The amylase IA: a pH optimum that doesn't match the textbook
A Higher Level student investigates the effect of pH on the rate of starch hydrolysis by amylase. She uses 1.0% starch, 0.5% amylase solution, five pH buffers (3, 4, 5, 6, 7) and a water bath set to 37 °C. Every 30 s she removes a drop, mixes it with iodine on a spotting tile, and records the time at which the blue-black colour is no longer visible. She runs one tube per pH in lesson 1, repeats the whole set twice more, and records:
| pH | Run 1 (s) | Run 2 (s) | Run 3 (s) |
|---|---|---|---|
| 3 | >600 | >600 | >600 |
| 4 | 305 | 288 | 190 |
| 5 | 96 | 84 | 61 |
| 6 | 210 | 195 | 172 |
| 7 | 480 | 512 | 460 |
The third run used a starch solution that had been kept at room temperature for eight days. A thermometer checked against a calibrated probe reads 2.0 °C high. All endpoints were judged by the same student, who knew the expected answer.
1. State the independent and dependent variables, and evaluate the use of 1/time as the measure of rate. Include how the pH 3 data must be handled.
Read the worked answer
Variables
- Independent variable: pH, at five discrete buffer values (3–7). It is nominal/ordinal, not continuous, so the data should be plotted as a bar chart or as points with the gaps acknowledged, not joined by a smooth curve implying values between the buffers.
- Dependent variable: rate of starch hydrolysis, measured operationally as the time for the iodine blue-black colour to disappear.
Is 1/time a valid rate?
- For a fixed amount of substrate in a fixed drop volume, rate = amount hydrolysed / time, so 1/t is proportional to the average rate over the assay. It is a defensible index.
- It is not an initial rate. The endpoint is the moment at which starch falls below the iodine detection threshold, so 1/t is an average over the whole reaction, during which substrate concentration and product concentration both change. Comparisons of average rate can rank pH values while still misrepresenting Vmax or Km.
- The reciprocal distorts the error structure: a 30 s timing resolution is a large relative error at t = 60 s but a small one at t = 480 s, so the short-time points dominate any mean of 1/t and the uncertainty is not constant.
The pH 3 data No endpoint was reached. These are censored observations, not zero-rate measurements. They must be reported as '>600 s' and either excluded from rate calculations or analysed with a non-parametric test. Computing 1/600 and treating it as a real rate invents data; treating it as 1/∞ = 0 asserts that no hydrolysis occurred, which the experiment has not shown.
2. Identify the sources of error and bias in this protocol and explain how each affects the conclusion that the optimum is pH 5.
Read the worked answer
1. The third run's starch batch (systematic error, run-specific) Starch kept at room temperature for eight days will have undergone some hydrolysis and microbial growth, so less intact starch remains and the endpoint arrives sooner. Run 3 is consistently the fastest at every pH (190, 61, 172, 460 s), which is exactly the signature of a batch effect rather than a pH effect. Consequence: the mean time at each pH is pulled down, and the within-pH variance is inflated, which reduces the power to detect differences between pH values and could manufacture the appearance of a peak if the effect were uneven.
2. Thermometer reading 2 °C high The bath is actually at 35 °C, not 37 °C. This is a systematic error applied equally to all tubes, so it compresses all rates but does not change the rank order of pH values. It does, however, invalidate the stated method and any comparison with published optima measured at 37 °C.
3. Unblinded, subjective endpoint One observer who knows the expected optimum judges a colour change on a spotting tile. This is a classic demand-characteristic bias: borderline drops are more likely to be called 'cleared' when the result is expected. Randomising the order of tubes and coding the samples, or using a colorimeter to measure absorbance of the starch–iodine complex, would remove it.
4. Design weaknesses One tube per pH per run, no measurement of the actual starch concentration, and no check that the enzyme is stable across pH 3–7 (a low rate at pH 3 may reflect denaturation rather than reduced catalytic efficiency). Any claim of a pH 5 optimum should therefore be treated as provisional pending a continuous, instrument-based assay.
3. She wants to claim that pH 5 and pH 6 differ significantly. Justify an appropriate statistical test, show what the test requires, and comment on whether her data support the claim.
Read the worked answer
Choice of test Two independent samples, one measurement per replicate, interval-scale data, three replicates at each pH: an unpaired two-sample t-test (Welch's version, since equal variances cannot be assumed with n = 3) is appropriate. A chi-square or ANOVA would answer a different question; ANOVA across all five pH values would actually be the better first step, with a post-hoc test for the pH 5 vs pH 6 pair, because testing only the pair she finds most interesting inflates the type I error rate.
Assumptions she must check Independent replicates (they are not - run 3 shares a starch batch, so run 3 at pH 5 and run 3 at pH 6 are not independent of each other); approximately normal distributions, which cannot be assessed with n = 3; and homogeneity of variance.
What the numbers show
- Mean pH 5 = (96 + 84 + 61)/3 = 80.3 s; mean pH 6 = (210 + 195 + 172)/3 = 192.3 s.
- Variance pH 5: deviations 15.7, 3.7, −19.3 → s² ≈ 316. Variance pH 6 → s² ≈ 366.
- t = (192.3 − 80.3) / √(316/3 + 366/3) = 112.0 / 15.1 ≈ 7.4, df ≈ 4. Critical value 2.78 at p = 0.05; the difference is significant.
Caveat The calculation is arithmetically correct but the design undermines it. With n = 3 and a contaminated third batch, the p value overstates the evidence. The defensible claim is 'times at pH 5 were shorter than at pH 6 in all three runs, consistent with a difference', supported by a repeat experiment with freshly prepared starch, coded samples and more replicates (n ≥ 10 per pH) before any significance claim is made.