A student examines a thin section of an onion-
Solution Strategy
What information is required in your answer to the problem?
The average duration of each stage of the cell cycle.
What information is provided to solve the problem?
The numbers of cells in different stages of the cell cycle and the time required for a complete cell cycle
For help with this problem, review:
The Cell Cycle and Mitosis in Section 2.2.
Solution Steps
This problem is solved in two steps. First, we calculate the proportions of cells in each stage of the cell cycle, which correspond to the amount of time that an average cell spends in each stage. For example, if cells spend 90% of their time in interphase, then, at any given moment, 90% of the cells will be in interphase. The second step is to convert the proportions into lengths of time, which is done by multiplying the proportions by the total time of the cell cycle (22 hours).
STEP 1 Calculate the proportion of cells at each stage.
The proportion of cells at each stage is equal to the number of cells found in that stage divided by the total number of cells examined:
Hint: The total of all the proportions should equal 1.0.
| Interphase | 94/120 = 0.783 |
| Prophase | 14/120 = 0.117 |
| Prometaphase | 3/120 = 0.025 |
| Metaphase | 3/120 = 0.025 |
| Anaphase | 5/120 = 0.042 |
| Telophase | 1/120 = 0.008 |
We can check our calculations by making sure that the proportions sum to 1.0, which they do.
STEP 2 Determine the average duration of each stage.
Hint: The total time for all stages should equal 22 hours.
To determine the average duration of each stage, multiply the proportion of cells in each stage by the time required for the entire cell cycle:
| Interphase | 0.783 × 22 hours = 17.23 hours |
| Prophase | 0.117 × 22 hours = 2.57 hours |
| Prometaphase | 0.025 × 22 hours = 0.55 hour |
| Metaphase | 0.025 × 22 hours = 0.55 hour |
| Anaphase | 0.042 × 22 hours = 0.92 hour |
| Telophase | 0.008 × 22 hours = 0.18 hour |