Linear-scaling electronic structure methods for biological macromolecules

Extension of theory to macromolecular problems requires computational methods that are efficient and have well behaved scaling properties. Conventional density-functional theory (DFT) and Hartree-Fock methods are limited to fairly small systems since the computational effort scales as the cubic of the number of atoms (or higher), making application of these methods to macromolecular systems unfeasible. The main scaling bottlenecks arise from (1) the order N³ problem of maintaining orthogonality of molecular orbitals (or equivalently the idempotency condition of the single-particle density matrix) in accord with the Pauli exclusion principle, and (2) the order N² problem of calculating long-range Coulomb interactions. The latter problem can be surmounted with fast-multipole techniques or linear-scaling Ewald methods that are also applicable in other important areas of computational chemistry such as molecular simulation and implicit solvation methods. A focus of the lab is to develop new "linear-scaling" electronic structure methods that are able to treat very large systems, and to apply them to exciting new areas such as the study of quantum mechanical effects on biological macromolecules in solution.

Recently it has become possible to perform fully self consistent electronic structure calculations of biological macromolecules up to 10,000 atoms in solution at the semiempirical level. It is a primary focus of the lab to extend these techniques to ab initio (Hartree-Fock and density-functional) methods, and apply them to important biological and pharmaceutical problems such as the elucidation of quantum mechanical electrostatic potential surfaces and reactivity indices, pKa shifts, density of electronic states, and the role of solute polarization in the process of solvation and ligand binding. More complex problems such as enzyme catalysis and long-range electron transfer events in biological macromolecules are areas of intense interest, and complimented by the molecular simulation and hybrid QM/MM component of the group's research.

Current Projects

CPU scaling for linear-scaling semiempirical method for several protein and DNA systems in the gas phase (solid line) and in solution (dotted line):

Relevent Publications

"Quantum mechanical treatment of biological macromolecules in solution using linear-scaling electronic structure methods," D. York, T.-S. Lee, and W. Yang, Phys. Rev. Lett., in press.

"Application of linear-scaling electronic structure methods to the study of polarization of proteins and DNA in solution," D. York, in Methods and Applications of Hybrid Quantum and Molecular Mechanical Potentials, (Jiali Gao and Mark Thompson, Eds), John Wiley, 1998.

"Quantum mechanical study of aqueous polarization effects on biological macromolecules using linear-scaling electronic structure and solvation methods," D. York, T.-S. Lee, W. Yang, J. Am. Chem. Soc. (communication) 118, 10940-10941 (1996).

"Linear-scaling semiempirical quantum calculations for macromolecules," T.-S. Lee, D. York, W. Yang, J. Chem. Phys. 105, 2744-2750 (1996).

"Parameterization and efficient implementation of a solvent model for linear-scaling semiempirical quantum mechanical calculations of biological macromolecules," D. York, T.-S. Lee, W. Yang, Chem. Phys. Lett. 263, 297-304 (1996).