Counting through the cycle

Counting chromosomes, chromatids and DNA

Three rules answer almost every question of this kind.

• Count the centromeres to count the chromosomes. A chromosome has one centromere, however many chromatids it has.
• Count the DNA molecules to count the chromatids. After S phase, each chromosome has two. After the centromeres split, each chromatid is a chromosome again.
• The DNA content is in C. S phase doubles it. A division halves it.

The table sets mitosis and meiosis side by side for a human cell, with 46 chromosomes and 2C of DNA in G1.

Reading a graph of DNA

A graph of DNA against time shows a staircase. It is flat at 2C in G1, rises in S phase, is flat at 4C in G2 and mitosis, and drops back to 2C when the cell divides. In meiosis there is a second drop to 1C.

Another picture of the same thing comes from flow cytometry. A machine measures the DNA of thousands of cells and plots a histogram.

The peak at 2C holds the cells in G1. The peak at 4C holds the cells in G2 and M. The cells in between are copying their DNA, so they are in S phase. If the cells are not dividing in step, the share of cells in a region is the share of the cycle that the phase takes. So the time in a phase is the share of cells multiplied by the length of the cycle.

The mitotic index

The mitotic index shows how many cells of a tissue are dividing.

The same idea gives the time of a phase. Suppose that 200 cells are counted, and 18 are in prophase. A cycle of 24 hours is 1440 minutes. Prophase takes $\dfrac{18}{200} \times 1440\ \text{min} = 129.6\ \text{min}$.

Use this only when the cells divide at random, not all together. If the cells are in step, the counts do not show the times.

How many cells after some divisions?

Each division makes two cells from one.

• After $n$ cycles, one cell gives $2^n$ cells, and $N_0$ cells give $N_0 \times 2^n$.
• To make $N$ cells from one, you need $\log_2 N$ cycles. Round up to a whole number.
• Each division adds exactly one cell. To go from 1 cell to $N$ cells, $N - 1$ divisions take place, whatever the number of cycles.

How many cells go through meiosis?

One primary spermatocyte makes four sperm. One primary oocyte makes one egg and the polar bodies. To make 100 sperm, 25 cells go through meiosis. To make 100 eggs, 100 cells go through meiosis.

You should see that the mitotic index is small, and that the time of each stage is in proportion to the number of cells caught in it. Prophase takes the longest of the four stages.

Try it in Python

The program finds the mitotic index and the minutes in each phase from a count of cells.

Practise with new numbers

Common mistakes

• Giving the cell in anaphase 2n chromosomes. It has 4n for a short time, as the chromatids are now chromosomes.
• Giving a cell in anaphase II n chromosomes. It has 2n chromosomes, but only 2C of DNA.
• Using the mitotic index for cells that divide in step. The method needs cells at random stages.
• Counting the cycles as the number of divisions. After 6 cycles from one cell there are 64 cells and 63 divisions.
• Forgetting the polar bodies. One primary oocyte makes one egg.

Remember these

• Count centromeres for chromosomes, DNA molecules for chromatids, C for the DNA.
• Share of cells in a phase times the cycle length gives the time in that phase.
• Mitotic index = cells in mitosis divided by cells counted, times 100.
• $N_0$ cells make $N_0 \times 2^n$ cells in $n$ cycles. One cell to $N$ cells needs $N - 1$ divisions.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A cell has 2n = 10 and 2C of DNA in G1. How many chromosomes and how much DNA does it have in anaphase of mitosis?

2. In a flow cytometry histogram, which cells lie between the 2C peak and the 4C peak?

3. In a field of 500 cells, 40 are in mitosis. What is the mitotic index?

4. How many cells are there after 5 cycles from one cell, and how many divisions have taken place?

5. How many cells must go through meiosis to make 60 sperm? How many to make 60 eggs?

References

• NCERT (2023). Biology, Textbook for Class XI, chapter 10.
• Clark M. A., Douglas M. and Choi J. (2018). Biology 2e, OpenStax, chapters 10.2 and 11.1.