Typically the 2-ddCt equation assumes that you have a target gene and a reference gene and a calibrator (control).  One measures the target and ref gene for the experimental samples, and also measures the target and ref gene for the calibrator sample and then plugs the values into the equation.  The 2-dCt equation doesn't include a reference gene and merely uses the target gene Ct values from the experimental sample and the control (calibrator) sample to provide the dCt values for each experimental sample. 

Use of a reference gene (or multiple ref genes) is the currently advised approach (with efficiency correction included as well; e.g., the Pfaffl Method; which is the 2-ddCt method - only corrected for efficiency).

Establishing high efficiency in the first place is your most important goal since poor amplification efficiency makes all of these approaches a shot in the dark at best sometimes.

Jack, :)

I'd like to respectfully correct you here:

"the 2-dCt equation doesn't include a reference gene and merely uses the Ct values from the experimental sample and the control (calibrator) sample to provide the dCt values for each experimental sample."

You did not specify the "equation". So far, you simply talk about the difference of two ct values - it is undefined if these two ct values are from the same gene (and different conditions/samples) or from different genes (same sample).

One can easily define (and to my knowledge this is quite common!):

Δct = ctref - ctgoi

(or even the other way around as Δct = ctgoi - ctref -- but for me that is counter-intuitive, as you know).

Calculated this way, the Δct is a measure proportional to the log expression of the gene-of-interest (goi), normalized to the expression of the reference gene (ref) that is used as "loading control".

One can calculate such Δct values for the different bacteria strains.

One can compare the Δct values between different bacteria strains. One might see if the Δct values for the different susceptible strains are systematically different to the Δct values for the resistance strains. And one might quantify the expected difference, which is a difference between Δct values, ie. a ΔΔct value.

Bottomline: a Δct value can be a normalized log expression measure - or it can be a log expression ratio. The latter would make sense only in highly standardized assays where one would not expect any relevant variation in sample loading (including cell preparation/isolation, RNA isolation, and RT efficiencies!).

Hi Jochen,

I just added the term 'target' to my above post.  We may be saying the same thing - but not absolutely certain.  See the attached Excel file for my understanding of the various equations and please comment if you see something out of place,  Thanks.  (The attached file here is now the corrected version).

In talking about these equations, we all have noticed that the vernacular of the words used to describe the quantities involved (in qPCR terminology) adds to more confusion. E.g.,  "normaliser" = "control gene" = "reference gene" which sometimes = "housekeeping gene."  And the term "endogenous control" has been used to connote a reference gene as well as the ROX endogenous reference dye on occasion.  Also "target gene" = "target" = gene of interest" = "goi." Also:  "CP" = "crossing point" = "threshold cycle" = "Ct" = "quantification cycle" = "Cq" and so on...

In other situations, terms like "control" has also been used to connote a reference gene or a calibrator (untreated control) sample.  So the terminology is all over the place.  A "calibrator" can also be any sample (treated or untreated) in an experiment (often not realized). 

So...  what are we to do but wring our hands in the meantime and hope that everyone eventually ends up on the same page ;].  Also, as Jochen points out, the "-" sign preceding an exponential subtraction can also be dealt with in two ways in accordance with the law of logs/mathematics and so on. Handling mercury seems simple but can be tricky especially when many of us are still using different words to describe the same thing.

Further, Dr. Laurence Stuart Hall on this forum states:

"Housekeeper refers to a subset of genes that are vital to cell metabolism and thus universally expressed in all cells. The other set are structural genes used to build cells, e.g. actin

Most control genes used in qPCR are therefore either metabolic housekeeping genes e.g. GAPDH or structural genes e.g. b actin or b tubular. That is because you need them expressed at high and constant levels

Therefore nearly all 'control' genes used in qPCR are housekeeping genes but not all housekeeping genes are internal control genes

They are essentially the same but with some minor distinctions as stated."

What is the differences between reference gene and housekeeping gene? - ResearchGate. Available from: https://www.researchgate.net/post/What_is_the_differences_between_reference_gene_and_housekeeping_gene [accessed Apr 16, 2016].

The Excel file I originally attached above had some typos in it.  The kind of typos that abound in the qPCR world.  "Relative quantity" should have instead been labeled "Fold-difference."  See now the same file attached again here, but now with this correction in terminology included.

"Relative quantity" actually implies the expressions: 10((Cq-b)/m)  or  EAMP(b-Cq) which are merely two alternate ways of expressing the same value in qPCR known as "relative quantity." 

Further, when "b" is known in terms of being the estimated Cq value for 1 copy of target initially in a qPCReaction, then the expressions 10((Cq-b)/m) and EAMP(b-Cq) indicate initial copies of target/qPCReaction.

Another precept in these endeavors is to be absolutely aware of how much sample is being loaded into each qPCReaction (as well as RT reactions preceding qPCR).

For two-step qPCR, generally it is a good idea to load all RT reactions (for cDNA synthesis) with the same amount of total RNA/uL.  This helps to keep the RT efficiencies as similar as possible from sample to sample, which further allows one to then load qPCReactions with the same amount of (cDNA) material for most targets of interest. As a correlate to this, for one-step qPCR (also called reverse transcription quantitative PCR or "RT-qPCR"), loading the same amount of total RNA per each RT-qPCReaction is a must as well.

However, realize that super-abundant targets such as 16S or 18S ribosomal RNA break this rule; and must be loaded into RT and qPCReactions up to 1000X more dilute than the RNA or cDNA sample is loaded for most other targets of interest. 

In order for any fold-change equation to hold any meaning, these things must first be observed.  In addition, one needs to prove one is working within the log linear range for each qPCR target or reference gene assay as well - something that should be done up front for every target or reference gene of interest by running e.g., 18-point serial 1:2 dilutions of a typical sample or sample mixture to reveal to the researcher what the best dynamic dilution range is for each target and reference gene of interest.  All qPCR targets and reference genes can be called "targets," but not all targets can be called a "reference gene," and not all reference genes are "housekeeping genes."  Reference genes (and housekeeping genes used as reference genes) must exhibit stable expression in the face of all experimental treatments/conditions. 

Again, once these several perfunctory features/facets have been observed and successfully carried out/addressed within the workflow, only then can one hope to use any of the various quantification equations with a reasonable degree of meaning/success. 

Another useful realization is that the error bars around relative or absolute quantities in qPCR are not linear about the geometric mean of the relative or absolute quantity.  So when converting (log transforming) from log scale to linear (normal) scale for relative or absolute quantity evaluations (whenever that is deemed necessary), one uses the attached equations to calculate the range of the upper standard error bar, and a separate equation to calculate the range of the lower standard error bar to attain this appropriate assymetry.

In Cq scale, technical replicate and/or treatment group individual Cq values are arithmetically averaged, whereas in quantity (linear/normal) scale, the geometric mean of technical replicates and/or treatment group individual (biological replicate) quantities is used. 

But, in Cq (log) scale, the error bars are symmetrical about the arithmetic Cq mean.  And this is not the case in linear absolute or relative quantity scale; therefore the attached file. This is the mathematical mercury that most often slips through most fingers in these mercurial matters.

Notce that the "10((Ct-b)/m)" expressions in each of the above attached file ("Error calc in qPCR quantity scale 4-15-16.doc") error calculations can be replaced by the expression:  EAMP(b-Cq) and "m" can be replaced with: -log10(EAMP)-1 if using log base 10 equations or -log2(EAMP)-1 if using log base 2 equations.  This shortens these standard error equational expressions even further.

The additional considerations often unaddressed in these matters involves the uncertainty in the error associated with amplification efficiency.  The attached publication does a good job of bringing this topic under proper scrutiny.

A more complete rendition of all the possible equations to use for qPCR fold-difference (or fold-change) calculations, quantification of relative quantities or absolute copy number estimates, and copy-number based estimates of fold-difference in gene expression is attached here.

Statistical analyses of all fold-change calculations and relative or absolute quantity estimates in qPCR is another matter entirely. A matter best left to expert statisticians - of which I am not one.