Dynamic Allometry of Nuclei in Early Embryos of Caenorhabditis elegans

Allometric relations between two observables are a widespread phenomenon in biology. The volume of nuclei, for example, has frequently been reported to scale linearly with cell volume, $V_N\sim V_C$, but conflicting, sublinear power-law correlations have also been found. Given that nuclei are vital organelles that harbor and maintain the DNA of cells, an understanding of allometric nuclear volumes that ultimately define the concentration and accessibility of chromatin is of great interest. Using the model organism Caenorhabditis elegans, we show here that the allometry of nuclei is a dynamically adapting phenomenon; i.e., we find $V_N\sim V_C^{\alpha }$ with a time-dependent scaling exponent $\alpha$ (“dynamic allometry”). This finding is due to relaxation growth of nuclear volumes at a rate that scales with cell size. If cell division stops the relaxation of nuclei in a premature stage, $\alpha <1$ is observed, whereas completion of relaxation yields $\alpha =1$ (“isometry”). Our experimental data are well captured by a simple and supposedly generic model in which nuclear size is determined by the available membrane area that can be integrated into the nuclear envelope to relax the expansion pressure from decondensed chromatin. Extrapolation of our results to growing and proliferating cells suggests that isometric scaling of cell and nuclear volumes is the generic case.

Popular Summary

In biology, allometric relations—in which two traits or processes in an organism scale with one another—are widespread. The size of cell nuclei, for example, has frequently been reported to be adapted to cell size: Small cells have small nuclei. Given that nuclei are vital organelles that harbor and maintain the DNA of cells, an understanding of allometric nuclear volumes is of great interest. Embryos of the nematode Caenorhabditis elegans are particularly well suited to study this relationship because they undergo a series of volume-conserving division cycles that result in progressively smaller cells. Using confocal and light-sheet fluorescence microscopy on this model organism, we show that the allometric relation between nuclear size and cell size depends explicitly on time.

Specifically, we find that the nuclei exhibit a relaxation growth toward an asymptotic volume after cell division, where the asymptotic volume is proportional to the cell volume (“isometry”) and the relaxation rate scales with cell size. Since division times and cell volumes are anticorrelated in C. elegans embryos, nuclei in large cells do not fully relax, but rather are stopped at a premature volume that scales sublinearly with cell volume. Our experimental data are well captured by a simple and generic model in which nuclear size is determined by the available membrane area that can be integrated into the nuclear envelope to relax the expansion pressure from decondensed chromatin.

Extrapolation of our results to growing and proliferating cells suggests that isometric scaling of cell and nuclear volumes is not limited to C. elegans embryos but rather is the case generically.

Figure 1

(a) Representative confocal image of a C. elegans embryo in the four-cell state with the green fluorescence highlighting plasma membrane and nuclear envelope (over a residual fluorescence background in the cytoplasm and nucleoplasm). (b) After manual segmentation of the entire image stack, the identified cell boundaries (green) and nuclear envelopes (red) allow for quantifying the respective volumes. (c) Representative data for the growth kinetics of the nuclear volume $V_N$ for single cells of the somatic (ABa, ABxxxx, MS) and germline (P1, P2) lineages in a single embryo. The experimental data (symbols) can be well fitted by Eq. (1) (solid lines, $0.81<R^2<0.99$). (d) Largest nuclear volume $V_N^{\max }$ observed experimentally before cell division (black circles, $n=5$ embryos), are linked to the cell volume $V_C$ by a sublinear relation $V_N^{\max }\approx 0.37V_C^{0.75}$ (black line, $R^2=0.76$). In contrast, the asymptotic steady-state volume $V_S=V_0+V_1$ (red open squares) obtained by Eq. (1) roughly follows an isometric relation $V_S=V_C/10$ (red line), albeit with considerable fluctuations (hence only $R^2=0.33$).

Figure 2

(a) Representative image sequence of fluorescently labeled chromatin in the P2 cell (1 min between consecutive frames, scale bar: $5\mathrm{\mu }\mathrm{m}$). In the first image (anaphase of the mother cell, P1), the chromatin of the second daughter cell (EMS) is marked with an asterisk. The area of the chromatin signal is approximately circular; i.e., nuclei were approximately spherical. (b),(c) Representative time course of nuclear volumes, $V_N(t)$, for differently sized cells of the somatic (AB, ABal, ABala) and germline (P1, P2, P3) lineages. Symbols represent the mean of $n=9$ untreated embryos. The standard error of the mean, reflecting embryo-to-embryo variation, was less than or equal to the symbol size for virtually all data points. Fits according to Eq. (1) are shown as solid lines ($0.92<R^2<0.99$). For large cells, the nuclear expansion was stopped by the next division event (dashed vertical lines), whereas nuclei of smaller cells had sufficient time to reach their final volume.

Figure 3

When the ambient temperature is lowered from 22.5 °C to 15 °C, the cell cycle time is prolonged [33], providing additional time for the nuclei to relax to their asymptotic volume. The example curves refer to EMS cells at the indicated temperatures. For better comparison of the relaxation, the fluctuating asymptotic volume $V_S$ is divided out since no consistent trend of the fit parameters in Eq. (1) as a function of temperature was observed (Fig. S2 in the Supplemental Material [48]). A single relaxation curve according to Eq. (1) (black line) is also shown for comparison.

Figure 4

(a) Starting volumes of nuclei, $V_0$, are, on average, constant for all cells (cf. gray dashed line); i.e., no dependency on cell volume $V_C$ is seen. (b) The asymptotic steady-state volume of nuclei, $V_S=V_0+V_1$, is in agreement with an isometric scaling $V_S=V_C/10$ (gray dashed line, $R^2=0.88$). Deviations at $V_C\approx {10}^4\mathrm{\mu }{\mathrm{m}}^3$ are most likely a consequence of an early interruption of the nuclear growth in cells AB and P1 [cf. Figs. 2 and 2], which truncates the time course $V_N(t)$ and leads to an increased uncertainty of the fit parameter $V_1$ in Eq. (1). (c) The typical relaxation time of nuclear growth, $\tau$, correlates with cell volume, following approximately a scaling $\tau =0.05V_C^{2/3}$ (gray dashed line, $R^2=0.51$). Note that the data for untreated embryos (black circles), eggshell-devoid embryos (red crosses), smaller embryos (green squares), and larger embryos (blue diamonds) follow the same trend in all plots; i.e., neither mechanical constraints from the eggshell nor the total length of the embryo have a distinct impact. For each condition, all available cell lineages are included here.

Figure 5

(a) Two-dimensional sketch of an idealized, spherical cell. The expanding chromatin (red) aims at increasing the nuclear envelope (gray circle in the center) whereas the connected and contiguous ER membrane tubules (gray lines) are spread along radially arranged microtubules (blue rods). Multiple interactions with the cytoskeleton and contact sites with the plasma membrane expand the vast ER network, hence limiting the available membrane pool for nuclear growth; see main text for details. (b) Fixing the ER membrane area in the vast network limits the available material for the nuclear envelope. The nucleus has to withstand the pressure from decondensed chromatin until nascent lipids (synthesized in the ER) diffuse to the nuclear envelope and get trapped there, hence relaxing the pressure by a surface area increase; see main text for details.