Nuclear to cellular volume ratio is maintained through interphase, in multinucleate cells and between fission yeast species

Different aspects of membrane bound organelles could scale with cell size, such as linear dimensions, surface area or volume. Nuclear volume and nuclear membrane surface area of Schizosaccharomyces pombe fission yeast cells were monitored by time lapse microscopy, measuring nuclear and cellular volumes (V) and surface areas (SA) at the beginning and end of interphase (Fig. 1A,B). The V_nuc/V_cell ratio was the same at the two time points, confirming results from an earlier pilot study of five cells (Neumann and Nurse, 2007), but both SA_nuc/SA_cell and SA_nuc/V_cell ratios were significantly altered, suggesting that nuclear size homeostasis operates through a V_nuc/V_cell mechanism. This was tested further using multinucleate cells where nuclear surface area and volume diverge more dramatically than in mononucleates. At the restrictive temperature, cdc11-119 cells undergo repeated nuclear division without septation, giving rise to multinucleate elongated cells (Nurse et al., 1976) (Fig. 1C). Both SA_nuc/SA_cell and SA_nuc/V_cell ratios were significantly higher in octonucleates than in mononucleates, whereas the V_nuc/V_cell ratio was not significantly different between mononucleates and octonucleates (Fig. 1D). In addition, the V_nuc/V_cell ratio appears to be conserved between S. pombe and Schizosaccharomyces japonicus, which are predicted to have diverged evolutionarily ∼200 million years ago (Rhind et al., 2011). Their interphase V_nuc/V_cell ratios were similar (Fig. 1E,F), despite divergent cell sizes and mitotic strategies, and significant evolutionary divergence (Gu et al., 2012).

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Fig. 1.

V_nuc/V_cell is maintained through interphase, in multinucleate cells and between related fission yeast species. (A) The nucleus to cell volume (V_nuc/V_cell), nuclear to cellular surface area (SA_nuc/SA_cell) and nuclear surface area to cell volume (SA_nuc/V_cell) ratio of wild-type cells early and late in interphase. n=100 cells. Wild-type cells were measured through time-lapse microscopy (the nuclear envelope marker was Cut11–GFP) at 25°C and 5 min intervals. Each cell was measured early and late in interphase. Early, time point of first image following cell division of parent cell. Late: time point before first image displaying a Cut11–GFP focus. Cut11 is the S. pombe Ndc1 orthologue that transiently associates with the spindle pole body (SPB) during mitosis (West et al., 1998). (B) Representative cell from time lapse described in A. Time (min) following the early interphase time point indicated. Bright field, magenta; Cut11–GFP, yellow. *Early interphase. **Late interphase. (C) Representative images of cdc11-119 cells grown at 25°C then incubated at 37°C for time indicated. Bright field, magenta; Cut11–GFP, yellow. (D) V_nuc/V_cell, SA_nuc/SA_cell and SA_nuc/V_cell ratios of mononucleate (labelled 1) and octonucleate (labelled 8) cdc11-119 cells. Ratios were normalized to the mean ratio of mononucleate population. n=100 cells/condition. For both mononucleates and octonucleates, the V_nuc/V_cell, SA_nuc/SA_cell and SA_nuc/V_cell ratios displayed were calculated from measurements of the same 100 cells. (E) Representative images of S. pombe and S. japonicus cells (32°C). Brightfield, magenta; Cut11–GFP, yellow. (F) Interphase N/C ratio of S. pombe and S. japonicus cells grown at 32°C (n=80 cells/species). Box plots represent the 25–75th percentiles, and the median is indicated. The whiskers show the 10–90th percentiles. Paired (A) or unpaired (D,F) Student's t-tests were used to calculate P-values. Scale bars: 10 µm.

Aberrant V_nuc/V_cell ratios undergo rapid correction

Having established that a constant nuclear to cellular volume (N/C) ratio is maintained, we sought to investigate the mechanism responsible for this homeostasis by assessing the response of individual cells to N/C ratio perturbation. Pom1Δ cells undergo symmetric nuclear division but asymmetric cell division. More than 80% of pom1Δ cells, compared with less than 5% of wild-type, divide asymmetrically (Bahler and Pringle, 1998). Consequently, pom1Δ cells exhibit a large range of birth N/C ratios. Time lapse microscopy was carried out, and the nuclear and cellular volume of individual cells displaying asymmetric cell division was measured every five minutes from nuclear division of the mother cell to nuclear division of the daughter cell. From this data, the N/C ratio was calculated for 156 cells (Fig. 2A–C). Birth N/C ratios had a mean value of 0.084, like wild-type cells, but that ratio was very variable, ranging from 0.053 to 0.132. The asymmetric cell divisions of pom1Δ cells lead to a range of cell cycle durations, so data was cycle time normalised. The 156 cells were assigned into cohorts according to the initial N/C ratio (N/C ratio of first 20 min time bin). The different N/C ratio cohorts of cells displayed rapid homeostasis towards the wild-type N/C ratio value (0.08), generally within one cell cycle (Fig. 2D). This experiment was repeated in wild-type cells where altered N/C ratios occur rarely, usually as a result of asymmetric nuclear division (Fig. 2E), and so fewer aberrant ratio cells could be analysed. However, like pom1Δ cells, they exhibited N/C ratio homeostasis (Fig. 2F).

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Fig. 2.

Rapid N/C ratio homeostasis observed in cells ‘born’ with aberrant N/C ratios. (A) Schematic of asymmetric cell division of a pom1Δ cell producing large (low N/C ratio) and small (high N/C ratio) daughters. (B) Images from time-lapse microscopy (32°C) of a representative pair of cells. Bright field, magenta; Cut11–GFP, yellow. Binucleate mother (grey), large (yellow) and small (blue) daughters are indicated. (C) Cell volume, nucleus volume and N/C ratio of cells in B. Cells were measured every 5 min from mother cell nuclear division to daughter cell nuclear division (assigned into 20 min bins). Colours as in B. (D) N/C ratio against cycle time for pom1Δ cells (32°C, n=156 cells). Cells were assigned into cohorts according to the initial N/C ratio (first time bin) (n≥10 cells per cohort). Linear regression lines are shown. (E) Representative wild-type cell that had undergone asymmetric nuclear division. Bright field, magenta; Cut11–GFP, yellow. (F) N/C ratio against cycle time for wild-type cells ‘born’ with aberrant N/C ratios (25°C, n=44). Cells were assigned into cohorts according to the initial N/C ratio (four cells/cohort). Regression lines are shown. Dashed lines represent the wild-type N/C ratio. Scale bars: 10 µm.

Nuclear and cellular growth rates are not directly coupled

The kinetics with which N/C ratios recover from perturbation are informative about the mechanisms by which nuclear size homeostasis is achieved as different mechanisms will lead to different recovery times. Therefore, we analysed the kinetics of the N/C ratio recovery to allow us to distinguish between potential models. The simplest model by which N/C ratio homeostasis could be achieved is direct coordination of nuclear and cellular growth rates. If nuclear growth rate was maintained at 8% of cellular growth rate then N/C ratio values would converge on a value of 0.08. Changes to N/C ratios with an initial range of 0.04 to 0.16 were simulated and demonstrate homeostatic behaviour; N/C ratios eventually converged on a wild-type value of 0.08 but only after around four generations (Fig. 3A). The experimental data in Fig. 2 was compared to modelled values. Experimental and modelled linear regression lines of N/C ratio of cohorts of cells over ∼0.8 of a cell cycle were compared (Fig. 3B). For seven of eight high N/C ratio cohorts, and five of seven low N/C ratio cohorts, the N/C ratio recovery towards the population mean observed experimentally was more rapid than that predicted by the model.

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Fig. 3.

Nuclear and cellular growth rate are not directly coupled across the population. (A) Simulated N/C ratios of cells with initial N/C ratios ranging from 0.04 to 0.16 over 11 generations. Cell volume doubles between successive generations. Nuclear growth rate (GR_nuc) is maintained at 8% of cellular growth rate (GR_cell). (B) Comparison of experimental data for cohorts of pom1Δ cells described in Fig. 2D (black), spanning ∼0.8 cell cycles for each cohort, to N/C ratio change predicted over 0.8 cell cycles by the model (grey dotted) in which GR_nuc is maintained at 8% of GR_cell. The dashed lines represent the wild-type N/C ratio.

A rapid control mechanism corrects aberrant N/C ratios

To test the homeostatic mechanism further, the kinetics of N/C ratio change during interphase were examined in more detail. Nuclear and cellular volumes of pom1Δ cells were assessed for a larger number of cells using a lower temperature (25°C), allowing greater time resolution. Cells and nuclei were measured for 200 min from the septation of the mother cell, or until nuclear division if this was sooner, and instantaneous growth rates calculated. A range of initial N/C ratios from 0.049 to 0.164 was observed (Fig. 4A). The kinetics of N/C ratio homeostasis and the parameters affecting the kinetics in individual cells at specific times as they correct, were analysed. For each 20 min time bin, cellular growth rate, nuclear growth rate and the N/C ratio change rate were calculated and assigned to a cohort according to the N/C ratio at the start of the bin. This indicated that correction towards an N/C ratio of 0.079 occurred, and that the more aberrant an N/C ratio was, the more rapidly it corrected (Fig. 4B). Experimental N/C ratio change rate values were compared to modelled values assuming direct coordination of nuclear growth rate and cellular growth rate (Fig. 4B). The experimental mean was not within 95% confidence intervals of the modelled mean in any of the 15 cohorts. Cells with both high and low N/C ratios, exhibited an N/C ratio change rate faster in the experimental than in the modelled data. Therefore, a homeostatic mechanism is operative, which is more rapid than simple coordination of nuclear and cellular growth rates, although it is possible that coordination of nuclear and cellular growth rates might form part of the N/C ratio homeostasis mechanism.

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Fig. 4.

Cells with more-aberrant N/C ratios correct more rapidly. (A) N/C ratio of pom1Δ cells (25°C) measured during the 200 min after septation (5 min intervals, 20 min bins) (n=180 cells). The dashed line represents wild-type N/C ratio. Data were assigned into cohorts according to the initial bin N/C ratio (10 cells/cohort). Linear regression of cohort N/C ratio coloured by cohort average initial N/C ratio (blue, high; grey, intermediate; yellow, low). (B) Experimental (blue) and modelled (grey) mean N/C ratio change rate (with 95% confidence intervals) of individual 20 min time bins from pom1Δ data described in A assigned into cohorts according to the N/C ratio at the start of the bin. Modelled data calculated from experimental cell and nuclear volumes at the start of bins and cellular growth rates assuming nuclear growth rate is 8% of cellular growth rate. (C,D) Mean nuclear growth rate (C) and cellular growth rate at the start of the bin (D) of individual 20 min time bins from data described in A assigned into cohorts according to the N/C ratio at start of bin. The dashed line represents the N/C ratio at the start of the bin at which no N/C ratio change is observed. (E–H) Cellular growth rate (E,F) and nuclear growth rate (G,H) of individual time bins from data described in A assigned into cohorts according to the cell (E,F) or nucleus (G,H) volume at the start of the bin. Linear regression lines are shown except for H as r²<0.2. (I) Experimental (blue), limiting components model (see Materials and Methods) (purple) and GR_nuc/GR_cell=0.08 model (grey) mean N/C ratio change rate (with 95% confidence intervals) of individual 20 min time bins. Time bins of pom1Δ data described in Fig. 4 are assigned into cohorts according to the N/C ratio at the start of the bin.

Nuclear growth rate correlates with cell volume, not nuclear volume

The relationships between growth rates and parameters of the cells were further assessed to gain understanding of how N/C ratio homeostasis is achieved. Average cellular and nuclear growth rates were calculated for cohorts of time bins assigned according to the N/C ratio at the start of the bin (Fig. 4C,D). Nuclear growth rate correlated near-linearly with the N/C ratio at the start of the bin in cells with both low and high N/C ratios, decreasing with increasing N/C ratio (Fig. 4C). Nuclear growth rate intercepted the x-axis at an N/C ratio ∼50% higher than the N/C ratio at which no correction is observed (0.079) suggesting that, at very high N/C ratios, nuclear growth ceases. Average cellular and nuclear growth rates were calculated for cohorts of time bins assigned into cohorts by nucleus or cell volume at the start of the bin. Cellular growth rate correlated with both the cell (Fig. 4E) and nucleus (Fig. 4F) volume at the start of the bin. Nuclear growth rate correlated with the cell volume at the start of the bin (Fig. 4G) but did not correlate with nucleus volume at the start of the bin (Fig. 4H). Therefore, nuclear growth rate was not determined by nuclear volume but instead correlated with cell volume and negatively with N/C ratio.

The kinetics of recovery observed are similar to those predicted by a limiting components model of nuclear size control

The observation that at very high N/C ratios (>0.12) nuclear growth rate is much decreased (Fig. 4C) suggested an alternative possible model for N/C ratio homeostasis. At N/C ratios above 0.12, nuclear growth may be prevented because a factor, or factors, required for nuclear growth becomes limiting, giving rise to a limiting components model (Goehring and Hyman, 2012; Marshall, 2015). In such a model, the amount of a component required for nuclear growth would be determined by cell volume. Nuclear growth rate would scale with the free cellular concentration of the component. In large cells with low N/C ratios, the component would not be limiting, so nuclear growth rate would be high, decreasing as the pool of excess component was depleted. In cells with mid-range N/C ratios, nuclear growth rate would generally scale with cellular growth rate, as the pool of limiting component was replenished by cellular growth. In small cells with extremely high N/C ratios, the free cellular concentration of the limiting component would rapidly become lower than that required for nuclear growth, so nuclear growth would reduce or even cease.

The kinetics of N/C ratio change predicted by such a limiting components model (Materials and Methods) were compared to experimental data and to those predicted by the alternative model described above in which nuclear and cellular growth rates are directly coupled (Fig. 3). The mean N/C ratio change rate was calculated for time bins assigned into cohorts according to the N/C ratio at the start of the bin (Fig. 4I). The limiting components model describes the experimental data well and predicts N/C ratio correction towards a value of ∼0.08. The modelled mean N/C ratio change rate is within 95% confidence intervals of the experimental mean in 14 of 15 N/C ratio cohorts. Therefore, the N/C ratio homeostasis observed in S. pombe cells is consistent with a limiting components model in which concentrations of nuclear components limit the nuclear growth rate. As a consequence, a nucleus in a low N/C ratio cell will undergo percentage size increase faster than a nucleus in a cell with a normal N/C ratio. The inverse is true for nuclei in high N/C ratio cells, as the percentage size increase would be slower than in cells with normal N/C ratios, giving rise to nuclear size homeostasis. A limiting component determining nuclear size has been proposed previously (Goehring and Hyman, 2012), and assumes that the amount of a factor required for nuclear growth is directly proportional to cell volume. This is reasonable given that biosynthesis rate (Schmoller and Skotheim, 2015) and protein amount (Crissman and Steinkamp, 1973; Newman et al., 2006; Williamson and Scopes, 1961) generally scale with cell size. In the case of nuclear size homeostasis, the amount of the limiting factor or factors in the cytoplasm determines nuclear volume growth. Increase in nuclear volume requires an increase in nuclear membrane surface area. As we have shown that nuclear membrane surface area does not scale simply with cell volume, we propose that the primary driver of nuclear size homeostasis is the amount of nuclear content, largely determined by the balance between nuclear import and export, and that changes in the nuclear membrane surface area are brought about indirectly by the nuclear contents. This is consistent with the observation that inhibition of nuclear export results in nuclear expansion (Neumann and Nurse, 2007) and, speculatively, might involve a pressure-sensing mechanism acting at the membrane. Our screens of fission yeast non-essential and essential gene deletion mutants for those with aberrant nuclear size phenotypes have implicated a range of factors and biological processes as being involved in this process, including nucleocytoplasmic transport, lipid biogenesis, LINC complexes and RNA processing in nuclear size control (Cantwell and Nurse, 2019; Kume et al., 2017). Thus, there could be multiple limiting components involved in the nuclear size homeostatic mechanism.