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The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Motivation: Thanks to the recent advances in structural biology, nowadays three-dimensional structures of various proteins are solved on a routine basis. A large portion of these contain structural repetitions or internal symmetries. To…
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 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…
Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the…
Studying the function of proteins is important for understanding the molecular mechanisms of life. The number of publicly available protein structures has increasingly become extremely large. Still, the determination of the function of a…
Tokenization is a promising path to multi-modal models capable of jointly understanding protein sequences, structure, and function. Existing protein structure tokenizers create tokens by pooling information from local neighborhoods, an…
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Emerging high-throughput technologies have led to a deluge of putative non-coding RNA (ncRNA) sequences identified in a wide variety of organisms. Systematic characterization of these transcripts will be a tremendous challenge. Homology…
Homologous gene shuffling between DNA promotes genetic diversity and is an important pathway for DNA repair. For this to occur, homologous genes need to find and recognize each other. However, despite its central role in homologous…
Accurately assigning folds for divergent protein sequences is a major obstacle to structural studies and underlies the inverse protein folding problem. Herein, we outline our theories for fold-recognition in the "twilight-zone" of sequence…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Identifying driver genes is crucial for understanding oncogenesis and developing targeted cancer therapies. Driver discovery methods using protein or pathway networks rely on traditional network science measures, focusing on nodes, edges,…
Despite the constant evolution of similarity searching research, it continues to face the same challenges stemming from the complexity of the data, such as the curse of dimensionality and computationally expensive distance functions.…
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…
Proteins are macromolecules that perform essential functions in all living organisms. Designing novel proteins with specific structures and desired functions has been a long-standing challenge in the field of bioengineering. Existing…
Protein sequences are abundant in repeating segments, both as exact copies and as approximate segments with mutations. These repeats are important for protein structure and function, motivating decades of algorithmic work on repeat…