Related papers: $\theta$-curves in proteins
Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
An effective model for protein structures is important for the study of protein geometry, which, to a large extent, determine the functions of proteins. There are a number of approaches for modelling; one might focus on the conformation of…
For the vast majority of naturally occurring, small, single domain proteins folding is often described as a two-state process that lacks detectable intermediates. This observation has often been rationalized on the basis of a nucleation…
Understanding why some cellular components are conserved across species, while others evolve rapidly is a key question of modern biology. Here we demonstrate that in S. cerevisiae proteins organized in cohesive patterns of interactions are…
Protein structure prediction and folding are fundamental to understanding biology, with recent deep learning advances reshaping the field. Diffusion-based generative models have revolutionized protein design, enabling the creation of novel…
Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic…
Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures…
Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…
Some natural proteins display recurrent structural patterns. Despite being highly similar at the tertiary structure level, repetitions within a single repeat protein can be extremely variable at the sequence level. We propose a mathematical…
Exploring the structural topology of genome-based large-scale metabolic network is essential for investigating possible relations between structure and functionality. Visualization would be helpful for obtaining immediate information about…
Proteins have regular tertiary structures but irregular amino acid sequences. This made it very difficult to decode the structural information in the protein sequences. Here we demonstrate that many small alpha protein domains have hidden…
Background: Networks in different domains are characterized by similar global characteristics while differing in local structures. To further extend this concept, we investigated network regularities on a fine scale in order to examine the…
In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological…
The theory of elastic rods can be used to describe certain geometric and topological properties of the DNA molecules. A similar effective field theory approach was previously suggested to describe the conformations and dynamics of proteins.…
We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they…
Understanding the observed variability in the number of homologs of a gene is a very important, unsolved problem that has broad implications for research into co-evolution of structure and function, gene duplication, pseudogene formation…