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An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
Motivation: Assessing the match between two biomolecular structures is at the heart of structural analyses such as superposition, alignment and docking. These tasks are typically solved with specialized structure-matching techniques…
Motivation: Protein folding is a dynamic process during which a protein's amino acid sequence undergoes a series of 3-dimensional (3D) conformational changes en route to reaching a native 3D structure; the resulting 3D structural…
Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design.…
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…
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…
Proteins perform much of the work in living organisms, and consequently the development of efficient computational methods for protein representation is essential for advancing large-scale biological research. Most current approaches…
Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive-zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in…
A new method for the Automated Protein Structure Analysis (APSA) is derived, which simplifies the protein backbone to a smooth curve in 3-dimensional space. For the purpose of obtaining this smooth line each amino acid is represented by its…
Crystallography may be the gold standard of protein structure determination, but obtaining the necessary high-quality crystals is also in some ways akin to prospecting for the precious metal. The tools and models developed in soft matter…
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…
The Automated Protein Structure Analysis (APSA) method is used for the classification of supersecondary structures. Basis for the classification is the encoding of three-dimensional (3D) residue conformations into a 16-letter code (3D-1D…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
We consider a generic representation problem of internal coordinates (bond lengths, valence angles, and dihedral angles) and their transformation to 3-dimensional Cartesian coordinates of a biomolecule. We show that 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…
Identification and alignment of three-dimensional folding of proteins may yield useful information about relationships too remote to be detected by conventional methods, such as sequence comparison, and may potentially lead to prediction of…
Protein structure determination has long been one of the primary challenges of structural biology, to which deep machine learning (ML)-based approaches have increasingly been applied. However, these ML models generally do not incorporate…
Various structures in human physiology follow a treelike morphology, which often expresses complexity at very fine scales. Examples of such structures are intrathoracic airways, retinal blood vessels, and hepatic blood vessels. Large…
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…
AlphaFold 3 represents a transformative advancement in computational biology, enhancing protein structure prediction through novel multi-scale transformer architectures, biologically informed cross-attention mechanisms, and geometry-aware…