IMAT Biology · Cell Structure and Membranes

Cell Theory, Cell Size and Microscopes

Every living thing is made of cells; cells are tiny because a small cell has more surface for its volume, and microscopes let us measure them.

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Why this matters

The older papers asked for cells and organelles put in order of size, a magnification calculation, and the features shared by all living things. The 2023 ministry paper asked how the surface area to volume ratio changes as a cell grows.

Concept 1 of 4: Cell theory and the features of living things

Look closely enough at any living thing, a tree, a mushroom or a person, and it turns out to be built of cells. Nothing smaller than a cell can stay alive on its own. A cell never appears from nowhere: it always comes from another cell dividing.

Definition

The cell theory grew from the work of Schleiden (plants, 1838), Schwann (animals, 1839) and Virchow (1855, "every cell from a cell").

All living things are made of one or more cells.
The cell is the smallest unit of structure and function that is alive.
New cells come only from existing cells, by division.
Cells pass on hereditary information as DNA.

Cells come in two basic kinds: prokaryotic (no nucleus: bacteria and archaea) and eukaryotic (DNA inside a nucleus: protists, fungi, plants, animals). The last page of this chapter compares them in detail. Every living organism shows all of these features: made of cells, DNA as its genetic material, metabolism (it uses energy to stay alive and keep its inside steady as the outside changes), growth and development, reproduction, and response to stimuli.

Statement	What it means	Exam angle
All living things are made of cells	One cell (unicellular) or many (multicellular)	Viruses are not made of cells, so they are not covered
The cell is the basic unit of life	It is the smallest thing that shows every feature of life	An organelle taken out of a cell cannot live on its own
Cells come only from cells	New cells form when existing cells divide	Rules out life arising from non-living matter today
Cells carry hereditary information	All cells use DNA as their genetic material	Some viruses use RNA, which is one reason they are not cells

Practice this conceptself-check · 4 quick reps

A cell does not need a nucleus to be a cell

Bacteria never have a nucleus, and mature red blood cells lose theirs. Options that make the nucleus part of the definition of a cell, or of life, are wrong. What every cell has is a plasma membrane, cytoplasm, ribosomes and DNA.

Concept 2 of 4: Sizes of cells, organelles and viruses

Biology runs across a huge range of sizes, so learn a few anchor values and place everything else between them. Each step from nanometres to micrometres to millimetres is a factor of a thousand. A light microscope cannot separate two points closer than about 0.2 µm, so anything smaller needs an electron microscope.

Definition

Units: $1\ \text{mm} = 10^{-3}\ \text{m}$ , $1\ \mu\text{m} = 10^{-6}\ \text{m}$ , $1\ \text{nm} = 10^{-9}\ \text{m}$ . So $1\ \text{mm} = 1000\ \mu\text{m}$ and $1\ \mu\text{m} = 1000\ \text{nm}$ .

Magnification is how many times larger the image is than the object.
Resolution is the smallest distance between two points that can still be seen as separate. It sets the detail you can see; enlarging a blurred image adds no detail.
Light microscope: resolution about 200 nm, useful magnification up to about ×1500. It can show living, coloured cells.
Electron microscope: resolution about 1 nm or better, magnification above ×100 000. Transmission EM shows thin sections; scanning EM shows surfaces in 3D. Samples must be dead and in a vacuum.

Structure	Typical size	Seen with
Ribosome	About 25 nm	Electron microscope only
Most viruses	About 20 to 300 nm	Electron microscope only
Bacterium such as E. coli	About 2 µm long, under 1 µm wide	Light microscope, but no inner detail
Mitochondrion	About 0.5 to 1 µm wide, 1 to 5 µm long	Light microscope as a speck; inner membranes need EM
Nucleus	About 5 to 10 µm	Light microscope
Human red blood cell	About 7 to 8 µm across	Light microscope
Typical animal cell (liver cell)	About 20 to 30 µm	Light microscope
Plant cell (onion epidermis)	A few hundred µm long	Light microscope, low power
Human egg cell	About 0.1 mm	Just visible to the naked eye

Rough order to remember: ribosome < virus < bacterium ≈ mitochondrion < nucleus < red blood cell < most animal cells < plant cells.

Practice this conceptself-check · 3 quick reps

More magnification does not mean more detail

A light microscope can enlarge a ribosome's image as much as you like, but it will never show it, because two points closer than about 200 nm blur into one. Resolution, not magnification, decides what can be seen. Ribosomes and viruses need an electron microscope.

Concept 3 of 4: Magnification: image size, actual size and scale bars

A micrograph is an enlarged picture, so the real object is the picture's size divided by the enlargement. The only hard part is the units. Put the image and the object in the same unit before dividing, and convert the answer to the unit that suits the object (µm for cells, nm for viruses).

Definition

Magnification = image size ÷ actual size. It has no unit.

Rearranged: actual size = image size ÷ magnification.
A scale bar is a line drawn on the image with its real length written beside it. Measure the bar on the page, then magnification = measured bar length ÷ the length written on it.
Convert first: $1\ \text{mm} = 1000\ \mu\text{m} = 10^6\ \text{nm}$ .

Magnification

M = \frac{I}{A}

$M$ magnification (no unit)
$I$ size of the image, as measured on the picture
$A$ actual size of the object, in the same unit as I

Worked example

An electron micrograph shows a mitochondrion 45 mm long at a magnification of ×15 000. Find its actual length. A second micrograph has a scale bar 10 mm long labelled 2 µm; what is its magnification?

Practice this conceptself-check · 3 quick reps

Divide by the magnification; do not multiply

The object is smaller than its image, so actual size = image size ÷ magnification. Multiplying gives an answer in metres or kilometres for a cell, which no living cell could be. Always check the answer against the size table.

Concept 4 of 4: Surface area to volume ratio and the limit on cell size

A cell takes in oxygen and food, and gets rid of waste, through its surface. What it needs depends on its volume. When a cell grows, its volume rises faster than its surface, so each unit of volume is served by less membrane. That is why cells stay small, and why big organisms need lungs, guts and blood vessels.

Definition

For any shape, scaling all lengths by $k$ multiplies the surface by $k^2$ and the volume by $k^3$ . So the surface area to volume ratio falls as $1/k$ .

Cube of side $L$ : surface $6L^2$ , volume $L^3$ , ratio $6/L$ .
Sphere of radius $r$ : ratio $3/r$ .
Cells raise the ratio by being flat (red blood cells), long and thin (neurons), or folded (microvilli on gut cells).
A large ratio means fast exchange by diffusion; this is the main reason cells divide rather than keep growing.

Ratio for a cube

\frac{\text{surface area}}{\text{volume}} = \frac{6L^2}{L^3} = \frac{6}{L}

$L$ length of one side of the cube

Worked example

Compare the surface area to volume ratios of cube-shaped cells with sides 1 µm, 2 µm and 4 µm.

Practice this conceptself-check · 3 quick reps

The ratio falls as a cell grows

Surface area and volume both increase when a cell grows, but volume increases faster, so their ratio gets smaller. Options saying the ratio stays the same, rises, or is unrelated to size are wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Magnification: image size, actual size and scale bars
Magnification
$M = \frac{I}{A}$
Surface area to volume ratio and the limit on cell size
Ratio for a cube
$\frac{\text{surface area}}{\text{volume}} = \frac{6L^2}{L^3} = \frac{6}{L}$

Reference tables (2)

Cell theory and the features of living things4 rows

Statement	What it means	Exam angle
All living things are made of cells	One cell (unicellular) or many (multicellular)	Viruses are not made of cells, so they are not covered
The cell is the basic unit of life	It is the smallest thing that shows every feature of life	An organelle taken out of a cell cannot live on its own
Cells come only from cells	New cells form when existing cells divide	Rules out life arising from non-living matter today
Cells carry hereditary information	All cells use DNA as their genetic material	Some viruses use RNA, which is one reason they are not cells

Sizes of cells, organelles and viruses9 rows

Structure	Typical size	Seen with
Ribosome	About 25 nm	Electron microscope only
Most viruses	About 20 to 300 nm	Electron microscope only
Bacterium such as E. coli	About 2 µm long, under 1 µm wide	Light microscope, but no inner detail
Mitochondrion	About 0.5 to 1 µm wide, 1 to 5 µm long	Light microscope as a speck; inner membranes need EM
Nucleus	About 5 to 10 µm	Light microscope
Human red blood cell	About 7 to 8 µm across	Light microscope
Typical animal cell (liver cell)	About 20 to 30 µm	Light microscope
Plant cell (onion epidermis)	A few hundred µm long	Light microscope, low power
Human egg cell	About 0.1 mm	Just visible to the naked eye

Rough order to remember: ribosome < virus < bacterium ≈ mitochondrion < nucleus < red blood cell < most animal cells < plant cells.

Watch out for (4)

A cell does not need a nucleus to be a cell
→ Cell theory and the features of living things
More magnification does not mean more detail
→ Sizes of cells, organelles and viruses
Divide by the magnification; do not multiply
→ Magnification: image size, actual size and scale bars
The ratio falls as a cell grows
→ Surface area to volume ratio and the limit on cell size

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