Related papers: Topological Solitons and Folded Proteins
Protein molecules can be approximated by discrete polygonal chains of amino acids. Standard topological tools can be applied to the smoothening of the polygons to introduce a topological classification of proteins, for example, using the…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
Apart from the knots formed by the main-chain, the proteins can form numerous topological structures, when included the covalent and ion-mediated interactions. In this work, we define the protein non-trivial $\theta$-curves and identify 7…
Coupled solitary waves in optics literature, are coined vector solitons to reflect their particle--like nature that remains intact even after mutual collisions. They are born from a nonlinear change in the refractive index of an optical…
Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small fast folding proteins. To investigate the extent of the…
The intrinsic property of proteins to form structural motifs such as alpha-helices and beta-sheets leads to a complex phase behavior in which proteins can assemble into various types of aggregates including crystals, liquidlike phases of…
We present a method to investigate the kinetics of protein folding on a long time-scale and the dynamics underlying the formation of secondary and tertiary structures during the entire reaction. The approach is based on the formal analogy…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended timescales. Our methodology involves simulating proteins with molecular…
Understanding the mechanism of protein secondary structure formation is an essential part of protein-folding puzzle. Here we describe a simple model for the formation of the $\beta$-hairpin, motivated by the fact that folding of a…
The paper presents a geometrical model for protein secondary structure analysis which uses only the positions of the $C_{\alpha}$-atoms. We construct a space curve connecting these positions by piecewise polynomial interpolation and…
Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in…
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…
We introduce a novel generalization of the discrete nonlinear Schr\"odinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both…
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…
This paper deepens into the analysis of the protein secondary structure using Frenet frame to describe the curvature and torsion of the discrete curve formed by the protein $\alpha$-carbons. We show how a simple criterion based on the…
Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there isn't a first-principle model to explain this different behaviour. We exploit the network properties of protein structures by introducing novel…
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…
Nearly a quarter of genomic sequences and almost half of all receptors that are likely to be targets for drug design are integral membrane proteins. Understanding the detailed mechanisms of the folding of membrane proteins is a largely…
Bacterial genomes are partitioned into kilobases long domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbours. This is made possible by proteins…