| Abstract |
This talk will present highlights of our group's recent research
developing numerical techniques for analyzing the electrostatic
interactions between biomolecules. These interactions play vital roles
in determining binding affinity and specificity; unfortunately,
constraints on computational resources severely limit simulation
accuracy, even when linear continuum electrostatics models are employed.
Our recent work has focused on highly accurate numerical techniques for
surface formulations of the electrostatics problem. I will present our
fast boundary-element-method (BEM) solver, called FFTSVD, which solves
these problems efficiently, and can also be applied to other domains. I
will describe methods for accurately representing biomolecule surfaces
and for numerically integrating singular functions over them. Our work
represents substantial progress towards a regime of unprecedented
accuracy. Finally, I will discuss the theory and practice of biomolecule
electrostatic optimization. This topic builds on the electrostatic
analysis methods discussed in the first part of the talk: in
computational drug design, for instance, one asks, "Is this drug optimal,
in some sense, to bind its target?" Such problems are well-posed but
computationally expensive. We have introduced a novel, highly efficient
PDE-constrained optimization technique for these problems. In
combination with preconditioned Krylov iterative methods, an implicit
representation of the Hessian dramatically reduces the computational
expense. I will conclude the talk by briefly describing several
promising areas for future work.
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