Related papers: Geometric and physical considerations for realisti…
Many types of peripheral and transmembrane proteins can sense and generate membrane curvature. Laterally isotropic proteins and crescent proteins with twofold rotational symmetry, such as Bin/Amphiphysin/Rvs superfamily proteins, have been…
Proteins have regular tertiary structures but irregular amino acid sequences. This made it very difficult to decode the structural information in the protein sequences. Here we demonstrate that many small alpha protein domains have hidden…
Proteins are intricate molecular machines whose complexity arises from the heterogeneity of the amino acid building blocks and their dynamic network of many-body interactions. These nanomachines gain function when put in the context of a…
We review algorithms for protein design in general. Although these algorithms have a rich combinatorial, geometric, and mathematical structure, they are almost never covered in computer science classes. Furthermore, many of these algorithms…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
Fundamental questions about the role of the quaternary structures are addressed using a statistical mechanics off-lattice model of a dimer protein. The model, in spite of its simplicity, captures key features of the monomer-monomer…
Predicting the structure of a protein from its sequence is a cornerstone task of molecular biology. Established methods in the field, such as homology modeling and fragment assembly, appeared to have reached their limit. However, this year…
The desirable properties when constructing collections of subspaces often include the algebraic constraint that the projections onto the subspaces yield a resolution of the identity like the projections onto lines spanned by vectors of an…
Proteins are miniature machines whose function depends on their three-dimensional (3D) structure. Determining this structure computationally remains an unsolved grand challenge. A major bottleneck involves selecting the most accurate…
Protein structure is central to biological function, and enabling multimodal protein models requires joint reasoning over sequence, structure, and function. A key barrier is the lack of principled protein structure tokenizers (PSTs):…
The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein…
Many researches have been working on the protein folding problem from more than half century. Protein folding is indeed one of the major unsolved problems in science. In this work, we discuss a model for the simulation of protein…
Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native…
Interactive molecular graphics applications facilitate analysis of three dimensional protein structures. Naturally, non-interactive 2-D snapshots of the protein structures do not convey the same level of geometric detail. Several 2-D…
The choice of structural resolution is a fundamental aspect of protein modelling, determining the balance between descriptive power and interpretability. Although atomistic simulations provide maximal detail, much of this information is…
We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C$_\alpha$ carbon of a protein backbone, and for this we develop new visualization techniques to…
We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic aminoacid-aminoacid potential is Lennard Jones for the native contacts and…
A model to describe the mechanism of conformational dynamics in secondary protein based on matter interactions is proposed. The approach deploys the lagrangian method by imposing certain symmetry breaking. The protein backbone is initially…
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…
Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are…