Week 4 · Chapter

Chapter 4 — Cell Structure & Function

Introduction to Biology Free sample edition

The module's primary reading · ~35–45 minutes · Objective 3 (compare prokaryotic and eukaryotic cells, relate each eukaryotic organelle to its function, explain how substances cross the plasma membrane by passive and active transport (including osmosis and tonicity), and use the surface-area-to-volume ratio to explain why cells stay small) · Read it first this week; the lecture, the slides, the tutorial, the quiz, and the lab all build on it.

In plain language

Every living thing is made of cells, and this week you look inside one. You will meet the two basic kinds of cell: prokaryotic cells (small cells with no nucleus, such as bacteria) and eukaryotic cells (larger cells with a nucleus and many inner compartments, such as yours). You will tour the organelles (the working parts inside a cell, each with one main job) and learn to read each one for the job it does. You will see how the plasma membrane (the thin border around every cell) decides what gets in and out, and why water moves the way it does. Finally, you will find out why cells stay so small, using nothing more than a few model cubes and some arithmetic.

Why you already care about this

Toss a pinch of salt onto a crisp lettuce leaf and leave it on the cutting board. Within minutes the leaf starts to droop. Wait a little longer and it goes limp and wet. Nothing tore it. Something left the leaf's cells, and here is the surprise: it was not the salt.

That limp leaf is the puzzle of this week. To solve it, you need to know what a cell is built like and what guards its border. Your own body is built from eukaryotic cells about 10 to 100 μm across. A bacterium is a prokaryotic cell about 0.1 to 5.0 μm across. Every cell, from the smallest bacterium to the largest cell in you, shares 4 basic parts. And every cell runs into the same size limit, for a reason you can work out with a cube.

You have seen this week's ideas many times without naming them. A houseplant that wilts when you forget to water it, then stands up again an hour after you do. A raisin that plumps up when it soaks overnight. A salad that goes soggy once it is dressed. This chapter gives each of them its biology.

By the end of this chapter you will be able to:

sort a cell as prokaryotic or eukaryotic by the deciding clue, and name the four things every cell shares;
match each organelle to its job and explain how its structure suits that job;
explain why a plant cell has both chloroplasts and mitochondria, and which kinds of cells have a cell wall;
describe the plasma membrane under the fluid mosaic model and explain what "selectively permeable" means;
tell diffusion, facilitated diffusion, and osmosis apart, and say which way water will move;
predict what happens to a cell in a hypotonic, hypertonic, or isotonic solution;
explain active transport and count the ions the sodium-potassium pump moves;
compute surface area, volume, and the surface-area-to-volume ratio of a cube cell, and use the ratio to explain why cells stay small.

Carry this line with you: a cell is a busy room with a guarded door — and it must stay small.

Where we are

Already covered: Week 1 named the cell as the smallest unit that is unambiguously alive; Week 2 covered atoms, ions, water, and pH; Week 3 covered the four classes of large biological molecules, including the phospholipid.
This week: the two kinds of cell, the organelles and their jobs, the plasma membrane, how substances cross it, and why cells stay small.
How they connect: the cell is built from Week 3's molecules, its membrane is Week 3's phospholipid put to work, and water and ions from Week 2 are what cross that membrane.
Where we're going next: Week 5, Energy, Enzymes & Metabolism, follows the ATP that this week's pump spends and the enzymes that run the cell's chemistry.

Week 1 put the cell on the ladder of life between the organelle and the tissue, and called it the smallest unit that is unambiguously alive. This week you open it up. Week 2 gave you ions, atoms that carry a charge, and you will meet two of them, sodium and potassium, at the membrane. It also gave you water as the solvent of every cell, the liquid that the molecules of life dissolve in. Week 3 gave you the phospholipid, a lipid with a water-loving head and two water-fearing tails. Here that molecule builds the border of every cell. Next week you will see where the cell's energy comes from and how enzymes use it.

1. Sort cells into two kinds: prokaryotic and eukaryotic

Picture two buildings you might walk into. One is a single open room: everything happens in one space, with no inner walls. The other is a large house with many rooms, each behind its own door, each set up for one kind of work. Every cell you will ever study follows one of the same two plans.

A prokaryotic cell is a cell with no nucleus and no membrane-bound organelles, whose DNA sits in a region called the nucleoid; bacteria and archaea are prokaryotes, typically about 0.1 to 5.0 μm across.

A eukaryotic cell is a cell with a true nucleus and membrane-bound organelles, typically about 10 to 100 μm across; animals, plants, fungi, and protists are built from eukaryotic cells.

Three terms make those definitions work:

The nucleoid is the region of a prokaryotic cell where its DNA sits; it has no membrane around it.
An organelle is a structure inside a cell that does one particular job, such as a mitochondrion or the Golgi apparatus; eukaryotic cells have many that are wrapped in their own membranes.
The nucleus is the membrane-wrapped compartment of a eukaryotic cell that holds its DNA and directs the making of proteins.

The sizes are ranges, and you should keep them as ranges. A prokaryote is about 0.1 to 5.0 μm across; a eukaryote is about 10 to 100 μm. The symbol μm stands for the micrometer, the unit used for cell sizes. Even the largest typical prokaryote, at 5.0 μm, is smaller than the smallest typical eukaryote, at 10 μm.

Whichever kind you look at, both kinds of cell share four things:

a plasma membrane, the thin border around every cell, built from a double layer of phospholipids with proteins set into it, that controls what enters and leaves;
cytoplasm, everything inside the plasma membrane apart from the nucleus: the jelly-like fluid of the cell and the structures that sit in it;
DNA, the cell's instructions;
ribosomes. A ribosome is a small structure, found in every cell, that builds proteins.

Worked example — sort three cells by the deciding clue. You look for one clue: is there a nucleus wrapped in a membrane?

A made-up cell about 2 μm across, with its DNA loose in a nucleoid and no inner compartments. No nucleus, so it is prokaryotic. Its size fits the 0.1 to 5.0 μm range, which agrees.
A cell from a mushroom, with a nucleus and many membrane-bound organelles. A true nucleus, so it is eukaryotic. Fungi are eukaryotes.
A cell that has a plasma membrane, cytoplasm, DNA, and ribosomes. Not enough to decide. Every cell has those four things, so they cannot tell the two kinds apart. You need to know whether there is a nucleus.

In words: the nucleus decides it for you. Size agrees with that call, but the four shared parts never decide it, because every cell has them.

Misconception check. Students often think a prokaryote is a eukaryote that lost its nucleus, a stripped-down version of a "real" cell. The idea is tempting because "no nucleus" sounds like something is missing. But a prokaryote is an older, distinct kind of cell, built on its own plan, not a broken copy of the other kind.

Memory hook: pro means no nucleus; eu means a true one.

2. Tour the eukaryotic cell: read each part for its job

Think of a busy restaurant kitchen. There is a recipe office, cooks at their stations, a prep line, a packing table, a delivery door, a generator in the back, and a cleanup crew. Each station has one main job, and the kitchen works because the stations work together. A eukaryotic cell, including each cell in your body, is organized in a similar way. The analogy is only a picture, but it helps you hold the tour in your head.

Here is your tour. At every stop you read the structure for the job it does, and you finish with one plain sentence naming both.

Nucleus. It holds the DNA and directs protein synthesis. It is the recipe office: the instructions stay safe here.
Ribosome. It builds proteins. Ribosomes are the cooks, and every cell has them.
Rough endoplasmic reticulum. The rough endoplasmic reticulum is a network of membranes studded with ribosomes that makes and folds proteins the cell will export or place in its membranes. The ribosomes on its surface give it the "rough" look.
Smooth endoplasmic reticulum. The smooth endoplasmic reticulum is a network of membranes without ribosomes that makes lipids and helps detoxify harmful substances.
Golgi apparatus. The Golgi apparatus is a stack of membrane sacs that modifies, sorts, and ships proteins and lipids to where they are needed. It is the packing table.
Mitochondrion. A mitochondrion is the organelle that makes ATP for the cell; plural mitochondria. Plant and animal cells both have them. It is the generator. ATP is the cell's energy currency, the molecule the cell spends to do work. The mitochondrion's inner membrane is folded many times. Those folds are the cristae, the folds of a mitochondrion's inner membrane, which add surface area for making ATP.
Chloroplast. A chloroplast is the organelle in plants and algae that carries out photosynthesis, using light energy to make sugar.
Lysosome. A lysosome is a membrane sac that breaks down waste, large molecules, and worn-out cell parts. It is the cleanup crew.
Central vacuole. The central vacuole is a large water-filled sac in a plant cell that stores water and presses outward to keep the cell firm. That firmness is turgor, the firmness of a plant cell when its water-filled central vacuole presses against the cell wall; a plant that loses it wilts.
Cell wall. A cell wall is a rigid layer outside the plasma membrane that gives support and shape to the cells of plants, fungi, and bacteria; animal cells have none.

Worked example — follow one protein out of the cell. A cell makes a protein it will send outside itself. You trace the protein's path, stop by stop.

Nucleus. The DNA holding the protein's instructions stays here, and the nucleus directs the job.
Ribosome on the rough endoplasmic reticulum. A ribosome builds the protein chain.
Rough endoplasmic reticulum. The new protein is folded inside this network of membranes.
Golgi apparatus. The protein is modified, sorted, and packed for shipping.
Plasma membrane. The protein leaves the cell at its border.

In words: the instructions stay in the nucleus, a ribosome builds, the rough ER folds, the Golgi ships, and the protein exits through the membrane. That ordered chain is the order-and-location habit this course asks of every process.

Worked example — structure to function in one organelle. You explain why the mitochondrion's inner membrane is folded. The mitochondrion makes ATP, and that work happens on its inner membrane. Folding the membrane into cristae packs far more membrane into the same small organelle. More membrane means more surface for the job. In words: the folds are the structure, and more room to make ATP is the function.

Misconception check. Students often think animal cells have a cell wall, because "cell" and "wall" seem to belong together. The idea is tempting because many diagrams of a plant cell show a thick outer wall. But a cell wall belongs to plants, fungi, and bacteria. An animal cell, like the ones in your own body, has a plasma membrane as its outer border and no wall at all.

Memory hook: office, cooks, prep line, packing table, generator, cleanup crew.

3. Fix the plant-cell trap: chloroplasts and mitochondria, both

Picture a houseplant on a sunny windowsill. In the day it makes sugar from light. At night, with the lamp off, it keeps living. It keeps growing roots, keeps moving water, keeps repairing itself. All of that work costs energy, day and night. So where, you might ask, does the night-time energy come from?

The plant's mitochondria supply it. A plant cell has chloroplasts and mitochondria, both. Chloroplasts make sugar, and mitochondria burn it, day and night. The chloroplast stocks the shelf; the mitochondrion spends from it.

Worked example — what does each kind of cell have? You check three structures against three kinds of eukaryotic cell.

Which of three structures are found in an animal cell, a plant cell, and a fungus cell
Structure	Animal cell	Plant cell	Fungus cell
Mitochondria	yes	yes	yes
Chloroplasts	no	yes	no
Cell wall	no	yes	yes

Mitochondria. Yes in all three, because all three need ATP.
Chloroplasts. Only in the plant cell, because chloroplasts belong to plants and algae, not to animals or fungi.
Cell wall. In the plant cell and the fungus cell, and in bacteria too, but never in an animal cell.

In words: every eukaryotic cell here has mitochondria; only the plant cell adds chloroplasts; and the wall goes with plants, fungi, and bacteria, not animals.

Misconception check. Students often say that plant cells have chloroplasts instead of mitochondria. The idea is tempting because chloroplasts are the famous plant organelle, so they seem to replace the energy organelle. But a plant cell has both. Chloroplasts make sugar, and mitochondria burn it, day and night.

Memory hook: chloroplasts stock the shelf; mitochondria spend from it.

4. Picture the plasma membrane: a gate, not a wall

Think of a soap bubble. Its skin is thin and flexible, it closes on itself, and it moves and shimmers as you watch. A cell's border is far more complex than a bubble, but it shares that fluid, self-sealing quality. You already know the molecule it is built from: you met it last week.

Here is the plasma membrane described as a labeled figure. Imagine a sandwich seen from the side. The two slices of bread are rows of phospholipid heads, the water-loving ends. One row faces the watery fluid outside the cell; the other row faces the watery cytoplasm inside. The filling is the phospholipid tails, the water-fearing ends, tucked inward away from water on both sides. Set into this sandwich, some passing all the way through it, are proteins. Some proteins form channels; some act as carriers or pumps.

A phospholipid bilayer is two layers of phospholipids arranged with their water-loving heads facing outward toward water on each side and their water-fearing tails tucked inward; the basic structure of a membrane.
The fluid mosaic model is the classroom model of the plasma membrane proposed by Singer and Nicolson in 1972: a fluid phospholipid bilayer with proteins set into it like pieces of a mosaic that can drift sideways.

"Fluid" means the parts are not locked in place; they can drift sideways. "Mosaic" means the surface is a patchwork of different pieces. Caveat: the fluid mosaic model is a model, a simplification you can hold in your head, not a photograph of every membrane in every cell.

The membrane does not let everything through, and it does not block everything either, as you will see in the next two sections. It is selectively permeable, letting some substances cross while holding others back, the way the plasma membrane works as a gate rather than a wall.

Worked example — read the bilayer from the outside in. You trace a straight path from the fluid outside a cell to the cytoplasm inside.

Outside fluid. Watery.
Outer row of heads. Water-loving, so they face the water.
Two layers of tails. Water-fearing, so they hide in the middle, away from water.
Inner row of heads. Water-loving, facing the watery cytoplasm.
Cytoplasm. Watery.

In words: water on both sides, so heads point out on both sides and tails hide in the middle. The structure follows from the molecule's two ends, which is structure determines function at the scale of a membrane.

Misconception check. Students often picture the membrane as a solid wall that seals the cell shut, or as an open net that lets anything through. Both pictures are tempting because "border" can suggest either one. But the membrane is selectively permeable: a gate, not a wall. It lets some things cross and holds others back.

Memory hook: heads out, tails in, proteins set in the layer.

5. Follow passive transport: downhill and free

Open a bottle of vanilla extract in one corner of a kitchen. A minute later someone across the room can smell it. Nobody carried the scent across. The molecules spread out on their own, from where there were many of them to where there were few.

You have watched diffusion, and that spreading has a name. Diffusion is the spreading of a substance from where it is more concentrated to where it is less concentrated, with no energy spent. The difference that drives it is a concentration gradient, a difference in how concentrated a substance is from one place to another, such as from one side of a membrane to the other. Moving from high to low is called moving "down" the gradient, like a ball rolling downhill.

When that movement happens across a membrane, it is passive transport. Passive transport is movement of a substance across a membrane down its concentration gradient, from high to low, with no energy spent by the cell. It comes in three forms:

Diffusion across the membrane itself, for substances the bilayer lets through.
Facilitated diffusion, passive transport in which a substance moves down its concentration gradient through a protein channel or carrier in the membrane. It is still downhill and still free; the protein only opens a path.
Osmosis, the diffusion of water across a selectively permeable membrane toward the side with more dissolved solute; osmosis moves water, not the solute.

A solute is a substance dissolved in a liquid, such as salt or sugar dissolved in water. Osmosis is the part that trips people up, so read it slowly and say it to yourself. Water moves toward the side with more solute. One way to hold it: where there is more dissolved stuff, there is relatively less free water, so water moves toward that side.

Worked example — which way does it move? You decide the direction and the type of transport in three cases.

A gas is more concentrated outside a cell than inside, and it slips through the bilayer. It moves from outside to inside, down its gradient, by diffusion. No energy is spent.
Sugar is more concentrated outside a cell, and it can cross only through a carrier protein. It moves from outside to inside, down its gradient, by facilitated diffusion. Still no energy; the protein only opens a path.
Two solutions are separated by a membrane that water can cross but salt cannot. Side A has more salt than side B. Water moves from side B toward side A, the side with more solute, by osmosis. The salt stays where it is.

In words: every case runs downhill and costs the cell nothing; only the path and the moving substance differ.

Misconception check. Students often say that osmosis moves the salt. The idea is tempting because the salt is what changed, so it seems like the thing that should move. But osmosis moves water. The salt sits still, and water moves toward it.

Memory hook: osmosis moves water, not the salt.

6. Read tonicity from the cell's side

Drop a few raisins into a glass of plain water and leave them overnight. By morning they are plump and smooth. Now think back to the salted lettuce leaf, which went limp. The same rule explains both, and you only need one habit to use it: always read the solution from the cell's point of view.

Three words name the outside solution compared with the inside of the cell:

Hypotonic describes a solution with less solute than the inside of the cell, so water moves into the cell; an animal cell placed in one swells and can burst.
Hypertonic describes a solution with more solute than the inside of the cell, so water moves out of the cell and the cell shrivels.
Isotonic describes a solution with the same solute concentration as the inside of the cell, so water moves in and out equally and there is no net change.

If you water a wilted houseplant, you see the next rule at work: a plant cell handles a hypotonic setting better than an animal cell. Water flows in, the central vacuole swells, and the cell presses against its cell wall. The wall holds firm, so the cell becomes firm instead of bursting. That firmness is turgor, and it is why a watered houseplant stands up straight.

Worked example — solve the lettuce puzzle. You read the salted lettuce from the cell's side.

Compare the solute. The salty film on the leaf has more solute than the inside of the lettuce cells.
Name the solution. More solute outside than inside means the outside is hypertonic.
Predict the water. Water moves toward the side with more solute, so water leaves the cells.
Predict the cell. The cells lose water and shrink, the central vacuoles lose their push, turgor drops, and the leaf goes limp.

In words: the salt stayed outside; the water left. That solves your opening puzzle.

Worked example — the raisin and the fish. You apply the same three steps twice.

A raisin in plain water. Plain water has less solute than the inside of the raisin's cells, so the water is hypotonic. Water moves in, and the raisin plumps up.
A freshwater fish placed in seawater. Seawater has more solute than the inside of the fish's cells, so the seawater is hypertonic. Water moves out of its cells, and the cells lose water.

In words: hypo means less solute outside, so water comes in; hyper means more solute outside, so water goes out.

Misconception check. Students often flip hypertonic and hypotonic, reading the word from the solution's side rather than the cell's. The idea is tempting because the words describe the solution, so it seems natural to start there. The cure is to compare the outside with the inside of the cell every time. Hyper means more solute outside than inside, so water leaves the cell.

Memory hook: hypo, water in; hyper, water out; iso, no net change.

7. Pay for active transport: uphill and paid

Picture pushing a bike up a steep hill. Rolling down needed no effort. Going up, you pay with your own energy every meter of the way. Your cells face the same hill. Some substances must go "up" across a membrane, from where they are scarce to where they are already plentiful, and the cell pays for that trip.

Active transport is movement of a substance across a membrane against its concentration gradient, from low to high, using a protein pump paid for with ATP. It is the opposite of passive transport in two ways: the direction is uphill, and the cell spends energy.

The best-known pump is the sodium-potassium pump, a membrane protein that uses one ATP in each cycle to move three sodium ions out of the cell and two potassium ions in. Sodium ions are written Na⁺ and potassium ions K⁺; each carries one positive charge.

Worked example — count the pump's work. You count what the sodium-potassium pump moves in 4 cycles.

One cycle. Each cycle of the sodium-potassium pump spends 1 ATP to move 3 Na⁺ out and 2 K⁺ in.
Sodium. 4 cycles move 4 × 3 = 12 Na⁺ out.
Potassium. 4 cycles move 4 × 2 = 8 K⁺ in.
Cost. 4 cycles spend 4 ATP, one per cycle.

In words: 4 cycles spend 4 ATP and move 4 × 3 = 12 Na⁺ out and 4 × 2 = 8 K⁺ in. The pump always sends out more sodium than it brings in potassium, 3 versus 2 each cycle.

Passive and active transport compared by direction, energy cost, and examples
Feature	Passive transport	Active transport
Direction	down the gradient, high to low	against the gradient, low to high
Energy	none spent	ATP spent
Examples	diffusion, facilitated diffusion, osmosis	the sodium-potassium pump

Misconception check. Students often confuse passive and active transport, especially facilitated diffusion, because it uses a protein, and a pump is a protein too. The idea is tempting because both involve a protein in the membrane. The cure is to ask two questions: which way is it going, and is ATP spent? Downhill and free is passive, even through a protein. Uphill and paid is active.

Memory hook: passive is downhill and free; active is uphill and paid.

8. Explain why cells stay small: surface area versus volume

Think about cooling a pot of soup. Leave it in one deep pot and it stays hot for a long time. Pour it into several shallow dishes and it cools much faster. The soup has not changed. What changed is how much surface each bit of soup has to work with. Each of your cells faces the same problem.

A cell trades with the outside world through its surface, the plasma membrane. Food, oxygen, and water come in that way; wastes go out that way. But the cell has to feed its whole volume, every bit of cytoplasm inside. As a cell grows, its surface area grows as the square of its size and its volume grows as the cube. So the volume races ahead of the surface.

The surface-area-to-volume ratio is a cell's surface area divided by its volume; it falls as a cell grows, because surface area grows as the square of the size and volume grows as the cube.

To see it with numbers, you can use the cube cell, an illustrative model built for this course, not real data. Real cells are not cubes; the cube is a model you can work with on paper. For a cube of side s:

surface area = 6s² (six square faces, each s × s);
volume = s³ (s × s × s);
the ratio of surface area to volume simplifies to 6 ÷ s.

Worked example — the cube cell. You compute surface area, then volume, then the ratio, for four cubes with sides 1, 2, 3, and 4 units.

Side 1. Surface area 6 × 1 × 1 = 6 square units; volume 1 × 1 × 1 = 1 cubic unit; ratio 6 ÷ 1 = 6, written 6:1.
Side 2. Surface area 6 × 2 × 2 = 24 square units; volume 2 × 2 × 2 = 8 cubic units; ratio 24 ÷ 8 = 3, written 3:1.
Side 3. Surface area 6 × 3 × 3 = 54 square units; volume 3 × 3 × 3 = 27 cubic units; ratio 54 ÷ 27 = 2, written 2:1.
Side 4. Surface area 6 × 4 × 4 = 96 square units; volume 4 × 4 × 4 = 64 cubic units; ratio 96 ÷ 64 = 1.5, written 1.5:1.
Shortcut check. 6 ÷ s gives 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 4 = 1.5, the same four ratios.

The cube cell model: side length, surface area, volume, and surface-area-to-volume ratio (illustrative, built for this course, not real data)
Side s	Surface area 6s²	Volume s³	Ratio 6 ÷ s
1	6	1	6:1
2	24	8	3:1
3	54	27	2:1
4	96	64	1.5:1

In words: the ratio falls as the cell grows, from 6:1 to 1.5:1, and the smallest cube has the highest ratio. A ratio of 2:1 means 2 units of surface for each 1 unit of volume.

Worked example — doubling the side. You double the side from 2 to 4 and compare the growth.

Surface area. It goes from 24 to 96, and 96 ÷ 24 = 4 times.
Volume. It goes from 8 to 64, and 64 ÷ 8 = 8 times.
Ratio. Volume grew twice as fast as surface, so the ratio fell from 3:1 to 1.5:1, half as much surface for each unit of volume.

In words: when you double a cell's width, its surface grows 4 times but its volume grows 8 times, so each bit of the inside gets half as much membrane to trade through. A large cell has too little membrane for the volume it must feed.

Real cells, including yours, cope with this limit in three ways: divide, flatten, or fold.

Divide. Split one big cell into smaller cells. Cut the side-2 cube into 8 side-1 cubes: the volume stays 8 cubic units, but the surface becomes 8 × 6 = 48 square units, so the ratio rises from 24 ÷ 8 = 3 to 48 ÷ 8 = 6.
Flatten. Spread the same volume into a thin shape. Here is an illustrative example, not real data: a flat slab 8 units long, 8 units wide, and 1 unit thick holds 8 × 8 × 1 = 64 cubic units, the same as the side-4 cube. Its top and bottom are 8 × 8 = 64 square units each, and its four edges are 8 × 1 = 8 square units each, so its surface is 64 + 64 + 8 + 8 + 8 + 8 = 160 square units. Its ratio is 160 ÷ 64 = 2.5, written 2.5:1, versus 1.5:1 for the cube of the same volume.
Fold. Crease the membrane to add surface without adding much volume. Microvilli are tiny finger-like folds of a cell's plasma membrane that add surface area without adding much volume. The cristae inside a mitochondrion use the same trick.

Limitation: the cube and the slab are models with clean numbers. A real cell is not a cube, and its exact surface and volume are messier, but the rule they show, that the ratio falls as size grows, holds for real cells.

Misconception check. Students often think a bigger cell has more surface, so it must work better. The idea is tempting because the surface really does grow: the side-4 cube has 96 square units against 6 for the side-1 cube. But volume grows faster, so the ratio falls. The bigger cell has less surface for each unit of volume it must feed. Two more slips to avoid: write 54 ÷ 27 = 2 as 2:1, never as 54:27, and never divide backwards as 27 ÷ 54.

Memory hook: surface grows as the square, volume as the cube — so stay small.

Pause and reflect. Choose one of these two prompts and think it through, or jot a few sentences in your notes.

(a) Think of a time you watched something wilt, shrivel, plump up, or go soggy, in the kitchen or the garden. Which way did water move, and was the outside hypotonic or hypertonic to the cells?
(b) Think of something you have seen that is flat, folded, or broken into small pieces, such as a radiator, a towel, or a bag of ice cubes. How does its shape give it more surface, and how is that like a cell coping with its size?

Key terms

Prokaryotic cell — A cell with no nucleus and no membrane-bound organelles, whose DNA sits in a region called the nucleoid; bacteria and archaea are prokaryotes, typically about 0.1 to 5.0 μm across. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Eukaryotic cell — A cell with a true nucleus and membrane-bound organelles, typically about 10 to 100 μm across; animals, plants, fungi, and protists are built from eukaryotic cells. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Nucleoid — The region of a prokaryotic cell where its DNA sits; it has no membrane around it. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Organelle — A structure inside a cell that does one particular job, such as a mitochondrion or the Golgi apparatus; eukaryotic cells have many that are wrapped in their own membranes. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Nucleus — The membrane-wrapped compartment of a eukaryotic cell that holds its DNA and directs the making of proteins. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Plasma membrane — The thin border around every cell, built from a double layer of phospholipids with proteins set into it, that controls what enters and leaves. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Cytoplasm — Everything inside the plasma membrane apart from the nucleus: the jelly-like fluid of the cell and the structures that sit in it. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Ribosome — A small structure, found in every cell, that builds proteins. (first used: 1. Sort cells into two kinds: prokaryotic and eukaryotic)
Rough endoplasmic reticulum — A network of membranes studded with ribosomes that makes and folds proteins the cell will export or place in its membranes. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Smooth endoplasmic reticulum — A network of membranes without ribosomes that makes lipids and helps detoxify harmful substances. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Golgi apparatus — A stack of membrane sacs that modifies, sorts, and ships proteins and lipids to where they are needed. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Mitochondrion — The organelle that makes ATP for the cell; plural mitochondria. Plant and animal cells both have them. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Cristae — The folds of a mitochondrion's inner membrane, which add surface area for making ATP. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Chloroplast — The organelle in plants and algae that carries out photosynthesis, using light energy to make sugar. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Lysosome — A membrane sac that breaks down waste, large molecules, and worn-out cell parts. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Central vacuole — A large water-filled sac in a plant cell that stores water and presses outward to keep the cell firm. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Turgor — The firmness of a plant cell when its water-filled central vacuole presses against the cell wall; a plant that loses it wilts. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Cell wall — A rigid layer outside the plasma membrane that gives support and shape to the cells of plants, fungi, and bacteria; animal cells have none. (first used: 2. Tour the eukaryotic cell: read each part for its job)
Phospholipid bilayer — Two layers of phospholipids arranged with their water-loving heads facing outward toward water on each side and their water-fearing tails tucked inward; the basic structure of a membrane. (first used: 4. Picture the plasma membrane: a gate, not a wall)
Fluid mosaic model — The classroom model of the plasma membrane proposed by Singer and Nicolson in 1972: a fluid phospholipid bilayer with proteins set into it like pieces of a mosaic that can drift sideways. (first used: 4. Picture the plasma membrane: a gate, not a wall)
Selectively permeable — Letting some substances cross while holding others back, the way the plasma membrane works as a gate rather than a wall. (first used: 4. Picture the plasma membrane: a gate, not a wall)
Diffusion — The spreading of a substance from where it is more concentrated to where it is less concentrated, with no energy spent. (first used: 5. Follow passive transport: downhill and free)
Concentration gradient — A difference in how concentrated a substance is from one place to another, such as from one side of a membrane to the other. (first used: 5. Follow passive transport: downhill and free)
Passive transport — Movement of a substance across a membrane down its concentration gradient, from high to low, with no energy spent by the cell. (first used: 5. Follow passive transport: downhill and free)
Facilitated diffusion — Passive transport in which a substance moves down its concentration gradient through a protein channel or carrier in the membrane. (first used: 5. Follow passive transport: downhill and free)
Osmosis — The diffusion of water across a selectively permeable membrane toward the side with more dissolved solute; osmosis moves water, not the solute. (first used: 5. Follow passive transport: downhill and free)
Solute — A substance dissolved in a liquid, such as salt or sugar dissolved in water. (first used: 5. Follow passive transport: downhill and free)
Hypotonic — Describes a solution with less solute than the inside of the cell, so water moves into the cell; an animal cell placed in one swells and can burst. (first used: 6. Read tonicity from the cell's side)
Hypertonic — Describes a solution with more solute than the inside of the cell, so water moves out of the cell and the cell shrivels. (first used: 6. Read tonicity from the cell's side)
Isotonic — Describes a solution with the same solute concentration as the inside of the cell, so water moves in and out equally and there is no net change. (first used: 6. Read tonicity from the cell's side)
Active transport — Movement of a substance across a membrane against its concentration gradient, from low to high, using a protein pump paid for with ATP. (first used: 7. Pay for active transport: uphill and paid)
Sodium-potassium pump — A membrane protein that uses one ATP in each cycle to move three sodium ions out of the cell and two potassium ions in. (first used: 7. Pay for active transport: uphill and paid)
Surface-area-to-volume ratio — A cell's surface area divided by its volume; it falls as a cell grows, because surface area grows as the square of the size and volume grows as the cube. (first used: 8. Explain why cells stay small: surface area versus volume)
Microvilli — Tiny finger-like folds of a cell's plasma membrane that add surface area without adding much volume. (first used: 8. Explain why cells stay small: surface area versus volume)

Summary

Prokaryotic cells have no nucleus; eukaryotic cells have a true nucleus and organelles.
Every cell has a plasma membrane, cytoplasm, DNA, and ribosomes.
Each organelle's structure suits its job; read every part for what it does.
A plant cell has both chloroplasts and mitochondria.
Cell walls belong to plants, fungi, and bacteria, never animal cells.
The plasma membrane is a phospholipid bilayer, described by the fluid mosaic model.
Passive transport runs down the gradient and costs no energy.
Osmosis moves water toward the side with more solute.
Read hypotonic, hypertonic, and isotonic from the cell's side.
Active transport runs against the gradient and spends ATP.
As a cell grows, its surface-area-to-volume ratio falls, so cells stay small.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A model cube cell has a side of 5 units. Compute its surface area, its volume, and its surface-area-to-volume ratio, and compare the ratio with a cube of side 1.
In a model run, the sodium-potassium pump completes 10 cycles. How many ATP does it spend, how many sodium ions does it move out, and how many potassium ions does it move in?
A gardener soaks a wilted stalk of celery in a glass of plain water, and an hour later it is crisp again. Name the solution from the celery cells' side, say which way water moved, and explain why the celery cells did not burst.
A classmate looks at a cell under a microscope and says, "It has ribosomes and DNA, so it must be eukaryotic." What is wrong with that reasoning, and what clue would settle it?

Answers (worked reasoning — read after attempting)

Surface area first: 6 × 5 × 5 = 150 square units. Volume second: 5 × 5 × 5 = 125 cubic units. Then divide: 150 ÷ 125 = 1.2, written 1.2:1. The shortcut agrees: 6 ÷ 5 = 1.2. A cube of side 1 has a ratio of 6:1, and 6 ÷ 1.2 = 5, so the side-1 cube has 5 times as much surface for each unit of volume as the side-5 cube. The bigger cube is worse at trading through its surface.
One ATP per cycle, so 10 cycles spend 10 ATP. Sodium out: 10 × 3 = 30 Na⁺. Potassium in: 10 × 2 = 20 K⁺. The pump moves both ions against their gradients, which is why it must spend ATP.
Plain water has less solute than the inside of the celery cells, so the water is hypotonic to them. Water moved into the cells by osmosis. The central vacuoles swelled and pressed against the cell walls, restoring turgor, so the celery became firm. The cells did not burst because a plant cell's wall holds firm against the push; an animal cell, with no wall, could burst.
Every cell has ribosomes and DNA, along with a plasma membrane and cytoplasm, so those parts cannot tell a prokaryote from a eukaryote. The deciding clue is a true nucleus with membrane-bound organelles. If the cell has a nucleus, it is eukaryotic; if its DNA sits in a nucleoid with no membrane around it, it is prokaryotic.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the laws of energy and the enzyme model explain the ATP your pumps spend.

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