Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

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Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules.

Exploring the dynamics of RNA molecules with multiscale Gaussian network model

Dynamical properties of proteins play an essential role in their function exertion. The elastic network model (ENM) is an effective and efficient tool in characterizing the intrinsic dynamical properties encoded in biomacromolecule structures. The Gaussian network model (GNM) and anisotropic network model (ANM) are the two often-used ENM models. Here, we introduce an equally weighted multiscale ENM (equally weighted mENM) based on the original mENM (denoted as mENM), in which fitting weights of Kirchhoff/Hessian matrixes in mENM are removed since they neglect the details of pairwise interactions. Then, we perform its comparison with the mENM, traditional ENM, and parameter-free ENM (pfENM) in reproducing dynamical properties for the six representative proteins whose molecular dynamics (MD) trajectories are available in http://mmb.pcb.ub.es/MoDEL/. In the results, for B-factor prediction, mENM performs best, while the equally weighted mENM performs also well, better than the traditional ENM and pfENM models. As to the dynamical cross-correlation map calculation, mENM performs worst, while the results produced from the equally weighted mENM and pfENM models are close to those from MD trajectories with the latter a little better than the former. Furthermore, encouragingly, the equally weighted mANM displays the best performance in capturing the functional motional modes, followed by pfANM and traditional ANM models, while the mANM fails in all the cases. This work is helpful for strengthening the understanding of the elastic network model and provides a valuable guide for researchers to utilize the model to explore protein dynamics.

Equally Weighted Multiscale Elastic Network Model and Its Comparison with Traditional and Parameter-Free Models

Configuration of DNA polyhedra of truncated tetrahedron, cuboctahedron, truncated octahedron.

In order to incorporate functionalization into synthesized DNA nanostructures, enhance their production yield, and utilize them in various applications, it is necessary to study their physical stabilities and dynamic characteristics. Although simulation-based analysis used for DNA nanostructures provides important clues to explain their self-assembly mechanism, structural function, and intrinsic dynamic characteristics, few studies have focused on the simulation of DNA supramolecular structures due to the structural complexity and high computational cost. Here, we demonstrated the feasibility of using normal mode analysis for relatively complex DNA structures with larger molecular weights, i.e., finite-size DNA 2D rings and 3D buckyball structures. The normal mode analysis was carried out using the mass-weighted chemical elastic network model (MWCENM) and the symmetry-constrained elastic network model (SCENM), both of which are precise and efficient modeling methodologies. MWCENM considers both the weight of the nucleotides and the chemical bonds between atoms, and SCENM can obtain mode shapes of a whole structure by using only a repeated unit and its connectivity with neighboring units. Our results show the intrinsic vibrational features of DNA ring structures, which experience inner/outer circle and bridge motions, as well as DNA buckyball structures having overall breathing and local breathing motions. These could be used as the fundamental basis for designing and constructing more complicated DNA nanostructures.

https://www.mdpi.com/1422-0067/19/7/1895/pdf

Fabrication and Characterization of Finite-Size DNA 2D Ring and 3D Buckyball Structures

DNA is a fundamental component of living systems where it plays a crucial role at both functional and structural level. The programmable properties of DNA make it an interesting building block for the construction of nanostructures. However, molecular mechanisms for the arrangement of these well-defined DNA assemblies are not fully understood. In this paper, the intrinsic dynamics of a DNA octahedron has been investigated by using two types of Elastic Network Models (ENMs). The application of ENMs to DNA nanocages include the analysis of the intrinsic flexibilities of DNA double-helices and hinge sites through the calculation of the square fluctuations, as well as the intrinsic collective dynamics in terms of cross-collective map calculation coupled with global motions analysis. The dynamics profiles derived from ENMs have then been evaluated and compared with previous classical molecular dynamics simulation trajectories. The results presented here revealed that ENMs can provide useful insights into the intrinsic dynamics of large DNA nanocages and represent a useful tool in the field of structural DNA nanotechnology.

https://www.mdpi.com/1420-3049/22/1/145/pdf

Lei He

Papers

Intrinsic Dynamics Analysis of a DNA Octahedron by Elastic Network Model.