A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography

Abstract

In this article, we report a method for coarse-grained normal mode analysis called the minimalist network model. The main features of the method are that it can deliver accurate low-frequency modes on structures without undergoing initial energy minimization and that it also retains the details of molecular interactions. The method does not require any additional adjustable parameters after coarse graining and is computationally very fast. Tests on modeling the experimentally measured anisotropic displacement parameters in biomolecular x-ray crystallography demonstrate that the method can consistently perform better than other commonly used methods including our own one. We expect this method to be effective for applications such as structural refinement and conformational sampling.all-atom normal modes ͉ elastic network model ͉ energy minimization ͉ normal mode analysis ͉ x-ray refinement N ormal mode analysis is a powerful tool for describing the global, collective, and functional motions of protein complexes (1-5). In this approach, the potential energy function of a protein is assumed to be harmonic so that protein motions can be described as a linear combination of a set of independent harmonic modes. Typically, only a few lowest-frequency modes with the largest amplitudes are sufficient to account for a majority of experimentally observed conformational fluctuations.Conventional normal mode analysis requires the calculation of an all-atom second-derivative matrix, the Hessian matrix, by using typical molecular mechanics force fields such as CHARMM (6-8) or AMBER (9-12). Thus, it requires substantial computer memory and processing power to perform the matrix diagonalization, which becomes a severe bottleneck in studies of supramolecular complexes. Moreover, to satisfy the harmonic approximation, the conventional method requires a lengthy initial energy-minimization step.To reduce the computational cost, many types of coarse-grained normal mode analyses have been developed (5,13,14). The most notable types include the rotations-translations of blocks (RTB) method (15) [also called block normal mode analysis (16)], allatom-derived coarse-grained methods (17, 18), and different variations of the elastic network model (19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29). The latter constructs the Hessian matrix from a highly simplistic Hamiltonian rather than a realistic molecular force field. Although elastic network models have been very successful, the quality of their modes is not optimal according to some recent studies, probably because of the usage of oversimplified Hamiltonians. In several reports that evaluated the use of low-frequency modes for interpreting crystallographic thermal parameters (28,30,31), the RTB approach with the CHARMM force field predicts anisotropic displacement parameters (ADPs) better than various elastic network models (28).Another limitation of the elastic network model is that it ignores molecular interaction details, which can be very important for certain cases (32). Also, in many a...

A force field for virtual atom molecular mechanics of proteins

“…4). Ma and colleagues have introduced alternative approaches to mitigate this ''tip effect'' problem by using a modified elastic potential function in ENM calculations (34) and a pairwise Hessian diagonalization scheme in BNM calculations (35). In practice, tip effects may not introduce a very serious problem because the important slow modes do not usually display this abnormality; however, it causes defects in analysis of the overall normal modes.…”

Measuring and modeling diffuse scattering in protein X-ray crystallography

“…Normal-mode analysis (NMA) provides a more detailed picture of the conformational ensemble than the LLM model, enabling a direct connection to putative mechanisms of protein function (25). The NM refinement methods that have been developed for Bragg analysis use few additional parameters (26)(27)(28)(29)(30); however, these methods are not currently available in the standard builds of the major refinement software. Reasonable qualitative agreement previously has been seen using NM to model diffuse intensity in individual diffraction images (31,32).…”

Ribosome Mechanics Informs about Mechanism

“…including several residues per node, have also proven satisfactory for determining the lower-frequency collective modes [57, 61] [62], as long as the overall shape of the molecule is preserved. The building block approach [63] and the minimalist network model [64] are other alternative efficient coarse-grained normal mode approaches.…”