Leaf Disk Assay: Investigation Model
Practice setting up a fair comparison, make predictions, and analyze simulated flotation. Then collect real observations and evaluate where the model agrees or falls short.
Key assumption: simplified equations connect the settings to gas accumulation and flotation. Their numerical values, variation, and resulting times have not been calibrated to a leaf disk dataset. A model result is not a measured result or an expected classroom answer.
Recommended use: before and after a real assay
- Before: choose a question. Begin with light intensity or bicarbonate, keeping the other settings constant. Use C as your comparison cup and A and B as treatments. Predict the pattern and explain your reasoning before running the model.
- Practice: watch infiltration, record counts, graph the results, and calculate ET₅₀. Repeat with a new seed to explore the model’s invented variability. Repeated simulations are not biological replicates.
- In class: follow your teacher’s real assay protocol. Record the actual preparation, light conditions, temperature, plant material, and counts. Include appropriate controls and independent replicate cups. Ten disks in one cup are subsamples, not ten independent treatment replicates.
- After: compare the direction and shape of your real results with the model. Keep the two datasets separately labeled. A disagreement may reveal an omitted factor, an unsuitable model assumption, or a procedural issue; it does not automatically mean your real experiment is wrong.
Use this activity for planning, analysis practice, and evaluating models. It accompanies hands-on work; it does not provide evidence that a particular treatment works in real plants or replace collecting real data.
Science foundations and model assumptions
Science foundation: infiltration replaces gas in spaces between cells with solution. In light, photosynthesis can produce oxygen while respiration also consumes oxygen. Gas accumulation changes buoyancy. The simulation represents this process with a simplified gas store and flotation threshold.
| Setting or process | What this model assumes | What you can conclude |
|---|---|---|
| Light intensity | A saturating response to relative intensity. No lamp heating or light damage. The percentage is an internal scale, not a measured photon flux. | Explore the assumed response; do not use its times to predict results under a particular lamp. |
| Bicarbonate | Added bicarbonate increases a saturating carbon factor. No added bicarbonate leaves a small, declining carbon supply. pH, dissolved-carbon chemistry, and salt effects are not calculated. | The slider represents bicarbonate concentration (% mass/volume), not dissolved CO₂ concentration. No added bicarbonate does not mean zero carbon. |
| Light color | Fixed illustrative weights: white 1.00; red 1.04; blue 0.85; green 0.68; amber 0.78. These are not fitted measurements. | This color ranking is a coding assumption, not a research finding. Neither green nor amber is modeled as inactive. |
| Temperature | A broad production optimum at 26°C and respiration multiplied by 1.8 per 10°C increase. These choices are not fitted to a species. | Do not infer a real plant’s optimum temperature or heat tolerance. |
| Plant type | Small invented differences in wetting and the gas needed for flotation; no measured species-specific photosynthesis rates. | These choices cannot establish which species performs best. Leaf history, thickness, and anatomy are not resolved. |
| Soap and infiltration | Soap and vacuum cycles change an invented chance of trapped air. “Excess” soap also multiplies production by 0.48. Two cycles with dilute soap always succeed in this model. | These probabilities and the soap penalty are unmeasured. Real preparation can fail despite following the modeled steps; vacuum damage is omitted. |
| Variation and flotation | Ten disks per cup, randomized gas thresholds and capacities, oxygen consumption, and a simple gas-loss term. Geometry, sticking, overlap, counting error, and changing light are omitted. | Randomness adds practice variation; it does not represent measured uncertainty. Flotation is an indirect indicator, not an oxygen measurement. |
Interpretation: zero floating disks does not establish zero photosynthesis. Equal final counts do not establish equal rates. ET₅₀ is the estimated time when 5 of 10 disks are floating; 1/ET₅₀ is a comparative flotation index, not an oxygen-production rate.
Inspect the numerical model
All constants below are illustrative model choices. Time t is in simulated minutes. U means an independent uniform random draw from 0 to 1.
L = (light percentage / 100) × color weight
C = (b / (b + 0.07)) / (0.2 / 0.27), when b > 0
C = 0.06 + 0.13 × exp(-t / 6), when b = 0
H = exp(-((temperature - 26) / 17)^2)
v = (0.92 + 0.16U) × (0.8 + 0.4U) × (0.86 + 0.28U)
r = 0.85 + 0.30U
P = 0.78 × L/(L + 0.7) × C × H × v
× soap factor × (1 - exp(-t / 1.1))
R = 0.052 × r × 1.8^((temperature - 25) / 10)
G(next) = max(0, G + (P - R - 0.012G) / 60)
Threshold = (1.45 + 1.05U) × plant capacity
Float when G/Threshold + initialAir × exp(-0.12t) ≥ 1
Plant: wetting factor, capacity
Spinach: 1.00, 1.00
Ivy: 0.90, 1.08
Arugula: 1.08, 0.97
Fast Plant: 0.96, 1.02
Chance of trapped air:
No soap: 0.55 × exp(-0.58 × cycles) × wetting factor
Excess soap: 0.14
Dilute soap: 0 when cycles ≥ 2; otherwise 0.07 × wetting factor
If trapped air: initialAir = 1.04 + 0.22U; otherwise 0
Soap factor = 0.48 for excess soap; otherwise 1
G is an arbitrary gas-store quantity. It is not milliliters or moles of oxygen. Settings stay fixed during each run; this version does not simulate transferring floating disks into darkness.
Sources for the assay’s procedure and interpretation: College Board, Investigation 5; Exploratorium, Photosynthetic Floatation; Brad Williamson’s assay guide. These sources do not validate this model’s numerical parameters.
C is your reference cup. Choose a control that answers your question; it is not automatically a dark control. All cups begin with the same settings.
The same settings and seed reproduce the same simulation. New run saves available counts for this visit and selects a new seed. Export your work before leaving this page.
Choose your settings, then infiltrate the disks.
Infiltration schematic
Shown for reference cup C; each cup uses its own preparation settings. The animation illustrates the sequence, not measured pressures, bubble sizes, or a guaranteed number of cycles.
Simulated results · 0.0 min
Counts are sampled every simulated minute. Disk positions between observations are illustrative.
| Cup | Latest sampled count | ET₅₀ (min) | 1/ET₅₀ (min⁻¹) |
|---|
ET₅₀ uses straight-line interpolation between one-minute counts around the first crossing of five. A cup with floating disks at time zero has an unsuitable starting baseline; its ET₅₀ is withheld.
Observation table · simulated counts
| Time (min) | C | A | B |
|---|
Look inside a leaf
An idealized broadleaf cross-section; cell sizes, numbers, and spaces are not to scale. Select a structure to read its role.
Air spaces between cells can fill with solution during infiltration. Gas accumulation later changes the disk’s buoyancy.
Investigation notebook
Use “The model produced…” for simulated evidence and “We observed…” for data from your real assay. Notes remain only for this page visit unless exported.
Saved simulations · this visit
Each saved entry is a simulation, not a real experimental trial. Saving again updates that run’s recorded progress.