The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.


Introduction and
: The figure is too small to read the data easily. As many of the earlier papers cited in the introduction 1-3, and especially the 2015 article, mostly consider the nucleus size and shape for cells attached to a surface and when released from the surface following chemical treatment. If the authors have generated the data in Figure 1A, it would be good to have more details about the experiment in the SI.

Modeling Assumptions and Initial Conditions (lines 231-260):
Can you briefly comment on any caveats on scaling up from Yeast growth related parameters to achieve initial conditions for Mammalian cells? Are the values given in Table 2

Figure 4:
Is the difference in the behavior of the increases in Cell Volume for the quiescence and poor amino acid cases in Yeast and HeLa cells primarily due to the difference in volume (HeLa > Yeast) between the two cells? If so, should this be stated in the text or is it more due to "the balance between protein synthesis and degradation" as you state in line 330? Fig.  6 and if X's or markers were placed on the exact conditions used in simulations (and Reported in Table 2) that are most appropriate. Figure 5: Out of curiosity, does CellV and doubling time ever plateau when increasing t1 (the amino acid transport rate, it does not seem that it does) or does CellV continue to increase for Yeast (as is shown in Fig. 5a and Fig.5f) with increasing t1 via your model parameters? -f respectively could benefit from having the same axes scales (which they do not, these seem to vary from 0.6-0.8 for the same quantity, i.e. t1), which would make a 1-to-1 comparison of growth conditions more amenable.

Figure 5 -Heatmap vs Contour maps: It may be clearer if this was made a 2D heatmap like
Lines 487-540: It is good that the authors eventually discuss the stochastic nature of gene expression and some of its effects on the cell cycle. I would like to have seen this mentioned earlier, perhaps in the introduction. It would also be good to discuss and cite some other work on stochastic gene expression, its impacts on various parts of the cell cycle, and combinations of analytic/deterministic processes with stochastic processes. Beside the early work of Elowitz on bacteria and Arkin, it would be good to mention both the existing analytical and computational studies. For example, the work of Ramon Grima in comparing analytic and stochastic simulations in a eukaryotic cell to obtain protein numbers (Cao and Grima, PNAS, 2020) could be an interesting discussion or comparison to make to this model. Additionally, of interest are the simulations ribosome biogenesis stochastically in a dividing E. coli cell (Earnest et al., Biopolymers, 2016) or the hybrid stochastic-deterministic simulation technique (Bianchi et al., IET Systems Biology, 2018) applied to the galactose switch in yeast.

Discussion and Conclusions:
Where you state "amino acid import coefficient t1 is more important for exponentially growing cells" in line 574 would be an opportune place in which to address my earlier question about the relationship between t1 and Volume Growth measured in Figure 5.
Minor 1.Where you state, "stochastic dynamical systems response to changes in environmental systems" in line 585 it should read "respond to changes". Also, a relevant citation for this statement would be: Wolf et al eLife 2015 among others. 2. line 305-307: Indicate whether replication initiation corresponds to DNA replication initiation or cell division initiation, as this could be unclear to readers less familiar with the budding process of yeast.