Related papers: II. Geometrical framework for thinking about globu…
We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry.…
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…
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…
Protein structure is generally conceptualized as the global arrangement or of smaller, local motifs of helices, sheets, and loops. These regular, recurring secondary structural elements have well-understood and standardized definitions in…
The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…
We present a simple physical model which demonstrates that the native state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and…
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…
A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed…
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…
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…
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…
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…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
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.…
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…
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,…
Proteins are linear chain molecules that play a central role in life and health. Protein native state folds are modular assemblies of space-filling building blocks of {\alpha}-helices, \{beta}-sheets and tight turns. Here we deduce the…
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…
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…