III-SGER: Algorithms for Next-Generation Protein Modeling: Beyond Pair-wise Interactions

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This work pursues the development of a new algorithmic framework whichallows for the first time efficient computation of higher-orderinteractions in biomolecules. Algorithms are created to demonstratetwo important applications on much larger scales than were previouslytractable, each representing a new door to a larger class of furtherpossibilities: Axilrod-Teller (3-body) simulation, and Hartree-Fock(4-index) quantum-level simulation. The multidisciplinary projectbrings together experts in computer science, protein folding, andquantum chemistry.Biomolecular simulations usually break down complex chemical systemsinto a balls-and-springs mechanical model augmented by torsionalterms, pair-wise point-charge electrostatic terms, and simplepair-wise dispersion (van der Waals) interactions. However such modelsoften fail to capture important, complex non-additive interactionsfound in real systems. Though the criticality of multi-bodypotentials for more accurate and realistic molecular modeling has beenargued by various authors, their evaluation in systems beyond tinysizes has not been previously possible due to the unavailability of anefficient way to realize the computation, which is cubic or higher.The work augments a framework for computational problems calledGeneralized N-Body Problems, which contains any such higher-orderphysical potential. The framework was originally developed toaccelerate common bottleneck statistical computations based ondistances, utilizing multiple kd-trees and other space-partitioningdata structures to bring down computation times both asymptoticallyand practically by multiple orders of magnitude. This work extendsthe framework with higher-order hierarchical series approximationtechniques, demonstrating how to do a fast multipole-type method forhigher-order interactions for the first time, effectively creating aGeneralized Fast Multipole Method.The algorithms are validated in biochemical systems chosen to clearlyillustrate many-body interactions: hydrogen bonds and three-bodydispersion interactions. Parameters for potential functions areobtained using customized machine learning methods on dual data setsgenerated by the co-PI's labs: high-quality quantum mechanicalbenchmark data and experimental protein structures.The goal is to demonstrate working many-body codes able to explore theeffect of modeling higher-order interactions on a larger scale andmore systematically than ever attempted previously. The intellectualmerit of the work is the elucidation of the first multi-tree multipolemethod capable of accurately and scalably performing these fundamentaltypes of higher-order physics computations. The potential broaderimpact is the ability to perform more accurate next-generationmolecular modeling, with implications for fundamental biology and drugdesign. For further information see the project web page at http://www.cc.gatech.edu/~agray/gfmm.html