Instead of attempting rational drug design, the evolutionary chemist simply generates a massive pool of variable DNA-like starting molecules (analogous to the variation that underlies biological natural selection). When these are then introduced to the target protein, only a small fraction of the molecules bind (the selection step). However, various chemical tricks then allow the chemist to amplify this population of molecules (the reproduction step). The amplified molecules are then used as the starting point for a subsequent round of selection and amplification. After several rounds of selection, the molecular mixture is greatly enriched for aptamers, molecules that bind tightly and specifically to the chosen target.
This evolutionary approach, called SELEX, has already led to the development of one useful drug, Pegaptanib (with the trade name Macugen), which has been licensed as a medicine to treat a common cause of blindness (age-related macular degeneration). But this is just the start: evolutionary chemistry is all set to deliver additional medically useful aptamers in the next few years that will target heart disease or cancer. For example, the US company Archemix has a developed lead aptamer, ARC1779, which acts as a potent, selective antagonist of von Willebrand Factor (vWF), with potential for use as an anticoagulant or antithrombotic agent (http://www.ncbi.nlm.nih.gov/pubmed/19479665). It is currently undergoing evaluation in clinical trials in patients diagnosed with acute coronary syndrome undergoing percutaneous coronary intervention.
For an unusual attempt to communicate how SELEX works (albeit applied to discovering new diagnostics rather than drugs), take a look at this video of the winning entry in the Dance you PhD competition of 2010!