IMAT Biology · Formula sheet

Cell Structure and Membranes formulas

4 formulas, 18 reference tables and 24 common traps for IMAT Biology Cell Structure and Membranes, grouped by subtopic.

Cell Theory, Cell Size and Microscopes

Magnification: image size, actual size and scale bars

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

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}

$L$ length of one side of the cube

Cell theory and the features of living things

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 viruses

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.

Common traps

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.

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.

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.

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.

The Plasma Membrane and the Fluid Mosaic Model

Learn this subtopic in the notes

Phospholipids and the lipid bilayer

Part	Made of	Behaviour in water	Position in the bilayer
Head	Phosphate group (plus glycerol, often choline)	Hydrophilic, polar	Faces the water on both surfaces
Tails	Two fatty acid chains	Hydrophobic, non-polar	Point inward, forming the core
Saturated tail	Only C-C single bonds, so straight	Hydrophobic	Packs tightly; makes the membrane less fluid
Unsaturated tail	One or more C=C double bonds, each making a kink	Hydrophobic	Packs loosely; makes the membrane more fluid

The fluid mosaic model: proteins, cholesterol and carbohydrates

Component	Where it sits	Main job
Phospholipids	The bilayer itself	Barrier to ions and polar molecules; gives fluidity
Integral proteins	Embedded in the bilayer, often spanning it	Channels, carriers, pumps, receptors
Peripheral proteins	On the inner or outer surface	Enzymes, links to the cytoskeleton, signalling
Cholesterol	Between phospholipids in both layers (animal cells)	Keeps fluidity within limits
Glycoproteins and glycolipids	Outer surface, sugar chains facing out	Cell recognition, receptors, blood group antigens

Membrane fluidity: temperature, unsaturated tails and cholesterol

Factor	Effect on fluidity	Why
Higher temperature	More fluid	Molecules have more kinetic energy
More unsaturated tails (C=C)	More fluid	Kinks stop the tails packing closely
Shorter fatty acid tails	More fluid	Fewer attractions between neighbouring tails
Cholesterol, at body or higher temperature	Less fluid	Its rigid rings restrict tail movement
Cholesterol, at low temperature	Stops the membrane setting solid	It spaces the tails so they cannot pack

Cell junctions and cell signalling

Junction	Structure	Job	Example
Tight junction	Rows of proteins that fuse neighbouring membranes	Seals the gap so fluid cannot leak between cells	Gut lining, kidney tubules, brain capillaries
Desmosome	Protein plaques joined across the gap, anchored to intermediate filaments	Holds cells together under stretching	Skin, heart muscle
Gap junction	Channels of connexin proteins linking two cytoplasms	Lets ions and small molecules pass straight between cells	Heart muscle, smooth muscle
Plasmodesma (plants)	Membrane-lined channel through two cell walls	Joins the cytoplasm of neighbouring plant cells	Almost all living plant tissues

Common traps

Phospholipids, not triglycerides, and two layers, not one

A triglyceride has three fatty acids and no polar head, so it cannot form a bilayer; it is a storage fat. The plasma membrane is a phospholipid bilayer, with tails inward. Options describing a single layer, a triglyceride layer or tails facing outward are wrong.

The membrane is not a protein sandwich

Proteins are dotted through and across the bilayer like tiles in a mosaic. They do not form continuous sheets on its two faces. Diagrams or options showing lipid enclosed between two protein layers describe an outdated model.

Cholesterol regulates fluidity; it is not an energy store or a universal hormone source

Cholesterol's job in the membrane is to keep fluidity steady across temperatures. It is not used as a fuel, and it is the source only of steroid hormones (cortisol, testosterone, oestrogen). Protein hormones such as insulin are made from amino acids.

Where the receptor is depends on the signal

Insulin is a protein and cannot cross the bilayer, so its receptor is in the plasma membrane. Steroid hormones are lipid-soluble and bind receptors inside the cell. Options putting the insulin receptor in the nucleus, or saying every hormone enters the cell, are wrong.

Diffusion, Osmosis and Active Transport

Learn this subtopic in the notes

Osmosis, osmolarity and tonicity

Osmolarity of a solution

\text{osmolarity} = i \times c

$i$ number of particles one formula unit gives when dissolved
$c$ molar concentration, in mol/L

Active transport and the sodium potassium pump

One cycle of the sodium potassium pump

3\,\mathrm{Na^+_{in}} + 2\,\mathrm{K^+_{out}} + \mathrm{ATP} \rightarrow 3\,\mathrm{Na^+_{out}} + 2\,\mathrm{K^+_{in}} + \mathrm{ADP} + \mathrm{P_i}

$\mathrm{P_i}$ inorganic phosphate released when ATP is split

Simple and facilitated diffusion: channels and carriers

Mechanism	Example of what crosses	Membrane protein?	ATP?	Direction
Simple diffusion	$\mathrm{O_2}$ , $\mathrm{CO_2}$ , steroid hormones	No	No	Down the gradient
Facilitated diffusion by channel	$\mathrm{Na^+}$ , $\mathrm{K^+}$ , $\mathrm{Cl^-}$ , water through aquaporins	Yes, channel	No	Down the gradient
Facilitated diffusion by carrier	Glucose into red blood cells	Yes, carrier	No	Down the gradient
Active transport	$\mathrm{Na^+}$ out and $\mathrm{K^+}$ in by the pump	Yes, carrier (pump)	Yes	Against the gradient

Common traps

"Uses a carrier protein" does not mean "active"

Carrier proteins work in both facilitated diffusion and active transport. The difference is the direction and the energy: facilitated diffusion goes down the gradient without ATP, active transport goes up it using ATP. Only active transport needs both a protein and ATP.

Water moves toward the higher solute concentration

In osmosis water goes from the dilute solution to the concentrated one, which is the side with less free water. Saying water moves "from high concentration to low" is only right if you mean the concentration of water. IMAT options often reverse this.

Count particles, not moles

0.1 mol/L NaCl gives 0.2 osmol/L because each unit splits into two ions; 0.1 mol/L glucose gives only 0.1 osmol/L. Comparing solutions by molar concentration alone gives the wrong tonicity.

Secondary active transport still depends on ATP

The sodium glucose cotransporter uses no ATP itself, but the sodium gradient it runs on is built by the ATP-driven pump. Stop the pump and glucose uptake stops too. It is active transport, not facilitated diffusion, because glucose moves against its gradient.

Nucleus, Ribosomes, ER, Golgi and Lysosomes

Learn this subtopic in the notes

The nucleus, nuclear envelope and nucleolus

Part	Structure	Job
Nuclear envelope	Two membranes; the outer one joins the rough ER	Separates DNA from the cytoplasm
Nuclear pores	Protein complexes through both membranes	Control traffic: mRNA out, proteins in
Chromatin	DNA wrapped round histones	Carries the genes
Nucleolus	Dense region with no membrane, containing DNA and RNA	Makes rRNA and assembles ribosome subunits

Ribosomes: what they are made of, their types and where they sit

Feature	Eukaryotic cytoplasm	Prokaryotes, mitochondria and chloroplasts
Whole ribosome	80S	70S
Subunits	60S and 40S	50S and 30S
Made of	rRNA and protein	rRNA and protein
Where found	Free in cytosol, or on rough ER and the outer nuclear membrane	Free in the cytoplasm, or in the mitochondrial matrix and chloroplast stroma

Endoplasmic reticulum and Golgi: the route of a secreted protein

Step	Structure	What happens
1	Ribosome on the rough ER	mRNA is translated; the growing chain is threaded into the ER lumen
2	Rough ER lumen	The protein folds and first sugar chains are added
3	Transport vesicle	Buds off the ER and carries the protein to the Golgi
4	Golgi apparatus	Modifies, sorts and packs the protein
5	Secretory vesicle	Moves to the plasma membrane and fuses with it, releasing the protein

Amino acids → ribosome → rough ER → vesicle → Golgi → vesicle → plasma membrane. The nucleus is not on the route.

Lysosomes, peroxisomes and vacuoles

Organelle	Membrane	Contents	Job
Lysosome	Single	Hydrolytic enzymes at about pH 5	Digestion of engulfed material and old organelles
Peroxisome	Single	Oxidases and catalase	Breaks down $\mathrm{H_2O_2}$ and fatty acids
Central vacuole (plants)	Single, the tonoplast	Cell sap	Turgor and storage
Contractile vacuole (protists)	Single	Water	Removes excess water

Endocytosis and exocytosis: moving large cargo in vesicles

Process	Direction	What moves	Example
Phagocytosis (cell eating)	Into the cell	Large particles or whole cells	Macrophages and neutrophils engulfing bacteria
Pinocytosis (cell drinking)	Into the cell	Small droplets of extracellular fluid	Most cells, continuously
Receptor-mediated endocytosis	Into the cell	Specific molecules bound to surface receptors	LDL (cholesterol) uptake by liver cells
Exocytosis	Out of the cell	Contents of secretory vesicles	Insulin from pancreas cells; neurotransmitter from neurons

Common traps

The nucleolus contains DNA and has no membrane

The nucleolus is built around the genes for ribosomal RNA, so it contains DNA as well as RNA. It is not wrapped in a membrane of its own. A question asking for a structure with RNA but no DNA wants the ribosome, not the nucleolus.

Ribosomes contain RNA but not DNA, and do not transcribe

Ribosomes are built of RNA and protein. Transcription, making RNA from DNA, happens in the nucleus; ribosomes do translation. Options saying ribosomes contain DNA or carry out transcription are wrong.

The Golgi modifies and ships proteins; it does not make them

Proteins are made on ribosomes. The Golgi receives them from the rough ER in vesicles, modifies and packs them, and sends them to the membrane, to lysosomes or out of the cell. Secreted proteins never return to the nucleus for checking.

Lysosomal enzymes work below pH 7, not above

The inside of a lysosome is acidic, about pH 4.5 to 5, and its enzymes work best there. Options giving an optimum above pH 7, saying lysosomes bud from the smooth ER, or saying their malfunction causes no disease are all wrong.

Neurons secrete too

Exocytosis is not only for gland cells. Every nerve ending releases neurotransmitter by exocytosis, and every neuron, like nearly every body cell, carries the full set of genes, including the insulin gene, even though it does not express it.

Mitochondria, Chloroplasts, the Cytoskeleton and the Cell Wall

Learn this subtopic in the notes

Mitochondria and chloroplasts: double membranes and their own DNA

Feature	Mitochondrion	Chloroplast
Found in	Almost all eukaryotic cells	Green cells of plants and algae
Membranes	Outer membrane plus a folded inner membrane (cristae)	Outer and inner membrane, plus thylakoids stacked in grana
Fluid inside	Matrix	Stroma
Job	Aerobic respiration, making most of the cell's ATP	Photosynthesis, making sugar from $\mathrm{CO_2}$ and water
Own genetic system	Circular DNA and 70S ribosomes	Circular DNA and 70S ribosomes

The cytoskeleton: microtubules, microfilaments and intermediate filaments

Fibre	Protein	Diameter	Main jobs
Microfilament	Actin	About 7 nm	Shape, muscle contraction, cell movement, cytokinesis in animals
Intermediate filament	Keratin, lamins and others	About 10 nm	Strength; anchors desmosomes; supports the nucleus
Microtubule	Tubulin	About 25 nm, hollow	Spindle, vesicle tracks, centrioles, cilia and flagella

Cell walls in plants, fungi and bacteria

Group	Main wall material	Key point
Plants	Cellulose	Resists turgor pressure; crossed by plasmodesmata
Fungi	Chitin	Same polysaccharide as insect exoskeletons
Bacteria	Peptidoglycan	Target of penicillin
Archaea	No peptidoglycan; other polymers or protein	Not affected by penicillin
Animals	No wall	Extracellular matrix of collagen instead

Common traps

Two membranes, not three

A mitochondrion has an outer and an inner membrane, with an intermembrane space between them. The space is not a third membrane, and the outer membrane is a normal bilayer, not a monolayer. In a chloroplast the thylakoids are a separate internal system, not part of the envelope.

Sugar units are in almost every organelle

Nucleotides contain a sugar (ribose in RNA and ATP, deoxyribose in DNA). So any structure with DNA, RNA or ATP contains carbohydrate monomers: the nucleolus, mitochondria and chloroplasts all do, as do the glycoproteins of every membrane and the cellulose of the wall.

Myosin, kinesin and dynein are motors, not cytoskeleton fibres

The three fibres of the cytoskeleton are microtubules, microfilaments and intermediate filaments. Myosin, kinesin and dynein are motor proteins that move along them, and collagen is an extracellular protein. Lists built from motors or collagen are wrong.

The outermost selective layer of a plant cell is the membrane, not the wall

A plant cell's wall is its outermost layer, but water and solutes pass through it freely. The selectively permeable barrier is the plasma membrane just inside it. An option calling the plant cell's outermost layer selectively permeable is wrong.

Prokaryotes, Eukaryotes, Plant and Animal Cells, and Viruses

Learn this subtopic in the notes

Prokaryotic and eukaryotic cells compared

Feature	Prokaryotic cell	Eukaryotic cell
Examples	Bacteria and archaea	Protists, fungi, plants, animals
Typical size	About 1 to 5 µm	About 10 to 100 µm
DNA	One circular chromosome in the nucleoid, often plasmids	Linear chromosomes with histones in a nucleus, plus circular DNA in mitochondria and chloroplasts
Membrane-bound organelles	None	Nucleus, mitochondria, ER, Golgi, lysosomes and others
Ribosomes	70S	80S in the cytoplasm; 70S in mitochondria and chloroplasts
Cell wall	Usually present; peptidoglycan in bacteria	In plants (cellulose) and fungi (chitin); none in animals
Cell division	Binary fission	Mitosis and meiosis

Plant and animal cells compared

Feature	Plant cell	Animal cell
Cell wall	Cellulose wall outside the membrane	None
Chloroplasts	In green, photosynthetic cells	None
Vacuole	One large permanent central vacuole	Small, temporary vacuoles, if any
Centrioles	Absent in most flowering plants	A pair in the centrosome
Storage carbohydrate	Starch	Glycogen
Shape	Fixed, often box-like	Variable, often rounded
Cytokinesis	Cell plate	Cleavage furrow

Viruses: structure and why they are not cells

Part	Made of	Note
Genome	DNA or RNA	HIV and influenza use RNA; herpes viruses use DNA
Capsid	Protein subunits	Protects the genome; helical or many-sided shapes
Envelope (some viruses)	Host phospholipid bilayer with viral glycoproteins	Present in HIV and influenza; absent in bacteriophages
Enzymes (some viruses)	Proteins such as reverse transcriptase	Carried in the particle, used once inside the host

Common traps

Circular DNA and ribosomes do not prove a cell is prokaryotic

Human cells contain circular DNA in their mitochondria, and every cell has ribosomes. To show a cell is eukaryotic, point to a membrane-bound organelle. To show it is prokaryotic, point to the absence of a nucleus, 70S ribosomes in the cytoplasm or a peptidoglycan wall.

Plant cells respire too

Plant cells have mitochondria as well as chloroplasts, and respire day and night. Only cells with chloroplasts photosynthesise; roots and other non-green parts only respire. An option saying all plant cells photosynthesise, or that plant cells lack mitochondria, is wrong.

Viruses are not prokaryotes

Prokaryotes are cells: they have a membrane, cytoplasm and ribosomes. Viruses have none of these, so they are not prokaryotes and not cells. They have no internal compartments either, so an option linking compartmentalisation to viruses is wrong.

Cell Structure and Membranes formulas

Cell Theory, Cell Size and Microscopes

Magnification: image size, actual size and scale bars

Surface area to volume ratio and the limit on cell size

Cell theory and the features of living things

Sizes of cells, organelles and viruses

Common traps

The Plasma Membrane and the Fluid Mosaic Model

Phospholipids and the lipid bilayer

The fluid mosaic model: proteins, cholesterol and carbohydrates

Membrane fluidity: temperature, unsaturated tails and cholesterol

Cell junctions and cell signalling

Common traps

Diffusion, Osmosis and Active Transport

Osmosis, osmolarity and tonicity

Active transport and the sodium potassium pump

Simple and facilitated diffusion: channels and carriers

Common traps

Nucleus, Ribosomes, ER, Golgi and Lysosomes

The nucleus, nuclear envelope and nucleolus

Ribosomes: what they are made of, their types and where they sit

Endoplasmic reticulum and Golgi: the route of a secreted protein

Lysosomes, peroxisomes and vacuoles

Endocytosis and exocytosis: moving large cargo in vesicles

Common traps

Mitochondria, Chloroplasts, the Cytoskeleton and the Cell Wall

Mitochondria and chloroplasts: double membranes and their own DNA

The cytoskeleton: microtubules, microfilaments and intermediate filaments

Cell walls in plants, fungi and bacteria

Common traps

Prokaryotes, Eukaryotes, Plant and Animal Cells, and Viruses

Prokaryotic and eukaryotic cells compared

Plant and animal cells compared

Viruses: structure and why they are not cells

Common traps

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