High School Biology · Grades 10–12

2Cells: The Common Unit of Life

Scrape the inside of your cheek with a cotton bud, smear it on a slide, add a drop of blue dye, and look through a microscope at four hundred times: a scatter of flat, irregular tiles, each with a darker spot near its centre. Peel the thin skin from inside an onion scale and look again: neat rectangular bricks, each with its own spot. Pond water shows oval creatures rowing past with a fringe of hairs. The three samples have nothing in common to the naked eye. Under the lens they are built from the same object — the cell — and this chapter is about what that object is, how it is seen, and why every living thing is made of it.

2.1 The cell theory

Definition 2.1 (Cell)

A cell is the smallest unit of a living thing that is itself alive: a volume of watery content, the cytoplasm, enclosed by a thin plasma membrane that separates it from its surroundings while letting selected substances cross. A cell takes in matter and energy, transforms them, grows, and divides into two cells.

Proposition 2.2 (The cell theory)

Three statements, established by microscopy in the nineteenth century, form the cell theory:

every living thing is made of one or more cells;
the cell is the basic unit of structure and function of living things — nothing smaller is alive on its own;
every cell comes from a pre-existing cell, by division.

Evidence. Statement 1 rests on the systematic examination of plants (Schleiden, 1838) and animals (Schwann, 1839) with improved microscopes: every tissue examined, however different in appearance, resolved into cells. Statement 3 was established by Virchow (1855) and by the observation of dividing cells in growing tissues; the alternative — cells forming spontaneously from fluid — was never observed, and Pasteur’s experiments on microbes (Chapter 18 returns to them) closed the question. Statement 2 follows from the first and from the fact that isolated cells, kept in a suitable liquid, go on living while any fragment of a cell does not. ∎

Example 2.3 (One cell or many)

A yeast, a paramecium or a bacterium is a single cell that does everything — feeds, moves, divides. An oak or a human is a cooperative of cells of many kinds, each doing a share of the work: a human body contains some $3 \times 10^{13}$ cells, of roughly two hundred kinds. Between the two lie colonies and simple multicellular organisms, but there is no living thing built of anything other than cells.

2.2 Seeing cells: scales and microscopes

Definition 2.4 (Magnification and resolution)

The magnification of an instrument is the ratio of the size of the image to the size of the object. Its resolution is the smallest distance between two points that it still shows as separate. Magnifying an image beyond what the resolution justifies enlarges the blur, not the detail.

Proposition 2.5 (Two instruments, two scales)

The light microscope magnifies up to about $\times 1500$ with a resolution of about $0.2\,\text{µ}\mathrm{m}$ : it shows cells, nuclei, chloroplasts and bacteria, in colour and alive. The electron microscope uses a beam of electrons instead of light: resolution below $1\,\mathrm{nm}$ , magnification up to $\times 10^6$ ; it reveals the inner structure of the cell — membranes, mitochondria, ribosomes, even large molecules — but on a sample that is dead, dried and cut into slices thinner than a micrometre.

Proof. Admitted at this level. ∎

Sizes on a logarithmic scale: each step is ten times larger. The naked eye resolves about 0.1\, mm; the light microscope reaches 0.2\, µ m and sees whole cells and bacteria; the electron microscope resolves nanometres and shows the parts inside. — Sizes on a logarithmic scale: each step is ten times larger. The naked eye resolves about $0.1\,\mathrm{mm}$ ; the light microscope reaches $0.2\,\text{µ}\mathrm{m}$ and sees whole cells and bacteria; the electron microscope resolves nanometres and shows the parts inside.

Method 2.6 (Measuring an object on a micrograph)

A micrograph carries either a magnification or a scale bar.

With a scale bar: measure the bar on the page (say $12\,\mathrm{mm}$ for a bar labelled $10\,\text{µ}\mathrm{m}$ ) and the object ( $30\,\mathrm{mm}$ ); the real size is $30 \times 10/12 = 25\,\text{µ}\mathrm{m}$ .
With a magnification: real size $=$ measured size divided by the magnification; a cell drawn $20\,\mathrm{mm}$ long at $\times 400$ is $20/400 = 0.05\,\mathrm{mm} = 50\,\text{µ}\mathrm{m}$ .
Always state the unit, and convert: $1\,\mathrm{mm} = 1000\,\text{µ}\mathrm{m}$ , $1\,\text{µ}\mathrm{m} = 1000\,\mathrm{nm}$ .

Example 2.7 (Cheek cells)

A cheek cell drawn $24\,\mathrm{mm}$ wide from a $\times 400$ image is $24/400 = 0.06\,\mathrm{mm} = 60\,\text{µ}\mathrm{m}$ across, and its nucleus, drawn $3\,\mathrm{mm}$ , is about $8\,\text{µ}\mathrm{m}$ . A red blood cell is $7\,\text{µ}\mathrm{m}$ ; the bacteria of the mouth, $1\,\text{µ}\mathrm{m}$ long, appear as barely resolved dots at the same magnification.

2.3 Inside the cell

Definition 2.8 (Organelle)

An organelle is a structure inside a cell, enclosed by its own membrane, that performs a specific task. The principal ones are:

the nucleus, which contains the chromosomes — the DNA of Chapter 3 — and controls the cell’s activity;
the mitochondria, some $1\,\text{µ}\mathrm{m}$ long, where organic molecules are broken down with oxygen to release usable energy (cellular respiration, Chapter 4);
in plant cells, the chloroplasts, green with chlorophyll, where photosynthesis takes place, and a large water-filled vacuole that keeps the cell taut.

Outside the membrane, a plant cell is boxed in a rigid cell wall of cellulose; animal cells have none. The cytoplasm of every cell also contains millions of ribosomes, particles of about $25\,\mathrm{nm}$ that assemble proteins, visible only with the electron microscope.

Two eukaryotic cells, schematically. Both have a membrane, a cytoplasm with mitochondria (orange) and a nucleus; the plant cell adds a cellulose wall, chloroplasts (green) and a large central vacuole. Neither is drawn to scale: a real nucleus is about a tenth of the cell’s width, and mitochondria are a hundred times smaller than the cell.

Definition 2.9 (Prokaryotes and eukaryotes)

A cell whose DNA is enclosed in a nucleus is a eukaryotic cell: animals, plants, fungi and many single-celled organisms are eukaryotes. A prokaryotic cell has no nucleus and no membrane-bound organelles: its DNA lies free in the cytoplasm, its size is around $1\,\text{µ}\mathrm{m}$ , and it is surrounded by a wall of its own kind. Bacteria are prokaryotes.

Example 2.10 (Reading a bacterium)

An electron micrograph of the gut bacterium Escherichia coli shows a rod $2\,\text{µ}\mathrm{m}$ long and $0.5\,\text{µ}\mathrm{m}$ wide: a wall, a membrane just inside it, a granular cytoplasm packed with ribosomes, and a paler central region where the single circular DNA molecule lies. No nucleus, no mitochondria. Yet the cell feeds, grows and divides every twenty minutes in a rich broth: everything the cell theory demands, in a thousandth of the volume of a cheek cell.

A plant cell cut open: the rigid wall, the thin membrane against it, the nucleus, the green chloroplasts and the vacuole that fills most of the volume.

2.4 Many cells, many shapes: specialisation

Proposition 2.11 (Specialised cells)

In a multicellular organism the cells share the same basic plan and the same DNA, but each kind has a shape and an equipment matched to its task: a neuron extends a fibre up to a metre long to carry signals; a red blood cell has lost its nucleus and is a flattened disc packed with haemoglobin; a muscle fibre is a giant cell full of contractile proteins; a root hair is a thin tube that maximises the surface for absorbing water; a guard cell of a leaf changes shape to open or close a pore. Specialisation is a matter of which parts of the shared plan are developed.

Proof. Admitted at this level. ∎

Example 2.12 (Surface and volume)

Why are cells so small? Everything a cell takes in or gives out crosses its membrane, whose area grows with the square of the size, while the needs grow with the volume, the cube. A cubic cell of side $10\,\text{µ}\mathrm{m}$ has a surface of $600\,\text{µ}\mathrm{m}^{2}$ for a volume of $1000\,\text{µ}\mathrm{m}^{3}$ : $0.6\,\text{µ}\mathrm{m}^{2}$ of membrane per cubic micrometre. At side $100\,\text{µ}\mathrm{m}$ the ratio drops to $0.06\,\text{µ}\mathrm{m}^{2}$ : ten times less membrane per unit of content. A large cell would starve at its centre; the cells that are large (a frog egg, a muscle fibre) are either mostly inert reserve or elongated so that no point is far from the surface.

A drop of pond water under the light microscope: a paramecium, a single cell a quarter of a millimetre long, rows past green algae with the beat of thousands of tiny hairs. One cell, and a whole organism.

Remark 2.13 (The cell as an open system)

A cell is not a sealed bag. Water, oxygen, glucose and ions cross its membrane continuously, and its wastes leave the same way; a cheek cell placed in pure water swells and bursts within minutes, and one placed in strong salt water shrivels. The membrane’s control of what enters and leaves is the subject of the Year 1 volume; for now, remember that a cell lives by exchanging with its surroundings, and dies when the exchanges stop.

2.5 Exercises

Exercise 2.1 ★

State the three statements of the cell theory.

Solution

Solution of Exercise 2.1.

Every living thing is made of one or more cells; the cell is the basic unit of structure and function; every cell comes from a pre-existing cell by division.

Exercise 2.2 ★

Convert: $0.05\,\mathrm{mm}$ to micrometres; $2500\,\mathrm{nm}$ to micrometres; $7\,\text{µ}\mathrm{m}$ to millimetres.

Solution

Solution of Exercise 2.2.

$50\,\text{µ}\mathrm{m}$ ; $2.5\,\text{µ}\mathrm{m}$ ; $0.007\,\mathrm{mm}$ .

Exercise 2.3 ★

A cell is drawn $36\,\mathrm{mm}$ long from a $\times 600$ image. What is its real length?

Solution

Solution of Exercise 2.3.

$36/600 = 0.06\,\mathrm{mm} = 60\,\text{µ}\mathrm{m}$ .

Exercise 2.4 ★

Name three structures found in a plant cell but not in an animal cell, and one structure found in every cell.

Solution

Solution of Exercise 2.4.

Plant only: cell wall, chloroplasts, large central vacuole. Every cell: a plasma membrane (also cytoplasm and ribosomes).

Exercise 2.5 ★

What is the difference between a prokaryotic and a eukaryotic cell? Give an example of each.

Solution

Solution of Exercise 2.5.

A eukaryotic cell keeps its DNA inside a nucleus and has membrane-bound organelles (a cheek cell, a yeast); a prokaryotic cell has neither, its DNA lies free in the cytoplasm, and it is about $1\,\text{µ}\mathrm{m}$ (a bacterium such as E. coli).

Exercise 2.6 ★★

On a micrograph a scale bar labelled $5\,\text{µ}\mathrm{m}$ measures $15\,\mathrm{mm}$ ; a mitochondrion measures $6\,\mathrm{mm}$ long. Compute the real length of the mitochondrion and the magnification of the image.

Solution

Solution of Exercise 2.6.

Real length $6 \times 5/15 = 2\,\text{µ}\mathrm{m}$ . Magnification: the bar is $15\,\mathrm{mm}$ for $5\,\text{µ}\mathrm{m}$ $= 0.005\,\mathrm{mm}$ , so $15/0.005 = 3000$ : $\times 3000$ .

Exercise 2.7 ★★

Why can a light microscope not show ribosomes, whatever its magnification? Use the two words of Definition 2.4.

Solution

Solution of Exercise 2.7.

A ribosome ( $25\,\mathrm{nm}$ ) is ten times smaller than the light microscope’s resolution ( $0.2\,\text{µ}\mathrm{m}$ $= 200\,\mathrm{nm}$ ): two neighbouring ribosomes, or a ribosome and its surroundings, cannot be told apart. More magnification only enlarges the blur.

Exercise 2.8 ★★

Iodine solution is added to a slice of potato under the microscope: the blue-black colour appears in oval grains inside the cells. Using Chapter 1, say what the grains are and what this shows about where a plant stores its reserves.

Solution

Solution of Exercise 2.8.

The grains are starch, stored inside the cells as solid grains (starch is insoluble). A plant’s reserves are kept inside its cells, not in some space between them.

Exercise 2.9 ★★

Onion skin cells show a nucleus and a wall but no chloroplast, while the cells of a moss leaf are full of them. Explain the difference from where each tissue lives.

Solution

Solution of Exercise 2.9.

The onion scale grows underground, in the dark, and stores reserves: chloroplasts would be useless there. The moss leaf lives in the light and makes its food by photosynthesis, so its cells are packed with chloroplasts. Same plan, different equipment.

Exercise 2.10 ★★

Compute the surface-to-volume ratio of a cubic cell of side $1\,\text{µ}\mathrm{m}$ (a bacterium) and of side $20\,\text{µ}\mathrm{m}$ (a typical animal cell). Which one can rely on simple diffusion through its membrane alone?

Solution

Solution of Exercise 2.10.

Side $1\,\text{µ}\mathrm{m}$ : surface $6\,\text{µ}\mathrm{m}^{2}$ , volume $1\,\text{µ}\mathrm{m}^{3}$ , ratio 6 per micrometre. Side $20\,\text{µ}\mathrm{m}$ : surface $2400\,\text{µ}\mathrm{m}^{2}$ , volume $8000\,\text{µ}\mathrm{m}^{3}$ , ratio 0.3. The bacterium has twenty times more membrane per unit of content and lives by diffusion alone; the larger cell needs internal transport and organelles.

Exercise 2.11 ★★

A bacterium in rich broth divides every $20\,\mathrm{min}$ . Starting from one cell, how many are there after $2\,\mathrm{h}$ ? After $4\,\mathrm{h}$ ?

Solution

Solution of Exercise 2.11.

$2\,\mathrm{h}$ is 6 divisions: $2^6 = 64$ cells. $4\,\mathrm{h}$ is 12: $2^{12} = 4096$ .

Exercise 2.12 ★★★

A red blood cell has no nucleus and no mitochondria. Does it satisfy Definition 2.1? Discuss, knowing that it lives about 120 days, cannot divide, and is produced by nucleated cells in the bone marrow.

Solution

Solution of Exercise 2.12.

It has a membrane, a cytoplasm and takes in and gives out substances, so it fits most of the definition, but it cannot divide and cannot renew its proteins: it is a cell that has given up part of the programme in exchange for room for haemoglobin, and it is made and replaced by complete cells. The definition describes the general case; the red blood cell is a specialised, terminal form of it.

Exercise 2.13 ★★★

In 1665 Hooke saw "cells" in a slice of cork — empty boxes with thick walls. Explain what he actually saw, in the vocabulary of this chapter, and why he could not have seen a nucleus in it.

Solution

Solution of Exercise 2.13.

Cork is dead tissue: Hooke saw the cellulose walls of cells whose living content had disappeared — empty boxes. A nucleus exists only in a living cell’s cytoplasm, and in any case his microscope’s resolution and the absence of stains would have hidden it.

Exercise 2.14 ★★★

Viruses are particles of $20\,\mathrm{nm}$ to $300\,\mathrm{nm}$ that contain nucleic acid and protein, cannot grow or divide on their own, and multiply only inside a cell. Are they cells? Are they alive? Argue from the cell theory.

Solution

Solution of Exercise 2.14.

A virus has no cytoplasm, no membrane of its own making, no metabolism, and cannot divide: it fails the definition of a cell. By the cell theory it is not alive on its own; it is a particle that borrows a cell’s machinery to make copies of itself. Whether to call it "alive" is a matter of definition; that it is not a cell is not.

Exercise 2.15 ★★★

A muscle fibre is a single cell $3\,\mathrm{cm}$ long and $50\,\text{µ}\mathrm{m}$ wide, containing hundreds of nuclei. Compute its volume and compare with that of a cubic $20\,\text{µ}\mathrm{m}$ cell; then explain, from Example 2.12, why its shape and its many nuclei make such a size workable.

Solution

Solution of Exercise 2.15.

Volume $\pi \times (25\,\text{µ}\mathrm{m})^2 \times 30000\,\text{µ}\mathrm{m} \approx 5.9 \times 10^{7}\,\text{µ}\mathrm{m}^{3}$ , about 7000 times the $8000\,\text{µ}\mathrm{m}^{3}$ of the cube. Being a thin cylinder, no point of the fibre is more than $25\,\text{µ}\mathrm{m}$ from the membrane, so exchanges remain fast; and each nucleus governs only its own stretch of the fibre, so no nucleus has to serve a volume larger than an ordinary cell’s.

2.6 Problem: Counting the Cells of a Body

Problem 2.1

Weekend problem — a microscopy session, from the onion skin on the slide to an estimate of the number of cells in a human body

A class spends an afternoon at the microscope. The objectives available give total magnifications of $\times 40$ , $\times 100$ and $\times 400$ ; the field of view at $\times 100$ is $1.8\,\mathrm{mm}$ across.

Part I — The onion.

At $\times 100$ , about 9 onion cells fit side by side across the field of view. Estimate the width of one cell, in micrometres.
At $\times 400$ the field of view is four times narrower. How wide is it, and how many of these cells fit across it?
A student draws one cell $28\,\mathrm{mm}$ wide from the $\times 400$ image. What is the magnification of the drawing relative to the real cell?
Iodine stains the nucleus yellow-brown; the student measures it at $4\,\mathrm{mm}$ on the drawing. Real diameter?
Name the structures the student should label on the drawing, and one structure present that cannot be seen at this magnification.

Part II — The cheek and the pond.

Cheek cells stained with methylene blue appear as flat polygons about $60\,\text{µ}\mathrm{m}$ across but only $5\,\text{µ}\mathrm{m}$ thick. Why are they flat, given where they come from?
A drop of pond water shows a paramecium $240\,\text{µ}\mathrm{m}$ long. Can it be seen with the naked eye? At which magnification does it fill a quarter of the field?
Tiny moving dots about $1\,\text{µ}\mathrm{m}$ long are visible near the paramecium at $\times 400$ . What are they, most probably, and what would an electron microscope add?
The paramecium is a single cell; the cheek cell is one of trillions. In one sentence each, say what "specialised" means for the cheek cell and why it cannot apply to the paramecium.
A student adds a drop of salt water to the cheek cells and sees them shrivel. Explain with Remark 2.13.

Part III — The size of a cell.

Take a typical human cell as a cube of side $20\,\text{µ}\mathrm{m}$ . Compute its volume in cubic micrometres, then in cubic millimetres ( $1\,\mathrm{mm}^{3} = 10^9\,\text{µ}\mathrm{m}^{3}$ ).
Compute its surface area and the ratio surface/volume.
Repeat for a bacterium taken as a cube of side $1\,\text{µ}\mathrm{m}$ . By what factor is its ratio larger?
Cells take up a mass roughly equal to that of an equal volume of water ( $1\,\mathrm{g}$ per $\mathrm{cm}^{3}$ ). Estimate the mass of the $20\,\text{µ}\mathrm{m}$ cell in nanograms ( $1\,\mathrm{g} = 10^9\,\mathrm{ng}$ ).
A red blood cell is a disc $7\,\text{µ}\mathrm{m}$ across and $2\,\text{µ}\mathrm{m}$ thick. Estimate its volume (treat it as a cylinder, $V = \pi r^2 h$ ) and compare with the cube of question 11.

Part IV — The number of cells in a body.

A student of mass $60\,\mathrm{kg}$ has a volume of about $60\,\mathrm{L}$ . If the body were made only of $20\,\text{µ}\mathrm{m}$ cubic cells, how many would it contain?
In fact about a third of the body’s volume is fluid between the cells and other non-cellular material. Correct the estimate.
Red blood cells alone number about $2.5 \times 10^{13}$ . Using the volume of question 15, what volume do they occupy? Is that consistent with a blood volume of about $4.5\,\mathrm{L}$ of which 45% is cells?
Combine questions 17 and 18: give an order of magnitude for the total number of cells in the body, and say why a precise count is impossible.
State the result: how many cells, roughly, make a human, and by what process — from which starting number — were they all produced?

Solution

Solution of Problem 2.1.

1. $1.8/9 = 0.2\,\mathrm{mm} = 200\,\text{µ}\mathrm{m}$ .

2. $1.8/4 = 0.45\,\mathrm{mm}$ ; about two cells fit across it.

3. $28/0.2 = 140$ : the drawing is $\times 140$ .

4. $4/140 \approx 0.029\,\mathrm{mm}$ , about $30\,\text{µ}\mathrm{m}$ .

5. Cell wall, plasma membrane (pressed against the wall), cytoplasm, nucleus, vacuole. Present but invisible at $\times 400$ : the ribosomes (and the mitochondria are at the limit).

6. They come from the surface of a lining that is several cells thick and constantly rubbed: the outermost cells are flattened and shed, which is why a cotton bud collects them.

7. $0.24\,\mathrm{mm}$ is just above the naked eye’s $0.1\,\mathrm{mm}$ limit: a barely visible speck. At $\times 100$ it spans $0.24/1.8 \approx 13\%$ of the field, at $\times 400$ more than half; no available objective gives exactly a quarter.

8. Bacteria. The electron microscope would show their wall, membrane, ribosomes and DNA region, and the absence of a nucleus.

9. The cheek cell does one job (protecting a surface) in a body where other cells feed it, oxygenate it and coordinate it; the paramecium has nobody else and must feed, move, sense and divide as a single cell.

10. The outside is now saltier than the cytoplasm, so water leaves the cell across the membrane; the cell loses volume and shrivels.

11. $20^3 = 8000\,\text{µ}\mathrm{m}^{3} = 8 \times 10^{-6}\,\mathrm{mm}^{3}$ .

12. $6 \times 20^2 = 2400\,\text{µ}\mathrm{m}^{2}$ ; ratio $2400/8000 = 0.3$ per micrometre.

13. Surface $6\,\text{µ}\mathrm{m}^{2}$ , volume $1\,\text{µ}\mathrm{m}^{3}$ , ratio 6: twenty times larger.

14. $8000\,\text{µ}\mathrm{m}^{3} = 8 \times 10^{-9}\,\mathrm{cm}^{3}$ , hence about $8 \times 10^{-9}\,\mathrm{g} = 8\,\mathrm{ng}$ .

15. $\pi \times 3.5^2 \times 2 \approx 77\,\text{µ}\mathrm{m}^{3}$ , about a hundredth of the cube.

16. $60\,\mathrm{L} = 6 \times 10^{16}\,\text{µ}\mathrm{m}^{3}$ ; divided by 8000: about $7.5 \times 10^{12}$ cells.

17. Two thirds of that: about $5 \times 10^{12}$ .

18. $2.5 \times 10^{13} \times 77 \approx 1.9 \times 10^{15}\,\text{µ}\mathrm{m}^{3} \approx 1.9\,\mathrm{L}$ . Blood cells: $0.45 \times 4.5 \approx 2.0\,\mathrm{L}$ — consistent.

19. About $5 \times 10^{12}$ large cells plus $2.5 \times 10^{13}$ red cells: some $3 \times 10^{13}$ , a few tens of trillions. Cell sizes span a factor of a hundred and the mix of kinds varies, so any count is an estimate to within a factor of two or three.

20. Roughly thirty trillion ( $3 \times 10^{13}$ ) cells, all produced by successive cell divisions from a single starting cell, the fertilised egg.

Terms defined in this chapter

See all 479 terms in the glossary