Related papers: III. Geometrical framework for thinking about glob…
This paper presents a method of reconstruction a primary structure of a protein that folds into a given geometrical shape. This method predicts the primary structure of a protein and restores its linear sequence of amino acids in the…
This survey for mathematicians summarizes several works by the author on protein geometry and protein function with applications to viral glycoproteins in general and the spike glycoprotein of the SARS-CoV-2 virus in particular. Background…
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.…
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):…
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…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
We study a minimal extension of the worm-like chain to describe polypeptides having alpha-helical secondary structure. In this model presence/absence of secondary structure enters as a scalar variable that controls the local chain bending…
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…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
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…
Intricate comparison between two given tertiary structures of proteins is as important as the comparison of their functions. Several algorithms have been devised to compute the similarity and dissimilarity among protein structures. But,…
The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral…
Since proteins carry out biological processes by interacting with other proteins, analyzing the structure of protein-protein interaction (PPI) networks could explain complex biological mechanisms, evolution, and disease. Similarly, studying…
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a…
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…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold…
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by…
The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete…
Predicting protein secondary structures such as alpha helices, beta sheets, and coils from amino acid sequences is essential for understanding protein function. This work presents a transformer-based model that applies attention mechanisms…