I guess the answer is about indirect one giving less error due to selectivity but how exactly does that happen?
It's often not necessarily an advantages vs disadvantages question, but one determined by available reagents and what question is being asked. For example, if you are developing a test for the antibody response to an antigen following immunization, you likely use a protocol like this:
- coat plates with antigen of interest (assume block / wash as appropriate going forward)
- add diluted serum from test animals / subjects
add a labelled secondary antibody specific for this animal/subject
- a labelled secondary antibody must be used because the animal's own antibody is not (of course) labelled.
if you are making your own labelled antibody in the lab and you have done this before you might do both a direct and indirect ELISA to verify that you have labeled the antibody and to determine the quality of the labeling. Assume you made a biotinylated mouse antibody.
do one direct ELISA (to quantitate label): 1. coat with target antigen 2. add dilution series of your antibody-biotin 3. add Streptavadin-Alkaline phosphatase to detect
a second indirect ELISA(to quantitate antibody): 1. coat with target antigen 2. add dilution series of your antibody-biotin 3. add biotinylated anti-mouse antibody 4. add Streptavadin-Alkaline phosphatase to detect
Now you know how much antibody (from the indirect ELISA) will give you how much signal (from the direct ELISA) against known amounts of your coating antigen.
One time you might actually have the option to do a direct or indirect assay is when you have all the reagents you need, but you need to amplify your signal sufficiently to detect low amounts. In that case a direct ELISA only has one antibody's worth of label, while coming in with a secondary (e.g. anti-heavy chain) can result in many antibodies worth of label per target.
Thermo has a nice page on this.
You are correct, the selectivity advantage of an indirect or sandwich ELISA comes from the fact that two antibodies are employed - one to capture the analyte, the other to detect it.
Here is the classic illustration of how this type of ELISA works. First (
), the capture antibody is coated onto the plate and bound via one of a number of different types of chemistry. The plate is then washed (this occurs between all steps).
, the analyte is added, sometimes in a homogenous solution (i.e., pure recombinant protein), other times in a matrix like serum, cell lysate, etc. The plate-bound antibody has a certain specificity for the analyte — let's say it binds the wrong epitope one time in 1000.
 The detection antibody is added, and let's say it has the same specificity of 1/1000. Finally,
 the secondary antibody (with the enzyme linked to it) is added, and
 the enzyme's substrate is added, producing the color or light output.
If we were to use a direct ELISA, the error rate would be 1/1000. However, by combining two antibodies, our error rate is now 1000 times lower — 1 in 1 million. Since both antibodies are required to bind properly in order to get a signal, this makes the results much more reliable.
I agree with the other answers and the biggest difference is indeed the specificity. An indirect ELISA is indeed more specific, but also for a reason which isn't described here yet: Using indirect ELISA means your plate is coated with the primary antibody. Since this primary AB is attached to the well surface with its heavy chain, the 2 light chains (= the parts which bind antigens, in this case the secondary ABs ) are available to bind the secondary AB. This means that each 1 of the primary ABs has the potential to bind 2 secondary ABs, thus increasing the specific signal considerably.