IMAT Biology · Formula sheet
Cell Division and Reproduction formulas
3 formulas, 10 reference tables and 18 common traps for IMAT Biology Cell Division and Reproduction, grouped by subtopic.
Chromosomes, the Cell Cycle and Mitosis
Learn this subtopic in the notesCounting cells, chromosomes, chromatids and DNA through mitosis
Cells after k rounds of mitosis
- number of cells at the start
- number of rounds of division
- number of cells at the end
Chromosome structure: chromatids, centromere and homologous pairs
| Term | What it is | Fact IMAT tests |
|---|---|---|
| Gene | A section of DNA on a chromosome that codes for a product | Each chromosome carries hundreds to thousands of genes |
| Centromere | The joining point of two sister chromatids | Spindle fibres attach here, at the kinetochore |
| Centriole | A small cylinder of microtubules; two make a centrosome | Organises the spindle in animal cells; plants have none |
| Sister chromatids | Two copies of one chromosome after S phase | Genetically identical (barring a copying error) |
| Homologous pair | Two chromosomes, one from each parent, same genes | Can carry different alleles; X and Y in a male pair only partly |
A replicated chromosome is still counted as ONE chromosome. Count centromeres to count chromosomes.
Phases of the cell cycle and their checkpoints
| Phase | Main events | Chromosomes and DNA |
|---|---|---|
| G1 | Cell grows, makes proteins and organelles | 2n chromosomes, each one chromatid; DNA content 2c |
| S | DNA replication; centrosome duplicates | Still 2n chromosomes, now two chromatids each; DNA rises to 4c |
| G2 | More growth, checks the copied DNA, prepares for division | 2n chromosomes, two chromatids each; 4c |
| M | Mitosis splits the nucleus, cytokinesis splits the cytoplasm | Each daughter: 2n, one chromatid each; 2c |
| G0 | Cell has left the cycle and does its job | Stays at 2n and 2c |
c is the DNA content of one unreplicated set of chromosomes.
The stages of mitosis in order: prophase, metaphase, anaphase, telophase
| Stage | What happens | How to spot it |
|---|---|---|
| Prophase | Chromatin condenses into visible chromosomes; nucleolus disappears; spindle forms; nuclear envelope breaks down at the end | Thick threads inside or just leaving the nucleus |
| Metaphase | Chromosomes line up singly on the equator; fibres from both poles attach to each kinetochore | One straight line of chromosomes across the middle |
| Anaphase | Centromeres split; sister chromatids are pulled to opposite poles as the fibres shorten | Two V-shaped groups moving apart |
| Telophase | Chromosomes reach the poles and uncoil; nuclear envelopes and nucleoli reform; spindle breaks down | Two clusters at the ends, new nuclei forming |
| Cytokinesis | Cytoplasm divides: furrow in animals, cell plate in plants | Two separate daughter cells |
Some books add prometaphase (envelope breaks, fibres attach) between prophase and metaphase.
Common traps
Spindle fibres attach at the centromere, not the centriole
The names are close, and IMAT uses that. The centromere is on the chromosome; its kinetochore is where the fibres grip. The centrioles are at the poles of an animal cell and help organise the spindle. A chromosome never attaches to a centriole.
Interphase is not a resting phase
Older books call interphase resting, but the cell is busy: it grows, copies its DNA and checks it. The true resting state is G0, which is outside the cycle.
In mitosis, chromatids separate, not homologous pairs
Homologous chromosomes never pair up in mitosis. Each chromosome lines up on its own and is split into its two sister chromatids in anaphase. Pairs of homologues lining up and separating is meiosis I.
DNA is copied before mitosis, not during it
DNA replication happens in S phase of interphase. An option placing DNA copying in prophase or anaphase is wrong: by prophase each chromosome already has two chromatids.
Ten divisions do not make ten or twenty cells
Every cell divides each round, so the count doubles every time: 2, 4, 8, 16 and so on. The total after k rounds is , not or .
Copying DNA does not double the chromosome number
After S phase a human cell still has 46 chromosomes, but 92 chromatids and twice the DNA. Counting each chromatid as a chromosome is the classic wrong row in IMAT tables.
Meiosis, Chromosome Numbers and Variation
Learn this subtopic in the notesChromosome number (n) and DNA content (c) at each stage of meiosis
Ploidy and DNA through meiosis
- haploid number: one set of chromosomes
- DNA content of one unreplicated set
Sources of variation in meiosis: crossing over, independent assortment, random fertilisation
Gamete combinations from independent assortment
- haploid number (number of homologous pairs)
The stages of meiosis I and meiosis II
| Stage | What happens | Chromosomes in each cell |
|---|---|---|
| Prophase I | Chromosomes condense, homologues pair into bivalents, crossing over | 2n, each with two chromatids |
| Metaphase I | Bivalents (pairs) line up on the equator, each pair facing a random pole | 2n, as pairs |
| Anaphase I | Homologous chromosomes go to opposite poles; sister chromatids stay joined | 2n in the cell, n moving to each pole |
| Telophase I | Two cells form | n, each still with two chromatids |
| Metaphase II | Chromosomes line up singly on the equator | n, each with two chromatids |
| Anaphase II | Centromeres split; sister chromatids go to opposite poles | n moving to each pole |
| Telophase II | Four haploid cells form | n, each with one chromatid |
Pairs on the equator means meiosis I; single chromosomes on the equator means mitosis or meiosis II.
Mitosis compared with meiosis
| Feature | Mitosis | Meiosis |
|---|---|---|
| Divisions after one S phase | One | Two |
| Cells made from one cell | Two | Four |
| Chromosome number | Same as parent (2n gives 2n) | Halved (2n gives n) |
| Genetic make-up | Identical to parent and to each other | Different from parent and from each other |
| Homologues pair, crossing over | Never | In prophase I |
| Where in humans | Somatic (body) cells everywhere | Germ cells in the testes and ovaries |
| Role | Growth, repair, asexual reproduction | Making gametes (animals) or spores (plants) |
Common traps
Homologous pairs moving apart means anaphase I
If whole chromosomes (each still two chromatids) are moving to the poles in pairs that have split, the cell is in anaphase I. In mitosis and in anaphase II it is single chromatids that move. Look at what is being separated, not just at the movement.
A cell after meiosis I is haploid, even though its DNA is 2c
Ploidy counts chromosome sets, not DNA. After meiosis I each cell has one chromosome from every pair, so it is haploid. Its chromosomes still have two chromatids, so its DNA content equals that of a diploid G1 cell. Calling it diploid because of the DNA is wrong.
Daughter cells of mitosis are not haploid
Mitosis keeps the parent's number: a 2n cell gives 2n daughters. Only meiosis halves it. A zygote is 2n, every cell mitosis makes from it is 2n, and only the cells meiosis makes are n.
Use n, not 2n, in 2 to the power n
Each homologous PAIR has two ways to face the poles, so the power is the number of pairs, which is the haploid number. Using the diploid number squares the true answer.
Crossing over is between non-sister chromatids
Sister chromatids are identical, so swapping between them would change nothing. Crossing over happens between a chromatid of the maternal chromosome and one of the paternal chromosome, in prophase I only. It does not happen in mitosis.
Meiosis is not limited to multicellular organisms or to special machinery
Single-celled eukaryotes such as yeast reproduce sexually using meiosis, and both mitosis and meiosis build a spindle from microtubules. The real differences are the number of divisions, pairing and crossing over, and haploid, varied products.
Making Sperm and Eggs, Fertilisation and the Early Embryo
Learn this subtopic in the notesSpermatogenesis: the stages of sperm production in the testis
| Cell | Ploidy | Made by |
|---|---|---|
| Spermatogonium | Diploid (2n) | Mitosis of germ cells |
| Primary spermatocyte | Diploid (2n), DNA copied | Growth of a spermatogonium |
| Secondary spermatocyte | Haploid (n), two chromatids per chromosome | Meiosis I (2 per primary) |
| Spermatid | Haploid (n) | Meiosis II (4 per primary) |
| Spermatozoon | Haploid (n) | Differentiation of a spermatid, no division |
Oogenesis: egg production and its pauses
| Cell | Ploidy | When |
|---|---|---|
| Oogonium | Diploid (2n) | Multiplies by mitosis before birth |
| Primary oocyte | Diploid (2n), DNA copied | Formed before birth; paused in prophase I until puberty |
| Secondary oocyte | Haploid (n), two chromatids per chromosome | Made by meiosis I; paused in metaphase II; ovulated |
| Polar bodies | Haploid (n) | Small cells from each unequal division; they degenerate |
| Ovum | Haploid (n) | Completed only after a sperm enters |
Fertilisation and early development of the human embryo
| Germ layer | Position | Gives rise to |
|---|---|---|
| Ectoderm | Outer | Epidermis of the skin, hair, nervous system (brain, spinal cord, nerves) |
| Mesoderm | Middle | Muscle, bone, heart, blood and vessels, kidneys, gonads |
| Endoderm | Inner | Lining of the gut and airways, liver, pancreas |
Common traps
Sperm are made by meiosis, not mitosis
Mitosis only builds up the stock of diploid spermatogonia. The step that makes haploid cells is meiosis. Saying sperm are formed by mitosis is wrong in animals (in plants it is different: see life cycles).
Spermatogenesis gives four gametes, oogenesis gives one
One primary spermatocyte gives four sperm. One primary oocyte gives one egg plus polar bodies, because the cytoplasm is divided unequally. Both still go through the same two meiotic divisions.
The secondary oocyte is already haploid
The halving happens in meiosis I, so the secondary oocyte is haploid even though meiosis is not finished. Only the oogonia and primary oocytes (and the body cells of the ovary) are diploid.
Identical twins share one zygote
Identical twins come from one fertilised egg that splits early, so they have the same genes. Non-identical twins come from two eggs and two sperm, so they are no more alike than other siblings.
Asexual and Sexual Reproduction and Life Cycles
Learn this subtopic in the notesAsexual and sexual reproduction: methods, advantages and costs
| Method | How it works | Example |
|---|---|---|
| Binary fission | One cell copies its DNA and splits in two | Bacteria, Amoeba |
| Budding | An outgrowth grows and breaks off | Yeast, Hydra |
| Fragmentation | A piece of the body regrows into a whole organism | Flatworms (planarians), starfish |
| Vegetative propagation | A new plant grows from a stem, root or leaf | Potato tubers, strawberry runners, onion bulbs |
| Parthenogenesis | An egg develops without being fertilised | Aphids, male honeybees, some lizards |
Sexual reproduction is favoured when the environment changes; asexual reproduction when it is stable.
Life cycles: where meiosis, mitosis and fertilisation fall
| Life cycle | Main body | Meiosis makes | Example |
|---|---|---|---|
| Diplontic | Diploid | Gametes | Humans and other animals |
| Haplontic | Haploid | Haploid cells from the zygote | Most fungi, Chlamydomonas |
| Alternation, gametophyte dominant | Haploid gametophyte | Spores | Mosses |
| Alternation, sporophyte dominant | Diploid sporophyte | Spores | Ferns, flowering plants |
Common traps
Variation is not only for sexual reproducers
Asexual populations also vary, through mutation, and natural selection acts on them (bacterial antibiotic resistance is the famous case). Sexual reproduction adds much more variation by recombining genes, but it is not the only source.
Gametes are not always made by meiosis
In animals, meiosis makes gametes. In plants, meiosis makes spores, and the haploid gametophyte then makes gametes by mitosis. An option saying gametes always come straight from meiosis is wrong for plants.