Control of nuclear size by osmotic forces in Schizosaccharomyces pombe

Article activity feed

1. 

   Version published to 10.7554/elife.76075 on eLife

   Jul 20, 2022
2. 

   eLife

   Jun 6, 2022

   Author Response

   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 …

   Author Response

   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.

   We appreciate these excellent points made by the reviewer and their numerous consultants. We amend the discussion of colloid osmotic pressure in the text to reflect these points.

   1. 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.

   1. 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.

   The citation is correct. It's a JTB paper by Park S. Nobel describing the BHV relation in biology.

   1. 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.

   This result was not trivial. Although both cells and nuclei volume change linearly with the inverse of the external osmotic concentration in protoplasts, it was not obvious whether the two volumes change with the same proportion (ie same slope on the BVH graph).

   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.

   In whole cells, the maintenance of the N/C ratio is in fact also maintained, consistent with the model. This result is now clarified in the manuscript (Figure 1C and D plus Figures 3D and S1C).

   1. 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.

   We agree that there are different possible interpretations for these results. We have carefully reconsidered the interpretation and have rewritten the entire text for Figure 5

   1. 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.

   We agree. We highlight the ribosomal subunit proteins as they are very abundant nuclear shuttling proteins that provide a good example for the dynamics of nuclear protein accumulation.

   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.

   We agree that these measurements are not so precise. We have carefully reworded this section and removed these specific comparisons.

   Reviewer #2 (Public Review):

   The goal of the paper is to test the idea that colloidal osmotic pressure controls nuclear growth as suggested by Tim Mitchison in a recent review.

   In fleshing out the idea, Lemiere and colleagues develop a simple mathematical model that focuses on the forces generated by the movement of macromolecules across the nuclear-cytoplasmic boundary, ignoring any contribution of ions or small molecules which they assume equilibrate across the nuclear envelope. In testing this model, they focus their quantitative analysis on the response of cells that lack a wall (protoplasts) to osmotic shocks and to perturbations of nuclear export, protein synthesis and symmetric cell division. They also analyse the motion of small 40nm particles to test how diffusion is affected by these perturbations in both compartments.

   Their analysis leads them to make some important observations that suggest that the system is even simpler than they might have hoped, since under the conditions tested nuclei (which lack lamins) behave as ideal osmometers. That is, the nuclei and cytoplasm grow and shrink in concert following sudden osmotic shocks. This suggests that the tension in the nuclear envelope, which gives nuclei their spherical shape, plays no role in constraining nuclear size.

   While most of the paper's claims are well supported by their data under the assumptions of the model, there are a few claims that are less convincing.

   For example, while their data are consistent with the idea that cells regulate their nuclear/cytoplasmic size ration using an adder type mechanism, in which a fix ratio of nuclear and cytoplasmic proteins are synthesised per unit time as cells grow, this has not been rigorously put to the test. In addition, while the diffusion analysis is very interesting, it does not fully support the authors' simple model linking diffusion, molecular crowding and colloidal osmotic pressure, something that could be more thoroughly discussed in the manuscript.

   We added new data showing that slowing growth rate leads to a proportionate decrease in N/C ratio correction. This strengthens this portion of the paper.

   We have added an improved discussion of the GEMs data and its limitations.

   Reviewer #3 (Public Review):

   This manuscript by Lemière and colleagues presents a view on how nuclear size is set by simple physical principles. The first part of the work describes a theoretical framework with the nucleus and the cell as two nested osmometers. Using fission yeast as a model, the authors then show that protoplasts and nuclei behave as ideal osmometers, i.e. show linear changes in volume upon change in external osmotic pressure. Consequently, the nuclear to cell volume ratio remains constant upon osmotic changes, but increases upon block of nuclear export, which leads to higher nuclear protein contents. Measurements of diffusion in the cytoplasm and nucleoplasm back these data. Finally, in the last part of the manuscript, the authors show that nuclear growth through a passive osmotic model can explain the previously described homeostasis of nuclear volume.

   The manuscript is clearly written, and the data are clean and overall solid. I very much liked the simple view on the phenomenon of constant nuclear to cytosol ratio and the mix of modelling and experiments supporting the model that nuclear size is set passively by osmotic principles.

   There are however a few points that are slightly at odds with the model and/or require further explanation to make the model compelling and discuss it in view of previous findings.

   1. Isn't the finding that diffusion rates are faster in the nucleus (line 298, Fig S4C), indicating lower crowding in the nucleus, at odds with the finding that the non-osmotic volumes are similar in the two compartments? If the nucleus is less crowded, does this not suggest a lower pressure than the cytosol? I would also like to see this finding appear in Figure 4, which only reports on the normalized diffusion rates in both nuclei and cytosol.

   We have added this figure to the main Figure 4, as requested. We agree that this raises some interesting questions. Our current interpretation is that composition of the nucleoplasm and cytoplasm are different and therefore affect GEMs diffusion and colloid osmotic pressure slightly differently.

   1. Similarly, I don't understand the observed change in diffusion rates of GEMs upon LMB treatment (Fig 5F). If the nucleus behaves as an ideal osmometer, then any change in protein density between the nucleus and the cytosol, leading to change in osmotic pressure, will lead to a change in nuclear size that should re-equilibrate the osmotic pressures between the two compartments. The prediction would thus be that, if LMB treatment does not change overall protein concentration, at equilibrium there is no change in either osmotic pressure or density as measured by GEM diffusion rates. This is indeed illustrated by the constant normalized non-osmotic volume of the nucleus after LMB treatment. Is the change in diffusion rates perhaps only transient until a new steady state is reached? Or is there a change upon total protein content in the cell after LMB treatment?

   1. In the experiments labelling proteins with FITC, are the reported values really those of protein concentrations or rather protein amounts? Isn't the enlargement of the nucleus upon LMB treatment compensating for this increase in amounts, returning the nucleus to a similar concentration as before treatment? A change in concentration is not in agreement with the reported constant non-osmotic volume of the nucleus.

   These measurements of intensity are of concentrations. We add in the text this prediction that changes in concentration will be compensated for by swelling in nuclear volume and now interpret the data in light of this prediction. We add new data that total FITC staining for protein and RNA shows no change in concentration in compartments, consistent with this model.

   1. The authors state that "a previous paper proposed a model for N/C ratio homeostasis based upon an active feedback mechanism (Cantwell and Nurse, 2019)" (lines 471-472). My understanding of this previous study is that nuclear size was proposed to be set by a limiting component, itself proportional to cell volume. No feedback was postulated. This previous model is in fact not too different from what the authors propose here, with the previously proposed limiting component now corresponding to the nuclear macromolecules that produce colloid osmotic pressure and thus set nuclear size. Though the present study goes significantly further in presenting the passive role of osmosis in setting nuclear size, it is a misrepresentation to portray this previous model as fundamentally different. Furthermore, it is not clear whether the new osmotic pressure-based model produces a better fit than the previous 'limiting component model'. Figure 7E here is very similar to Fig 4I in Cantwell and Nurse 2019, but it is difficult to judge the similarity of the fits.

   The Cantwell and Nurse paper tested two models. The first was based upon nuclear growth being a fraction of cell growth. This model is qualitatively similar to ours. However, they discarded this initial model because it fitted poorly with their data. They then went to propose a second model, which contains a critical equation in which nuclear growth rate is a function of the N/C ratio, i.e. the system is sensing the N/C ratio and adjusting nuclear growth rate as a function of the N/C ratio. In other words, this is a feedback mechanism. The Cantwell paper does not describe this "feedback" term explicitly in the text, but it is clearly present in the equations. Therefore, our model which lacks any feedback term is fundamentally different from the Cantwell limiting component model.

   We show that our model fits our data much better than the Cantwell model. We believe that the different views in these studies arise from differences in the experimental data. These differences may arise from two technical differences: 1) Their use of binning could be responsible for flattening the nuclear growth rate as a function of the nuclear volume at start. 2) Their estimates of cell and nuclear volumes using a 2D image and geometric assumptions may be less accurate than our automated 3D volume method.

   1. If nuclear size is set purely by osmotic regulation, how do you explain that mutants in membrane regulation (such as nem1 and spo7, see Kume et al 2017; or lem2, see Kume et al 2019) previously shown to have an enlarged nucleus, display increased nuclear size?

   This is an interesting question that we are currently pursuing. It is likely that these mutants affect multiple processes besides nuclear envelope expansion. For example, at least some of these mutants have altered chromatin organization could cause increase in colloid pressure. There may also be significant defects in chromosome segregation, which leads to production of different-sized nuclei with abnormal number of chromosomes. Some of the N/C ratio defects reported in these papers may arise from their 2D measurement methods, which are not accurate for misshapen nuclei. In our preliminary results, lem2 mutants do not have N/C ratio defects.

   Read the original source
3. 

   eLife

   Jun 6, 2022

   Evaluation Summary:

   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.

   (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

   Read the original source
4. 

   eLife

   Jun 6, 2022

   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 …

   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.

   1. 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.

   2. 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.

   3. 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.

   4. 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.

   5. 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.

   Read the original source
5. 

   eLife

   Jun 6, 2022

   Reviewer #2 (Public Review):

   The goal of the paper is to test the idea that colloidal osmotic pressure controls nuclear growth as suggested by Tim Mitchison in a recent review.

   In fleshing out the idea, Lemiere and colleagues develop a simple mathematical model that focuses on the forces generated by the movement of macromolecules across the nuclear-cytoplasmic boundary, ignoring any contribution of ions or small molecules which they assume equilibrate across the nuclear envelope. In testing this model, they focus their quantitative analysis on the response of cells that lack a wall (protoplasts) to osmotic shocks and to perturbations of nuclear export, protein synthesis and symmetric cell division.
   They also analyse the motion of small 40nm particles to test how diffusion is affected by these perturbations in both compartments.

   Their …

   Reviewer #2 (Public Review):

   The goal of the paper is to test the idea that colloidal osmotic pressure controls nuclear growth as suggested by Tim Mitchison in a recent review.

   In fleshing out the idea, Lemiere and colleagues develop a simple mathematical model that focuses on the forces generated by the movement of macromolecules across the nuclear-cytoplasmic boundary, ignoring any contribution of ions or small molecules which they assume equilibrate across the nuclear envelope. In testing this model, they focus their quantitative analysis on the response of cells that lack a wall (protoplasts) to osmotic shocks and to perturbations of nuclear export, protein synthesis and symmetric cell division.
   They also analyse the motion of small 40nm particles to test how diffusion is affected by these perturbations in both compartments.

   Their analysis leads them to make some important observations that suggest that the system is even simpler than they might have hoped, since under the conditions tested nuclei (which lack lamins) behave as ideal osmometers. That is, the nuclei and cytoplasm grow and shrink in concert following sudden osmotic shocks. This suggests that the tension in the nuclear envelope, which gives nuclei their spherical shape, plays no role in constraining nuclear size.

   While most of the paper's claims are well supported by their data under the assumptions of the model, there are a few claims that are less convincing.

   For example, while their data are consistent with the idea that cells regulate their nuclear/cytoplasmic size ration using an adder type mechanism, in which a fix ratio of nuclear and cytoplasmic proteins are synthesised per unit time as cells grow, this has not been rigorously put to the test. In addition, while the diffusion analysis is very interesting, it does not fully support the authors' simple model linking diffusion, molecular crowding and colloidal osmotic pressure, something that could be more thoroughly discussed in the manuscript.

   Overall, the paper is well written in a manner that will make clear to any reader the aims and relevant background. In addition, the paper controls an impressive amount of data and includes clever controls (e.g. labelled ribosomal proteins of different sizes). The inconsistencies in the use of graph axes in Figures are likely to confuse readers though.

   Read the original source
6. 

   eLife

   Jun 6, 2022

   Reviewer #3 (Public Review):

   This manuscript by Lemière and colleagues presents a view on how nuclear size is set by simple physical principles. The first part of the work describes a theoretical framework with the nucleus and the cell as two nested osmometers. Using fission yeast as a model, the authors then show that protoplasts and nuclei behave as ideal osmometers, i.e. show linear changes in volume upon change in external osmotic pressure. Consequently, the nuclear to cell volume ratio remains constant upon osmotic changes, but increases upon block of nuclear export, which leads to higher nuclear protein contents. Measurements of diffusion in the cytoplasm and nucleoplasm back these data. Finally, in the last part of the manuscript, the authors show that nuclear growth through a passive osmotic model can explain the previously …

   Reviewer #3 (Public Review):

   This manuscript by Lemière and colleagues presents a view on how nuclear size is set by simple physical principles. The first part of the work describes a theoretical framework with the nucleus and the cell as two nested osmometers. Using fission yeast as a model, the authors then show that protoplasts and nuclei behave as ideal osmometers, i.e. show linear changes in volume upon change in external osmotic pressure. Consequently, the nuclear to cell volume ratio remains constant upon osmotic changes, but increases upon block of nuclear export, which leads to higher nuclear protein contents. Measurements of diffusion in the cytoplasm and nucleoplasm back these data. Finally, in the last part of the manuscript, the authors show that nuclear growth through a passive osmotic model can explain the previously described homeostasis of nuclear volume.

   The manuscript is clearly written, and the data are clean and overall solid. I very much liked the simple view on the phenomenon of constant nuclear to cytosol ratio and the mix of modelling and experiments supporting the model that nuclear size is set passively by osmotic principles.

   There are however a few points that are slightly at odds with the model and/or require further explanation to make the model compelling and discuss it in view of previous findings.

   1. Isn't the finding that diffusion rates are faster in the nucleus (line 298, Fig S4C), indicating lower crowding in the nucleus, at odds with the finding that the non-osmotic volumes are similar in the two compartments? If the nucleus is less crowded, does this not suggest a lower pressure than the cytosol? I would also like to see this finding appear in Figure 4, which only reports on the normalized diffusion rates in both nuclei and cytosol.

   2. Similarly, I don't understand the observed change in diffusion rates of GEMs upon LMB treatment (Fig 5F). If the nucleus behaves as an ideal osmometer, then any change in protein density between the nucleus and the cytosol, leading to change in osmotic pressure, will lead to a change in nuclear size that should re-equilibrate the osmotic pressures between the two compartments. The prediction would thus be that, if LMB treatment does not change overall protein concentration, at equilibrium there is no change in either osmotic pressure or density as measured by GEM diffusion rates. This is indeed illustrated by the constant normalized non-osmotic volume of the nucleus after LMB treatment. Is the change in diffusion rates perhaps only transient until a new steady state is reached? Or is there a change upon total protein content in the cell after LMB treatment?

   3. In the experiments labelling proteins with FITC, are the reported values really those of protein concentrations or rather protein amounts? Isn't the enlargement of the nucleus upon LMB treatment compensating for this increase in amounts, returning the nucleus to a similar concentration as before treatment? A change in concentration is not in agreement with the reported constant non-osmotic volume of the nucleus.

   4. The authors state that "a previous paper proposed a model for N/C ratio homeostasis based upon an active feedback mechanism (Cantwell and Nurse, 2019)" (lines 471-472). My understanding of this previous study is that nuclear size was proposed to be set by a limiting component, itself proportional to cell volume. No feedback was postulated. This previous model is in fact not too different from what the authors propose here, with the previously proposed limiting component now corresponding to the nuclear macromolecules that produce colloid osmotic pressure and thus set nuclear size. Though the present study goes significantly further in presenting the passive role of osmosis in setting nuclear size, it is a misrepresentation to portray this previous model as fundamentally different. Furthermore, it is not clear whether the new osmotic pressure-based model produces a better fit than the previous 'limiting component model'. Figure 7E here is very similar to Fig 4I in Cantwell and Nurse 2019, but it is difficult to judge the similarity of the fits.

   5. If nuclear size is set purely by osmotic regulation, how do you explain that mutants in membrane regulation (such as nem1 and spo7, see Kume et al 2017; or lem2, see Kume et al 2019) previously shown to have an enlarged nucleus, display increased nuclear size?

   Read the original source
7. 

   Version published to 10.1101/2021.12.05.471221v2 on bioRxiv

   Dec 14, 2021
8. 

   Version published to 10.1101/2021.12.05.471221v1 on bioRxiv

   Dec 7, 2021