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The Calvin cycle: three steps, and the arithmetic behind them

Carbon dioxide is fixed, the product is reduced, and most of what is made is spent putting the acceptor back. Six turns for one hexose, twelve triose phosphate made and only two allowed to leave. The numbers are half the marks in this topic, and the other half comes from working out what happens when you take something away.

Before this The light-dependent stage and its products · Chloroplast structure · Reduction as gain of hydrogen

Before you start

The light-independent stage does not need light, which is why it is called the dark stage and why it carries on all night. The first half is true in a narrow sense: no step in the cycle absorbs a photon, and it will run in a darkened flask if you supply it. The conclusion is wrong. Every turn spends ATP and reduced NADP, both of which are made only in the light and neither of which is stored in quantity, so the cycle stalls within seconds of the lights going out. 'Dark stage' is a misleading name for a stage that stops in the dark.

What you should be able to do

Describe the three stages of the Calvin cycle and say where each takes place.
State what rubisco does and how many molecules of GP one turn produces.
Explain what reduced NADP and ATP each contribute to the reduction of GP.
Work out how many turns, how many TP and how much ATP a molecule of glucose costs.
Predict and explain the changes in GP, TP and RuBP when light or carbon dioxide is withdrawn.

Where it happens, and what it is waiting for

The Calvin cycle runs in the stroma, the fluid around the thylakoids, and every step is catalysed by an enzyme dissolved in it. That placement is not an accident: the ATP and reduced NADP made by the light-dependent stage are released into the stroma, so the cycle sits directly downstream of them with no membrane in between.

Three things arrive. Carbon dioxide diffuses in from the air through the stomata and across the chloroplast envelope. ATP and reduced NADP arrive from the thylakoid membranes a few nanometres away. Everything else the cycle needs, it makes itself.

RuBP: Ribulose bisphosphate, a five-carbon compound; the molecule that accepts carbon dioxide.
Rubisco: RuBP carboxylase, the enzyme that joins carbon dioxide to RuBP. Slow, easily out-competed by oxygen, and probably the most abundant protein on Earth.
GP: Glycerate 3-phosphate, a three-carbon compound; the first stable product of fixation.
TP: Triose phosphate, a three-carbon sugar phosphate; the product of reducing GP, and the molecule that either leaves the cycle or rebuilds RuBP.

The name to be careful with is fixation. It means taking carbon from an inorganic molecule in the air and locking it into an organic one, and the moment it happens is the moment carbon dioxide joins RuBP. Everything after that is rearranging carbon that has already been fixed.

Three steps, and where the carbon goes

Rubisco joins one molecule of carbon dioxide to one molecule of RuBP. The six-carbon compound that results is so unstable that it has never been isolated; it splits immediately into two molecules of GP. One carbon in, two three-carbon molecules out — and 5 + 1 = 3 + 3, which is the check worth doing every time you draw this.

Watch how little leaves. Six turns of the cycle make twelve TP and only two of them are allowed out; the other ten are spent rebuilding the RuBP that made them possible. A cycle that let all twelve go would stop after one round.

GP is then reduced to TP, and the two inputs do different jobs. Reduced NADP supplies the hydrogen — that is what reduction means here — and ATP supplies the energy for the reaction. Questions ask which does which, so keep them separate: hydrogen from reduced NADP, energy from ATP. The stripped NADP and the ADP go straight back to the thylakoid membranes to be used again.

TP now faces a fork. A small fraction leaves the cycle and is built into the substances the plant actually wants: two TP condense to form a hexose sugar such as glucose, which can be polymerised into starch for storage or cellulose for walls; other TP are converted into glycerol and fatty acids for lipids, or, with nitrate taken up from the soil, into amino acids. The rest of the TP is spent on regeneration: a sequence of rearrangements, costing more ATP, that turns TP back into RuBP so the cycle can accept the next carbon dioxide.

Costing one molecule of glucose

Glucose has six carbons and each turn of the Calvin cycle fixes one carbon dioxide. Work out how many turns are needed, how many TP are made in that time, how many of them leave, and how much ATP and reduced NADP the whole thing costs.

Six carbons in glucose, one carbon fixed per turn, so six turns. Those six turns start from six RuBP, which is 30 carbons, and add six more, giving 36 carbons in play.

Each turn makes two GP and each GP is reduced to one TP, so six turns make twelve TP. Twelve TP is 36 carbons, which matches — nothing has appeared or vanished.

Only two TP leave, carrying six carbons, and those two form the hexose. The remaining ten TP hold 30 carbons, exactly the amount needed to rebuild the six RuBP the cycle began with.

The reduction of twelve GP uses twelve ATP and twelve reduced NADP, one of each per molecule. Regenerating six RuBP costs a further six ATP, giving eighteen ATP in total. If a question asks why photosynthesis needs so much ATP, that ratio — eighteen ATP for one hexose — is the answer.

Two features of this arrangement are worth noticing because examiners build questions on them. The first is how wasteful it looks: five sixths of the product goes on maintenance. The second is why it has to. RuBP is not supplied from outside, so if the cycle ever stops making it, the acceptor runs out and no more carbon can be fixed at all.

Taking something away, and reasoning it out

This is the question that appears most often in this topic and the one most often learned as a list of four facts that then get muddled under pressure. There is no need to memorise it. Two rules generate every version of the answer.

Rule one: work out which single step has been blocked. Rule two: the substance immediately before the block accumulates, because it is still being made and no longer used; the substance immediately after the block falls, because it is still being used and no longer made.

Notice that GP and RuBP always move in opposite directions. They sit on either side of the fixation step, so anything that blocks one route piles up on one side and drains from the other.

Light switched off. The blocked step is the reduction of GP, because ATP and reduced NADP stop arriving within seconds. GP is immediately before the block, so GP rises — rubisco carries on fixing carbon dioxide onto the RuBP that is still there. TP is immediately after the block, so TP falls. RuBP falls as well, and for a reason worth spelling out: it is still being consumed by fixation, but it is regenerated from TP, and there is no longer any TP to regenerate it from.

Carbon dioxide removed. Now the blocked step is fixation itself. RuBP is immediately before that block, so RuBP rises: TP keeps arriving and keeps being converted into RuBP, while nothing is using it up. GP is immediately after, so GP falls sharply — it is still being reduced to TP but nothing is replacing it. TP falls too, a little later, once the supply of GP it is made from has run out.

Change	GP	TP	RuBP	Step that is blocked
Light removed	rises	falls	falls	Reduction of GP to TP
CO₂ removed	falls	falls	rises	Fixation of CO₂ onto RuBP
Light intensity increased	falls	rises	rises	None: reduction speeds up
CO₂ increased	rises	rises	falls	None: fixation speeds up

The bottom two rows are the same reasoning run forwards instead of backwards, and they catch people out because the instinct is to say everything goes up when conditions improve. More light means faster reduction, so GP is consumed faster than it is replaced and its level falls even though the cycle as a whole is running quicker. Levels are not rates.

TRY IT — A sudden change, explained in full

A plant is photosynthesising steadily in bright light with a normal supply of carbon dioxide. The carbon dioxide concentration around it is suddenly reduced to almost zero, the light being left on. Describe and explain what happens to the concentrations of RuBP and of GP in the stroma over the next minute.

Check your answer

RuBP rises. RuBP is used up when rubisco fixes carbon dioxide onto it, and with almost no carbon dioxide available that reaction nearly stops. It is still being regenerated from TP, using ATP that the light reactions are still supplying, so it is made and not used, and it accumulates.

GP falls. GP is produced only by fixation, which has stopped, but it continues to be reduced to TP because reduced NADP and ATP are still arriving in the light. Made no longer, used still, so its concentration drops quickly.

Both changes level off rather than continuing indefinitely. RuBP cannot rise for ever because the pool of TP available to make it is finite, and once GP has been used up there is nothing left to reduce, so TP stops being made as well.

The phrase to reach for in this sort of answer is 'still being made but no longer used', or its mirror image. Naming the reaction on each side of the block is what turns a guess into an explanation.

Why rubisco is the weak link

Rubisco is unhurried. A single molecule fixes something like three carbon dioxide molecules per second, which for an enzyme is close to sluggish, and plants compensate by making enormous quantities of it — it can account for half the soluble protein in a leaf.

It also has an awkward habit. The active site accepts oxygen as well as carbon dioxide, and when it takes oxygen instead, the products are one GP and a two-carbon compound that the plant has to spend energy recovering. On a hot dry day, when stomata close to conserve water, carbon dioxide inside the leaf falls and oxygen from photosynthesis builds up, so the odds tip further towards oxygen and productivity drops.

This is the reason raising carbon dioxide concentration in a glasshouse works so well, and the reason it stops working once the concentration is high enough to keep rubisco busy. It is also why C4 plants such as maize and sugarcane, which concentrate carbon dioxide around their rubisco before the Calvin cycle sees it, outproduce wheat in a hot climate.

In the exam

Say that rubisco catalyses the reaction and that one turn gives two molecules of GP. Both are single marks and both are regularly thrown away.
Reduced NADP supplies hydrogen; ATP supplies energy. A question asking for the role of each wants them separated, not lumped together as 'they are used in the reduction'.
Six turns per hexose, twelve TP made, two leave, eighteen ATP spent. Quantitative questions in this topic are almost always one of those four numbers.
For levels-after-a-change questions, name the blocked step before you say anything goes up or down. The explanation is the marks; the direction alone usually is not.
Do not call it the dark stage in an answer. Say light-independent, and if you have room, say that it stops in the dark because ATP and reduced NADP stop arriving.

Check yourself

In an experiment, algae photosynthesising in bright light were given carbon dioxide labelled with the isotope carbon-14. Samples were killed at intervals of a few seconds and their compounds separated. After five seconds the label was found almost entirely in GP; after thirty seconds it was in GP, TP and RuBP; after two minutes it was also in glucose and starch. Explain this sequence.

Answer

Labelled carbon dioxide is fixed by rubisco onto RuBP, and the six-carbon product splits at once into two molecules of GP. GP is therefore the first compound the label can possibly appear in, which is why after five seconds it is almost the only one labelled.

By thirty seconds the labelled GP has been reduced to TP using reduced NADP and ATP, so the label appears in TP. Some of that labelled TP has then been used to regenerate RuBP, so the label reaches RuBP as well — and that also shows RuBP is rebuilt from TP rather than supplied from outside.

By two minutes, some labelled TP has left the cycle. Two TP condense into a hexose, and hexoses are polymerised into starch, so the label finally turns up in the products the plant stores.

The order of appearance is the evidence for the order of the pathway, which is how the cycle was worked out in the first place. Notice how long the label takes to reach glucose compared with GP: most of the TP never leaves the cycle at all.

Questions

Written to the command words the boards use. Try them on paper before opening a scheme: the marks go to points made, not to length.

Question 15 marks

Calculate the number of turns of the Calvin cycle, the number of molecules of triose phosphate made, the number of molecules of ATP used and the number of molecules of reduced NADP used in producing two molecules of glucose.

Mark scheme

M1 each turn fixes one carbon dioxide and a hexose holds six carbons, so six turns are needed per hexose and 6 × 2 = 12 turns in all
M1 each turn makes two GP and each GP is reduced to one triose phosphate, so 2 × 12 = 24 molecules of triose phosphate
A1 reducing 24 molecules of GP uses 24 ATP and 24 reduced NADP, one of each per molecule
M1 regenerating RuBP costs one further ATP per turn, so 12 more ATP
A1 36 molecules of ATP and 24 molecules of reduced NADP in total, which is eighteen ATP per hexose

Question 24 marks

Describe the three stages of the Calvin cycle, naming the compounds involved and saying what reduced NADP and ATP each contribute.

Mark scheme

B1 fixation: rubisco joins one molecule of carbon dioxide to the five-carbon RuBP, and the six-carbon product is so unstable that it splits immediately into two molecules of GP
B1 reduction: GP is reduced to triose phosphate, with reduced NADP supplying the hydrogen and ATP supplying the energy for the reaction
B1 the oxidised NADP and the ADP go straight back to the thylakoid membranes to be used again
B1 regeneration: most of the triose phosphate is rearranged, at a further cost in ATP, back into RuBP, while the rest leaves the cycle to be built into hexose sugars, lipids or amino acids

Question 34 marks

A plant photosynthesising steadily in bright light is placed in complete darkness, with its carbon dioxide supply unchanged. Explain what happens to the concentrations of GP, of triose phosphate and of RuBP in the stroma over the following minute.

Mark scheme

B1 ATP and reduced NADP are made only in the light and are not stored in quantity, so within seconds the blocked step is the reduction of GP to triose phosphate
B1 GP rises, because it lies immediately before the block: rubisco carries on fixing carbon dioxide onto the RuBP still present, so GP is still being made and is no longer being used
B1 triose phosphate falls, because it lies immediately after the block: it is still being used and is no longer being made
B1 RuBP falls as well, because it is still being consumed by fixation but is regenerated from triose phosphate, and there is no longer any triose phosphate to regenerate it from

Question 43 marks

Six turns of the Calvin cycle make twelve molecules of triose phosphate, and only two of them leave the cycle. Explain why the other ten cannot be allowed to leave.

Mark scheme

B1 the ten that remain hold thirty carbons, which is exactly the number needed to rebuild the six molecules of RuBP the six turns started from
B1 RuBP is not supplied from outside the chloroplast, so the only source of it is the regeneration of triose phosphate
B1 if all twelve left, there would be no acceptor for the next carbon dioxide and the cycle would stop after a single round, so no further carbon could be fixed

Question 53 marks

On a hot, dry, bright day the productivity of a wheat crop falls even though light intensity is high. Suggest how the properties of rubisco account for this.

Mark scheme

B1 the stomata close to conserve water, so carbon dioxide entering the leaf falls while the oxygen made by photosynthesis builds up inside it
B1 the active site of rubisco accepts oxygen as well as carbon dioxide, so with the ratio of the two gases shifted the enzyme takes up oxygen more often
B1 when it does, the products are one GP and a two-carbon compound the plant has to spend energy recovering, so less carbon is fixed into the cycle and productivity drops

Question 62 marks

State the name of the enzyme that catalyses the fixation of carbon dioxide in the Calvin cycle, and state how many molecules of GP one turn of the cycle produces.

Mark scheme

B1 the enzyme is rubisco, also called RuBP carboxylase
B1 one turn produces two molecules of GP

Worth remembering

Rubisco fixes one CO₂ onto one RuBP and the product splits immediately into two GP.
Reduced NADP gives the hydrogen, ATP gives the energy, and GP becomes TP.
Six turns, twelve TP, two out and ten back into RuBP, eighteen ATP spent.
Whatever comes before a blocked step accumulates; whatever comes after it falls.
GP and RuBP always move in opposite directions.

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