Erratum to: Quartz-Seq: a highly reproducible and sensitive single-cell RNA sequencing method, reveals non-genetic gene-expression heterogeneity

Erratum

After publication of our article [1], we noticed some errors. In this manuscript, we amplified cDNA with 41.67 nmol/l RT primer and 70 nmol/l tagging primer for single-cell Quartz-Seq, and not pmol/l as originally stated. In addition, two mathematical expressions were inadvertently omitted.

Thus, in the section Whole-transcript amplification for single-cell Quartz-Seq, the following are correct:

Immediately after the second centrifugation, 0.8 μl of priming buffer (1.5× PCR buffer with MgCl2 (TaKaRa Bio), 41.67 nmol/l of the RT primer (HPLC-purified; Table 1), 4 U/μl of RNase inhibitor (RNasin Plus; Promega Corp., Madison, WI, USA), and 50 μmol/l dNTPs were added to each tube.

And

We then added 23 μl of the second-strand buffer (1.09× MightyAmp Buffer v2 (TaKaRa), 70 nmol/l tagging primer (HPLC-purified; Table 1), and 0.054 U/μl MightyAmp DNA polymerase (TaKaRa)) to each tube.

In the section Bioinformatics analysis, the equations should appear as follows:

The MI is considered the Kullback–Leibler distance from the joint probability density to the product of the marginal probability densities as follows:

$$MI\left(X,Y\right)=E_{f\left(x,y\right)}\left\{log\frac{f\left(x,y\right)}{f\left(x\right)f\left(y\right)}\right\}$$ 1

The MI is always non-negative, symmetric, and equal to 0 only if × and Y are independent. The MI can be represented as a summation of entropies:

$$MI\left(X,Y\right)=H\left(X\right)+H\left(Y\right)-H\left(X,Y\right)$$ 2