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Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their…
Local protein structure analysis is informative to protein structure analysis and has been used successfully in protein structure prediction and others. Proteins have recurring structural features, such as helix caps and beta turns, which…
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we…
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…
As protein folding is a NP-complete problem, artificial intelligence tools like neural networks and genetic algorithms are used to attempt to predict the 3D shape of an amino acids sequence. Underlying these attempts, it is supposed that…
An increasing number of proteins are being discovered with a remarkable and somewhat surprising feature, a knot in their native structures. How the polypeptide chain is able to knot itself during the folding process to form these highly…
Context-dependent nature of biological phenomena are well documented in every branch of biology. While there have been few previous attempts to (implicitly) model various facets of biological context-dependence, a formal and general…
Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow…
We present a new lattice model for proteins that incorporates a tube-like anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.
We review theoretical approaches, experiments and numerical simulations that have been recently proposed to investigate the folding problem in single-domain proteins. From a theoretical point of view, we emphasize the energy landscape…
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learnt how to extract this information so as to predict the detailed, biological active, three-dimensional structure of…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
Predicting protein secondary structure using lattice model is one of the most studied computational problem in bioinformatics. Here secondary structure or three dimensional structure of protein is predicted from its amino acid sequence.…
Woven shell structures are beneficial for applications requiring lightweight, damage resilience, and design tunability, such as in wearable devices, soft robotics, and aerospace systems. A fundamental component of woven structures is the…
Proteins contain a large fraction of regular, repeating conformations, called secondary structure. A simple, generic definition of secondary structure is presented which consists of measuring local correlations along the protein chain.…
Mechanical stretching of six proteins is studied through molecular dynamics simulations. The model is Go-like, with Lennard-Jones interactions at native contacts. Low temperature unfolding scenarios are remarkably complex and sensitive to…
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…
Protein-protein binding enables orderly and lawful biological self-organization, and is therefore considered a miracle of nature. Protein-protein binding is steered by electrostatic forces, hydrogen bonding, van der Waals force, and…