Single-cell data and correlation analysis support the independent double adder model in both Escherichia coli and Bacillus subtilis

The reference point for cell-size control in the cell cycle is a fundamental biological question. We previously reported that we were unable to reproduce the conclusions of Witz et al.s eLife paper (Witz, van Nimwegen, and Julou 2019) entitled, "Initiation of chromosome replication controls both division and replication cycles in E. coli through a double-adder mechanism", despite extensive efforts. In this replication double adder (RDA) model, both replication and division cycles are determined via replication initiation as the sole implementation point of size control. Witz et al. justified the RDA model using a type of correlation analysis (the "I-value analysis") that they developed. By contrast, we previously showed that, in both Escherichia coli and Bacillus subtilis, replication initiation and cell division are determined by balanced biosynthesis of key cell cycle proteins (e.g., DnaA for initiation and FtsZ for cell division) and their accumulation to their respective threshold numbers, which Witz et al. coined the independent double adder (IDA) model. The adder phenotype is a natural quantitative consequence of these mechanistic principles. In a recent bioRxiv response to our report, Witz and colleagues explicitly confirmed two important limitations of the I-value analysis: (1) it is only applicable to non-overlapping cell cycles, wherein E. coli is known to deviate from the adder principle, and (2) it is only applicable to select biological models and, for example, cannot evaluate the IDA model. These limitations of the I-value analysis were not explained in the original eLife paper and were overlooked during the review process. In this report, we show using data analysis, mathematical modeling, and experiments why the I-value analysis - in its current implementation - cannot compare different biological models. Furthermore, the RDA model is incompatible with the adder principle and is not broadly supported by experimental data. For completeness, we also provide a detailed point-by-point response to Witz et al.s response (Witz, Julou, and van Nimwegen 2020) in the Supplemental Information.