Intrinsic Dynamics Analysis of a DNA Octahedron by Elastic Network Model

Topological structures of DNA octahedrons determined by the number of ssDNA strands

How to control the nontrivial topological structures of DNA nanocages by the number of ssDNA strands is a fundamental problem for polyhedra assembly. In this paper, oriented octahedral links have been established as topological structure models to characterize DNA octahedrons with double helix edges assembled from one or more ssDNA strands. Here a program "Octa-links" has been developed in Python language to give all octahedral links and their components (number). There are 1566 types of octahedral links generated by considering all orientations calculated and the allowable tangle types on each edge. Note that all same orientations and links have been excluded by introducing 24 symmetric operations of octahedra. Furthermore, a new algorithm is proposed to give each component of each octahedral link as a series of vertex arcs, obtaining that the component number of all links fills the integer interval [1, 8]. Hence our program designed according to this algorithm paves an effective approach to calculate the component number of polyhedral links, making up the gap in the computer program on this aspect. Also, our work provides a complete list of topological structures with different component number for new DNA octahedrons assembled by adjusting the number of ssDNA strands.

Elastic network models and molecular dynamic simulations reveal the molecular basis of allosteric regulation in ubiquitin-specific protease 7 (USP7)

Ubiquitin-specific protease 7 (USP7) is one of the most abundant deubiquitinases and plays an important role in various malignant tumors. However, the molecular mechanisms underlying USP7's structures, dynamics, and biological significance are yet to be investigated. In this study, we constructed the full-length models of USP7 in both the extended and compact state, and applied elastic network models (ENM), molecular dynamics (MD) simulations, perturbation response scanning (PRS) analysis, residue interaction networks as well as allosteric pocket prediction to investigate allosteric dynamics in USP7. Our analysis of intrinsic and conformational dynamics revealed that the structural transition between the two states is characterized by global clamp motions, during which the catalytic domain (CD) and UBL4-5 domain exhibit strong negative correlations. The PRS analysis, combined with the analysis of disease mutations and post-translational modifications (PTMs) further highlighted the allosteric potential of the two domains. The residue interaction network based on MD simulations captured an allosteric communication path which starts at CD domain and ends at UBL4-5 domain. Moreover, we identified a pocket at the TRAF-CD interface as a high-potential allosteric site for USP7. Overall, our studies not only provide molecular insights into the conformational changes of USP7, but also aid in the design of allosteric modulators that target USP7.

Simulative Analysis of a Family of DNA Tetrahedrons Produced by Changing the Twisting Number of Each Double Helix

In this paper, three tetrahedral nanocages, composed of six DNA double helix edges with all having the twist number 1, 2 or 3, have been characterized using classical molecular dynamics simulation to measure the specific structural and conformational features produced by only changing the twisting number of each double helix. The simulation result indicates that three tetrahedral cages are relatively stable and are maintained along the entire trajectory. Each double helix is more inclined to behave as a whole in the 2TD and 3TD cages than in the 1TD cage according to the cross-correlation maps for three nanocages, and also their local motions are more easily induced by the conformational variability of the thymidine linkers due to the increased flexibility of each helix. Hence, the double helices become the important factors on the structural stability of total cages with the DNA twisting number, and also give the signification contributions to the sizes of these cages conferring the larger spaces of the 2TD and 3TD cages than the 1TD cage. Our result provides an insight into which roles the double helix edges play in assembling DNA polyhedron, and also contribute to improving the loading capacity of DNA tetrahedron in drug delivery.

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

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.

Construction and Analysis of Double Helix for Triangular Bipyramid and Pentangular Bipyramid

DNA cages can be joined together to make larger 3D nanostructures on which molecular electronic circuits and tiny containers are built for drug delivery. The mathematical models for these promising nanomaterials play important roles in clarifying their assembly mechanism and understanding their structures. In this study, we propose a mathematical and computer method to construct permissible topological structures with double-helical edges for a triangular bipyramid and pentangular bipyramid. Furthermore, we remove the same topological links, without eliminating the nonrepeated ones for a triangular bipyramid and pentangular bipyramid. By analyzing characteristics of these unique links, some self-assembly and statistic rules are discussed. This study may obtain some new insights into the DNA assembly from the viewpoint of mathematics, promoting the comprehending and design efficiency of DNA polyhedra with required topological structures.

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

The synthesis of DNA polyhedra has attracted more interest because of its wide application prospect, but its formation mechanism from mathematical viewpoint remains poorly understood. This paper presents the assembly process and mechanism of DNA truncated tetrahedron, cuboctahedron and truncated octahedron by the means of mathematics and computer program. Firstly, based on the assumption that the total number of all the crossings within each face of a DNA polyhedron must be an even number, potential types for three DNA polyhedra above are calculated by computer programs; Secondly, the projections of the truncated tetrahedron, the cuboctahedron and the truncated octahedron are plotted based on data fetched by the program; Thirdly, the component number, the odd-crossing edge number and even-crossing edge number for the corresponding polyhedral links are computed by analysis of their projections. This study gets some assembly mechanism on the structure of DNA double helix, promoting the comprehending and design efficiency of DNA polyhedra.

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

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.

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

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.