Limiting factors sim
Drag the lamp along the rule, pour a stronger or weaker sodium hydrogencarbonate solution and set the water bath, count the bubbles from a pondweed sprig for one minute at a time, and build your own rate graphs, where each plateau is marked with the factor that limits it.
Photosynthesis: limiting factors (light intensity, carbon dioxide concentration, temperature) · covers the O-Level, IGCSE, GCSE topic
What the sim shows
Limiting factors in photosynthesis. A sprig of pondweed (Elodea) in sodium hydrogencarbonate solution stands in a thermostatic water bath. Drag the lamp along the rule (light intensity), drag a bottle to the tube to change the solution (more sodium hydrogencarbonate gives more dissolved carbon dioxide), or slide the bath's set-point (temperature). Then press Count for 1 min: the bubbles that leave the cut end of the stem in that minute are drawn in the close-up and counted. Each factor allows the pondweed at most a certain rate; the rate is set by the factor in shortest supply, the limiting factor. Raising the limiting factor raises the rate. Raising a factor that is not limiting makes little or no difference, so the graph levels off in a plateau, and a plateau is higher when the factor that limits it is raised. Temperature works through the enzymes that control photosynthesis: up to the optimum (about 35 °C) the rate about doubles for each 10 °C rise; above it, more and more of the enzymes are denatured and the rate falls. Light intensity follows the inverse square law: halving the lamp's distance gives four times the light, so relative light intensity = (40/d)², with d in cm (1 at 40 cm, ≈ relative). Simplified on purpose: the numbers are illustrative (≈) and each count is exact, with none of the scatter of a real count; the model is a smooth minimum of three ceilings (rate = (cL⁻⁹ + cC⁻⁹ + cT⁻⁹)^(−1/9) bubbles per minute, where each c is the most that factor allows); the bubbles stand for the oxygen made, but they are not pure oxygen (they also hold some nitrogen and carbon dioxide from the water) and real bubbles differ in size, so a gas syringe or capillary tube that measures the volume is more accurate; a lamp also heats the water, but in this sim the water bath holds the tube at exactly the set temperature, so the lamp does not warm it (in a real practical, use an LED lamp or a clear heat shield, such as a beaker of water, and check the thermometer); the bath cools as well as heats (a real one needs ice below room temperature); denaturing is permanent: a minute at 40 °C or above destroys some of the enzyme for good, so after it the most the enzymes allow is lower at every temperature, and cooling the sprig never brings the rate back; a sprig that has been counted at 40 °C keeps about 71 % of its enzyme, and one counted at 45 °C only about 17 % (a sixth); these surviving shares are illustrative; press Fresh sprig for a new one, and use a fresh sprig for each setting at or above 40 °C; here a second minute at the same temperature does no further damage (in a real plant, damage builds up with time spent hot); in this sim the damage happens only during a count, because time passes only then; the pondweed is assumed to have had 5 minutes to adjust after each change; the lamp is treated as a point source, and the light lost in the glass and water is ignored; the apparatus on the bench is drawn to scale, and the close-up is not to scale.
- Lit: the lamp's index tab on the rule and the bath's set-point
- Close-up: the cut end of the stem, magnified, and what each factor allows
- Close-up bars: dashed line, the rate you counted
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