Mitotic Index and a Colchicine Block: Proportion Is Not Rate
Students squashed the tips of onion roots (2n = 16) and counted 2000 cells in one slide: 1780 in interphase, 120 in prophase, 45 in metaphase, 25 in anaphase and 30 in telophase. A previous experiment using labelled thymidine had shown that the whole cell cycle in these roots takes 20 hours.
A second batch of roots was grown in 0.05% colchicine for 3 hours. In 2000 cells from these roots, 360 were dividing, of which 300 were in metaphase and none in anaphase.
One student wrote in her report: "Colchicine-treated roots have a higher mitotic index (18% against 11%), so colchicine makes cells divide faster."
1. Calculate the mitotic index for both sets of roots and estimate the duration of each mitotic phase in the untreated roots. State the assumption your calculation depends on.
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Mitotic index. Untreated: dividing cells = 120 + 45 + 25 + 30 = 220, so MI = 220/2000 = 0.11 (11%). Treated: 360/2000 = 0.18 (18%).
Duration of each phase. In a population of cells that is not synchronised, the proportion of cells in a phase equals the proportion of the cycle spent in that phase. With a 20-hour cycle:
- Prophase: 120/2000 × 20 h = 1.2 h (72 min)
- Metaphase: 45/2000 × 20 h = 0.45 h (27 min)
- Anaphase: 25/2000 × 20 h = 0.25 h (15 min)
- Telophase: 30/2000 × 20 h = 0.30 h (18 min)
- Mitosis in total: 2.2 h; interphase: 17.8 h
Assumption. The cells must be asynchronous and in a steady state: every phase is entered and left at the same rate, so the count is a snapshot of a stable distribution. If the root had been partly synchronised, or if a phase were unusually long or short-lived, the proportions would not reflect time. A second assumption is that all phases are equally easy to recognise on the squash, which anaphase cells, with their compact separated groups, may not be.
2. Explain the effect of colchicine on the treated roots, with reference to the spindle, and predict the chromosome number of the daughter cells produced.
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Mode of action. Colchicine binds tubulin and prevents it from polymerising into microtubules. The spindle cannot form, so the chromosomes, although they condense and line up, are never pulled to opposite poles. The cell arrests in metaphase, which is why 300 of the 360 dividing cells are in metaphase and no anaphase figures are seen: anaphase cannot begin because the structure that performs it has not been built.
Why the index rises. More cells appear to be dividing not because the cycle has speeded up but because cells accumulate in metaphase. The duration of metaphase is extended, so a larger fraction of the population is caught in mitosis at the moment of squashing. The mitotic index measures a proportion, not a rate of division, and can rise simply because a phase has been lengthened.
Chromosome number. The chromosomes have replicated in interphase but cannot be separated, so the cell either remains arrested or escapes into a new interphase with one doubled nucleus. Onion cells would then contain 32 chromosomes (4n), and if that cell later divided by mitosis, all its descendants would be polyploid (32). This is the basis of using colchicine to induce polyploidy in plant breeding.
3. Evaluate the student's conclusion that colchicine makes cells divide faster. What additional measurement would you need before accepting or rejecting it?
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Why the conclusion does not follow. The student has used a proportion as if it were a rate. The mitotic index is the fraction of cells that happen to be in mitosis when the root is fixed. It rises if mitosis lengthens, if interphase shortens, or if cells accumulate at one stage - and colchicine demonstrably does the third. The distribution of stages in the treated roots (300 of 360 in metaphase, zero in anaphase) is direct evidence of a block rather than acceleration.
Additional complications. Colchicine is a drug, not a nutrient: at 0.05% it may kill some cells or slow the cycle, so the 18% is an average over a population that may be dying and dividing at the same time. A higher index in a partly dead root tip is not evidence of faster division.
What to measure instead. Measure the rate of cell production directly: the number of new cells formed per root tip per hour, or the increase in cell number in the meristem over time. Alternatively, determine the length of the cycle in treated roots (for example by labelling dividing cells, or by counting cells over a time series) and compare it with the 20-hour control. Only if the cycle were shown to be shorter would the word "faster" be justified.