Related papers: Planar diagrams from optimization
Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have…
We study a heteropolymer model with random contact interactions introduced some time ago as a simplified model for proteins. The model consists of self-avoiding walks on the simple cubic lattice, with contact interactions between nearest…
Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be…
Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple…
The tube model is a central concept in polymer physics, and allows to reduce the complex many-filament problem of an entangled polymer solution to a single filament description. We investigate the probability distribution function of…
The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical…
Protein chains of the (FG)$_n$ ($n \simeq$ 300) type cap the cytoplasmatic side of the nucleopore complex, which connects the nucleus to the remainder of an eukaryotic cell. We study the properties of three fundamental polymer models that…
We present an analytical theory for heteropolymer deformation, as exemplified experimentally by stretching of single protein molecules. Using a mean-field replica theory, we determine phase diagrams for stress-induced unfolding of typical…
We present an exactly solvable model of a Gaussian (flexible) polymer chain in a quenched random medium. This is the case when the random medium obeys very long range quadratic correlations. The model is solved in $d$ spatial dimensions…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
Random heteropolymers do not display the typical equilibrium properties of globular proteins, but are the starting point to understand the physics of proteins and, in particular, to describe their non-native states. So far, they have been…
We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…
We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number,…
We propose a coarse-grained model for polymer chains and polymer networks based on the meso-scale dynamics. The model takes the internal degrees of freedom of the constituent polymer chains into account using memory functions and colored…
We investigate the time evolution of the heteropolymer model introduced by Iori, Marinari and Parisi to describe some of the features of protein folding mechanisms. We study how the (folded) shape of the chain evolves in time. We find that…
We propose new polymer models for Monte Carlo simulation and apply them to a polymer chain confined in a relatively thin box which has both curved and flat sides, and show that either an ideal or an excluded-volume chain spends more time in…
Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long…
We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The…
In-vivo DNA organization at large length scales ($\sim 100nm$) is highly debated and polymer models have proved useful to understand the principle of DNA-organization. Here, we show that $<2$% cross-links at specific points in a ring…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…