Unlocking Biology With Math

Oct. 7, 2013 — Scientists at USC have created
a mathematical model that explains and
predicts the biological process that creates
antibody diversity -- the phenomenon that
keeps us healthy by generating robust immune
systems through hypermutation.
The work is a collaboration between Myron
Goodman, professor of biological sciences and
chemistry at the USC Dornsife College of
Letters, Arts and Sciences; and Chi Mak,
professor of chemistry at USC Dornsife.
"To me, it was the holy grail," Goodman said.
"We can now predict the motion of a key
enzyme that initiates hypermutations in
immunoglobulin (Ig) genes."

Goodman first described the process that
creates antibody diversity two years ago. In
short, an enzyme called "activation-induced
deoxycytidine deaminase" (or AID) moves up
and down single-stranded DNA that encodes
the pattern for antibodies and sporadically
alters the strand by converting one nitrogen
base to another, which is called "deamination."

The change creates DNA with a different
pattern -- a mutation.
These mutations, which AID creates a million-
fold times more often than would otherwise
occur, generate antibodies of all different sorts
-- giving you protection against germs that
your body hasn't even seen yet.
"It's why when I sneeze, you don't die,"
Goodman said.
In studying the seemingly random motion of
AID up and down DNA, Goodman wanted to
understand why it moved how it did, and why
it deaminated in some places much more than
others.

"We looked at the raw data and asked what the
enzyme was doing to create that," Goodman
said. He and his team were able to develop
statistical models whose probabilities roughly
matched the data well, and were even able to
trace individual enzymes visually and watch
them work.

But they were all just
approximations, albeit reasonable ones.
Collaborating with Mak, however, offered
something better: a rigorous mathematical
model that describes the enzyme's motion and
interaction with the DNA and an algorithm for
directly reading out AID's dynamics from the
mutation patterns.
At the time, Mak was working on the
mathematics of quantum mechanics. Using
similar techniques, Mak was able to help
generate the model, which has been shown
through testing to be accurate.

"Mathematics is the universal language behind
physical science, but its central role in
interpreting biology is just beginning to be
recognized," Mak said. Goodman and Mak
collaborated on the research with Phuong
Pham, assistant research professor, and Samir
Afif, a graduate student at USC Dornsife. An
article on their work, which will appear in
print in the Journal of Biological Chemistry on
October 11, was selected by the journal as a
"paper of the week."

Next, the team will generalize the
mathematical model to study the "real life"
action of AID as it initiates mutations during
the transcription of Ig variable and constant
regions, which is the process needed to
generate immunodiversity in human B-cells.