A study of rats showed variations in brain structure pre-dated their first exposure to narcotics, and made them more likely to opt for cocaine.
Writing in Science, the team say genes may affect these differences in humans.
Treatments to reduce their effect may be found - but a test of vulnerability to drugs is unlikely, they add.
Up to 500,000 people are currently addicted to Class A drugs such as cocaine, heroin and amphetamines, according to government figures.
One of the most important questions in the science of addiction surrounds the origin of differences noticed in the brains of human drug users.
While these differences are thought to be important in the way humans respond to drugs, it is difficult to prove whether they are a part of the natural brain chemistry of that individual, or have developed as a result of taking the drugs themselves.