Investigation of limiting factors

1. Overview

Photosynthesis needs a supply of light energy, carbon dioxide and a suitable temperature. At any moment one of these is usually in shortest supply, and this limiting factor sets the overall rate: increasing it speeds up photosynthesis, while increasing the others has no effect until the limiting one is raised. This topic explains how light intensity, carbon dioxide concentration and temperature each change the rate, and how to investigate them both in the test tube using isolated chloroplasts with redox indicators ($DCPIP$ or methylene blue) and in living material using whole aquatic plants such as pondweed.

Key Definitions

• Limiting factor: the factor that, at a particular moment, is in shortest supply and so directly controls the rate of a process such as photosynthesis.
• Light intensity: a measure of the amount of light energy reaching a given area, which provides the energy for the light-dependent reactions.
• Compensation point: the light intensity at which the rate of photosynthesis exactly equals the rate of respiration, so there is no net exchange of carbon dioxide or oxygen.
• Redox indicator: a dye that changes colour when it is reduced (gains electrons or hydrogen), used to follow the light-dependent reactions; examples are DCPIP and methylene blue.
• DCPIP: a blue redox indicator that becomes colourless when reduced, acting as an artificial electron acceptor in place of NADP in the Hill reaction.
• Hill reaction: the light-driven reduction of an electron acceptor by illuminated chloroplasts, releasing oxygen from water.
• Action spectrum: a graph showing the rate of photosynthesis at different wavelengths of light.
• Absorption spectrum: a graph showing how strongly a pigment absorbs each wavelength of light.

Content

The idea of a limiting factor

A metabolic pathway has several stages, each needing a particular input. At any moment the factor in shortest supply holds back the whole process, so it is called the limiting factor. For photosynthesis, the three main limiting factors are:

• light intensity
• carbon dioxide concentration
• temperature

If you raise the limiting factor the rate climbs; if you raise a factor that is not limiting, the rate stays the same because something else is still holding it back. On a rate graph this gives a line that rises steeply and then levels off (plateaus) once a different factor has taken over as the limit.

Effect of light intensity

Light energy drives the light-dependent reactions, producing the $ATP$ and reduced $NADP$ needed to fix carbon dioxide in the Calvin cycle.

• At low light intensity, light is limiting, so the rate increases roughly in proportion to intensity.
• As intensity rises further the rate plateaus, because some other factor (such as carbon dioxide concentration or temperature) has become limiting.
• At very low intensities, respiration releases more carbon dioxide than photosynthesis fixes. The intensity at which the two exactly balance is the compensation point. Below the compensation point the plant is a net consumer of oxygen and net producer of carbon dioxide (respiration exceeds photosynthesis); only above it does the plant show a net release of oxygen and net uptake of carbon dioxide. This is why a deeply shaded plant can give out carbon dioxide overall even in daylight.

Effect of carbon dioxide concentration

Carbon dioxide is the substrate fixed by the enzyme Rubisco in the light-independent reactions (Calvin cycle), where it combines with the 5-carbon acceptor ribulose bisphosphate ($RuBP$). At low concentrations, raising carbon dioxide increases the rate steeply. The rate then plateaus when another factor becomes limiting. Atmospheric air contains only about $0.04\%$ carbon dioxide, so in bright, warm conditions carbon dioxide is often the limiting factor - which is why commercial greenhouses enrich the air with extra carbon dioxide.

A useful extension is the difference between C3 and C4 plants. In C4 plants the enzyme PEP carboxylase in the mesophyll cells first fixes carbon dioxide efficiently, even at low concentrations, before passing it on as a 4-carbon compound to the bundle sheath cells, where Rubisco completes the Calvin cycle. Be careful here: PEP carboxylase is in the mesophyll, while Rubisco is restricted to the bundle sheath cells.

Reading a graph with two curves

A common question plots two curves for the same factor (e.g. rate against light intensity) measured at a higher and a lower carbon dioxide concentration, or at two temperatures. The mark-earning points are:

• On the initial steep section the two curves overlap, because light is limiting for both - the extra carbon dioxide (or higher temperature) makes no difference while light is in short supply.
• The curves separate at the plateau: the higher-carbon-dioxide (or higher-temperature) curve plateaus at a higher rate, and its plateau begins at a higher light intensity, because light stays limiting for longer before carbon dioxide (or temperature) takes over as the limiting factor.

Effect of temperature

Temperature affects the enzyme-controlled light-independent reactions far more than the (mainly photochemical) light-dependent reactions. As temperature rises, enzyme and substrate molecules gain kinetic energy, collide more often, and form more enzyme-substrate complexes, so the rate rises - roughly doubling for each 10 °C rise up to the optimum. Above the optimum the enzymes (especially Rubisco) begin to denature: the tertiary structure changes, active sites are no longer complementary to their substrate, and the rate falls sharply. Remember too that respiration continues at all temperatures, in both light and dark - plants do not "switch off" respiration in the light.

Investigating the light-dependent reactions with redox indicators

Isolated chloroplasts can be made to carry out the Hill reaction: when illuminated, they split water and pass electrons to an artificial electron acceptor (a redox indicator) instead of $NADP$. As the indicator is reduced it changes colour:

• DCPIP goes from blue to colourless as it is reduced.
• Methylene blue also goes from blue to colourless as it is reduced - it is simply an alternative artificial electron acceptor, so the colour change you look for is exactly the same as for DCPIP.

A faster colour change means a faster rate of the light-dependent reactions.

Method outline:

1. Extract a cold chloroplast suspension by grinding leaf tissue in chilled isotonic buffer and filtering it.
2. Mix a fixed volume of the suspension with a fixed volume of the redox indicator.
3. Shine light of a chosen intensity or wavelength on the tube.
4. Record the time taken for a set colour change, or use a colorimeter to measure the falling absorbance at regular intervals.
5. Keep the suspension cold and use a buffer throughout, to protect the chloroplasts and hold the pH constant.

To vary the factor under test, change one thing at a time: vary light intensity by changing the lamp distance, and vary wavelength by placing coloured filters between the lamp and the tube, keeping everything else constant.

Action spectrum and absorption spectrum

Investigating different wavelengths produces an action spectrum (rate against wavelength); photosynthesis is fastest in red and blue light and slowest in green, which is reflected. As the graph below shows, the action spectrum of photosynthesis and the absorption spectrum of chlorophyll track each other closely, both peaking in blue and red light and dipping in green. The figure illustrates the general shape and overlap of the two curves; the axes are relative, so use it to compare the pattern of the curves rather than to read off exact values.

Comparing the action spectrum with the absorption spectrum of a single pigment such as chlorophyll a is powerful: where the action spectrum is higher than the absorption spectrum of one pigment, it shows that accessory pigments (such as chlorophyll b and carotenoids) must also be absorbing light and contributing to photosynthesis. Argue this from the shape and overlap of the curves, not just from isolated numerical differences between two points.

Investigating whole plants, including aquatic plants

A convenient system is an aquatic plant such as Elodea (pondweed), because the oxygen it produces can be counted or collected. Two common approaches:

• Counting bubbles: cut the stem, place it in water containing dissolved carbon dioxide (e.g. sodium hydrogencarbonate solution), and count oxygen bubbles released per minute.
• Measuring oxygen volume: collect the gas in a capillary tube or gas syringe and measure the volume or length of gas produced in a set time - more reliable than counting, since bubble size varies.

To study light intensity, change the distance of the lamp (intensity follows the inverse square law); to study carbon dioxide concentration, vary the concentration of hydrogencarbonate solution; to study temperature, use a thermostatically controlled water bath. Always control the other two factors, allow time for the plant to acclimatise at each setting, and use a heat filter (a beaker of water between lamp and plant) so the lamp does not warm the water when only light is being varied. A measured rate of bubble or oxygen production is net photosynthesis, because the plant is also respiring.

Worked example

Exam-style question: A student adds equal volumes of a cold chloroplast suspension and blue DCPIP solution to several tubes. Each tube is placed at a different distance from a lamp, and the time for the blue colour to disappear is recorded. The tubes closest to the lamp lose their colour fastest. Explain these results, and suggest one variable that is difficult to control in this investigation. [4]

Model answer:

• The illuminated chloroplasts carry out the light-dependent reactions and pass electrons to DCPIP, which becomes colourless as it is reduced (the Hill reaction).
• Tubes closer to the lamp receive a higher light intensity, so the light-dependent reactions run faster; DCPIP is reduced more quickly and the colour disappears in a shorter time.
• At greater distances light intensity is the limiting factor, so the rate is lower and the colour change is slower.
• A variable that is hard to control is the temperature of the tubes (the lamp also warms them); a heat filter or water bath would reduce this.

Worked example

Exam-style question: A student measured the rate of photosynthesis of pondweed by counting the oxygen bubbles released per minute at four lamp distances. The results are shown below. Calculate the relative light intensity ($1/d^{2}$) at each distance, describe how the rate responds, identify the limiting factor on the steep and level parts of the response, and explain why the bubble count gives the net rather than the gross rate of photosynthesis. [5]

Distance, $d$ (cm)	Bubbles per minute
10	30
20	30
40	16
80	4

Model answer:

• Relative light intensity is $1/d^{2}$: at 10 cm, $1/10^{2} = 0.0100$; at 20 cm, $1/20^{2} = 0.0025$; at 40 cm, $1/40^{2} = 0.000625$; at 80 cm, $1/80^{2} = 0.000156$ (arbitrary units).
• At the higher intensities (10 cm and 20 cm) the bubble count is the same (30 per minute) even though the intensity has fallen fourfold, so light is not limiting here; another factor, such as carbon dioxide concentration or temperature, is the limiting factor on this level (plateau) part.
• As the lamp is moved further away (to 40 cm then 80 cm) the rate falls steeply (16 then 4 bubbles per minute) as the intensity drops, so on this steep part light intensity is the limiting factor.
• The bubble count measures net photosynthesis because the plant is respiring at the same time; some of the oxygen made is used internally in respiration, so the oxygen released understates the gross rate.

Key Equations

This topic is largely qualitative. The only quantitative relationship needed is for light intensity from a point source, which falls with the square of the distance from the lamp: $$\text{light intensity} \propto \frac{1}{d^{2}}$$ where $d$ is the distance between the lamp and the plant. Rate of photosynthesis is usually calculated as a count or volume per unit time, for example: $$\text{rate} = \frac{\text{number of bubbles (or volume of oxygen)}}{\text{time}}$$

Common Mistakes to Avoid

• Listing "contamination" as a source of error. Properly washing the apparatus removes contamination, so it is not a genuine experimental error. Instead discuss variables that are genuinely hard to keep constant, such as the temperature rise from the lamp.
• Putting PEP carboxylase in the wrong cells of a C4 plant. PEP carboxylase fixes carbon dioxide in the mesophyll cells; Rubisco is confined to the bundle sheath cells.
• Drying living tissue in an oven before measuring. Oven-drying removes water from inside cells and damages them. For living material, gently blot dry with a paper towel instead.
• Using only odd numbers to claim accessory pigments are present. Argue from the curves: if the action spectrum lies above the absorption spectrum of one pigment, other (accessory) pigments must also be absorbing light and driving photosynthesis.
• Saying the plateau happens because the enzyme is "used up". Enzymes are catalysts and are not consumed; the rate levels off because the active sites are saturated or because a different factor has become limiting.
• Thinking a saturated enzyme means the reaction has stopped. When active sites are saturated and substrate is still plentiful, the enzyme keeps working at its maximum turnover: a roughly constant (steady-state) number of enzyme-substrate complexes is forming and breaking apart all the time. So the rate stays high and constant at the plateau - it does not stall - and the enzyme amount, not the substrate, is now the limit.
• Claiming plants stop respiring in the light. Respiration occurs continuously, in both light and dark, so a measured oxygen release is net photosynthesis.
• Forgetting that a rate may level off because something else is now limiting. Always state which factor has taken over as the limiting factor at the plateau.

Exam Tips

• When you explain a curve, name the limiting factor at each part - "light is limiting on the steep portion; another factor limits at the plateau."
• For the redox-indicator practical, link the colour change directly to reduction of the indicator by electrons from the light-dependent reactions (the Hill reaction).
• Prefer measuring the volume of oxygen over counting bubbles, and say why (bubble size varies), to gain reliability marks.
• When controlling variables, mention a heat filter or water bath so that changing the lamp distance does not also change the temperature.
• Quote the inverse square law when asked how lamp distance affects light intensity, and explain that doubling the distance quarters the intensity.
• Use precise vocabulary: denatured (not "killed"), active site complementary to substrate, and net versus gross photosynthesis.
• For "compare the spectra" questions, describe the overlap and difference in shape of the action and absorption spectra rather than picking single readings.