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The interconnected processes of protein folding, mutations, epistasis, and evolution have all been the subject of extensive analysis throughout the years due to their significance for structural and evolutionary biology. The origin…
Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function…
The primitive data for deducing the Miyazawa-Jernigan contact energy or BLOSUM score matrix consists of pair frequency counts. Each amino acid corresponds to a conditional probability distribution. Based on the deviation of such conditional…
Many fundamental biological processes are regulated by protein-DNA complexes called {\it synaptosomes}, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation remain not…
Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…
Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have…
Starting from linear chains of amino acids, the spontaneous folding of proteins into their elaborate three-dimensional structures is one of the remarkable examples of biological self-organization. We investigated native state structures of…
Protein aggregates exhibit diverse morphology, exemplified by amyloid fibrils, gel-like structures, and liquid-like condensates. Differences in the morphologies in identical proteins play important functional roles in several diseases.…
Genomes evolve as modules. In prokaryotes (and some eukaryotes), genetic material can be transferred between species and integrated into the genome via homologous or illegitimate recombination. There is little reason to imagine that the…
The genetic blueprint for the essential functions of life is encoded in DNA, which is translated into proteins -- the engines driving most of our metabolic processes. Recent advancements in genome sequencing have unveiled a vast diversity…
Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at…
The sequence of amino acids in a protein is believed to determine its native state structure, which in turn is related to the functionality of the protein. In addition, information pertaining to evolutionary relationships is contained in…
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…
Modern Protein Language Models (PLMs) apply transformer-based model architectures from natural language processing to biological sequences, predicting a variety of protein functions and properties. However, protein language has key…
Protein function is driven by cohesive substructures, such as catalytic triads, binding pockets, and structural motifs, that occupy only a small fraction of a protein's residues. Yet existing pipelines built on protein encoders do not model…
Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory,…
We review the development of thermodynamic protein hydropathic scaling theory, starting from backgrounds in mathematics and statistical mechanics, and leading to biomedical applications. Darwinian evolution has organized each protein family…
Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show…
Apart from the knots formed by the main-chain, the proteins can form numerous topological structures, when included the covalent and ion-mediated interactions. In this work, we define the protein non-trivial $\theta$-curves and identify 7…
Each and every biological function in living organism happens as a result of protein-protein interactions.The diseases are no exception to this. Identifying one or more proteins for a particular disease and then designing a suitable…