researchers in understanding protein folding
by Steven Schultz
For Christodoulos Floudas, professor of chemical engineering,
the watchwords of his research are "divide and conquer."
This has nothing to do with heavy-handed politics--it's a
bold mathematical technique he is applying to a question that
has tantalized scientists for years: how do proteins fold?
Understanding the way proteins fold--what three-dimensional
shape they have--is a problem that rears its head in fields
from biology and chemistry to engineering and math and has
major implications for medical science. The bumps and valleys
in a protein's shape determine how it reacts with other proteins.
The shapes also give drug-makers clues about how to design
medicines that latch on to a bump, or a valley and interfere
with the proteins involved in disease. Comprehending the way
proteins fold could result in new medicines, new understanding
of disease, and insights into the basic mechanisms of life.
Photo by Frank Wojciechowski
Chemical Engineering Professor Christodoulos
Floudas works to understand how proteins fold.
Proteins are fundamental elements of life. They send the
messages, transport the chemicals, and build the structures
that allow living things to exist. Scientists have known for
a long time the precise chemical makeup of proteins. But that's
only half the story. What really determines the function of
a particular protein is the precise and intricate way it is
When cells manufacture proteins, they start off as long strings
of chemical blocks but quickly fold up into ringlets and loops
like ribbons on a birthday present.
What puzzles scientists is that the sequence of chemicals
in a protein does not offer obvious clues about the shape
that the protein assumes.
For example, if one protein includes chemicals A, B, and
C and they bend into a right angle, another protein may have
the same ABC sequence in a straight line or a loop. For decades,
scientists have tried to understand why a particular chemical
sequence leads to a particular fold. Their ultimate goal is
to predict the complete three-dimensional structure of a protein
based solely on knowing the sequence of chemicals that go
"It is a fascinating problem, because nature does it
so quickly and efficiently, and we all fail to predict it,"
said Professor Floudas, who is one of a growing number of
scientists trying to tackle the problem using mathematics,
rather than experimental methods.
The mathematical approach is part of a field of applied mathematics
called optimization. This is a process of looking at complex
situations affected by many variables and understanding what
values for the variables will produce the desired result.
With proteins, the variables are the positions of atoms of
the chemical units.
The chemical units in proteins, the As, Bs, and Cs, are amino
acids; there are 20 amino acids that can be used in any combination.
A typical protein may be madeup of hundreds of amino acids,
but for the purposes of studying protein folding, scientists
often look at relatively short segments, called peptides.
Even a pentapeptide, a protein with just five amino acids,
could fold in any of 100 billion possible structures, Professor
"How can you develop accurate mathematical models that
capture all the interactions?" he asked.
Like many scientists, Professor Floudas thinks about protein
folding in terms of how much energy is needed to hold a protein
together in a particular shape. A folded protein is analogous
to a person sitting crosslegged on the floor, compared to
the person standing bent over at the waist; one position requires
less energy than the other.
In theory, the same protein could assume many different stable,
low-energy shapes. In nature, however, proteins always head
down the one path that leads to the very lowest level of energy.
Scientists want to know which path nature will select. Which
is the lowest of the low? There are far too many to compare
one at a time.
That's where the principle of "divide and conquer"
comes in. Professor Floudas has figured out a way to divide
the problem in half repeatedly, so that he searches for the
highest energy conformations and then looks for the theoretical
lowest limit on what the protein's energy could be, a number
that is below the actual lowest-energy state. He then uses
a mathematical process that makes the two numbers converge
on the correct answer. In technical language this method is
called "branch and bound global optimization approach."
Professor Floudas said it provides a "theoretical guarantee
for locating the global solution to a given problem."
He has had good preliminary results with a 28-amino-acid
protein and is now working on one with 58 amino acids. One
validation of his method came last year when a group from
Columbia University used it to make good predictions about
the shape of several proteins ranging in size from 54 to 183
"There is strong evidence we're on the right track,"
Professor Floudas said.
Ken Dill, professor of pharmaceutical chemistry at the University
of California, San Francisco was a keynote speaker at a conference
on computational approaches to protein folding, co-organized
by Professor Floudas and held at Princeton in May.
"Chris's work is an important new contribution to this
field," Professor Dill said.
He added that Professor Floudas is the first to use rigorous
computing methods to achieve global optimization ("global"
because it doesn't just find a good answer, it finds the best
answer). Professor Dill, however, believes there is still
a lot of work to be done. He likens the protein-folding problem
to finding a needle in a haystack: what Professor Floudas
has done is find a very good way of sorting through all the
hay; what is not yet clear is how good is the description
of the needle itself.
In other words, do computational modelers have a good enough
description of how much energy is associated with a particular
Despite these unresolved issues, Professor Floudas' techniques
already are finding practical applications. He is collaborating
with two groups at the University of Pennsylvania that are
using his optimization tools to tackle specific medical research
questions, one having to do with how the immune system works
and the other with the working of the protein compstatin.
These collaborations combine Professor Floudas' mathematical
approach with more commonly used experimental methods.
In addition, research conducted in Professor Floudas' Computer
Aided Systems Laboratory addresses fundamental problems in
nonlinear mixed-integer and deterministic global optimization,
and their important applications in the synthesis, design,
control, and operation of chemical processes.
Graduate students John Klepeis and Heather Schafroth,
and postdoctoral associate Karl Westerberg are working
with Professor Floudas on the protein folding problem. Dr.
Westerberg, a National Institutes of Health fellow, investigates
the transition states, pathways, and dynamics of protein-folding.
Mr. Klepeis, a Wallace Memorial Honorific Fellow, studies
the ab initio secondary and tertiary structure prediction
of polypeptides. Ms. Schafroth, a National Science Foundation
Graduate Research Fellow and a Gordon Wu Fellow in Engineering,
investigates interactions of proteins in peptide docking.
Professor Floudas acknowledges that it is too early to claim
the protein-folding problem has been solved, but he believes
his approach includes several technical elements that others
omit, and the results are getting better and better.
"I'm encouraged," he said, "because rigorous
computational methods can advance our understanding of protein
structure prediction and elucidate the dynamics of protein
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This story first appeared in the Sept. 27,
1999 issue of the Princeton Weekly Bulletin and is
reprinted here with permission.