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A number of important technologies have made it possible to measure nucleic acids.  The most important of these are outlined below.

Polymerase Chain Reaction (PCR)

Measuring DNA or RNA requires several steps to isolate the molecules from the organism.  Once we have a DNA or RNA sample, there are several requirements to obtain good measurements: the molecules must be stable enough to be maintained throughout the measurement process, the molecules must be present in quantities above detection level, and for some measurement devices, molecules must be tagged with a label.  PCR provides all of these requirements.

In the cell, DNA is synthesized during cell division using enzymes which attach to the unzipped DNA and attach matching nucleotides to each base from the 5' to 3' end of the DNA molecule.  Mimicking this in the lab was a very slow process until the development of the polymerase chain reaction in the late 1970's.  Modern use of PCR seems to have started in 1983 with the process devised by Mullis. Advances in this technology have led to more efficient and accurate duplication (amplification).

Basically, the DNA reproduction enzymes are attached to locations on the DNA using primers, which are short segments of DNA which complement the piece that you want to replicate.  Each cycle of PCR duplicates the segment of DNA, so there is an exponential growth in the quantity of DNA in the sample.  For whole genome work, a large set of primers are used so that every region of the DNA can be duplicated in each cycle.  During PCR, the nucleotides in the newly synthesized DNA can be labeled so that after several cycles of duplication most of the DNA is labeled.

Duplication proceeds from the 5' to 3' end of the molecule.  Since the binding of the duplication mechanism is not perfect, the length of the molecule that can be accurately and completely duplicated is limited.  A common result of sample amplification is loss of sequence at the ends of the molecule.  This is one of the reason that shot-gun methods are used - the DNA is fragmented into shorter pieces that can be duplicated.   Over time, reagents and processes have been improved to improve the length of fragments that can be duplicated.

The duplication process is not perfect.  As amplification proceeds, errors may be introduced into the synthesized DNA.  The more amplification is done, the more errors are introduced.  For this reason there is a trade-off between starting from very small samples of DNA (such as the DNA from a single cell or a small region such as a tissue interface) which need to be amplified so that the DNA can be detected by the measurement instrument, and starting from a larger sample that comes from a less homogeneous biological sample.

Because the number of duplications is controlled during the PCR reaction, PCR can be used to quantify the amount of DNA of a specific type in a sample using a method called real time or quantitative PCR (RT-PCR or qPCR).  A primer is used to select a single region of DNA.  At each PCR cycle, the amount of label detected in the sample is recorded.  Since this should be a logarithmic growth curve, it can be extrapolated back to the zero-th cycle to assess the amount of DNA in the original sample - even if the label is below detection limits for the first few cycles.  This method is often used as the gold standard for quantification.  These days it is pretty cheap if a primer is already available.  Note however that it is a "one feature at a time" method as opposed to the methodologies we use in bioinformatics (although it is usually performed in sets of 96 wells).

PCR acts only on DNA.  We want to measure DNA when we are sequencing the genome, looking for genomic variants such as SNPs and microsatellites or looking at DNA modifications such as protein binding and methylation.  However, for gene expression, ncRNA and isoform detection we need to measure the RNA in the cell.