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DOCTORS are watching helplessly as HIV, tuberculosis and many other deadly
infections grow resistant to drugs. Now two mathematicians believe they have
pinned down the conditions that allow viruses and bacteria to mutate into these
resistant strains.

For a pathogen to develop resistance to a drug, the drug must tread a very
fine line. It must be effective enough to kill much of the normal strain, giving
drug-resistant mutants an evolutionary advantage. But it must not be so
effective that it completely stops the normal strain reproducing and mutating.
鈥淚t seems like the window of opportunity is incredibly narrow,鈥� says Thomas
Kepler, a biomathematician at North Carolina State University at Raleigh.

This made Kepler wonder why drug resistance is so common, with some bugs
developing resistance to several drugs. He and Alan Perelson have developed a
mathematical model that mimics the way viruses and other pathogens reproduce in
the body (Proceedings of the National Academy of Sciences, vol 95, p 11
514).

By plugging various numbers into the model, the researchers showed that if a
patient takes medicine regularly and the drug penetrates the body evenly,
resistance is unlikely to develop. But if there are 鈥渟anctuaries鈥� in the body
where the drug does not penetrate well, the pathogen can reproduce in safety.
When resistant mutants enter the bloodstream they reproduce better than
non-resistant varieties.

Kepler says this may explain how HIV, for instance, has developed resistance
to several antiviral drugs. 鈥淭here must be places where the drug is not
penetrating completely,鈥� he says. He suggests that drug designers should focus
on trying to solve this problem.

鈥淭he arguments make a lot of sense,鈥� says Jon Condra, a virologist with Merck
Pharmaceuticals in West Point, Pennsylvania. 鈥淚 don鈥檛 really think that they
have told us anything we didn鈥檛 know intuitively, but it鈥檚 nice to see and great
to show that mathematical modelling makes biological sense.鈥� He hopes the
results can be confirmed by clinical data.