Related papers: Topology, Geometry, and Stability: Protein Folding…
A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein…
Proteins have evolved through mutations, amino acid substitutions, since life appeared on Earth, some 109 years ago. The study of these phenomena has been of particular significance because of their impact on protein stability, function,…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…
The native state structures of globular proteins are stable and well-packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry…
It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other…
Natural protein sequences somehow encode the structural forms that these molecules adopt. Recent developments in structure-prediction are agnostic to the mechanisms by which proteins fold and represent them as static objects. However, the…
A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native…
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…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural…
Scaling of folding properties of proteins is studied in a toy system -- the lattice Go model with various two- and three- dimensional geometries of the maximally compact native states. Characteristic folding times grow as power laws with…
The functionality of proteins is related to their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube…
We propose a protein model based on a hierarchy of constraints that force the protein to follow certain pathways when changing conformation. The model exhibits a first order phase transition, cooperativity and is exactly solvable. It also…
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…
The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
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 the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a…
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…