NEWS | IN DEPTH
By Jennifer Couzin-Frankel
Why? That’s the first word on many lips after a cancer diagnosis. “It’s a perfectly reasonable question,” says Bert Vogelstein, a cancer geneticist at Johns Hopkins Uni- versity in Baltimore, Maryland,
who has spent a lifetime trying to answer
it. Thanks to his friendship with a recently
minted Ph.D. in applied mathematics, the
two now propose a framework arguing that
most cancer cases are the result of biological
In a paper published on page 78 this week
in Science, Vogelstein and Cristian Tomasetti,
who joined the biostatistics department at
Hopkins in 2013, put forth a mathematical
formula to explain the genesis of cancer.
Here’s how it works: Take the number of
cells in an organ, identify what percentage
of them are long-lived stem cells, and determine how many times the stem cells divide.
With every division, there’s a risk of a cancer-causing mutation in a daughter cell. Thus,
Tomasetti and Vogelstein reasoned, the tissues that host the greatest number of stem
cell divisions are those most vulnerable to
cancer. When Tomasetti crunched the numbers and compared them with actual cancer
statistics, he concluded that this theory explained two-thirds of all cancers.
“Using the mathematics of evolution, you
can really develop an engineerlike under-
standing of the disease,” says Martin Nowak,
Harvard University and has worked with
Tomasetti and Vogelstein. “It’s a baseline
risk of being an animal that has cells that
need to divide.”
The idea emerged during one of the pair’s
weekly brainstorming sessions in Vogelstein’s
office. They returned to an age-old question:
How much of cancer is driven by environ-
mental factors, and how much by genetics?
To solve that, Tomasetti reasoned, “I first
need to understand how much is by chance
and take that out of the picture.”
By “chance” Tomasetti meant the roll of
the dice that each cell division represents,
leaving aside the influence of deleterious
genes or environmental factors such as
smoking or exposure to radiation. He was
most interested in stem cells because they
endure—meaning that a mutation in a stem
cell is more likely to cause problems than a
mutation in a cell that dies more quickly.
Tomasetti searched the literature to find
the numbers he needed, such as the size of
the stem cell “compartment” in each tissue.
Plotting the total number of stem cell divisions over a lifetime against the lifetime risk
of cancer in 31 different organs revealed a
correlation. As the number of divisions rose,
Colon cancer, for example, is far more common
than cancer of the duodenum, the first stretch of the
small intestine. This is true
even in those who carry
a mutated gene that puts
their entire intestine at risk.
Tomasetti found that there
are about 1012 stem cell divisions in the colon over a
lifetime, compared with 1010
in the duodenum. Mice, by
contrast, have more stem
cell divisions in their small
intestine—and more cancers—than in their colon.
The line between mutations and cancer isn’t necessarily direct. “It may not just
be whether a mutation occurs,” says Bruce
Ponder, a longtime cancer researcher at
the University of Cambridge in the United
Kingdom. “There may be other factors in
the tissue that determine whether the mutation is retained” and whether it triggers
That said, the theory remains “an ex-
tremely attractive idea,” says Hans Clevers,
a stem cell and cancer biologist at the Hu-
brecht Institute in Utrecht, the Netherlands.
Still, he points out, the result “hinges entirely
on how good the input data are.”
Tomasetti was aware that some of the
published data may not be correct. In 10,000
runs of his model, he skewed where various
points on the graph were plotted. Always,
“the result was still significant,” he says, sug-
gesting the big picture holds even if some of
the data points do not. In mathematical jar-
gon, the graph showed a correlation of 0.81.
(A correlation of 1 means that by knowing
the variable on the x-axis—in this case, the
lifetime number of stem cell divisions—one
can predict the y-axis value 100% of the time.)
Squaring that 0.81 gives 0.65—an indicator of
how much of the variation in cancer risk in
a tissue is explained by variation in stem cell
divisions (see graph).
For Vogelstein, one major message is that
cancer often cannot be prevented, and more
resources should be funneled into catching
it in its infancy. “These cancers are going to
keep on coming,” he says.
Douglas Lowy, a deputy director of the
National Cancer Institute in Bethesda, Maryland, agrees, but also stresses that a great
deal of “cancer is preventable” and efforts to
avert the disease must continue.
Although the randomness of cancer might
be frightening, those in the field see a positive side, too. The new framework stresses
that “the average cancer patient … is just unlucky,” Clevers says. “It helps cancer patients
to know” that the disease is not their fault. ■
105 107 109 1011
Total stem cell divisions
The bad luck
Analysis suggests most
cases can’t be prevented
Charting cancer risk
As the number of stem cell divisions in a tissue rises, so does
the chance of cancer striking that site.
Random mutations in healthy cells may explain
two-thirds of cancers, like this one in the colon.