DNA sequence-dependent formation of heterochromatin nanodomains

The mammalian epigenome contains thousands of heterochromatin nanodomains (HNDs) marked by di- and trimethylation of histone H3 at lysine 9, which have a typical size of 3-10 nucleosomes. However, the (epi)genetic determinants of their location and boundaries are only partly understood. Here, we compare four HND types in mouse embryonic stem cells, that are defined by histone methylases SUV39H1/2 or GLP, transcription factor ADNP or chromatin remodeller ATRX. Based on a novel chromatin hierarchical lattice framework termed ChromHL, we are able to predict HND maps with singe-nucleotide resolution. We find that HND nucleation can be rationalized by DNA sequence specific protein binding to PAX3/9, ADNP and LINE1 repeats. Depending on type of microdomains, boundaries are determined either by CTCF binding sites or by nucleosome-nucleosome and nucleosome-HP1 interactions. Our new framework allows predicting how patterns of H3K9me2/3 and other chromatin nanodomains are established and changed in processes such as cell differentiation.

Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

EIGENTIME IDENTITY FOR WEIGHT-DEPENDENT WALK ON A CLASS OF WEIGHTED FRACTAL SCALE-FREE HIERARCHICAL-LATTICE NETWORKS

In this paper, we construct a class of weighted fractal scale-free hierarchical-lattice networks. Each edge in the network generates [Formula: see text] connected branches in each iteration process and assigns the corresponding weight. To reflect the global characteristics of such networks, we study the eigentime identity determined by the reciprocal sum of non-zero eigenvalues of normalized Laplacian matrix. By the recursive relationship of eigenvalues at two successive generations, we find the eigenvalues and their corresponding multiplicities for two cases when [Formula: see text] is even or odd. Finally, we obtain the analytical expression of the eigentime identity and the scalings with network size of the weighted scale-free networks.