Related papers: Sequence determines degree of knottedness in a coa…
A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable.…
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…
We have exactly enumerated all sequences and conformations of HP proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the hydrophobic-polar (HP) model, where only two types of monomers are…
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence…
Entangled knots form spontaneously in flexible filaments, yet the influence of the surrounding environment on this process is poorly understood. Here we demonstrate that free-moving particles act as kinetic catalysts for spontaneous…
Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Go model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a…
We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and…
In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against…
The hydrophobic/polar HP model on the square lattice has been widely used to investigate basics of protein folding. In the cases where all designing sequences (sequences with unique ground states) were enumerated without restrictions on the…
We simulate the evolution of a protein-like sequence subject to point mutations, imposing conservation of the ground state, thermodynamic stability and fast folding. Our model is aimed at describing neutral evolution of natural proteins. We…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that…
We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a…
Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
Approximately 1% of the known protein structures display knotted configurations in their native fold but their function is not understood. It has been speculated that the entanglement may inhibit mechanical protein unfolding or transport,…
Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a…
Protein structures are a very special class among all possible structures. It was suggested that a ``designability principle'' plays a crucial role in nature's selection of protein sequences and structures. Here we provide a theoretical…
Knotted molecules occur naturally and are designed by scientists to gain special biological and material properties. Understanding and utilizing knotting require efficient methods to recognize and generate knotted structures, which are…