Reviewer #1 (Public Review):
This work offers a simple explanation to a fundamental question in cell biology: what dictates the volume of a cell and of its nucleus, focusing on yeast cells. The central message is that all this can be explained by an osmotic equilibrium, using the classical Van't Hoff's Law. The novelty resides in an effort to provide actual numbers experimentally.
In this work, Lemière and colleagues combine physical modeling and quantitative measures to establish the basic principles that dictate the volume of a cell and of its nucleus. By doing so, they also explain an observation reported many times and in many different types of cells, of a proportionality between the volume of the cell and of its nucleus. The central message is that all this can be explained by an osmotic equilibrium, using the classical Van't Hoff's Law. This is because, in yeast cells, while the cell has a wall that can contribute to the equilibrium, the nucleus does not have a lamina and there is thus no elastic contribution in the force balance for the nucleus, as the authors show very nicely experimentally, using both cells and protoplasts and measuring the cell and nucleus volume for various external osmotic pressures (the Boyle Van't Hoff Law for a perfect gas, also sometimes called the Ponder relation) - this was performed before for mammalian cells (Finan et al.), as cited and commented in the discussion by the authors, showing that mammalian cells have no significant elastic wall (linear relation) while the nucleus has one (non linear relation). This is well explained by the authors in the discussion. It is one of the clearer experimental results of the article. Together, the data and model presented in this article offer a simple explanation to a fundamental question in cell biology. In this matter, the principles are indeed seemingly simple, but what really counts are the actual numbers. While this article sheds some light on this aspect, it does not totally solve the question. The experiments are very well done and quantified, but some approximations made in the modeling are questionable and should at least be discussed in more length. Overall, this article is extremely valuable in the context of the recent effort of the cell biology and biophysics communities to understand the fundamental question of what dictates the size of cells and organelles. I have a few concerns detailed below. Importantly, there are many very interesting points of the article that I am not discussing below, simply because I completely agree with them.
1) The main concern is about the assumption made by the authors that the small osmolytes do not count to establish the volume of the nucleus. It was shown that small osmolytes such as ions are a vast majority of the osmolytes in a cell (more than ten times more abundant than proteins for example, which represent about 10 mM, for a total of 500 mM of osmolytes). This means that just a small imbalance in the amount of these between the nucleus and cytoplasm might have a much larger effect than the number of proteins, which is the osmolyte that authors choose to consider for the nuclear volume.
The point of the authors to disregard small osmolytes is that they can freely diffuse between the cytoplasm and the nucleus through the nuclear pores. They thus consider that the nuclear volume is established thanks to the barrier function of the nuclear envelope, which would retain larger osmolytes inside the nucleus and that the rest is balanced. This reasoning is not correct: for example, the volume of charged polymers depends on the concentration of ions in the polymer while there is no membrane at all to retain them. This is because of an important principle that the authors do not include in their reasoning, which is electro-neutrality.
Because most large molecules in the cell are charged (proteins and also DNA for the nucleus), the number of counterions is large, and is probably much larger than the number of proteins. So it is hard to argue that this could be ignored in the number of osmotically active molecules in the nucleus. This is known as the Donnan equilibrium and the question is thus whether this is actually the principle which dictates the nuclear volume.
The question then becomes whether the number of counterions differs between the cytoplasm and the nucleus, and more precisely whether the difference is larger than the difference considered by the authors in the number of proteins.
How is it possible to estimate this number? One of the numbers found in the literature is the electric potential across the nuclear envelope (Mazanti Physiological Reviews 2001). The number is between 1 and 10 mV, with more cations in the nucleus than in the cytoplasm. This number could correspond to much more cations than the number of proteins, although the precise number is not so simple to compute and the precision of the measure matters a lot, since there is an exponential relation between the concentrations and the potential.
This point above is simply made to explain that the authors cannot rule out the contribution of small osmolytes to the nuclear volume and should at least leave this possibility open in the discussion of their article.
As a conclusion, I totally agree with equation 3 which defines the N/C ratio, but I think that the Ns considered might not be the number of large macromolecules which cannot pass the nuclear envelope, but rather the small ones. Whether it is the case or not and what is actually the important species to consider depends on the actual numbers and these numbers are not established in this article. It is likely out of the scope of the article to establish them, but the point should at least be discussed and left open for future studies.
2) The authors refer to the notion of colloidal pressure, discussed in the review by Mitchison et al. This term could be confusing and the authors should either explain it better or just not use it and call it perfect gas pressure or Van't Hoff pressure. Indeed, what is meant by colloidal pressure is simply the notion that all molecules could be considered as individual objects, independently of their size, and that it is then possible to apply the Van't Hoff Law just as it was a perfect gas, hence the notion of 'colloidal' pressure, which would be the osmotic pressure of all the individual molecules. The authors might want to discuss, or at least mention, that it is a bit surprising that all these crowded large macromolecules would behave like a perfect osmometer and that the Van't Hoff law applies to them. Alternatively, it could be simpler to consider that what actually counts for the volume is mostly small freely diffusing osmolytes, to which this law applies well, and which are much more numerous.
3) Very small point: on page 7 the authors refer to BVH's Law (Nobel, 1969). It is not clear what they mean. If they refer to the Nobel prize of Van't Hoff, it dates from 1901 (he died in 1911) and not 1969. I am not sure if there is something in one of the Nobel prizes delivered in 1969 which relates to this law. I checked but it does not seem to be the case, so it is probably a mistake in the date.
4) On page 11, bottom, the result of the maintenance of the N/C ratio in protoplast is presented as an additional result, while it is a simple consequence of the previous results: both the cell and nuclear volume change linearly with the external osmotic pressure, so it is obvious that their ratio does not change when the external pressure is changed. Another result, not commented by the authors, is that this should be true only in protoplasts, since in whole cells, the cell wall is affecting the response of the cell volume, but not the nucleus, so the ratio should change.
5) The results in Figure 5, with the inhibition of export from the nucleus, are presented as supporting the model. It is not really clear that they do. First the effect is very small, even if very clear. Again, the numbers matter here, so the interpretation of this result is not really direct and more calculation should be made to understand whether it can really be explained by a change of number of proteins. The result in panel F is even more problematic. The authors try to argue that the nucleus transiently gets denser, based on the diffusion of the GEMs and then adapts its density. It rather seems that it is overall quite constant in density, while it is the cell which has a decreasing density - maybe, as suggested by the authors, because there are less ribosomes in the cytoplasm, so protein production is reduced. This could have an indirect effect on the number of amino acids (which would then be less consumed). A recent article by Neurohr et al (Trends in cell biology, 2020) suggests that such an effect can lead to cell dilution, in yeast, because the number of amino acids increases. In this particular case, this increase would affect the nuclear volume rather than the cell volume because of the presence of the cell wall and the rather small change.
6) Page 16: it seems to me that the experiments presented in the chapter lines 360 to 376, on the ribosomal subunits, simply confirm that export is impaired, and they do not really contribute to confirm the hypothesis of the authors that it is the number of proteins in the nucleus which counts.
The next paragraph with the estimation of the number of proteins in the nucleus and cytoplasm and how they change relatively upon export inhibition also appears to mostly demonstrate that export has been inhibited.
The authors propose to use the number they find, 8%, to compare it to the change in the N/C ratio, which is of the same order. Given how small these numbers are, and the precision of such measures, it is very hard to believe that these 8% are really precise at a level which could allow such a comparison. The authors should really estimate the precision of their measures if they want to claim that. It is more likely that what they observe is a small but significant change in both cases; a small change means it is small compared to the total, so it is a fraction of it, and it is measurable, which means it is more than just a few percent, which is usually not possible to measure. So it means that it is in the order of 10%. This is the typical value of any small but measurable change given a method for the measure which can detect changes around 10%. In conclusion, these numbers might not prove anything.
It could also be that the numbers match not just by chance, but that the osmolyte which matters is, for this type of experiment, changing in proportion to the amount of proteins (which would be possible for counter ions for example). But determining all that requires precise calculations and additional measures. It is thus more a matter of discussion and should be left more open by the authors.