Large Eigenvalue Problems in Coarse-Grained Dynamic Analyses of Supramolecular Systems

Scalable computation of anisotropic vibrations for large macromolecular assemblies

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.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Spike Proteins of SARS-CoV and SARS-CoV-2 Utilize Different Mechanisms to Bind With Human ACE2

The ongoing outbreak of COVID-19 has been a serious threat to human health worldwide. The virus SARS-CoV-2 initiates its infection to the human body via the interaction of its spike (S) protein with the human Angiotensin-Converting Enzyme 2 (ACE2) of the host cells. Therefore, understanding the fundamental mechanisms of how SARS-CoV-2 S protein receptor binding domain (RBD) binds to ACE2 is highly demanded for developing treatments for COVID-19. Here we implemented multi-scale computational approaches to study the binding mechanisms of human ACE2 and S proteins of both SARS-CoV and SARS-CoV-2. Electrostatic features, including electrostatic potential, electric field lines, and electrostatic forces of SARS-CoV and SARS-CoV-2 were calculated and compared in detail. The results demonstrate that SARS-CoV and SARS-CoV-2 S proteins are both attractive to ACE2 by electrostatic forces even at different distances. However, the residues contributing to the electrostatic features are quite different due to the mutations between SARS-CoV S protein and SARS-CoV-2 S protein. Such differences are analyzed comprehensively. Compared to SARS-CoV, the SARS-CoV-2 binds with ACE2 using a more robust strategy: The electric field line related residues are distributed quite differently, which results in a more robust binding strategy of SARS-CoV-2. Also, SARS-CoV-2 has a higher electric field line density than that of SARS-CoV, which indicates stronger interaction between SARS-CoV-2 and ACE2, compared to that of SARS-CoV. Key residues involved in salt bridges and hydrogen bonds are identified in this study, which may help the future drug design against COVID-19.

Determining Optimal Coarse-Grained Representation for Biomolecules Using Internal Cluster Validation Indexes

The development of ultracoarse-grained models for large biomolecules needs to derive the optimal number of coarse-grained (CG) sites to represent the targets. In this work, we propose to use the statistical internal cluster validation indexes to determine the optimal number of CG sites that are optimized based on the essential dynamics coarse-graining method. The calculated curves of Calinski-Harabasz and Silhouette Coefficient indexes exhibit the extrema corresponding to the similar CG numbers. The calculated ratios of the optimal CG numbers to the residue numbers of fine-grained models are in the range from 4 to 2. The comparison of the stability of index results indicates that Calinski-Harabasz index is the better choice to determine the optimal CG representation in coarse-graining. © 2019 Wiley Periodicals, Inc.

The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses

In the last three decades, many giant DNA viruses have been discovered. Giant viruses present a unique and essential research frontier for studies of self-assembly and regulation of supramolecular assemblies. The question on how these giant DNA viruses assemble thousands of proteins so accurately to form their protein shells, the capsids, remains largely unanswered. Revealing the mechanisms of giant virus assembly will help to discover the mysteries of many self-assembly biology problems. Paramecium bursaria Chlorella virus-1 (PBCV-1) is one of the most intensively studied giant viruses. Here, we implemented a multi-scale approach to investigate the interactions among PBCV-1 capsid building units called capsomers. Three binding modes with different strengths are found between capsomers around the relatively flat area of the virion surface at the icosahedral 2-fold axis. Furthermore, a capsomer structure manipulation package is developed to simulate the capsid assembly process. Using these tools, binding forces among capsomers were investigated and binding funnels were observed that were consistent with the final assembled capsid. In addition, total binding free energies of each binding mode were calculated. The results helped to explain previous experimental observations. Results and tools generated in this work established an initial computational approach to answer current unresolved questions regarding giant virus assembly mechanisms. Results will pave the way for studying more complicated process in other biomolecular structures.