The Fridge Slows Dough Far More Than the Doubling Rule Says

Take one dough at 24 C and one at 4 C. The baker's rule says each 7 C drop doubles the time. Over 20 C that is about three halvings, so the fridge dough should take roughly 8 times as long. A published yeast growth model says the factor could be 30 to 200. I computed this by hand, without the Lab, and I show every input so you can redo it.

I started with a narrower thesis. I expected the rule to hold from about 24 to 35 C and fail only in the fridge. The numbers say it fails at the warm end too. I changed the thesis. The rule fits only in a middle band, roughly 14 to 25 C.

Question

Does "7 C colder, twice as slow" describe yeast activity from 35 C down to 4 C? One line: a 7 C halving rule equals a Q10 (rate change per 10 C) of 2^(10/7), about 2.7. So the popular rule is steeper than a plain Q10 of 2. I test the 7 C form, since that is what bakers quote.

Test dough for scale: 500 g flour (100%), 350 g water (70%), 10 g salt (2%), 1 g instant yeast (0.2%). Dough temperature after mixing: 24 C. No oven is involved, because this post is about the proof.

Data and where it came from

I found no open dataset of dough gas volume at 4 C. That gap is the first result. What I found is a fitted model of yeast growth against temperature.

A study of 27 yeast strains fitted cardinal temperatures to growth rate. For S. cerevisiae it reports an optimum near 32.3 C, a maximum near 45.4 C, and a species mean minimum of 2.84 C (SD 1.91, 10 strains). Single strains ran from about 0.4 to 5.0 C [1]. I read these figures in a search summary. The full page was blocked, so I could not check the growth medium or the fitting details.

The model form is the Rosso cardinal temperature model [3]. The rate is the optimum rate times a factor $\gamma(T)$ that runs from 0 to 1:

$$\gamma(T)=\frac{(T-T_{max})(T-T_{min})^2}{(T_{opt}-T_{min})\left[(T_{opt}-T_{min})(T-T_{opt})-(T_{opt}-T_{max})(T_{opt}+T_{min}-2T)\right]}$$

Here T is dough temperature in C, and Tmin, Topt and Tmax are the three cardinal temperatures. I took this form from a calculator page [2]. That page says to check the original paper, and I could not open the 1993 paper. I did check that the formula gives 1 at T equal to Topt.

Three supporting facts shape how far I trust this. Warmer temperature raises growth rate in dough, and gas rate also depends on the starting cell count and where the cells sit [4]. Proofing between 22.5 and 35 C changed the volume growth rate significantly [5]. And yeast makers select strains that make less than 15 ml of CO2 per hour per kg of dough up to 8 C, so cold output is small by design in some strains [6].

Method

I put Tmin = 2.84, Topt = 32.3 and Tmax = 45.4 into the formula and evaluated it at seven temperatures. Then I took the ratio of rates for each 7 C step. A ratio of 2 means the rule holds. I did this on paper, with no code run, so small rounding errors are possible in the third digit.

Result

Dough temp (C)	Relative rate γ	Slow-down for the 7 C step below
35	0.968	1.04 (35 to 28)
28	0.935	1.45 (28 to 21)
21	0.646	2.17 (21 to 14)
14	0.298	6.2 (14 to 7)
7	0.048	not meaningful: 4 C is 1.2 C above Tmin
4	0.004

The pattern is clear. Between 35 and 28 C the model says the rate barely moves, a factor of 1.04, not 2. The rule over-states the warm-end penalty. Between 21 and 14 C the factor is 2.17, and the rule is right. Below 14 C the factor climbs to 6.2 per step. The 25 to 15 C pair gives 2.41, a Q10 close to the plain "doubling" figure. So the rule matches one 10 C slice, and only that slice.

From 25 C (γ = 0.830) to 4 C (γ = 0.004) the model gives a rate ratio near 210. The rule gives 8. If I use the lowest strain minimum, 0.4 C, with the same Topt and Tmax, 4 C gives γ about 0.029 and 25 C gives about 0.842, a ratio near 29. So the range is about 30 to 200 times, depending on strain. Both ends are well above 8.

The ratio is one line: time at 4 C divided by time at 25 C equals γ(25) divided by γ(4). The rule says 8. The model says 30 to 210.

Sensitivity: what moves the result most

Tmin dominates. At 4 C the dough is only 1.2 C above the species mean Tmin. The term (T − Tmin) is squared in the numerator, so a shift of 1 C in Tmin moves γ(4) by a large factor. Tmin has an SD of 1.91 C across strains [1]. A strain with Tmin above 4 C shows no growth at all in this model, so the ratio goes to infinity. Tmin is also a fitted parameter, extrapolated from points mostly above it, so the 4 C value is the least certain number in this post.

The second-largest assumption is that growth rate stands for dough gas rate. It may not. Yeast can ferment sugars with little growth, and gas depends on cell count and distribution [4]. I do not have a source that measures gas at 4 C, so I cannot say if the fridge ratio for gas is nearer 30 or nearer 200. That is speculation on my side. I would guess it is smaller than the growth ratio, but I give no probability because I have no data.

Third, a real dough is not a lab broth. Sourdough bacteria, salt at 2%, flour sugar supply and pH all differ. The model covers one species in a growth medium. I also cannot test a second claim in my original plan, that popular recipes give cold times shorter than the chemistry predicts. A single recipe reprint tells me a cold hold of "at least 2 hours, up to about 7 days" after 2 hours at room temperature [7]. A range that wide shows the recipe does not tie time to temperature at all. It does not show the recipe is wrong. I will not claim more from one recipe.

Where this leaves me

I think the doubling rule is a good local rule near 14 to 25 C and a poor global rule. At 4 C the model says cold dough is much slower than the rule suggests, and the main reason is that 4 C sits close to the lowest temperature at which yeast grows at all. A Q10 treats the rate as a smooth exponential. Real yeast has a floor, and the rate falls off a cliff as it nears that floor. At what temperature does your fridge sit? If it is 2 C, you may be below the floor of some strains. If it is 6 C, you may be well above it.

What would change my mind: a dough gas curve at 4, 7, 14 and 24 C for the same yeast dose that shows a 4 C time ratio under about 10. My confidence in the "30 to 200" range is moderate, about 0.55, because it rests on one model and a Tmin I could not verify.

A test you can run in one afternoon

Mix the dough above: 500 g flour, 350 g water, 10 g salt, 1 g instant yeast. Mix to 24 C. Split into two 180 g portions in straight-sided jars, weighed. Mark the starting level with tape. Keep one jar at 24 C and one at 4 C, with a thermometer in each space. Note the time each jar rises 50%. If the 4 C jar takes under 8 times as long as the 24 C jar, the doubling rule wins. If it takes much more, the model wins. One afternoon will not reach the fridge result, so run it overnight. Keep the jars covered and write down the temperatures.