相关论文: Intricate Knots in Proteins: Function and Evolutio…
We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce…
The idea that structural disorder might be a novel mechanism of protein interaction is widespread in the Literature, although the number of statistically significant structural studies supporting this is surprisingly low. At variance with…
Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can…
The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological…
Metamorphic proteins like Lymphotactin are a notable exception of the empirical principle that structured natural proteins possess a unique three dimensional structure. In particular, the human chemokine lymphotactin protein (Ltn) exists in…
In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our…
Proteins perform a large variety of functions in living organisms, thus playing a key role in biology. As of now, available learning algorithms to process protein data do not consider several particularities of such data and/or do not scale…
The Knot Entropy Conjecture states that the exponential growth rate of the number of $n$-edge lattice polygons with knot-type $K$ is the same as that for unknot polygons. Moreover, the next order growth follows a power law in $n$ with an…
In this paper we analyze the vibrational spectra of a large ensemble of non-homologous protein structures by means of a novel tool, that we coin the Hierarchical Network Model (HNM). Our coarse-grained scheme accounts for the intrinsic…
This paper, to be regularly updated, lists those prime knots with the fewest possible number of crossings for which values of basic knot invariants, such as the unknotting number or the smooth 4-genus, are unknown. This list is being…
Lattice-model simulations and experiments of some small proteins suggest that folding is essentially controlled by a few conserved contacts. Residues of these conserved contacts form the minimum set of native contacts needed to ensure…
The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify…
It is becoming clear that traditional, single-structure models of proteins are insufficient for understanding their biological function. Here, we outline one method for inferring, from experiments, not only the most common structure a…
One of the most puzzling and unsolved challenges in molecular biology is understanding how proteins fold. Despite having advanced predictive tools that can accurately estimate the native structures of proteins, we still lack a comprehensive…
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local" and, for several ring polymer models, we provide both theoretical and numerical…
Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance…
Intrinsically disordered proteins are fascinating the community of protein science since the last decade, at least. There is a well-established line of research that intends to reveal the crucial role played by intrinsically disordered…
The subject of this report is the dynamics of elastic system in conjunction with hydrogen bonds of the DNA. We draw attention to the draw-back of the familiar rod model of the DNA, and make a case of constructing models that could…
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…
A ribbon is, intuitively, a smooth mapping of an annulus $S^1 \times I$ in 3-space having constant width $\varepsilon$. This can be formalized as a triple $(x,\varepsilon, \mathbf{u})$ where $x$ is smooth curve in 3-space and $\mathbf{u}$…