Related papers: The geometry of chromatin
The importance of the notion of symmetry in physics is well established: could it also be the case for the genetic code? In this spirit, a model for the Genetic Code based on continuous symmetries and entitled the "Crystal Basis Model" has…
The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be…
One-dimensional arrays of nucleosomes (DNA-bound histone octamers separated by stretches of linker DNA) fold into higher-order chromatin structures which ultimately make up eukaryotic chromosomes. Chromatin structure formation leads to…
Proteins are central to biological systems, participating as building blocks across all forms of life. Despite advancements in understanding protein functions through protein sequence analysis, there remains potential for further…
An approach based on using the idea of distinguished coding phase in explicit form for identification of protein-coding regions (exons) in whole genome has been proposed. For several genomes an optimal window length for averaging GC-content…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
Dynamics of nucleosomes, the building blocks of the chromatin, has crucial effects on expression, replication and repair of genomes in eukaryotes. Beside constant movements of nucleosomes by thermal fluctuations, ATP-dependent chromatin…
Researchers in the field of DNA-based chaotic cryptography have recently proposed a set of novel and efficient image encryption algorithms. In this paper, we present a comprehensive summary of those techniques, which are available in the…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
The huge amount of data acquired by high-throughput sequencing requires data reduction for effective analysis. Here we give a clustering algorithm for genome-wide open chromatin data using a new data reduction method. This method regards…
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…
While the structure of chromatin has been studied in great detail on length scales below 30 nm, amazingly little is known about the higher-order folding motifs of chromatin in interphase. Recent experiments give evidence that the folding…
A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick…
Understanding chromatin dynamics across multiple spatiotemporal scales requires models that reconcile biological specificity with physics-based interactions and computational tractability. We present a modular, recognition-enabled…
The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…
Each human genome is a 3 billion base pair set of encoding instructions. Decoding the genome using deep learning fundamentally differs from most tasks, as we do not know the full structure of the data and therefore cannot design…
The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…
We present a simple physical model which demonstrates that the native state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…