The ability to introduce exogenous DNA into an organism to alter its genetic program is one of the most crucial tools in modern biology. Early work showed that certain bacteria could acquire the traits of a related strain through the addition of heat-killed cells. Although it was not well understood at the time, the transfer of gene-encoding DNA from one strain to another facilitated this. This concept was turned into a useful tool upon the advent of bacterial plasmid transformations in the early 1970's, which allowed genes of interest to be easily inserted into E. coli. Over the years, methods have been developed to introduce exogenous genes into a wide range of useful organisms, including bacteria, yeasts, plants, and animal tissues. These methods vary enormously in efficiency however, necessitating a way to identify and isolate cells which contain the DNA of interest. This can be accomplished either by screening for successfully modified cells, or through selection.
Screening vs. Selection
In the case of bacterial transformations, it's possible to plate cells post-transformation on non-selective media and screen each individual colony to identify those that have been successfully modified. Because each colony arises from a single cell present during transformation, the colony is made up of a set of identical clones. Screening can involve testing for the desired DNA itself or for the product of an inserted gene. This process is extremely difficult however, as the vast majority of cells will not be successfully transformed, so many colonies need to be tested to identify even a single transformant. A much more efficient strategy is to use a selectable genetic marker that allows only those cells which have been transformed to survive under certain growth conditions. These marker genes may be combined with the DNA of interest on a single plasmid, thus ensuring that any cells that survive selection contain the gene(s) of interest. The most commonly used selectable markers in bacteria are genes that provide resistance to a specific antibiotic upon transformation, allowing for positive selection of cells containing the marker.
Antibiotic Resistance Markers: ampR
Perhaps the most commonly used selectable marker in bacteria is the ampR gene, which provides resistance to certain beta-lactam antibiotics such as ampicilllin (amp) and its more stable relative carbenicillin (carb). Beta-lactam antibiotics are penicillin derivatives that inhibit synthesis of bacterial peptidoglycan cell walls, arresting cell division and ultimately leading to cell death. Although beta-lactams are primarily functional against gram-positive bacteria due to their larger cell walls, some examples, such as amp and carb, are capable of killing gram-negative E. coli. All antibiotics in the family share a central four atom ring structure known as the beta-lactam ring, which serves as a cleavage target for enzymes known as beta-lactamases. Due to the shared structural features of becta-lactam antibiotics, these enzymes often have promiscuous activities that target multiple drugs. Upon cleavage of the lactam ring, antibiotics such as amp lose their toxicity, allowing cell growth and division to resume.
The common ampR gene, as used in the E. coli pBR322 plasmid, was naturally derived from Salmonella bacteria through transposition. Because it efficiently cleaves amp and carb, it's one of the most useful markers in E. coli. One downside to the use of ampR is that removal of antibiotic from selective media by beta-lactamase can allow for growth of cells that lack resistance. This is often witnessed in the form of satellite colonies on amp plates.
Antibiotic/Non-Antibiotic Dual Selection: tetA(C)
Tetracycline Positive Selection
The tetA(C) gene is primarily used for positive selection in bacteria, similar to ampR. tetA(C) encodes a membrane-bound transporter that rapidly pumps the antibiotic tetracycline out of bacterial cells. This process is energy dependent, as the protein uses the influx of H+ ions from the surrounding environment to drive the process. Tetracycline is a broad-spectrum, polyketide antibiotic derived from Streptomyces that inhibits bacterial translation. The antibiotic binds the 30s subunit of bacterial ribosomes, blocking entry of aminoacyl-tRNAs to the A site of the ribosome.
Because tetracycline resistance is gained through expression of a transporter and not a modifying enzyme, selective media maintains its antibiotic levels during growth of resistant cells. High levels of tetA expression can have a detrimental effect on the cells however, due the energy cost of pumping tetracycline and increased vulnerability to certain extracellular conditions. 
Nickel Salt Negative Selection
Expression of tetA in bacteria has the side effect of making cells more vulnerable to poisoning by either lipophilic chelating agents or metal salts.
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Background on the ampR gene from pBR322
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The tetA(C) gene from pBR322
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Nickel selection with tetA
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Riboswitch selection/screening using a tetA-GFP fusion marker