---
title: "Lipids"
book: "University Biology — Year 1"
subject: biology
language: en
chapter: 9
exercises: 12
source: https://one-course.com/books/biology/3/en/chapter/9-lipids
---

# Chapter 9 — Lipids

A camel crossing a desert carries thirty kilograms of [fat](#def-b1-lipids-triglyceride) in its hump and no water there at all; a trout in a mountain stream at $4\,{}^{\circ}\mathrm{C}$ has membranes as fluid as a carp’s in a warm pond; and a drop of olive [oil](#def-b1-lipids-triglyceride) shaken into water breaks into a cloud of droplets that, left alone, gather back into one. All three are [lipids](#def-b1-lipids-fattyacid) at work: the densest store of chemical energy an [organism](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#def-b1-organism-environment-organism) can carry, the film that bounds every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and every [organelle](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-prokeuk), and the class of molecule that water refuses to dissolve. This chapter describes [fatty acids](#def-b1-lipids-fattyacid) and the [fats](#def-b1-lipids-triglyceride) built from them, the [amphiphilic](#def-b1-lipids-amphiphilic) [lipids](#def-b1-lipids-fattyacid) that assemble into membranes, what makes a membrane more or less fluid, and the other [lipids](#def-b1-lipids-fattyacid) — [sterols](#def-b1-lipids-amphiphilic), pigments, hormones — that a few carbons arranged in rings and chains can be.

## 9.1 Fatty acids

**Definition 9.1 (Lipid, fatty acid).**

*Lipids* are the biological molecules defined not by a common structure but by a common property: they are insoluble in water and soluble in non-polar solvents. Most are built on *fatty acids*: carboxylic acids with an unbranched hydrocarbon chain of $12\text{ to }24\,$ carbons, almost always an even number (they are assembled two carbons at a time, [Chapter 16](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#ch-b1-biosyntheses-integration)). A *saturated* fatty acid has only single bonds and a straight, flexible chain; an *unsaturated* one has one or more double bonds, in the *cis* configuration, each putting a rigid kink of about $30^\circ$ in the chain. Notation: C18:1 $\Delta^9$ is an 18-carbon acid with one double bond after carbon 9 (oleic acid); an *omega-3* acid has its last double bond three carbons from the methyl end.

![Two 18-carbon fatty acids. The saturated chain is straight and packs closely against its neighbours; the cis double bond of oleic acid bends the chain and keeps neighbours apart, which is why oleic acid is liquid at room temperature and stearic acid a solid.](https://one-course.com/images/onecourse/chapters/biology-3/b1-lipids/fig-7ae593710e17.svg)

*Two 18-carbon [fatty acids](#def-b1-lipids-fattyacid). The saturated chain is straight and packs closely against its neighbours; the *cis* double bond of oleic acid bends the chain and keeps neighbours apart, which is why oleic acid is liquid at room temperature and stearic acid a solid.*

**Proposition 9.2 (Melting points).**

The melting point of a [fatty acid](#def-b1-lipids-fattyacid), and the [fluidity](#def-b1-lipids-fluidity) of any [lipid](#def-b1-lipids-fattyacid) assembly it belongs to, is set by how closely the chains can pack: it rises with chain length ($44\,{}^{\circ}\mathrm{C}$ for C12:0, $63\,{}^{\circ}\mathrm{C}$ for C16:0, $70\,{}^{\circ}\mathrm{C}$ for C18:0) and falls sharply with each *cis* double bond (C18:0 $70\,{}^{\circ}\mathrm{C}$, C18:1 $13\,{}^{\circ}\mathrm{C}$, C18:2 $-5\,{}^{\circ}\mathrm{C}$, C18:3 $-11\,{}^{\circ}\mathrm{C}$). Animal [fats](#def-b1-lipids-triglyceride), rich in saturated acids, are solid at room temperature; plant and fish [oils](#def-b1-lipids-triglyceride), rich in unsaturated ones, are liquid.

**Proof.** Straight chains lie side by side and every $\mathrm{CH_2}$ makes [van der Waals](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-bonds) contacts with its neighbours, each worth a few kilojoules per mole, summed along the chain: more carbons, more contacts, more heat to separate them. A kink prevents close contact over several carbons on each side and removes many contacts at once. ∎

## 9.2 Fats: the energy store

**Definition 9.3 (Triglyceride).**

A *triglyceride* (triacylglycerol, a *fat* when solid, an *oil* when liquid) is glycerol — a three-carbon alcohol — esterified on its three hydroxyls by three [fatty acids](#def-b1-lipids-fattyacid). It has no charge and no polar group left: it is entirely hydrophobic, and it is stored as anhydrous droplets in *adipocytes*, [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of the adipose [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue) that are little more than a droplet of fat with a nucleus pushed to one side.

![White adipose tissue: each cell is one droplet of triglyceride, up to 100\, µ m across, with its cytoplasm and nucleus squeezed into a thin rim. Capillaries run between the cells to deliver and collect fatty acids.](https://one-course.com/images/onecourse/chapters/biology-3/b1-lipids/img-37ce09e955a4.jpg)

*White adipose [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue): each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) is one droplet of [triglyceride](#def-b1-lipids-triglyceride), up to $100\,\text{µ}\mathrm{m}$ across, with its [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and nucleus squeezed into a thin rim. Capillaries run between the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) to deliver and collect [fatty acids](#def-b1-lipids-fattyacid).*

**Proposition 9.4 (Fat is the densest energy store).**

Oxidising $1\,\mathrm{g}$ of [fat](#def-b1-lipids-triglyceride) releases $38\,\mathrm{kJ}$, against $17\,\mathrm{kJ}$ for $1\,\mathrm{g}$ of carbohydrate or protein: the carbons of a [fatty acid](#def-b1-lipids-fattyacid) are more reduced (more C–H bonds, fewer C–O) and so give up more electrons to oxygen. Moreover [fat](#def-b1-lipids-triglyceride) is stored dry, whereas glycogen binds about $3\,\mathrm{g}$ of water per gram: $1\,\mathrm{g}$ of stored glycogen yields $4\,\mathrm{kJ}$ per gram of stored mass, [fat](#def-b1-lipids-triglyceride) nine times more. A lean human carries $0.5\,\mathrm{kg}$ of glycogen (a day’s energy) and $12\,\mathrm{kg}$ of [fat](#def-b1-lipids-triglyceride) (more than a month’s).

**Example 9.5 (Why not store everything as fat).**

[Fat](#def-b1-lipids-triglyceride) can only be burnt with oxygen, slowly, and cannot be turned back into glucose in animals ([Chapter 16](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#ch-b1-biosyntheses-integration)); the brain and the red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) need glucose, and a sprinting muscle needs it faster than [fat](#def-b1-lipids-triglyceride) can supply. Glycogen is the fast, oxygen-free, glucose store for hours; [fat](#def-b1-lipids-triglyceride), the dense store for weeks. A migrating bird, a hibernating dormouse and a camel are [fat](#def-b1-lipids-triglyceride); a sprinter’s legs are glycogen.

**Definition 9.6 (Waxes).**

*Waxes* are esters of a [fatty acid](#def-b1-lipids-fattyacid) with a long-chain alcohol: solid, entirely hydrophobic, and used as coatings — the [cuticle](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) of [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ([Chapter 3](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#ch-b1-flowering-plant-organization)), the surface of insects, the waterproofing of feathers and fur, the comb of bees.

## 9.3 Membrane lipids and self-assembly

**Definition 9.7 (Amphiphilic lipids).**

The [lipids](#def-b1-lipids-fattyacid) of membranes are *amphiphilic*: a polar *head* that water solvates and one or two non-polar *tails* that it excludes. *Glycerophospholipids* are glycerol bearing two [fatty acids](#def-b1-lipids-fattyacid) and, on the third carbon, a phosphate linked to a small polar alcohol (choline, ethanolamine, serine, inositol): phosphatidyl-choline is the commonest [lipid](#def-b1-lipids-fattyacid) of animal membranes. *Sphingolipids* are built on the amino-alcohol sphingosine instead of glycerol, with one [fatty acid](#def-b1-lipids-fattyacid) and a head of phosphocholine (sphingomyelin) or of sugars (glycolipids), and are enriched in the outer leaflet and in nerve sheaths. *Sterols* — *cholesterol* in animals, related sterols in plants and fungi — are rigid four-ring molecules with a single hydroxyl as their head, lying among the tails of the other [lipids](#def-b1-lipids-fattyacid).

**Proposition 9.8 (Self-assembly).**

In water, [amphiphilic molecules](#def-b1-lipids-amphiphilic) assemble spontaneously so as to hide their tails and expose their heads. The shape of the molecule decides the structure: single-tailed [lipids](#def-b1-lipids-fattyacid) ([fatty acids](#def-b1-lipids-fattyacid), detergents), shaped like cones, form *micelles* — spheres a few nanometres across with the tails inside; double-tailed [phospholipids](#def-b1-lipids-amphiphilic), shaped like cylinders, form *bilayers*, which close on themselves into *liposomes* (vesicles) to leave no edge exposed. The assembly is driven by the [hydrophobic effect](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-properties) ([Chapter 8](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#ch-b1-water-small-molecules)): it costs no energy and needs no enzyme, and a torn bilayer reseals by itself. Membranes are self-healing sheets that grow by insertion of new [lipids](#def-b1-lipids-fattyacid) and never form from nothing: every membrane comes from a membrane.

**Evidence.** Dried [phospholipid](#def-b1-lipids-amphiphilic) dispersed in water forms closed vesicles with bilayer walls visible in the [electron microscope](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#prop-b1-cell-unit-of-life-microscopes) (Bangham, 1965); their permeability to ions and water matches that of [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) membranes, and they can be loaded with drugs and fused with [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). Adding a detergent (single-tailed, cone-shaped) dissolves the bilayer into mixed micelles; removing it by dialysis lets the bilayer reform. ∎

![Three assemblies of amphiphilic lipids in water. Cone-shaped single-tailed molecules pack into micelles; cylindrical double-tailed phospholipids form a bilayer, which closes into a vesicle to hide its edges.](https://one-course.com/images/onecourse/chapters/biology-3/b1-lipids/fig-d899cd65be43.svg)

*Three assemblies of [amphiphilic](#def-b1-lipids-amphiphilic) [lipids](#def-b1-lipids-fattyacid) in water. Cone-shaped single-tailed molecules pack into micelles; cylindrical double-tailed [phospholipids](#def-b1-lipids-amphiphilic) form a bilayer, which closes into a vesicle to hide its edges.*

![Oil shaken into water: a cloud of droplets that will coalesce within minutes unless an amphiphile — a detergent, a bile salt, a phospholipid — coats them. Emulsification is what the gut does to dietary fat before its enzymes can reach it.](https://one-course.com/images/onecourse/chapters/biology-3/b1-lipids/img-1d12de162146.jpg)

*[Oil](#def-b1-lipids-triglyceride) shaken into water: a cloud of droplets that will coalesce within minutes unless an amphiphile — a detergent, a bile salt, a [phospholipid](#def-b1-lipids-amphiphilic) — coats them. Emulsification is what the gut does to dietary [fat](#def-b1-lipids-triglyceride) before its enzymes can reach it.*

**Example 9.9 (Bile salts).**

Dietary [fat](#def-b1-lipids-triglyceride) arrives in the intestine as [oil](#def-b1-lipids-triglyceride); the lipase that digests it works only at the oil–water interface. Bile salts, [amphiphilic](#def-b1-lipids-amphiphilic) derivatives of [cholesterol](#def-b1-lipids-amphiphilic), coat the [fat](#def-b1-lipids-triglyceride) into droplets a micrometre across, multiplying the interface a thousandfold, and then carry the [fatty acids](#def-b1-lipids-fattyacid) released, in micelles, to the absorbing [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ([Chapter 22](https://one-course.com/books/biology/3/en/chapter/22-digestion-and-absorption#ch-b1-digestion-absorption)). The same trick is used by soap.

## 9.4 Membrane fluidity

**Definition 9.10 (Fluidity, phase transition).**

A [lipid bilayer](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-membrane) has a *phase transition temperature* $T_m$: below it the chains are packed in an ordered, gel-like state in which [lipids](#def-b1-lipids-fattyacid) barely move; above it they are disordered and the bilayer is a two-dimensional fluid in which a [lipid](#def-b1-lipids-fattyacid) changes places with its neighbour a million times a second and crosses the membrane’s plane at $1\,\text{µ}\mathrm{m}/\mathrm{s}$. [Cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) keep their membranes above $T_m$: the *fluidity* lets proteins diffuse and rotate, vesicles bud and fuse, and the bilayer reseal.

**Proposition 9.11 (What sets the fluidity).**

$T_m$ rises with the length of the chains and falls with their unsaturation, as for free [fatty acids](#def-b1-lipids-fattyacid); a bilayer of C18:0 chains melts at $55\,{}^{\circ}\mathrm{C}$, one of C18:1 chains at $-20\,{}^{\circ}\mathrm{C}$. [Cholesterol](#def-b1-lipids-amphiphilic), inserted among the tails, has a double effect: above $T_m$ its rigid rings restrict the motion of the chains and stiffen the membrane; below $T_m$ they prevent the chains from packing and keep it from freezing. It broadens the transition into a gradual change and keeps the [fluidity](#def-b1-lipids-fluidity) nearly constant over a wide range of temperature — a [buffer](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-buffer) of [fluidity](#def-b1-lipids-fluidity). Animal plasma membranes are up to one [cholesterol](#def-b1-lipids-amphiphilic) for every [phospholipid](#def-b1-lipids-amphiphilic).

![Fluidity against temperature for three bilayers. Saturated chains freeze sharply near 40\, C; one double bond per lipid lowers the transition below zero; cholesterol smooths the transition into a gentle slope, keeping the membrane neither solid nor too fluid across the physiological range.](https://one-course.com/images/onecourse/chapters/biology-3/b1-lipids/fig-fe1271ff5cc6.svg)

*[Fluidity](#def-b1-lipids-fluidity) against temperature for three bilayers. Saturated chains freeze sharply near $40\,{}^{\circ}\mathrm{C}$; one double bond per [lipid](#def-b1-lipids-fattyacid) lowers the transition below zero; [cholesterol](#def-b1-lipids-amphiphilic) smooths the transition into a gentle slope, keeping the membrane neither solid nor too fluid across the physiological range.*

**Proposition 9.12 (Homeoviscous adaptation).**

[Organisms](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#def-b1-organism-environment-organism) that cannot regulate their temperature adjust the composition of their membranes to keep the [fluidity](#def-b1-lipids-fluidity) constant: as the temperature falls, they replace saturated by [unsaturated fatty acids](#def-b1-lipids-fattyacid) and long chains by shorter ones, and the reverse when it rises.

**Evidence.** *E. coli* grown at $10\,{}^{\circ}\mathrm{C}$ has twice the proportion of [unsaturated fatty acids](#def-b1-lipids-fattyacid) of the same strain grown at $40\,{}^{\circ}\mathrm{C}$, and the membranes of the two cultures, measured by the mobility of a probe, are equally fluid at their growth temperatures. Trout acclimated to $5\,{}^{\circ}\mathrm{C}$ carry more polyunsaturated acids in their membrane [lipids](#def-b1-lipids-fattyacid) than trout at $20\,{}^{\circ}\mathrm{C}$; the [fat](#def-b1-lipids-triglyceride) of reindeer legs, close to the snow, is more unsaturated than the [fat](#def-b1-lipids-triglyceride) of the trunk. Plants that survive frost enrich their membranes in unsaturated [lipids](#def-b1-lipids-fattyacid) in autumn, and mutants unable to do so die when chilled. ∎

**Example 9.13 (Butter, olive oil, fish oil).**

Butter ($65\,\%$ saturated) is solid in the refrigerator and soft at room temperature; olive [oil](#def-b1-lipids-triglyceride) ($75\,\%$ oleic acid) is liquid at room temperature and clouds in the refrigerator; fish [oil](#def-b1-lipids-triglyceride), rich in omega-3 acids with five and six double bonds, stays liquid at $-20\,{}^{\circ}\mathrm{C}$, which is what a cod’s membranes need in the North Atlantic.

## 9.5 Sterols, pigments and signals

**Definition 9.14 (Steroids, isoprenoids).**

*Steroids* share [cholesterol](#def-b1-lipids-amphiphilic)’s four fused rings: [cholesterol](#def-b1-lipids-amphiphilic) itself (membranes, and the precursor of the rest), the bile salts, vitamin D, and the steroid hormones — cortisol, aldosterone, the sex hormones — small, hydrophobic molecules that cross membranes freely and act on receptors inside the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). *Isoprenoids* (terpenes) are chains and rings of five-carbon isoprene units: the *carotenoids* that colour carrots and protect [chloroplasts](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plastid) ([Chapter 14](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#ch-b1-photosynthesis)), the side chain of chlorophyll, the quinones of the electron-transport chains, rubber, and the fat-soluble vitamins A, E and K.

**Proposition 9.15 (What lipids do).**

Energy storage ([triglycerides](#def-b1-lipids-triglyceride)); membranes ([phospholipids](#def-b1-lipids-amphiphilic), [sphingolipids](#def-b1-lipids-amphiphilic), [sterols](#def-b1-lipids-amphiphilic)); insulation and waterproofing ([fat](#def-b1-lipids-triglyceride), [waxes](#def-b1-lipids-wax)); light absorption and protection (carotenoids); electron carriage (quinones); signalling between [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ([steroid](#def-b1-lipids-steroids) hormones, prostaglandins) and within them (inositol [phospholipids](#def-b1-lipids-amphiphilic), diacylglycerol); vitamins. One property — insolubility in water — underlies all of them: a [lipid](#def-b1-lipids-fattyacid) stays where it is put, in a droplet, a film or a membrane, or crosses a membrane without a carrier.

**Example 9.16 (A hormone that needs no receptor at the surface).**

Cortisol, secreted by the adrenal gland, travels in the blood bound to a carrier protein, [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) it at a target [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), dissolves through the plasma membrane in seconds, and binds a receptor in the [cytosol](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-organelle) that then enters the nucleus and switches genes on ([Chapter 20](https://one-course.com/books/biology/3/en/chapter/20-control-of-gene-expression#ch-b1-expression-control)). A protein hormone such as insulin, water-soluble and too large to cross, must bind a receptor on the outside and have its message relayed inward. The chemistry of the messenger decides the route of the message.

## 9.6 Exercises

**Exercise 9.1 ★.**

Define a [lipid](#def-b1-lipids-fattyacid) and explain why the definition is by property rather than by structure.

**Solution of Exercise 9.1.**

A [lipid](#def-b1-lipids-fattyacid) is a biological molecule insoluble in water and soluble in non-polar solvents. [Fats](#def-b1-lipids-triglyceride), [phospholipids](#def-b1-lipids-amphiphilic), [sterols](#def-b1-lipids-amphiphilic) and carotenoids share no common skeleton, only this behaviour toward water, which is what gives them their common roles (stores, films, membranes).

**Exercise 9.2 ★.**

Write the notation of linoleic acid (18 carbons, double bonds after carbons 9 and 12) and say whether it is an omega-3 or an omega-6 acid.

**Solution of Exercise 9.2.**

C18:2 $\Delta^{9,12}$. The last double bond starts at carbon 12 from the carboxyl, i.e. at carbon 6 from the methyl end: omega-6.

**Exercise 9.3 ★.**

Why does a [triglyceride](#def-b1-lipids-triglyceride) form droplets while a [phospholipid](#def-b1-lipids-amphiphilic) forms bilayers? What structural difference is responsible?

**Solution of Exercise 9.3.**

A [triglyceride](#def-b1-lipids-triglyceride) has no polar head: entirely hydrophobic, it is excluded from water as a bulk phase, a droplet. A [phospholipid](#def-b1-lipids-amphiphilic) is [amphiphilic](#def-b1-lipids-amphiphilic): its polar head must stay in water while its tails must leave it, which only a sheet two molecules thick can satisfy.

**Exercise 9.4 ★.**

From the [fluidity](#def-b1-lipids-fluidity) figure, at what temperature is each of the three bilayers half-way through its transition? Which would you expect in a bacterium living at $10\,{}^{\circ}\mathrm{C}$?

**Solution of Exercise 9.4.**

About $41\,{}^{\circ}\mathrm{C}$, $-5\,{}^{\circ}\mathrm{C}$ and $20\,{}^{\circ}\mathrm{C}$ (the [cholesterol](#def-b1-lipids-amphiphilic) curve has no sharp transition; half its rise is near $20\,{}^{\circ}\mathrm{C}$). A bacterium at $10\,{}^{\circ}\mathrm{C}$ needs the unsaturated composition, fluid well below its growth temperature.

**Exercise 9.5 ★★.**

A person stores $15\,\mathrm{kg}$ of [fat](#def-b1-lipids-triglyceride). Compute the energy it holds, the number of days it could sustain a resting expenditure of $8\,\mathrm{MJ}/\mathrm{d}$, and the mass of hydrated glycogen that would hold the same energy.

**Solution of Exercise 9.5.**

$15\,000\times 38 = 570\,\mathrm{MJ}$; $570/8 = 71$ days. Glycogen: dry $570\,000/17 = 33.5\,\mathrm{kg}$, hydrated $134\,\mathrm{kg}$.

**Exercise 9.6 ★★.**

Rank by melting point: C14:0, C18:0, C18:1, C18:3, C22:0, and justify each step of the ranking.

**Solution of Exercise 9.6.**

C22:0 $>$ C18:0 $>$ C14:0 $>$ C18:1 $>$ C18:3. Among saturated acids, longer chains make more [van der Waals](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-bonds) contacts; one *cis* double bond removes more packing than four extra carbons add (C18:1 melts below C14:0); each further bond lowers it again.

**Exercise 9.7 ★★.**

A red blood [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) has a surface of $140\,\text{µ}\mathrm{m}^{2}$; a [phospholipid](#def-b1-lipids-amphiphilic) head occupies $0.6\,\mathrm{nm}^{2}$. Compute the number of [phospholipid](#def-b1-lipids-amphiphilic) molecules in the membrane (two leaflets) and, at $750\,\mathrm{g}/\mathrm{mol}$, their total mass in picograms.

**Solution of Exercise 9.7.**

$2\times140\,\text{µ}\mathrm{m}^{2}/0.6\,\mathrm{nm}^{2} = 2\times 1.4\times
10^{-10}/6\times 10^{-19} = 4.7 \times 10^{8}$ molecules; mass $4.7 \times 10^{8}\times 750/6 \times 10^{23} = 5.8 \times 10^{-13}\,\mathrm{g} = 0.58\,\mathrm{pg}$.

**Exercise 9.8 ★★.**

$1\,\mathrm{g}$ of olive [oil](#def-b1-lipids-triglyceride) (density $0.9\,\mathrm{g}/\mathrm{mL}$) is emulsified into droplets of $1\,\text{µ}\mathrm{m}$ diameter. Compute the total interface area. Repeat for a single drop. Why does the pancreatic lipase need the emulsion?

**Solution of Exercise 9.8.**

Volume $1.11\,\mathrm{mL}$ $= 1.11 \times 10^{-6}\,\mathrm{m}^{3}$; surface of spheres $= 6V/d = 6\times 1.11\times 10^{-6}/10^{-6} = 6.7\,\mathrm{m}^{2}$. One drop of that volume: $d = 1.28\,\mathrm{cm}$, surface $5.2\,\mathrm{cm}^{2}$: the emulsion has thirteen thousand times more interface. Lipase is water-soluble and acts only at the interface; the rate is proportional to it.

**Exercise 9.9 ★★.**

Explain the two opposite effects of [cholesterol](#def-b1-lipids-amphiphilic) on [membrane fluidity](#def-b1-lipids-fluidity) and why a membrane with [cholesterol](#def-b1-lipids-amphiphilic) has no sharp transition.

**Solution of Exercise 9.9.**

Above $T_m$ its rigid rings hinder the motion of the neighbouring chains and reduce [fluidity](#def-b1-lipids-fluidity); below $T_m$ its bulk prevents the chains from packing into the ordered gel and prevents freezing. With no cooperative packing possible, there is no temperature at which the whole bilayer changes state at once: the transition is spread out.

**Exercise 9.10 ★★★.**

A mutant plant cannot make [unsaturated fatty acids](#def-b1-lipids-fattyacid). Predict its membranes at $25\,{}^{\circ}\mathrm{C}$ and at $5\,{}^{\circ}\mathrm{C}$, what happens to its [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) on a cold night, and why the wild type survives.

**Solution of Exercise 9.10.**

All-saturated chains: at $25\,{}^{\circ}\mathrm{C}$ the membranes are already close to their transition and stiff; at $5\,{}^{\circ}\mathrm{C}$ they gel. Gelled membranes let proteins stop working and, on rewarming or mechanical stress, crack and leak: the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) lose their contents and the [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue) dies (chilling injury). The wild type desaturates its [lipids](#def-b1-lipids-fattyacid) in autumn and stays fluid at $5\,{}^{\circ}\mathrm{C}$.

**Exercise 9.11 ★★★.**

[Fat](#def-b1-lipids-triglyceride) gives $1.07\,\mathrm{g}$ of water per gram oxidised (glycogen $0.56\,\mathrm{g}$, protein $0.4\,\mathrm{g}$). Compute the water produced by a camel oxidising $1\,\mathrm{kg}$ of [fat](#def-b1-lipids-triglyceride). The oxygen needed is $2\,\mathrm{L}$ per gram of [fat](#def-b1-lipids-triglyceride); breathing it in dry desert air costs about $0.03\,\mathrm{g}$ of water per litre of air ventilated, at $5\,\%$ oxygen extraction. Compute the water lost in breathing and say whether the hump is a water store.

**Solution of Exercise 9.11.**

$1.07\,\mathrm{kg}$ of water per kilogram of [fat](#def-b1-lipids-triglyceride). Oxygen: $2000\,\mathrm{L}$; at $5\,\%$ extraction of $21\,\%$ oxygen, air needed $2000/(0.21\times 0.05) = 190\,\mathrm{m}^{3}$; water lost at $30\,\mathrm{g}/\mathrm{m}^{3}$: $5.7\,\mathrm{kg}$. The camel loses five times more water breathing than the [fat](#def-b1-lipids-triglyceride) yields: the hump is an energy store, not a water store.

**Exercise 9.12 ★★★.**

“A membrane assembles itself, but a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) cannot make a membrane from nothing.” Reconcile the two halves of the sentence in a paragraph, using the [hydrophobic effect](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-properties), the growth of membranes by insertion, and the continuity of membranes through [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) division.

**Solution of Exercise 9.12.**

Given a bilayer, the [hydrophobic effect](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-properties) makes it reseal, close into vesicles and accept new [lipids](#def-b1-lipids-fattyacid) with no energy input: assembly is spontaneous. But the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) makes its [lipids](#def-b1-lipids-fattyacid) with enzymes sitting in an existing membrane (the ER), which insert them in place; a new membrane grows by expansion of an old one and is partitioned at division, so that every membrane of every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) descends from the membranes of the previous [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). Self-assembly explains the physics of the sheet, not its origin in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell).

## 9.7 Problem: Cold Water and Desert Fat

**Problem 9.1.**

Weekend problem — a trout’s membranes in a mountain stream and a camel’s hump in the desert: unsaturation, transition temperatures, energy density and metabolic water, ending on the mass that storing fat instead of glycogen saves

Part I concerns a trout whose membrane [phospholipids](#def-b1-lipids-amphiphilic) carry chains of C16:0, C18:1 and C22:6 (an omega-3 acid with six double bonds). Part II concerns a dromedary of $500\,\mathrm{kg}$ with a $30\,\mathrm{kg}$ hump of [triglyceride](#def-b1-lipids-triglyceride), crossing a desert at a [metabolic rate](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#def-b1-organism-environment-allometry) of $60\,\mathrm{MJ}/\mathrm{d}$. Energy: [fat](#def-b1-lipids-triglyceride) $38\,\mathrm{kJ}/\mathrm{g}$, glycogen $17\,\mathrm{kJ}/\mathrm{g}$ dry, stored with $3\,\mathrm{g}$ of water per gram. Metabolic water: $1.07\,\mathrm{g}/\mathrm{g}$ of [fat](#def-b1-lipids-triglyceride). Oxygen: $2.0\,\mathrm{L}$ per gram of [fat](#def-b1-lipids-triglyceride); air is $21\,\%$ oxygen; the camel extracts $5\,\%$ of the oxygen it breathes; exhaled air carries $30\,\mathrm{g}/\mathrm{m}^{3}$ of water more than the desert air inhaled.

**Part I — The trout.** Trout acclimated to $20\,{}^{\circ}\mathrm{C}$ have membrane chains that are $40\,\%$ C16:0, $45\,\%$ C18:1 and $15\,\%$ C22:6; trout at $5\,{}^{\circ}\mathrm{C}$, $25\,\%$, $40\,\%$ and $35\,\%$.

1. Write the notation of the three acids and count the double bonds per chain in each.
2. Compute the mean number of double bonds per chain at each temperature.
3. Explain, from chain packing, why the change lowers the transition temperature of the membrane.
4. A bilayer’s $T_m$ falls by about $20\,{}^{\circ}\mathrm{C}$ for each additional $0.5\,$ double bond per chain on average. Estimate the shift of $T_m$ between the two trout.
5. The warm trout’s membrane is fluid at $20\,{}^{\circ}\mathrm{C}$ but would gel at $5\,{}^{\circ}\mathrm{C}$ . What would happen to its transport proteins, its pumps and its nerve conduction on a sudden cold night?
6. The adaptation takes days. Name the enzymes the trout must make more of, and where in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) they act ( [Chapter 6](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#ch-b1-eukaryotic-cell) ).
7. [Cholesterol](#def-b1-lipids-amphiphilic) is at one molecule per two [phospholipids](#def-b1-lipids-amphiphilic) in both trout. Explain what it contributes in each case.

**Part II — The camel’s energy.**

8. Compute the energy stored in the hump.
9. For how many days of the crossing does it suffice?
10. Compute the mass of dry glycogen holding the same energy, and the mass of hydrated glycogen.
11. Compute the mass saved by storing [fat](#def-b1-lipids-triglyceride) rather than glycogen, and express it as a fraction of the camel’s body mass.
12. [Fat](#def-b1-lipids-triglyceride) is stored in a hump rather than spread under the skin. Propose a reason, from the [heat budget](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#prop-b1-mammal-organization-heatbudget) of [Chapter 2](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#ch-b1-mammal-organization) .

**Part III — Is the hump a water store?**

13. Compute the metabolic water produced by oxidising the whole hump.
14. Compute the oxygen needed, in litres.
15. Compute the volume of air the camel must ventilate to obtain it.
16. Compute the water lost in exhaling that air.
17. Compare the water gained with the water lost, and conclude.
18. Instead of sweating, the camel lets its body temperature rise by $6\,{}^{\circ}\mathrm{C}$ during the day and cool at night. Compute the heat it stores this way (heat capacity $3.5\,\mathrm{kJ}\,\mathrm{kg}^{-1}\,\mathrm{K}^{-1}$ ) and the water that evaporating the same heat would cost ( $2.4\,\mathrm{kJ}/\mathrm{g}$ ).
19. A camel can lose $25\,\%$ of its body water and survive, and its red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) swell to twice their volume without bursting when it drinks $100\,\mathrm{L}$ in ten minutes. Relate the second property to the membranes of [Chapter 7](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#ch-b1-membranes-transport) .

**Part IV — The bilayer’s arithmetic.** A [phospholipid](#def-b1-lipids-amphiphilic) head occupies $0.65\,\mathrm{nm}^{2}$; a bilayer is $5\,\mathrm{nm}$ thick; the camel’s red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) have a surface of $80\,\text{µ}\mathrm{m}^{2}$ and number $8 \times 10^{12}$ per litre of blood.

20. Compute the number of [phospholipids](#def-b1-lipids-amphiphilic) in one [red-cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) membrane.
21. Compute the number in all the red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of $40\,\mathrm{L}$ of blood.
22. At $750\,\mathrm{g}/\mathrm{mol}$ , compute the mass of that [lipid](#def-b1-lipids-fattyacid) in grams.
23. A [phospholipid](#def-b1-lipids-amphiphilic) flips from one leaflet to the other spontaneously about once a week, but diffuses laterally $1\,\text{µ}\mathrm{m}$ in a second. Explain both numbers from the [hydrophobic effect](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-properties) .
24. Explain why, given the flip rate, the two leaflets of a membrane can stay different in composition for the life of a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) .
25. State the result: the mass the camel saves by carrying $30\,\mathrm{kg}$ of [fat](#def-b1-lipids-triglyceride) rather than the glycogen of equal energy, and the verdict on the hump as a water store.

**Solution of Problem 9.1.**

**1.** C16:0 (0), C18:1 $\Delta^9$ (1), C22:6 $\Delta^{4,7,10,13,16,19}$ (6). **2.** Warm: $0.40\times 0 + 0.45\times 1 + 0.15\times 6 = 1.35$; cold: $0 + 0.40 + 2.10 = 2.50$ double bonds per chain. **3.** Each *cis* bond kinks the chain and prevents close packing with neighbours; fewer [van der Waals](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-bonds) contacts, less heat needed to disorder the chains, lower $T_m$. **4.** $1.15$ more bonds per chain: about $45\,{}^{\circ}\mathrm{C}$ lower. **5.** In a gel the [lipids](#def-b1-lipids-fattyacid) cannot move: carriers cannot change conformation, pumps stop, [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) stick; ion gradients decay, nerve conduction fails, and the fish is paralysed and dies of the cold that a cold-acclimated fish tolerates. **6.** Desaturases, which introduce double bonds into fatty acyl chains; they are [integral proteins](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-proteins) of the [endoplasmic reticulum](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-endomembrane), where the [lipids](#def-b1-lipids-fattyacid) are made. **7.** In both it [buffers](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-buffer) [fluidity](#def-b1-lipids-fluidity): stiffening the very unsaturated cold membrane above its low $T_m$, and keeping the warm membrane from gelling on a cool day. **8.** $30\,000\times 38 = 1140\,\mathrm{MJ}$. **9.** $1140/60 = 19$ days. **10.** Dry: $1.14 \times 10^{6}/17 = 67\,\mathrm{kg}$; hydrated: $268\,\mathrm{kg}$. **11.** $268 - 30 = 238\,\mathrm{kg}$, nearly half the camel’s mass. **12.** A layer of [fat](#def-b1-lipids-triglyceride) under the whole skin would insulate the body and prevent it from shedding heat in the desert; concentrating the [fat](#def-b1-lipids-triglyceride) in one hump [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) the rest of the skin free to lose heat. **13.** $1.07\times 30 = 32\,\mathrm{kg}$ of water. **14.** $2.0\times 30\,000 = 60\,000\,\mathrm{L} = 60\,\mathrm{m}^{3}$ of oxygen. **15.** $60/(0.21\times 0.05) = 5700\,\mathrm{m}^{3}$ of air. **16.** $5700\times 30 = 171\,\mathrm{kg}$ of water. **17.** Lost five times what is gained: oxidising the hump costs water. The hump is a store of energy that lets the camel go without food; its water economy comes from its kidneys, its tolerance of dehydration and its ability to let its temperature rise. **18.** $500\times 3.5\times 6 = 10.5\,\mathrm{MJ}$ stored as heat and released at night; evaporating it away would have cost $10\,500/2.4 = 4.4\,\mathrm{kg}$ of water a day. **19.** A membrane can stretch only a few percent, so doubling the volume of a red [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) requires a large excess of membrane folded into the resting biconcave shape, and a [cytoskeleton](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) that lets it unfold without tearing: the camel’s red [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) are oval, with more membrane per volume than a human’s. **20.** $2\times 80\times 10^{-12}/0.65\times 10^{-18} = 2.5 \times 10^{8}$. **21.** $2.5 \times 10^{8}\times8 \times 10^{12}\times 40 = 7.9 \times 10^{22}$. **22.** $7.9 \times 10^{22}\times 750/6 \times 10^{23} = 99\,\mathrm{g}$. **23.** Lateral diffusion keeps the head in water and the tails in [oil](#def-b1-lipids-triglyceride) at every step, costing nothing; flipping requires the polar head to cross the hydrophobic core, a large energy barrier that thermal agitation surmounts once a week. **24.** A difference between leaflets decays only as fast as [lipids](#def-b1-lipids-fattyacid) flip; at once a week per molecule, an asymmetry set up by enzymes that move specific [lipids](#def-b1-lipids-fattyacid) across (flippases) persists indefinitely against spontaneous flipping. **25.** About $240\,\mathrm{kg}$ saved — nearly half its body mass — by carrying $30\,\mathrm{kg}$ of [fat](#def-b1-lipids-triglyceride) instead of $270\,\mathrm{kg}$ of hydrated glycogen; and the hump is not a water store: oxidising it loses five times more water in the breath than it produces.