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way to puzzle out how a machine works is to disassemble it, then
put it together again. If that machine contains millions of pieces
that require a precise, yet flexible fit with other parts, with
all those pieces constantly jiggling around, changing shape, attracting
and repelling one another, the problem becomes infinitely complex.
Researchers using NPACI computing resources at SDSC have used electrostatic
modeling to tackle the construction of such a dynamic machine, figuring
out how all the pieces fit together in a device that only nature
could build. J. Andrew McCammon, the Joseph E. Mayer Professor of
Theoretical Chemistry at UCSD, and his colleagues at UCSD and Washington
University have reconstructed biomolecules of unprecedented size,
revealing new insights into the function of key structures inside
cells.
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Molecular
Electrostatics
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Animated Microtubule
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“Creating
a blueprint of intricate biological machines in order to understand
how they can perform such functions as transporting the anti-cancer
drug taxol requires a mix of expertise in biology, mathematics,
computer science, and the use of a massively parallel machine. A
group led by McCammon has been fine-tuning a method called parallel
focusing, which provides an atom-by-atom rendering of extremely
large biomolecules.
In a paper published in the August 28 issue of Proceedings of the
National Academy of Sciences, the researchers describe a milestone
in biomolecular visualization. The work is considered a triumph
for the use of the “digital test tube”—computational
work that provides atomic, molecular, and cellular details that
can elude normal laboratory experiments. The scientists’ improved
methods for computational modeling allow them to increase the size
of the systems they are capable of modeling from fewer than 50,000
atoms to more than one million—an unprecedented number in such
a simulation. “We’ve achieved a new landmark in the scale
of cellular structures that we can model from a molecular perspective,”
said McCammon. “The work signals a new era of calculations
on cellular-scale structures in biology.”
The atomic-scale maps of large biomolecules give a fine portrait
of the structures found within cells: microtubules (Figures 1–3),
hollow fibers that are involved in intracellular transport and shape,
and ribosomes, which manufacture proteins. The electrostatic potential
describes the way in which the landscape of electrical charge is
laid out in a molecular environment. Such charges are vitally important
in a variety of biochemical processes. For example, electric forces
tug a tRNA molecule into place on a ribosome during translation,
and they draw a taxol molecule through a microtubule to a binding
site. McCammon likens the ability to pick out one atom within such
a large 3-D system to being able to describe one cherry dangling
from an entire fruit tree.
The work of McCammon and his colleagues is based on creating a new
method for solving what is known as the Poisson-Boltzmann equation,
a mathematical construction that allows a computer to determine
the framework vital to creating accurate electrostatic models. Electrostatic
modeling typically represents the biomolecule and the Poisson-Boltzmann
equation on a Cartesian grid. The solution of the equation on the
array of grid points is then used to represent the electrostatic
potential around the large biomolecules.
“One can think of these electrostatic equations as being solved
in a very big box that contains the grid and which is several times
larger than the molecule to be modeled,” said Nathan Baker,
a postdoctoral researcher in McCammon’s lab. “In the parallel
focusing method, we divide up that box, so that even if it’s
very large, the calculations can be done on a single processor.
We have each processor solve the equations for that coarse grid
and then use that low-accuracy solution to provide the boundary
conditions to focus on a much smaller and finer problem on a particular
partition of the mesh allocated to that particular processor.”
Eventually, the scientists plan to make their software available
to the scientific community.
In the past, calculating electrostatic potential has been a cumbersome
process that requires a tremendous amount of computing resources,
even for the simplest of models, said Baker. In 2000, Mike Holst,
associate professor of mathematics at UCSD, and Randolph Bank, professor
of mathematics at UCSD, found that the Poisson-Boltzmann equation
could be broken into independent parts. “One of the problems
with traditional molecular dynamics methods for simulating large
systems is that they require considerable computational effort to
simulate the surrounding atoms of the aqueous solvent,” said
McCammon. “The Poisson-Boltzmann equation circumvents this
by treating the solvent as one featureless polarizable medium—essentially
a big cloud of charge around a molecule such as a protein.”
To model the structures, McCammon and a group that included Baker,
Holst, Simpson Joseph, assistant professor of biochemistry at UCSD,
and David Sept, assistant professor of biomedical engineering at
Washington University, created algorithms and wrote computer codes
to solve equations that describe the electrostatic contributions
of individual atoms within a system. Utilizing parallel processing
produces significantly more computing power and allows far more
complex models to be created than ever before.
The new algorithm assigns a small portion of the calculation to
individual processors available on a supercomputer. Each of those
processors independently solves its portion of the equation and
passes its results along to a master processor that gathers and
processes the data. The IBM Blue Horizon supercomputer at SDSC completed
the calculations for the equation relating to the microtubule in
less than one hour using 686 processors out of 1,152 available.
The researchers estimated that the old method would have required
at least 350 times more memory and time to solve. That simulation
couldn’t have been completed in a practical amount of time.
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Opposite Ends
of a Microtubule
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“Applying
the technique to model a 1.25-million-atom microtubule composed
of 90 units of the protein tubulin revealed that electrostatic variations
in the microtubule were much larger in scale than those seen in
individual tubulin molecules. The variations in electrical potential
demonstrate the value of this type of modeling technique in understanding
the collective properties of large molecules, said Baker.
While the overall negative charge of the microtubule likely plays
a strong role in intracellular transport, the topographical picture
also highlights regions where such drugs as taxol and colchicine
may bind. The researchers discovered small islands of positive potential
around the microtubule. The electrostatic heterogeneity may provide
clues to the stability of microtubules, Baker said. In addition,
the variations in electrostatic potential around binding sites provide
new insights about drug performance. “Understanding microtubule
instability and the mechanism by which microtubules dissociate could
have therapeutic applications because many anti-cancer drugs act
to stabilize microtubules,” said McCammon.
"The researchers
also examined the electrostatic model of the two ribosomal subunits—the
30s subunit with 88,000 atoms and the 50s subunit with 94,854—revealing
an intricate terrain of positive and negative potentials. The researchers
speculate that one of the areas, revealed on an electrostatic map
of the ribosome in an area on the smaller 30s subunit, might play
a role in stabilizing tRNA and mRNA during translation. The system
could be enlarged further according to Baker and McCammon. “The
calculations were done in a highly scalable fashion and would be
suited to even larger runs. We hope to push the envelope even further
and to tackle a number of large-scale problems in intracellular
activity such as antibiotic binding to ribosomes,” said Baker.
—CF
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PRINCIPAL INVESTIGATORS
J. Andrew McCammon
Nathan Baker
Simpson Joseph
Michael Holst
UCSD
David Sept
Washington University
nbcr.sdsc.edu/mccammon/
mccammon.html
mccammon.ucsd.edu |
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