PH}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}}(2{k}_{{{{\rm{off}}}}}+{k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}+2{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})}{{k}_{{{{\rm{off}}}}}^{{{{\rm{PPH}}}}}(2{k}_{{{{\rm{off}}}}}+{c}_{{{{\rm{P}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})({c}_{{{{\rm{H}}}}}{k}_{{{{\rm{on}}}}}+{c}_{{{{\rm{PH}}}}}{k}_{{{{\rm{on}}}}}^{{{{\rm{PPH}}}}})}$$

This has been corrected in both the PDF and HTML versions of the Article.