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SDSC’s Blue Horizon Paints Electrostatic Landscapes of Cellular Structures

ne 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.


Molecular Electrostatics

Animated Microtubule

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.

Opposite Ends of a Microtubule

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

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