Scalable computation of anisotropic vibrations for large macromolecular assemblies

Jordy Homing Lam; Aiichiro Nakano; Vsevolod Katritch

doi:10.1038/s41467-024-47685-8

Scalable computation of anisotropic vibrations for large macromolecular assemblies

Nat Commun. 2024 Apr 24;15(1):3479. doi: 10.1038/s41467-024-47685-8.

Authors

Jordy Homing Lam^{1

2

3}, Aiichiro Nakano^{4

5

6}, Vsevolod Katritch^{7

8

9

10}

Affiliations

¹ Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA.
² Bridge Institute and Michelson Center for Convergent Biosciences, University of Southern California, Los Angeles, CA, USA.
³ Center for New Technologies in Drug Discovery and Development, University of Southern California, Los Angeles, CA, USA.
⁴ Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA. anakano@usc.edu.
⁵ Department of Physics and Astronomy, University of Southern California, Los Angeles, CA, USA. anakano@usc.edu.
⁶ Department of Computer Science, University of Southern California, Los Angeles, CA, USA. anakano@usc.edu.
⁷ Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA. katritch@usc.edu.
⁸ Bridge Institute and Michelson Center for Convergent Biosciences, University of Southern California, Los Angeles, CA, USA. katritch@usc.edu.
⁹ Center for New Technologies in Drug Discovery and Development, University of Southern California, Los Angeles, CA, USA. katritch@usc.edu.
¹⁰ Department of Chemistry, University of Southern California, Los Angeles, CA, USA. katritch@usc.edu.

Abstract

The Normal Mode Analysis (NMA) is a standard approach to elucidate the anisotropic vibrations of macromolecules at their folded states, where low-frequency collective motions can reveal rearrangements of domains and changes in the exposed surface of macromolecules. Recent advances in structural biology have enabled the resolution of megascale macromolecules with millions of atoms. However, the calculation of their vibrational modes remains elusive due to the prohibitive cost associated with constructing and diagonalizing the underlying eigenproblem and the current approaches to NMA are not readily adaptable for efficient parallel computing on graphic processing unit (GPU). Here, we present eigenproblem construction and diagonalization approach that implements level-structure bandwidth-reducing algorithms to transform the sparse computation in NMA to a globally-sparse-yet-locally-dense computation, allowing batched tensor products to be most efficiently executed on GPU. We map, optimize, and compare several low-complexity Krylov-subspace eigensolvers, supplemented by techniques such as Chebyshev filtering, sum decomposition, external explicit deflation and shift-and-inverse, to allow fast GPU-resident calculations. The method allows accurate calculation of the first 1000 vibrational modes of some largest structures in PDB ( > 2.4 million atoms) at least 250 times faster than existing methods.