Reviewer #2 (Public Review):

Summary
This work investigates how multiple regulatory elements combine to regulate gene expression. The authors use an episomal reporter assay which measures the transcriptional output of the reporter under the regulation of an enhancer-enhancer-promoter triple. The authors test all combinations of 8 promoters and 59 enhancers in this assay. The main finding is that enhancer pairs generally combine additively on reporter output. The authors also find that the extent to which enhancers increase reporter output is inversely related to the intrinsic strength of the promoter.

This manuscript presents a compact experiment that investigates an important open question in gene regulation. The results and data will be of interest to researchers studying enhancers. Given that my expertise is in modeling and computation, I will take the experimental results at face value and focus my review on the interpretation of the results and the computational methodology. I find the result of additivity between enhancers to be well supported. The findings on differential responsiveness between promoters are very interesting but the interpretation of such responses as 'non-linear' or 'following a power-law' may be misleading. More broadly, I think a more rigorous description of the mathematical methodology would increase the clarity and accessibility of this manuscript. A major unanswered question is whether the findings in this study apply to enhancers in their native genomic context. Regardless, investigating such questions in an episomal reporter assay is valuable.

Main comments
Applicability to native genomic context: The applicability of the results in this paper to enhancers in their native genomic context is unclear. As the authors state in the discussion section, the reporter gene is not integrated into the genome, the spacing between enhancers does not match their native context etc. It is thus unclear whether this experimental design is able to detect the non-additivity between enhancers which is known to be present in the genome. This could be investigated by testing the enhancer-enhancer-promoter tuples for which non-additivity has been observed in the genome (references are given in the introduction) in this assay.

Interpretation of promoter responses as non-linear and following a power-law: In Fig 5, the authors demonstrate that enhancer-enhancer pairs boost reporter output more for weak promoters as opposed to strong promoters. I agree the data supports this finding, but I find the interpretation of such data as promoters scaling enhancers according to a power-law (as stated in the abstract) to be misleading. As mentioned on line 297, it is not possible to define an intrinsic measure of enhancer strength, thus the authors assign the base of the power-law to be the average boost index of the enhancer-enhancer pair across the 8 promoters. But this measure incorporates some aspect of a promoter and is not solely a property of enhancers. It would also be useful to know whether the results in Fig 5 apply to only enhancer-enhancer-promoter triples or also to enhancer-promoter pairs.

Enhancer-promoter selectivity: As a follow-up to a previous study (Martinez-Ara et al, Molecular Cell 2022) the authors mention that the data in this study also shows that enhancers show selectivity for certain promoters. The authors mention that both studies use the same statistical methodology and the data in this study is consistent with the data from the 2022 paper. However, I think the statistical methodology in both studies needs further exposition. This section of the review is thus meant to ensure that I understand the author's methodology, to guide the reader in understanding how the authors define 'selectivity', and to probe certain assumptions underlying the methodology.

My understanding of the approach is as follows: The authors consider an enhancer to be not selective if its 'boost index' is the same across a set of promoters. 'Boost index' is defined to be the ratio of the reporter output with the enhancer and promoter divided by the reporter output with just the promoter. Conceptually, I think that considering the boost index is a reasonable way to quantify selectivity.

The authors use a frequentist approach to classify each enhancer as selective or not selective. The null hypothesis is that the boost index of the enhancer is equal across a set of promoters. This can be visualized in Fig. 2C where the null hypothesis is that the mean of each vertical distribution is equal. Note that in Figure S4 of this paper (and in Figure 4B of their 2022 paper) the within-group variance is not plotted. Statistical significance is assessed using a Welch F-test. This is a parametric test that assumes that the observations within each vertical distribution in Fig 2C are normally distributed (this test does allow for heteroskedasticity - which means that the variance may differ within each vertical distribution). Does the normality assumption hold? This analysis should be reported. If this assumption does not hold, is the Welch test well calibrated?

Figures and data