Related papers: The Ramachandran number: an order parameter for pr…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
In this paper we experiment with using neural network structures to predict a protein's secondary structure ({\alpha} helix positions) from only its primary structure (amino acid sequence). We implement a fully connected neural network…
Predicting protein structure from amino acid sequence is one of the most important unsolved problems of molecular biology and biophysics.Not only would a successful prediction algorithm be a tremendous advance in the understanding of the…
Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is…
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…
A protein is traditionally visualised as a piecewise linear discrete curve, and its geometry is conventionally characterised by the extrinsically determined Ramachandran angles. However, a protein backbone has also two independent intrinsic…
The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters…
The protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature $\kappa(s)$ and torsion $\tau(s)$ both expressed as a function of arc length s. It is shown that the…
Protein one-dimensional (1D) structures such as secondary structure and contact number provide intuitive pictures to understand how the native three-dimensional (3D) structure of a protein is encoded in the amino acid sequence. However, it…
The correct prediction of protein secondary structures is one of the key issues in predicting the correct protein folded shape, which is used for determining gene function. Existing methods make use of amino acids properties as indices to…
The Gene or DNA sequence in every cell does not control genetic properties on its own; Rather, this is done through translation of DNA into protein and subsequent formation of a certain 3D structure. The biological function of a protein is…
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…
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…
The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein…
Structural relationships among proteins are important in the study of their evolution as well as in drug design and development. The protein 3D structure has been shown to be effective with respect to classifying proteins. Prior work has…
Proteins are essential for life, and their structure determines their function. The protein secondary structure is formed by the folding of the protein primary structure, and the protein tertiary structure is formed by the bending and…
In this study, the distributions of protein structure classes (or folding types) of experimentally determined structures from a legacy dataset and a comprehensive database (SCOP) are modeled precisely with geometric constructs such as…
A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the…
The structures of proteins exhibit secondary elements composed of helices and loops. Comparison of several water-only hydrophobicity scales with the functionalities of two repeat proteins shows that these secondary elements possess…
The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in 3-dimensional space and characterizes it by curvature kappa and torsion tau as a function of arc length s, was applied on 77…