Exercises: The phases of the cell cycle

Explain what the cell cycle is and name its two main periods, stating what generally happens in each.

The diagram represents the cell cycle as a circle divided into four numbered stages. Name stages 1, 2, 3 and 4, and explain why the cycle is represented as a circle rather than a line with a beginning and an end.

What fundamental event occurs during the S phase of the cell cycle? Explain why it is essential for it to occur before the cell divides.

Order these phases of the cell cycle as they occur over time: M phase, G1 phase, G2 phase, S phase. Briefly describe what the cell does in each.

In a cell culture, the complete cell cycle lasts $24\ \text{h}$ and interphase takes up $90\ \%$ of the time. Calculate how many hours each cell spends in interphase and how many in the division phase.

A cell in G1 phase has a certain amount of DNA. State at what point in the cycle this amount has doubled and at what point it is halved again in each daughter cell.

In an oncology lab, two tumor cell cultures are analyzed:

• Line A: has an inactivated p53 gene, so the cells pass the $G_1/S$ checkpoint even if their DNA shows breaks and damage caused by ultraviolet radiation.

• Line B: has an inactivated metaphase checkpoint (spindle assembly checkpoint), so the cells enter anaphase even if there are chromosomes that have not properly attached to the microtubules.

1. a) Predict which type of genetic alteration will predominate in the daughter cells of each culture after several divisions: point mutations at the DNA sequence level or karyotypic alterations in chromosome number (aneuploidies)? Justify your deduction in each case.
2. b) An antitumor drug that destabilizes spindle microtubules is tested. Justify with reasoning in which of the two cell lines ($A$ or $B$) this drug will be unable to halt cell cycle progression.

After a stroke (cerebrovascular accident), destroyed neurons do not regenerate and permanent neurological damage usually remains. In contrast, after a superficial burn that destroys thousands of epidermal cells, the skin is capable of regenerating completely within a few days.

1. a) Justify this medical difference by explaining the cell cycle state of the mature cells in both tissues.
2. b) A research team proposes reactivating the cell cycle in adult neurons to repair brain injuries by forcing them out of the G0 phase. Predict what difficulties or functional risks forcing mitosis could entail in highly specialized cells integrated into stable synaptic circuits.

Consider two spherical model cells: cell A (radius = 1 µm) and cell B (radius = 3 µm).

1. a) Knowing that the surface area of a sphere is $S = 4\pi r^2$ and its volume is $V = \frac{4}{3}\pi r^3$, calculate the surface-to-volume ratio ($S/V$) for each of them.
2. b) The exchange of gases and nutrients with the environment depends on membrane surface area, while metabolic demand depends on cytoplasmic volume. Based on your numerical calculations, justify why cell B is at a critical limit of viability if it does not divide.
3. c) Certain highly active human cells, such as the enterocytes of the intestinal epithelium, reach a considerable size without dividing. Deduce what morphological adaptation in their membrane allows them to maintain a high $S/V$ ratio.