Biophysics and Computational Biology Correction for “Evolved interactions stabilize many coexisting phases in multicomponent liquids,” by David Zwicker and Liedewij Laan, which published July 6, 2022; 10.1073/pnas.2201250119 (Proc. Natl. Acad. Sci. U.S.A. 119, e2201250119).
Authors note that Fig. 3 and its corresponding legend appeared incorrectly. Authors state, “We found a mistake in the code that evaluates the performance g (defined by Eq. 5) in the script that we used to produce Fig. 3B. Consequently, the published version of Fig. 3B reported too low values of the performance g. Using these data, we wrongly reported that structured interaction matrices have low performance, while the corrected plot suggests that they are performing alright (although not as well as the optimized ones).” The corrected figure and its corrected legend appear below. The online version has been corrected.
Fig. 3.
Interaction matrices with block structure can target specific phase counts K reliably. (A and B) Mean phase count 〈K〉 and performance g (for w = 1) as functions of the interaction χ+ between different blocks and the interaction χ− within blocks for N = 10 components arranged in K∗ = 5 equal blocks (Insets in A show example matrices). (C) Distribution of composition angles θ shown as histograms and using kernel density estimation (lines) for several χ+ at χ− = 0. (D) Distribution of the number of components enriched in phases for several χ+ at χ− = 0. A–D show averages over 104 initial compositions. Distribution means are indicated by vertical bars.]
As a result of the above, the following corrections have been made to the text:
The authors note that on page 4, left column, second full paragraph, line 227, “Naively structured interactions also do not lead to reliable phase counts” should instead appear as “Structured interactions can lead to reliable phase counts.” The online version has been corrected.
The authors note that on page 4, left column, second full paragraph, line 240, “However, while these designed matrices display expected behavior, they still have significant variations and the resulting performance is only marginally better than that of random matrices (Fig. 3B).” should instead appear as “These designed matrices display expected behavior, and the resulting performance is high, particularly for large χ+ (Fig. 3B).” The online version has been corrected.
The authors note that on page 4, left column, second full paragraph, line 244, “This is also visible in the distribution of the composition angles θ shown in Fig. 3C: even for strong repulsion (large χ+), there is a significant fraction of phases with similar composition (θ ≈ π/4), even though exactly two components are enriched in each phase (Fig. 3D).” should instead appear as “However, the segregation into distinct phases is not perfect, which is also visible in the distribution of the composition angles θ shown in Fig. 3C: even for strong repulsion (large χ+), there is a significant fraction of phases with similar composition (θ ≈ π/4), even though exactly two components are enriched in each phase (Fig. 3D).” The online version has been corrected.
The authors note that on page 4, right column, first paragraph, line 252, “We thus find that creating interaction matrices with desired behavior is not as straightforward as we had hoped.” should instead appear as “Taken together, structured interaction matrices perform much better than random matrices, but they can still exhibit significant variations in phase counts.” The online version has been corrected.
The authors note that on page 5, left column, first paragraph, line 297, “In any case, we showed in Fig. 3 that block matrices are not optimal, so any obvious clustering might actually be detrimental.” should be removed. The online version has been corrected.
Authors assert that “the corrected data actually answers a question that [they] sometimes got when talking about the project, where people were surprised that structured interaction matrices had such low performances g. With the corrected code, the performance is much closer to peoples’ intuition. The error had no impact on the main part of our paper, where we show that evolutionary optimization can discover interaction matrices with optimal performance.”