  Drug gradients are believed to play an important role in the evolution of
bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We
use a statistical physics model to study the evolution of a population of
malignant cells exposed to drug gradients, where drug resistance emerges via a
mutational pathway involving multiple mutations. We show that a non-uniform
drug distribution has the potential to accelerate the emergence of resistance
when the mutational pathway involves a long sequence of mutants with increasing
resistance, but if the pathway is short or crosses a fitness valley, the
evolution of resistance may actually be slowed down by drug gradients. These
predictions can be verified experimentally, and may help to improve strategies
for combatting the emergence of resistance.
