Power law relationship between cell cycle duration and cell volume in the early embryonic development of Caenorhabditis elegans

Abstract

Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <0.39 in radius, respectively). Thus, the power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures.

Keywords: cell cycle duration; cell size; ima-3/Importin α; nuclear-cytoplasmic volume ratio; power law.

Figure 1

Cell division timing of C. elegans embryos. (A) The cell division timings in an embryo cultured at 25°C. Cell identity is indicated on the horizontal axis. Cell division timing was determined by nuclear envelope breakdown (NEBD). The numbers in parentheses indicate the cell generation in each founder cell lineage. For example, AB(1) indicates the AB cell, and AB(2) indicates the AB daughter cells. (B) The average and standard deviation (SD) of cell division timings in the same generation in AB and MS lineages in an embryo were obtained; data obtained from six embryos were aligned on the horizontal axis in order (the leftmost of AB and in the leftmost of MS were obtained from an embryo). The CV of cell division timings in the same generation in AB and MS lineages in an embryo were averaged among the six embryos and were shown with SD [the average CV ± SD (%)] in the right side of data in the graphs after the third generation. The NEBD of the AB cells was set as time 0. AB, MS, C, P, E, and D are indicated with a green dot, blue square, light green triangle, magenta triangle, orange x-mark, and gray cross, respectively. The EMS cell was indicated by a light blue square.

Figure 2

Relationship between cell cycle duration and cell volume. This relationship of cells in embryos is shown in a double logarithmic plot (A) and a linear plot (B). The relationship of cells in AB [green dot, (C)], MS [blue square, (D)], C [light green triangle, (E)], P [magenta triangle, (F)], E [orange x-mark, (G)], and D [gray cross, (H)] lineages are shown in the double logarithmic plot. Cell volume and cell cycle duration data were obtained from four wild-type embryos. Data in the logarithmic scale were fitted to the formula, y = a + bx, by the linear least-squares method. (G) E cells are indicated by squares, and their descendants are indicated by orange x-marks. Downward bracket indicates the daughter cells of E cells. Regression analysis of cells in E lineage was performed without the E cells. Degrees of freedom in fitting in (C–H) were 68, 19, 10, 11, 8, and 4, respectively.

Figure 3

Powers of the T–V relationship could be classified into three classes. T–V relationships in each lineage in the logarithmic (A) or linear (B) scale were fitted by a power law model. Statistical analysis combining regression analysis and a bootstrap method were performed 10,000 times, using the same data used in Figure 2. The estimated power is indicated in the horizontal axis, while the appearance frequencies of the values of power is indicated in the vertical axis. The 95% CIs of the power of the T–V relationship were determined by the appearance frequency and are shown by long horizontal bars. Data for AB, MS, C, P, E, and D lineages are shown in green, blue, light green, magenta, orange, and gray, respectively.

Figure 4

The duration of cell cycle phases in C. elegans embryos. The duration of the (A) intermitotic phase or (B) mitotic phase in the size-correlated class; AB (green dot), MS (blue square), C (light green triangle), and P (magenta triangle) lineages are shown in linear plots in the vertical axis. The cell generations in each founder cell lineage are shown in the horizontal axis. Data points are displaced along the horizontal axis to avoid overlap (A,B). This data displacement does not affect exponentiation of data. Duration data were obtained from three wild-type embryos.

Figure 5

Power law relationship between the nuclear and cell volume. Relationship between nuclear and cell volume in size-correlated classes (AB, MS, C, and P) is shown in linear (A) and double logarithmic (B) plots. Cell volumes were determined by the integral approach with error correction, whereas nuclear volumes were determined by the formula approach in three wild-type embryos. Data in logarithmic scale were fitted to the formula, y = a + bx, by the linear least-squares method. Degree of freedom in fitting was 75.

Figure 6

Relationship between cell cycle duration and cell volume in loss-of-function embryos. (A) Images of embryos at the two-cell stage for wild-type, ptp-2(op194), and ima-3 RNAi embryos were obtained by differential interference contrast (DIC) microscopy. Scale bar = 20 μm. Relationship between cell cycle duration and cell volume in AB lineage in ptp-2(op194) [filled circles in (B)] and ima-3(RNAi) [filled circles in (C)] embryos are shown with that in wild-type embryos [open circles in (B,C)] in double logarithmic plots. Cell volume and cell cycle duration data in loss-of-function embryos were obtained from each of three embryos. Data in the logarithmic scale were fitted to the formula, y = a + bx, by the linear least-squares method. Degrees of freedom in fitting (B,C) were 19 and 19, respectively.