August 21, 2001
Providing a New Look at Large Biomolecules
A new method for studying the electrical landscape of large
biological molecules may enable researchers to make a leap from
modeling molecules of 50,000 atoms to those of more than a million
atoms.
The technique, developed by Howard Hughes Medical Institute (HHMI)
researchers at the University of California, San Diego (UCSD), was used
to model the electrostatic properties of microtubules, which are part
of the cell's structural and transport systems, and ribosomes, which
are the cell's protein-making factories. The scientists say their new
computer modeling method, called parallel focusing, will provide
molecular biologists with a useful tool for exploring the dynamic
behavior of complex biomolecules. The scientists plan to make their
software widely available to the scientific community.
“Electrostatic models portray how the charges on individual atoms of a molecule interact to produce a distribution of electric fields throughout the molecule. Shown here are two images that illustrate the electrostatic properties of the microtubule. Potential isocontours are shown along the solid blue surface and the translucent red surface of the microtubule. The "negative" and "positive" ends of the microtubule are shown in the left and right figures, respectively.”
Electrostatic models portray how the charges on individual atoms of
a molecule interact to produce a distribution of electric fields
throughout the molecule. These models have proven useful to researchers
analyzing the stability and dynamic motions and interactions of
biological molecules, including proteins, DNA and RNA.
In an article published online on August 21, 2001, in Proceedings
of the National Academy of Sciences, researchers led by HHMI
investigator J.
Andrew McCammon report that parallel focusing is a new approach to
solving the Poisson-Boltzmann equation (PBE), a fundamental equation in
the field of electrostatics.
"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,"
he said.
According to McCammon, the effectiveness of the PBE, which is called
an "implicit solvent method," has made it one of the most popular bases
for electrostatic modeling. But while the popularity of the PBE has
increased, methods to solve the equation have been limited to molecules
of about 50,000 atoms because of their considerable computational
demands.
In the PNAS article, however, McCammon, HHMI predoctoral
fellow Nathan A. Baker and their colleagues at UCSD describe how the
parallel focusing method enables solution of the PBE to be run
efficiently and flexibly on parallel computers. By using massively
parallel computers, researchers can divide large computations among
many processors, and drastically reduce the time required to create
complex models.
Electrostatic modeling typically represents the biomolecule and the
PBE on a Cartesian grid, explained Baker. Very fast numerical methods,
such as the multigrid, are then used to solve the equation on this
grid. The solution on the array of grid points is then used to
represent the electrostatic potential around the biomolecule.
"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 Baker. “In the
parallel focusing method, we divide that box up, so that even if it's a
very large box, 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."
Parallel focusing is based on theoretical work by UCSD
mathematicians Randolph E. Bank and Michael J. Holst, who proved that
solving a problem with a low level of accuracy over an entire domain
would enable one to use that solution to get a more accurate picture on
a subset of that domain, Baker said. According to Baker and McCammon,
their approach enables each processor to arrive at a highly precise
solution for a tiny part of a molecule, without the need to communicate
with other processors in the parallel computer. Reducing or eliminating
such communications is critical if parallel machines are to tackle the
problems efficiently.
Parallel focusing allows electrostatic modeling of molecules with a
very high resolution, in which each partition of the mesh represents
about 0.5 Angstroms. McCammon and Baker say that the method can be used
on a range of parallel computers — from networks of workstations with
relatively low-speed connections to high-performance
supercomputers.
To demonstrate the utility of their approach, the scientists modeled
the electrostatic charges on microtubules and ribosomes. Microtubules
are hollow polymers of protein that provide a rigid support structure
in the cell and serve an important role in transporting proteins
throughout the cell. Ribosomes are large molecular complexes of RNA and
protein that are the site of protein synthesis in the cell.
Applying their technique to a model of a 1.25-million-atom
microtubule, which was 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
large-scale "undulations" in electrical potential demonstrate the value
of this type of modeling technique in revealing the collective
properties of large molecules, said Baker. The scientists also found
that the electrostatic potential at each end of the microtubule was
different. This may provide clues to the stability of microtubules,
Baker said.
The scientists also explored the variation in electrostatic
potential over the sites on the microtubules where drugs like Taxol
bind. "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 electrostatic model of the two ribosomal subunits — one with
88,000 atoms and the other with 94,854, revealed an intricate map of
positive and negative potential that could yield insights into the
function of ribosomes, said the scientists.
According to McCammon, software using the new approach will soon be
made available to researchers to help guide their experiments on large
molecules. The scientists will also begin extending their method to
model dynamic changes in molecules over time. "This approach enables
investigators to do all the things they could do with electrostatic
models before — for example, exploring binding energies and
associations of proteins — on a far larger scale that is much more
relevant to cellular processes," said McCammon.
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