What photosynthesis does
Plants, algae and cyanobacteria use the energy of light to build sugar from carbon dioxide and water, giving off oxygen:
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
It happens in two linked parts. In the light-dependent reactions, in the thylakoid membranes of the chloroplast, chlorophyll absorbs light and the energy is used to split water, which releases the oxygen, and to make ATP and NADPH. In the Calvin cycle, in the stroma around the thylakoids, the enzyme Rubisco fixes carbon dioxide and the ATP and NADPH turn it into sugar. The first part needs light; the second needs carbon dioxide and, like every set of enzyme reactions, runs faster when warm.
Limiting factors
In 1905 Frederick Blackman pointed out that when a process depends on several factors, its rate is held back by the one in shortest supply, the limiting factor. Give a plant more light when it is short of carbon dioxide and nothing much happens; give it more carbon dioxide and the rate climbs until light, or temperature, becomes the limit instead. That is why every rate curve for photosynthesis rises and then levels off: the plateau is where another factor has taken over.
- Light intensity limits the light reactions. In dim light the rate is close to proportional to the light.
- Carbon dioxide limits the Calvin cycle. Water plants take it up as dissolved CO₂ and as hydrogencarbonate ions, which is why adding sodium hydrogencarbonate (NaHCO₃) speeds them up.
- Temperature sets the speed of the enzymes: roughly doubling for every 10 °C rise (a Q₁₀ of about 2) until, above an optimum, the enzymes begin to be damaged and the rate falls steeply.
Light and distance: the inverse square law
Light from a small lamp spreads out over a sphere whose area grows with the square of the distance, so the intensity falls as 1 ÷ d². Moving a lamp from 10 cm to 20 cm leaves a quarter of the light; to 30 cm, a ninth. Results from the lamp experiment are therefore often plotted against 1 ÷ d², which is proportional to the light intensity, rather than against the distance itself.
Respiration and the compensation point
A plant respires all the time, using oxygen, day and night. What you measure as oxygen given off is the net rate: gross photosynthesis minus respiration. In dim light the two can balance, so no oxygen leaves the plant at all. The light intensity at which this happens is the compensation point. Below it the plant uses more sugar than it makes.
The pondweed experiment
A sprig of pondweed (Elodea or Cabomba) is put upside down in a tube of water, cut end up, with a lamp beside it. Oxygen from photosynthesis collects in the air spaces of the stem and escapes from the cut end as a stream of bubbles. Count the bubbles in a minute at several lamp distances, or collect the gas in a capillary tube and measure its length, and you have a measure of the rate. Sodium hydrogencarbonate in the water keeps the plant from running short of carbon dioxide, and a beaker of water around the tube keeps the temperature steady.
A worked example
The simulation starts with the lamp 20 cm away, white light, 1 g of sodium hydrogencarbonate per liter and water at 25 °C.
- Light: the lamp gives 800 µmol of photons per m² per second at 10 cm, so at 20 cm I = 800 × (10 ÷ 20)² = 200.
- Light alone could support J = 0.1 × 0.75 × 200 = 15 bubbles a minute (0.75 for white light).
- Carbon dioxide: 1 g of NaHCO₃ (84 g per mole) is 11.9 mM, plus 0.5 mM from the water, so C = 12.4 mM and C ÷ (C + 2) = 0.86.
- Temperature: at 25 °C the enzymes run at 0.65 of their best, so the most they could manage is P_max = 60 × 0.65 × 0.86 = 33.6 bubbles a minute.
- J is well below P_max, so light limits the rate. Gross photosynthesis comes to 14.0, respiration takes 3, and 11 bubbles a minute are given off.
Move the lamp to 10 cm and the light quadruples to 800, J becomes 60, and the net rate rises to 27.4 bubbles a minute: not four times as much, because the rate is now close to P_max. The light is no longer limiting; at 25 °C temperature is. Warming the water to 35 °C raises the net rate to 34.6, while raising the sodium hydrogencarbonate to 10 g/L only takes it to 30.9.
Using the simulation
In the Photosynthesis and Limiting Factors Simulator, things to try:
- Plot the rate against the lamp distance and count the bubbles at 10, 20, 40 and 80 cm; then plot the same against light intensity to see the curve level off.
- Move the lamp past about 45 cm: below the compensation point the bubbles stop, though the plant is still photosynthesizing.
- Set the sodium hydrogencarbonate to 0 with the lamp close: carbon dioxide limits the rate to under 5 bubbles a minute however bright the lamp.
- Plot against temperature: the rate rises to an optimum near 33 °C and collapses by 45 °C, where respiration outruns photosynthesis.
- Switch to green light: the rate drops to a fraction of what red light gives at the same distance.
What the model assumes
- A point source of light following the inverse square law exactly, with no light from the room.
- The rate is the smaller of what light and the enzymes allow, with a smooth bend between the two (a non-rectangular hyperbola with a curvature θ of 0.9), as in the usual models of leaf photosynthesis.
- Carbon dioxide follows a saturating curve, C ÷ (C + 2 mM), with dissolved CO₂ and hydrogencarbonate treated as equally usable.
- Temperature speeds the enzymes with a Q₁₀ of 2 and damages them with a midpoint at 37 °C; damage is instant and fully reversible.
- Respiration is 3 bubbles a minute at 25 °C, doubling every 10 °C, and the same in light and dark.
- Every bubble is the same size and made only of oxygen from photosynthesis; counts scatter as random (Poisson) numbers around the model rate.
- Color enters as a single efficiency for each lamp: red 1, white and blue 0.75, green 0.3, at the same photon flux.
Edge cases
- Lamp very close: at 5 cm the light is 3,200 µmol m⁻² s⁻¹, more than full sunlight, but the rate rises only from 27.4 to 30 bubbles a minute compared with 10 cm: the curve has saturated.
- Compensation point: below it the net rate is shown as zero; the plant is not doing nothing, but it uses all its oxygen itself.
- No sodium hydrogencarbonate: only the 0.5 mM in the water is left, and carbon dioxide limits everything.
- Hot water: from about 42 °C the enzymes fail and respiration, still rising, exceeds photosynthesis, so there are no bubbles however bright the lamp.
- Near freezing: at 0 °C the enzymes run at about a tenth of their best, so even bright light gives few bubbles.
Where the model stops being right
- Lamps heat the water. A filament or halogen lamp close to the tube warms it, so moving the lamp changes temperature as well as light. LED lamps or a tank of water between lamp and plant avoid this.
- Close lamps are not points. Within a few lamp-diameters of the plant, the light no longer falls as 1 ÷ d², and parts of the plant are shaded by others.
- Bubbles are a rough measure. They vary in size, some oxygen dissolves before it can form bubbles, and the gas also contains nitrogen and carbon dioxide. Measuring gas volume, or dissolved oxygen with a probe, is more accurate.
- Damage is not reversible. Enzymes denatured by heat do not recover when the water cools, and very bright light damages the photosystems (photoinhibition), lowering the rate instead of holding it at a plateau.
- Green light is not useless. Thin pondweed leaves absorb little green light, but in thicker leaves green light is absorbed on repeated passes; McCree's measurements on crop leaves found green photons around 70% as effective as red.
- The plant changes. Over hours, plants close their light-harvesting machinery in bright light, use up carbon dioxide in still water, and acclimatize to the temperature, so a long experiment drifts from the model.
- Photorespiration. Rubisco also reacts with oxygen, wasting energy, more so when warm and when carbon dioxide is low; the simple temperature curve folds this into one factor.
Related tools
Make up the sodium hydrogencarbonate solution with the Molarity Calculator and the Molar Mass Calculator, as described in How to Make a Solution of a Given Molarity. The Enzyme Kinetics Simulator shows how enzymes respond to temperature and substrate, and the Spectrophotometer and Beer-Lambert Law Simulator measures how pigments such as chlorophyll absorb light of each color. The Temperature Converter converts the water temperature.