Although the simulation data as well as the conclusion on the proportionality between Vip(i) and Vg(i) in the work
 is correct, interpretation of some data therein should be corrected. As the sampling number (L = 200) to measure the average gene expression level is not large enough, there is a bias in the estimate in Vg(i). Finiteness in the number of sampling L will generally cause a bias of the order of Vip(i)/L, in the estimate of the variance Vg(i). The too good proportionality between Vip(i) and Vg(i) for large σ, shown in Figure two (a)(b) of
 (especially for small Vg(i)), is due to this artifact. Accordingly, the sharp peak at ∼1/L = 1/200 in Figure three of
 is due to this insufficiency by the sample number.
Still, the proportionality between the two variances Vip(i) and Vg(i), albeit not so sharp, holds, as already observed in the region with larger Vg(i) in
. We have simulated the model with a larger number of samples, i.e., N = L = 1000. As is shown in Figure
1, the proportionality is well discernible, where the proportion coefficient Vg(i)/Vip(i) decreased with the increase in the noise level σ, which was already observed in the broad peak beyond 1/L in Figure three of
. This broad peak beyond 1/L in Figure three of
 was found to be sharper as N was increased, from 200 to 1000. This peak indeed corresponds to the proportion coefficient extracted from Figure
1 in the present Correction. As the noise level σ was increased, the peak position ρ = Vg(i)/Vip(i) decreased. Hence for larger σ, larger L is needed to get reliable estimate in the proportion coefficient. As for Figure five and Figure six of
, the sharp proportionality for Vg(i) ≲ 0.001 is due to the above bias, while the discussion therein concerns with the approach of Vg(i) to Vip(i) at larger Vg(i), which is not affected by the bias here.
To sum up, the main claim of
, i.e., proportionality between Vip(i) and Vg(i) is valid, but the value of the proportion coefficient ρ = Vg(i)/Vip(i) should be corrected. It decreases with the noise level, in contrast to the discussion in
 for large σ. Major factor on this proportionality is attributed to the correlation of each variance with the average value
: In other words, a state with an intermediate expression level (i.e., smaller
) can be more easily switched on or off, both by noise and also by mutation, and hence the variances generally increase as
approaches 0. Still, some correlation between Vip(i) and Vg(i) remains even after removing this correlation through
I regret any inconvenience that misintepretation of the data with an insufficient sample size may have caused.
Department of Basic Science, Univ. of Tokyo
Kaneko K: Proportionality between variances in gene expression induced by noise and mutation: consequence of evolutionary robustness.BMC Evol Biol 2011, 11:27.PubMedView Article
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