The cell cycle, mitosis and meiosis, and capstone: a cell biology investigation

The third statement of the cell theory says every cell comes from a pre-existing cell (lesson 1). This final lesson asks how. It follows the cell cycle that copies and divides a cell, the mitosis that shares its chromosomes equally, the meiosis that makes eggs and sperm with half the chromosomes, and the controls whose failure leads to cancer. It ends with a capstone that pulls the course together: planning a small cell biology investigation, analyzing its data, and thinking about the ethics of research with human cells. Genetics (BIOL-201), developmental biology (BIOL-360) and cancer biology (BIOL-450) build on these foundations.

Why cells divide, and what they must copy

Cell division serves different purposes. A bacterium or yeast cell divides to reproduce. A fertilized human egg divides to build a body of trillions of cells. Adult tissues divide to replace cells: your gut lining renews itself every few days, and you make about two million red blood cells every second. Whatever the purpose, a dividing cell must copy its DNA exactly and share the copies evenly between two daughter cells.

The amount of DNA to copy is large. A human cell has 46 chromosomes holding about 6 billion base pairs, roughly 2 meters of DNA if stretched out, packed into a nucleus about 6 µm across. In a non-dividing cell, DNA is loosely packed as chromatin. Before division, each chromosome is copied into two identical sister chromatids joined at a constriction called the centromere, and the chromatin condenses into the compact X-shaped chromosomes seen in textbook pictures. Bacteria, with a single circular chromosome, divide by the simpler process of binary fission: the chromosome is copied, the copies move apart, and the cell pinches in two.

The eukaryotic cell cycle

The life of a dividing eukaryotic cell is a repeating cycle with two main parts: interphase, when the cell grows and copies its DNA, and the mitotic (M) phase, when it divides. Interphase takes most of the time and has three stages.

Here C is the DNA content of one complete set of chromosomes in an egg or sperm (for humans about 3 billion base pairs). A typical human cell in culture completes the cycle in about 24 hours, with M phase taking only about an hour. Early frog embryos skip the gap phases and divide every 30 minutes; some liver cells divide only about once a year.

Because the time a cell spends in a phase is proportional to the fraction of cells found in that phase in a growing population, biologists can estimate phase lengths by counting. The mitotic index is the fraction of cells in mitosis.

Mitosis: sharing chromosomes equally

Mitosis is the division of the nucleus into two genetically identical nuclei. It is a continuous process, but biologists divide it into stages for description:

The spindle is built from the microtubules of lesson 11, and its motors and dynamic instability move the chromosomes. The result is two daughter cells with the same number and kind of chromosomes as the parent.

Growth of cell populations

When cells divide steadily, their numbers grow exponentially, doubling every generation time. After \(t\) hours with a doubling time \(t_d\), a population that started with \(N_0\) cells has \(N = N_0 \cdot 2^{t/t_d}\) cells. Exponential growth explains why a single bacterium can become billions overnight and why a small tumor can grow rapidly.

import math
# Exponential growth of a cell culture: N = N0 * 2**(t / td)
def cells(N0, t, td):
    return N0 * 2 ** (t / td)

print("E. coli, td = 20 min, from 1 cell after 8 h:", f"{cells(1, 480, 20):.2e}")
print("Human cells, td = 24 h, from 1e5 after 5 days:", f"{cells(1e5, 120, 24):.2e}")

# Estimating doubling time from two counts
N1, N2, hours = 2.0e5, 1.6e6, 72
td = hours * math.log(2) / math.log(N2 / N1)
print(f"Doubling time from counts {N1:.1e} -> {N2:.1e} in {hours} h: {td:.1f} h")

E. coli, td = 20 min, from 1 cell after 8 h: 1.68e+07
Human cells, td = 24 h, from 1e5 after 5 days: 3.20e+06
Doubling time from counts 2.0e+05 -> 1.6e+06 in 72 h: 24.0 h

Real cultures do not grow forever. Bacteria in a flask show a lag phase, an exponential phase, a stationary phase when nutrients run low, and a death phase. Normal animal cells in culture stop dividing when they touch their neighbors (contact inhibition) and, after a limited number of divisions (about 40 to 60 for human fibroblasts, the Hayflick limit), stop dividing altogether, partly because the protective ends of their chromosomes, telomeres, shorten with each division.

Controlling the cycle and the origins of cancer

The cell cycle is driven by a control system based on proteins called cyclins and cyclin-dependent kinases (Cdks). Cdks are protein kinases (lesson 11) that are active only when bound to a cyclin; cyclin levels rise and fall through the cycle, switching on the events of each phase in turn. Leland Hartwell, Tim Hunt and Paul Nurse shared the 2001 Nobel Prize in Physiology or Medicine for discovering this system in yeast and sea urchin eggs. At checkpoints, the cell checks conditions before continuing: at the end of G1 (is the cell big enough, are conditions favorable, is DNA undamaged?), at the end of G2 (is DNA fully and correctly copied?), and in metaphase (are all chromosomes attached to the spindle?). The protein p53 halts the cycle when DNA is damaged and can trigger apoptosis if the damage cannot be repaired; it is mutated in about half of all human cancers.

Cancer is a disease of cells that divide when they should not. It arises when mutations accumulate in two kinds of genes: proto-oncogenes, which normally promote division and become overactive oncogenes (like a stuck accelerator), and tumor suppressor genes such as p53, which normally restrain division and are inactivated (like failed brakes). Usually several mutations are needed, which is one reason cancer risk rises with age. Cancer cells ignore contact inhibition, evade apoptosis, divide indefinitely (often by reactivating telomerase), attract a blood supply and can spread to other tissues (metastasis). Many treatments target dividing cells, which is why chemotherapy also affects fast-dividing normal tissues such as hair follicles and the gut lining.

Meiosis: halving the chromosome number

Humans have 23 pairs of chromosomes: one set of 23 from each parent. Cells with two sets are diploid (2n = 46 in humans); eggs and sperm have one set and are haploid (n = 23). Each pair of matching chromosomes, one from each parent, carrying the same genes in the same order, is a homologous pair. If eggs and sperm were made by mitosis, the chromosome number would double every generation. Meiosis prevents that: it is a special pair of divisions that turns one diploid cell into four haploid cells, each genetically different.

Meiosis creates variety in two ways. In crossing over, homologous chromosomes swap segments during prophase I, producing chromosomes with new combinations of the parents' versions of genes. In independent assortment, each pair of homologues lines up at random in metaphase I, so each gamete gets a random mix of maternal and paternal chromosomes. With 23 pairs, independent assortment alone gives \(2^{23}\), over 8 million, combinations per parent, before counting crossing over and the random meeting of egg and sperm. Mistakes in separating chromosomes, called nondisjunction, produce gametes with an extra or missing chromosome; Down syndrome, with three copies of chromosome 21, usually arises this way. Genetics (BIOL-201) follows what this means for inheritance.

# Chromosome number and DNA content through mitosis and meiosis (human, n = 23)
n = 23
rows = [("G1 (diploid cell)",        2*n, "2C"),
        ("after S phase (G2)",       2*n, "4C"),
        ("each mitotic daughter",    2*n, "2C"),
        ("after meiosis I (each)",   n,   "2C"),
        ("after meiosis II (each)",  n,   "1C")]
for stage, chromosomes, dna in rows:
    print(f"{stage:<26} chromosomes: {chromosomes:>2}   DNA: {dna}")
print("Combinations from independent assortment:", f"{2**n:,}")

G1 (diploid cell)          chromosomes: 46   DNA: 2C
after S phase (G2)         chromosomes: 46   DNA: 4C
each mitotic daughter      chromosomes: 46   DNA: 2C
after meiosis I (each)     chromosomes: 23   DNA: 2C
after meiosis II (each)    chromosomes: 23   DNA: 1C
Combinations from independent assortment: 8,388,608

Capstone: a cell biology investigation

Science is a way of asking questions and testing answers. To finish the course, we plan and analyze an investigation of the kind you might run in a first-year laboratory, using ideas from several lessons. The data below are invented for teaching.

The question: does a microtubule-disrupting drug change the mitotic index of onion root tip cells? Lesson 11 predicts that blocking spindle microtubules should trap cells in metaphase, so more cells should appear to be in mitosis. A hypothesis is a testable explanation: the drug blocks spindle formation, arresting cells in mitosis. From it we make a prediction: treated root tips will have a higher mitotic index than untreated ones. The null hypothesis, which statistics tests, is that there is no difference.

import numpy as np
from scipy import stats

rng = np.random.default_rng(107)
# Invented data: mitotic index (%) from 8 root tips per group, 400 cells each
control = np.round(rng.normal(11.5, 1.6, 8), 1)
treated = np.round(rng.normal(19.0, 2.4, 8), 1)
for name, x in [("control", control), ("treated", treated)]:
    print(f"{name:<8} {x}  mean {x.mean():.2f}  SD {x.std(ddof=1):.2f}")

t, p = stats.ttest_ind(treated, control, equal_var=False)   # Welch's t-test
diff = treated.mean() - control.mean()
pooled = np.sqrt((control.var(ddof=1) + treated.var(ddof=1)) / 2)
print(f"Difference in means: {diff:.2f} percentage points")
print(f"Welch t = {t:.2f}, p = {p:.2g}")
print(f"Effect size (Cohen's d) = {diff / pooled:.1f}")

control  [12.1  8.5 11.4 14.3  9.1 12.5 10.6 14. ]  mean 11.56  SD 2.10
treated  [17.9 17.5 23.1 22.2 18.2 14.2 15.  20.1]  mean 18.52  SD 3.15
Difference in means: 6.96 percentage points
Welch t = 5.19, p = 0.00021
Effect size (Cohen's d) = 2.6

Interpreting the output takes care. The mean and standard deviation (SD) summarize each group; the SD shows how much individual root tips vary. The t-test asks how likely a difference at least this large would be if the null hypothesis were true; a small p-value (conventionally below 0.05) means the data would be surprising if the drug had no effect, so we reject the null hypothesis. A small p-value does not prove the hypothesis, does not measure how big the effect is, and does not rule out a flaw in the design. The effect size, here the difference in means divided by the pooled SD, shows how large the difference is relative to the natural variation.

A good report would go further. Is the result consistent with the mechanism? Looking at which phase the extra cells are in would test it: if the drug blocks the spindle, the excess should be in prometaphase or metaphase, with few in anaphase. What are the limitations? Eight root tips is a small sample; counting can be biased (hence blinding); one drug concentration and one time point say nothing about dose or timing. What next? A dose–response experiment, a time course, or fluorescence microscopy of microtubules (lesson 4) to see the spindle directly.

Research ethics and human cells

Much cell biology uses human cells, and the most famous human cell line raises ethical questions every student should know. In 1951, cells were taken from a tumor of Henrietta Lacks, a 31-year-old Black woman being treated for cervical cancer at Johns Hopkins Hospital in Baltimore, without her knowledge or consent, as was common practice then. Her cells, named HeLa, were the first human cells to grow indefinitely in culture. They have been used in tens of thousands of studies and contributed to the polio vaccine, cancer research and many other advances, while her family for decades knew nothing of their use and received no benefit. In 2013 the US National Institutes of Health reached an agreement with the Lacks family giving them a say over access to HeLa genome data, and in 2023 her estate settled a lawsuit with a biotechnology company over the commercial use of her cells. Her story is now widely taught as a lesson about consent, privacy and fairness in research, especially toward communities that have been exploited in the past.

Today, research involving human participants or identifiable human biological materials in the United States is governed, for federally funded research, by the Federal Policy for the Protection of Human Subjects (the Common Rule, revised in 2018). Projects must be reviewed by an institutional review board (IRB), participants must give informed consent, and privacy must be protected. The revised rule added an option for broad consent for storing and reusing identifiable specimens. Research with tribal nations increasingly follows tribal research codes and data sovereignty principles, such as the CARE principles for Indigenous data governance.

Ethics also covers how you handle data. Record observations as you make them, keep raw data, never adjust results to fit expectations, report experiments that did not work, and credit others' work. Using AI tools to help write a lab report is governed by your institution's academic integrity policy; whatever the policy, the data and the conclusions must be your own and honestly described.