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Question 15 of 20 Intermediate Practical

How does the delta-delta Cq method calculate fold change, and what does it assume?

Short answer

It subtracts a reference gene's Cq from the target's in each sample, subtracts the control group's value from the treated group's, and raises 2 to the negative of that difference. It assumes both assays run at about 100 percent efficiency and that the reference gene does not change with treatment.

Why

The method, described by Livak and Schmittgen in 2001, turns two subtractions into a fold change. The first subtraction normalizes each sample for how much RNA went into the reverse transcription. The second compares treated with control.

The base of 2 encodes the assumption that product exactly doubles every cycle. If the real efficiency is 90 percent, every cycle of difference is a 1.9-fold change, and the error compounds with the size of the difference. Pfaffl's efficiency-corrected ratio uses each assay's measured efficiency instead.

MIQE 2.0 goes further and recommends converting Cq values to efficiency-corrected quantities and normalizing to the geometric mean of several validated reference genes. The method also assumes the reference gene is stable across conditions, which has to be shown rather than assumed. Statistics belong on per-sample normalized values, before averaging per group.

How to work it through

  1. Confirm that target and reference efficiencies are known and similar, from a dilution series in the same sample type.
  2. Average technical replicate Cq values for each sample and each assay.
  3. Compute delta Cq for each sample as target Cq minus reference Cq.
  4. Subtract the mean control-group delta Cq from each sample's delta Cq to get delta-delta Cq.
  5. Convert with 2 raised to minus delta-delta Cq, or use measured efficiencies if they are not near 100 percent.
  6. Run statistics on the per-sample values, usually on the log scale, and report fold change with an interval.

An example

A control sample has target Cq 26.0 and reference Cq 18.0, so its delta Cq is 8.0. A treated sample has target Cq 24.0 and reference Cq 18.1, so its delta Cq is 5.9. The delta-delta Cq is 5.9 minus 8.0, which is minus 2.1.

Two raised to 2.1 gives a fold change of about 4.3. If the target assay actually ran at 90 percent efficiency and the reference at 100 percent, the Pfaffl ratio is 1.9 to the power 2.0 divided by 2.0 to the power minus 0.1, about 3.9. The difference is small here but grows with larger Cq gaps.

Where the answer stops holding

The result is only as good as the reference gene. If treatment shifts the reference by half a cycle, the fold change is off by about 40 percent. Differences in efficiency between assays bias every result in the same direction.

Late Cq values near the detection limit carry large sampling noise that the formula ignores. The method gives relative change only, never copy number.

A strong answer covers

  • Two subtractions: normalize to reference, then compare to control
  • Base 2 assumes 100 percent efficiency for both assays
  • Reference gene stability must be demonstrated
  • Efficiency-corrected alternatives such as the Pfaffl ratio
  • Statistics on per-sample log values, not on group means of fold change

Common mistakes

  • Averaging fold changes across samples on the linear scale instead of the log scale
  • Using the method without measuring whether the two assays have similar efficiencies
  • Choosing a single housekeeping gene without testing whether it moves with treatment