Related papers: Computation of protein geometry and its applicatio…

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…

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…

Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a…

The asymmetry in the shapes of folded and unfolded states are probed using two parameters, one being a measure of the sphericity and the other that describes the shape. For the folded states, whose interiors are densely packed, the radii of…

This chapter deals with approaches for protein three-dimensional structure prediction, starting out from a single input sequence with unknown struc- ture, the 'query' or 'target' sequence. Both template based and template free modelling…

In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…

Learning on 3D structures of large biomolecules is emerging as a distinct area in machine learning, but there has yet to emerge a unifying network architecture that simultaneously leverages the graph-structured and geometric aspects of the…

Identifying novel functional protein structures is at the heart of molecular engineering and molecular biology, requiring an often computationally exhaustive search. We introduce the use of a Deep Convolutional Generative Adversarial…

After AlphaFold won the Nobel Prize, protein prediction with deep learning once again became a hot topic. We comprehensively explore advanced deep learning methods applied to protein structure prediction and design. It begins by examining…

As protein folding is a NP-complete problem, artificial intelligence tools like neural networks and genetic algorithms are used to attempt to predict the 3D shape of an amino acids sequence. Underlying these attempts, it is supposed that…

Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein's linear sequence of amino acids folds into its specific three dimensional structure.This structure is…

We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…

Structure-based drug design uses three-dimensional geometric information of macromolecules, such as proteins or nucleic acids, to identify suitable ligands. Geometric deep learning, an emerging concept of neural-network-based machine…

Protein folding is the intricate process by which a linear sequence of amino acids self-assembles into a unique three-dimensional structure. Protein folding kinetics is the study of pathways and time-dependent mechanisms a protein undergoes…

We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details…

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.…

Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…

AI algorithms have proven to be excellent predictors of protein structure, but whether and how much these algorithms can capture the underlying physics remains an open question. Here, we aim to test this question using the Alphafold2 (AF)…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…