Related papers: The geometry of chromatin
Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
Understanding the three-dimensional (3D) structure of the genome is essential for elucidating vital biological processes and their links to human disease. To determine how the genome folds within the nucleus, chromosome conformation capture…
Designing novel proteins with desired functions is crucial in biology and chemistry. However, most existing work focus on protein sequence design, leaving protein sequence and structure co-design underexplored. In this paper, we propose…
Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function…
A simple and surprisingly accurate description of spectral diffusion in deeply frozen globular proteins is constructed directly using the concept of ultrametricity of protein dynamics. Earlier the similar concept has been used for…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
Modeling of DNA-protein interactions is a complex process involving many important time and length scales. This can be facilitated through the use of coarse-grained models which reduce the number of degrees of freedom and allow efficient…
We calculate the mutual information function for each of the 24 chromosomes in the human genome. The same correlation pattern is observed regardless the individual functional features of each chromosome. Moreover, correlations of different…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Mapping conformational heterogeneity of macromolecules presents a formidable challenge to X-ray crystallography and cryo-electron microscopy, which often presume its absence. This has severely limited our knowledge of the conformations…
The paper investigates the problem of fitting protein complexes into electron density maps. They are represented by high-resolution cryoEM density maps converted into overlapping matrices and partly show a structure of a complex. The…
The discovery of molecules with tailored optoelectronic properties such as specific frequency and intensity of absorption or emission is a major challenge in creating next-generation organic light-emitting diodes (OLEDs) and photovoltaics.…
Modelising the translation errors by suitable mathematical operators in the crystal basis model of the genetic code and requiring that codons prone to be misread encode the same amino-acid, the main features of the organisation in…
To support comparative genomics, population genetics, and medical genetics, we propose that a reference genome should come with a scheme for mapping each base in any DNA string to a position in that reference genome. We refer to a…
The nucleotide sequence representation of DNA can be inadequate for resolving protein-DNA binding sites and regulatory substrates, such as those involved in gene expression and horizontal gene transfer. Considering that sequence-like…
Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural…
An approach that combines Self-Organizing maps, hierarchical clustering and network components is presented, aimed at comparing protein conformational ensembles obtained from multiple Molecular Dynamic simulations. As a first result the…
Understanding chromatin organization and dynamics is important since they crucially affect DNA functions. In this study, we investigate chromatin dynamics by statistically analyzing single-nucleosome movement in living human cells. Bi-modal…
We have presented the basic knowledge on the structure of molecules coding the genetic information, mechanisms of transfer of this information from DNA to proteins and phenomena connected with replication of DNA. In particular, we have…
Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological…