PREreview of Cell size scaling laws: a unified theory

In the paper Cell size scaling laws: a unified theory by Rollin et al., a tuned simplified Pump-Leak model (PLM) in combination with order of magnitude estimations serves as physical basis for the derivation of various cell size scaling laws, a highly relevant biological topic with medical applications.

The first sections introduce the simplified PLM together with the necessary assumptions and present the results of the order of magnitude estimations, highlighting the dominance of metabolites in the wet volume and the dominance of proteins in the dry volume.

Under additional consideration of a growth model and an amino-acid biosynthesis model, the authors find a constant dry mass density during growth and dilution at senescence.

A similar phenomenon with a different origin, mitotic swelling, can be explained taking into account Manning condensation.

The last three sections deal with reasonable extensions and considerations that allow the authors to explain nuclear scaling and to identify influential parameters of the NC ratio, in particular the role of metabolites. Apart from relying on the simplified PLM, these sections on nuclear scaling are self-contained and therefore, given their abundance of insights, potentially more suitable for a separate research paper.

Embedded in an excellent structure, and based on an introduction that is accessible for a general scientific audience, the authors carefully introduce simplifications and justifications. While physical basics seem to be properly explained for biologists, this does not always apply for the opposite case. Biological explanations are in places insufficiently provided to readers from a physics background, indicating that physicists are not the primary target group of this paper. At least in the discussion, more biological intuition is provided (e.g., the Sec. The nucleoskeletal theory). The authors' efforts to make explanations of their results intuitive are clearly visible but not in every aspect successful. That does not diminish the understanding of the authors' conclusions which are well supported and properly explained.

Major comments

• Schematic drawings of biological processes are barely understandable without the caption. I would strongly encourage to add legends to Figs. 1A, 2A, 4A to be able to understand the presented mechanisms at one glance.

• To avoid confusion, it should be specified that the physical dimension of dry mass is volume.

• In Fig. 2D, errorbars are shown together with more than one data point for each time. In general, errorbars should only be displayed together with the mean value. It is unclear whether the mean value is displayed. If so, it should be highlighted, for example in boxplot style. Otherwise, not an error bar, but a violin style plot would be appropriate.

• Fig. 4B displays simulation results with parameters from experiments. This is correctly described in the respective caption. However, in the main text, the authors ambiguously refer to this figure in the context of an experimental verification.

• Although Fig. 4B is certainly capable of showing a correlation between variations of NC ratio and variations of the NEP, mirroring one plot is a detour. Computing and/or displaying the cross correlation between the slopes would be more informative and support this statement more directly.

• To conceptually link the Sec. Mitotic swelling with the following ones, it should already in Sec. Mitotic swelling be specified when effects concerning the nucleus (i.e., the relevance of chromatin) are considered, especially for non-biologist readers.

• In Sec. Mitotic swelling, the 5th defining feature (nuclear envelope breakdown) is not sufficiently explained. Without further elaboration, it remains unclear why one could expect it to be an explanation for mitotic swelling.

• The idea to include explanatory sections, e.g., on Manning condensation in the appendix, is very helpful.

• When reporting that the actual NC ratio lies closer to NC1 than to NC2, the conclusion that metabolites are relevant since their role is considered in NC1 appears obvious but is not proven in the main text. The authors should explicitly point out that there is no underlying nonlinearity governing the relation between the influence of metabolites and the NC ratio, if necessary, by referring to additional calculations.

Minor comments

• Symbols that have superscripted subscripts, such as z_{A^f} , are hard to decipher, especially in nested fractions, e.g., Eq. 5.

• The inset in Fig. 4D is too small to be properly readable in print.

Competing interests

The author declares that they have no competing interests.