Investigation of limiting factors

A limiting factor is the factor in shortest supply that controls the rate of a process when other factors are present in excess. Blackman's law of limiting factors (Blackman, 1905) states that when a process is influenced by several factors, the rate is determined by the factor that is closest to its minimum value — increasing any other factor will have no effect on the rate until the limiting factor itself is increased.

For photosynthesis, the three main limiting factors are:

• Light intensity — drives the light-dependent reactions; controls the supply of ATP and NADPH to the Calvin cycle.
• CO₂ concentration — the substrate of Rubisco; controls how fast RuBP can be carboxylated to GP.
• Temperature — controls the rate of all enzyme-catalysed steps, especially in the Calvin cycle.

Water, mineral ions (Mg²⁺ for chlorophyll; N for amino acids and chlorophyll; PO₄³⁻ for ATP and nucleic acids) and chlorophyll concentration can also influence rate, but on the time scale of a single experiment they are usually constant.

Identifying a limiting factor from a graph. When rate is plotted against a single environmental variable, the rising portion of the curve shows that variable is the limiting factor. The plateau shows that some other factor is now limiting. To identify which other factor, repeat the experiment with that suspected factor at a higher level — if the plateau rises, that factor was indeed limiting.

A classic example: plot rate vs light intensity at low CO₂ and at high CO₂. At low light both curves coincide (light is limiting). At high light they diverge — the high-CO₂ curve plateaus higher (showing CO₂ was the second limiting factor).

At low light intensity the rate of photosynthesis is directly proportional to light intensity. Light is the limiting factor: more photons → more electrons excited at PSII and PSI → more ATP and NADPH produced → more RuBP regenerated and more GP reduced → more CO₂ fixed.

At intermediate light intensity the curve flattens. The light reactions are saturated and supplying ATP and NADPH faster than the Calvin cycle can use them. Some other factor (CO₂ or temperature) is now limiting.

At very high light intensity (above ~1500 μmol photons m⁻² s⁻¹, similar to bright noon sunlight) two effects can lower the rate:

• Photoinhibition — excess light energy damages PSII proteins (especially the D1 subunit) by generating reactive oxygen species. Plants have photoprotection mechanisms (xanthophyll cycle, photorespiration acts as an energy 'safety valve'), but at extreme intensities damage exceeds repair.
• Stomatal closure — high light raises leaf temperature and accelerates water loss; the plant closes stomata, reducing CO₂ supply.

Compensation point. At very low light intensity, photosynthesis is slower than respiration. As light increases, photosynthesis speeds up. The light intensity at which photosynthesis exactly equals respiration is the compensation point. Below it, the plant respires more than it photosynthesises (net biomass loss). Above it, the plant has net biomass gain.

• Sun plants (e.g. dandelion, grass) have high compensation points (~50-200 μmol photons m⁻² s⁻¹) but very high maximum rates of photosynthesis.
• Shade plants (e.g. wood sorrel, ferns) have low compensation points (~5-20 μmol photons m⁻² s⁻¹) but low maximum rates — adapted to consistent low light in forest understories.

Carbon dioxide is the substrate of Rubisco and therefore directly limits the Calvin cycle.

At low CO₂ rate rises with concentration — CO₂ is limiting. More CO₂ → more substrate for Rubisco → more RuBP carboxylated → more GP → more TP. The relationship is nearly linear at very low CO₂.

At higher CO₂ the rate plateaus. Rubisco's active sites are saturated with CO₂; further increase has no effect. The new limiting factor is either light (insufficient ATP / NADPH) or temperature (slow Calvin cycle enzymes).

Atmospheric CO₂ in 2026 is about 420 ppm (0.042%) — well below the saturation point of most C3 crops, which lies near 1000 ppm (0.1%). Photosynthesis in most agricultural systems is therefore CO₂-limited most of the time. This is why CO₂ enrichment in glasshouses pays for itself.

Note on photorespiration. Rubisco is not perfectly specific for CO₂ — it can also catalyse the reaction of RuBP with O₂ (its 'oxygenase' activity). At high O₂ : CO₂ ratios (high T, low CO₂ inside the leaf), photorespiration consumes RuBP without fixing carbon, lowering net photosynthesis. Maintaining a high CO₂ concentration favours the carboxylase activity and reduces photorespiration — another reason CO₂ enrichment in glasshouses raises yield.

C4 plants (maize, sugarcane, sorghum) overcome the low atmospheric CO₂ problem by concentrating CO₂ at Rubisco using PEP carboxylase in mesophyll cells. They are more efficient in hot, dry, high-light conditions than C3 plants but require specialist anatomy.

Temperature affects the Calvin cycle strongly because it is enzyme-catalysed (especially by Rubisco). The light-dependent reactions are largely temperature-independent because they are photochemical (driven by light energy rather than enzymatic kinetic energy in the conventional sense). However, ATP synthase and the cytochromes are proteins, so extremely low or high temperatures do affect the light reactions to some extent.

Below the optimum (typically 0-25°C). Rate rises approximately exponentially with temperature. The Q₁₀ for the Calvin cycle is about 2 — rate roughly doubles per 10°C rise. This is because:

• Substrate molecules (CO₂, RuBP) have more kinetic energy → more successful collisions.
• Enzyme molecules (Rubisco etc.) have more kinetic energy → faster cycling.

Optimum (25-35°C for most temperate C3 plants; higher for tropical species). Maximum enzyme activity; rate at its highest provided light and CO₂ are non-limiting.

Above the optimum (35-45°C). Rate falls sharply. Three reasons:

1. Enzyme denaturation. Rubisco and other Calvin cycle enzymes have their tertiary structure disrupted by excessive thermal vibration. The active site changes shape and can no longer bind RuBP / CO₂ effectively. By ~50°C most enzymes are irreversibly denatured.

2. Photorespiration increases. Rubisco's oxygenase activity (the side reaction in which O₂ rather than CO₂ binds RuBP) becomes proportionally more important as temperature rises. This wastes RuBP and lowers net photosynthesis.

3. Stomatal closure. High leaf temperature accelerates transpirational water loss. The plant senses water stress, releases ABA, and closes stomata — reducing CO₂ uptake. CO₂ then becomes the dominant limiting factor.

Below 0°C. The Calvin cycle is effectively halted (cytoplasm may freeze; enzymes are very slow). Photosynthesis stops.

Practical implication. In a glasshouse, temperature is controlled to remain within the optimum band (typically 20-25°C for lettuce, 22-28°C for tomato). Heating in winter; ventilation and shading in summer.

The classical Cambridge 9700 practical investigation uses an aquatic plant — usually Cabomba (preferred for ease of bubble release) or Elodea (Canadian pondweed) — in sodium hydrogencarbonate (NaHCO₃) solution.

Why hydrogencarbonate? NaHCO₃ dissolves to release CO₂ in the water (HCO₃⁻ ⇌ CO₂ + OH⁻), supplying a constant excess of CO₂ so that CO₂ is not the limiting factor. The plant's photosynthesis then depends on the variable being tested (light intensity or temperature).

Apparatus.

• Boiling tube with 0.2% NaHCO₃ solution (50 cm³).
• ~5 cm length of Cabomba / Elodea with the stem cut at an angle under water (to release any trapped air bubbles and to ensure the cut surface bubbles freely).
• Water bath at controlled temperature (e.g. 25°C).
• Bench lamp (60-100 W or equivalent LED).
• Heat sink — a beaker of water between the lamp and the boiling tube to absorb infrared and keep temperature constant when the lamp distance changes.
• Stopwatch and either:
  • Counting: an inverted funnel and capillary to count bubbles per minute.
  • Volume: an inverted measuring cylinder or gas syringe to collect O₂ and measure volume after a known time.

Procedure — varying light intensity (independent variable).

1. Set lamp at distance $d_1$ (e.g. 10 cm).
2. Allow 5 min equilibration.
3. Count bubbles in 2 min OR record volume of O₂ collected in 5 min.
4. Repeat twice more; take mean.
5. Move lamp to $d_2 = 20$ cm; repeat.
6. Continue at $d_3 = 30$, $d_4 = 40$, $d_5 = 50$ cm.

Calculating light intensity. For a point-source lamp, intensity follows the inverse square law: $I \propto 1/d^2$. Calculate relative intensity = $1/d^2$. Or use a light meter (lux meter) for direct measurement.

Procedure — varying CO₂ concentration. Use NaHCO₃ at 0.0, 0.1, 0.2, 0.5, 1.0 and 2.0% w/v; keep light constant.

Procedure — varying temperature. Use the water bath at 5, 15, 25, 35, 45°C; keep light and NaHCO₃ constant. Note: above ~40°C the plant may be damaged.

Calculating the rate. Rate = volume of O₂ ÷ time (cm³ min⁻¹) OR bubbles per minute. Volume measurement is preferred — bubble size varies with rate.

Control variables (always). Same piece of plant, same volume of NaHCO₃, same temperature (water bath + heat sink), same orientation, same equilibration time.

Expected results. A typical light-intensity curve rises steeply at low intensity, then plateaus. A CO₂ curve rises steeply at low concentration, then plateaus. A temperature curve has a typical bell shape with an optimum around 25-30°C.

Commercial glasshouses (greenhouses) are large enclosed structures where the environment can be controlled to remove or raise every limiting factor of photosynthesis. The economic goal is to grow crops year-round and to maximise yield per square metre.

Light. Sunlight is supplemented with artificial lighting (high-pressure sodium lamps or modern white-LED panels) for several hours per day, especially in winter and at high latitudes. Reflective wall coverings increase light to lower leaves. Light intensity is monitored to stay above the saturation point.

CO₂. The atmosphere is enriched to 1000-1200 ppm CO₂ (vs ~420 ppm outside). Two common sources:

• Burning natural gas (methane) inside the glasshouse — produces CO₂ AND heat as a dual benefit. The waste heat is used in winter.
• Compressed CO₂ from cylinders — used when the climate is warm but extra CO₂ is needed. Enrichment increases yield by 20-40% for crops such as tomato, cucumber and lettuce.

Temperature. Heating systems (gas, biomass or geothermal) raise temperature in winter; thermostatically-controlled vents and shading reduce temperature in summer. Target range: 20-28°C depending on crop. Computer-controlled environmental management.

Water. Drip irrigation supplies water directly to the roots, minimising waste and disease. Misting systems maintain humidity to slow transpiration. Sensors monitor soil moisture.

Mineral nutrients. Fertigation (fertilisers dissolved in irrigation water) supplies N, P, K, Mg and trace elements. Many commercial glasshouses use hydroponics — plants are grown without soil, with roots in nutrient solution or inert media (rockwool, perlite). This gives precise control over nutrition and excludes soil-borne pathogens.

Pest and disease control. Closed environment allows biological control (e.g. Phytoseiulus predator mites against red spider mites) to be highly effective.

Economic balance. Each input has a cost. Growers compute the marginal return — does the extra yield from more CO₂ / light / heat exceed the input cost? The optimal strategy is the one that maximises profit per square metre, not the absolute photosynthesis rate.

Examples. The Netherlands produces ~6 million tonnes of glasshouse tomatoes per year; UK and Spanish glasshouse lettuce; Japanese strawberry farms. The Westland region in the Netherlands has 90 km² of glasshouses — visible from space.

At very low light intensity, photosynthesis is slower than respiration: the plant uses up its sugar reserves and loses biomass. As light intensity increases, photosynthesis speeds up. The light intensity at which photosynthesis exactly equals respiration is called the compensation point.

At the compensation point:

• O₂ produced by photosynthesis = O₂ consumed by respiration → no net O₂ release.
• CO₂ fixed by photosynthesis = CO₂ released by respiration → no net CO₂ uptake.
• No net change in glucose / starch reserves.

Above the compensation point photosynthesis exceeds respiration → net biomass gain.

Below the compensation point respiration exceeds photosynthesis → net biomass loss; the plant is using reserves.

Sun vs shade plants. Different plant species have evolved different compensation points to match their habitat:

Plant type	Compensation point	Maximum rate
Sun plant (e.g. grass)	High (50-200 μmol m⁻² s⁻¹)	Very high
Shade plant (e.g. fern)	Low (5-20 μmol m⁻² s⁻¹)	Lower

Shade plants have a lower compensation point because:

• They have more chlorophyll per unit leaf area (more pigment per chloroplast, more chloroplasts per cell).
• They have a lower rate of respiration (smaller, thinner leaves with fewer mitochondria).

This allows shade plants to survive in low-light forest understories where sun plants would lose biomass.

Practical importance. A houseplant placed in a dark corner below its compensation point will gradually wither — even if you 'water it'. Conversely, exposing a shade plant to full sun can cause photoinhibition damage.

The compensation point is reached briefly at dawn and dusk in the field — at very low light intensities just after sunrise and just before sunset.