There's an old saying about curing the common cold that Biophysicist Shankar Subramaniam likes to recall when explaining why he models antibodies and antigens: "With medicine, it takes a week to cure a cold; without it, seven days."
During the early stages of infection, says Subramaniam, "your body is really trying to learn and grope and adapt to the foreign particle that is coming in. It's a way of maturing to a stage where the immune system is able to tackle the infection."
In the past several decades, biological and medical research has deciphered many of the biochemical reactions by which the human immune system recognizes a particle as foreign and launches an attack. Where things get fuzzy, however, is in deciphering the basis underlying this recognition. This knowledge is essential to accelerating relief and to targeting medicines more accurately.
To fine tune the process of biological recognition, NCSA Research Scientist Subramaniam is leading a team of computational biologists and computer scientists at NCSA who are modeling how one of the body's key defensive mechanisms, the antibodies, recognize and bind with one of the largest of microbial invaders, the antigens. Recently, the group successfully computed the complete nonlinear Poisson-Boltzmann equation and combined the electrostatic steering forces obtained from this equation with the diffusive motion of Brownian dynamics.
The Poisson-Boltzmann equation is a fundamental equation in electrostatics once considered so difficult to solve as to be intractable. Previous efforts had solved the linear version of the equation, which does not account for the electrostatic affects of the ionic medium on the antigen's diffusion in the blood stream. The added realism of the nonlinear equation made it possible for Subramaniam and his colleagues to model the monoclonal antibody HyHEL-5 binding to the hen-egg lysozome at a rate that replicated experimental results--a first for antibody-antigen modelers.
The key to the system's success--as well as the reason for its seemingly slow pace--is its capacity to be flexible yet specific. Rather than having a billion different lymphocytes patrolling your blood vessels, the immune system sends out a few lookouts who, upon detecting an invader, rapidly sort through its genetic library to construct the suitable T cells or B cells to replicate and eventually subdue the invader. T cells are lymphocytes that originate primarily in the thymus and destroy fungi, viruses, and parasites by engulfing and digesting them. B cells are formed in the bone marrow and give rise to antibodies, which confer resistance against most bacteria.
Antibodies are Y-shaped chains of polypeptides that are identical for a small section of amino acids at the forked end of the Y. The attractive and repulsive interactions between the tip of the fork of the antibody and the reactive portion of the antigen determines whether the two will bond weakly or strongly. The binding affinity between an antibody and antigen is the basis of molecular recognition.
Their model depicts an antibody surrounded by an ionic medium. Antigens were placed around the edges of a box at 500,000 different points and, one at a time, allowed to diffuse randomly just as they would in blood. If an antigen bonded strongly (in the correct orientation) with the antibody during one of these trajectories, Subramaniam considered the reaction over. If it bounced back or wandered off, the encounter was considered unsuccessful. By averaging these trajectories, he generated a rate of reaction for the antibody-antigen encounter. Because it would be impossible to model the entire antibody-antigen complex, only the 4,000 atoms involved in bonding were modeled.
To model the two forces that propel antigens toward antibodies--the electrostatic forces represented in the full nonlinear Poisson- Boltzmann equation and Brownian motion--Subramaniam teamed up with Faisal Saied, assistant professor in the UIUC Department of Computer Science, graduate student Michael Holst, and postdoctoral associate Richard Kozack. The new method that arose from their collaboration employed a multigrid technique, a methodology that more efficiently solves equations on grids by resolving them at different levels of detail. The large memory required for this equation is amenable to a solution on NCSA's CONVEX C3880, or C3.
The linear Poisson-Boltzmann equation had been solved before using a single-mesh approach, but not with a nonlinear technique. The existing methods were so slow as to discourage people from doing so. "Our method is so fast that it translates into a new capability," says Saied, who developed the algorithm for running the equation on NCSA's machines.
Once the electrostatic forces were obtained, Kozack and Subramaniam used Brownian dynamics to model the diffusional motion of the antigen to the antibody.
"Brownian motion is what we call an embarrassingly parallel equation," says Subramaniam in explaining why they chose to model this force responsible for diffusion on NCSA's Thinking Machines CM-5 and SGI POWER CHALLENGE. Brownian motion is the seemingly random motion of small particles as they are buffeted about by collisions with other molecules in a solution. Each of the 500,000 trajectories were basically calculations of Brownian motion.
By combining the nonlinear Poisson-Boltzmann equation with Brownian motion, Subramaniam says they now have quantitative rates of reaction they can use to look at absolute values of reaction rates.
Rational design, he says, "will constitute genuine protein engineering rather than where we stand now, which is often so unpredictable that is has been referred to as 'protein terrorism'."
Understanding how a protein's structure influences its actions is essential for developing immunotoxins, biosensors, and in industrial applications such as bacterial organisms genetically altered to degrade oil spills. Who knows? It may even help biologists beat Mother Nature in curing the common cold.
NOTE: Papers based on this research have appeared in the following journals.
R. E. Kozack, M. J. D'Mello, and S. Subramaniam. "Computer modeling of electrostatic steering and orientational effects in antibody-antigen association." Biophys. J. (in press).
M. Holst, R. E. Kozack, F. Saied, and S. Subramaniam. 1994. "Treatment of electrostatic effects in proteins: Multi-grid-based Newton iterative method for solution of the full nonlinear Poisson-Boltzmann equation." Proteins: Structure, Function, and Genetics 18(3): 231-245.
M. Holst, R. E. Kozack, F. Saied, S. Subramaniam. 1994. "Protein electrostatics: Rapid multigrid-based Newton algorithm for solution of the full nonlinear Poisson-Boltzmann equation." J. Biomol. Struct. Dyn. 11(6): 1437-1445.
S. P. Slagle, R. E. Kozack, and S. Subramaniam. 1994. "Role of electrostatics in antibody-antigen association: anti-hen egg lysozyme/lysozyme complex (HyHEL-5HEL)." J. Biomol. Struct. Dyn. 12:439-456.
R. E. Kozack and S. Subramaniam. 1993. "Brownian dynamics simulations of molecular recognition in an antibody-antigen system." Protein Science 2:915-926.
Holly Korab is a science writer in the Publications Group.
