Related papers: Discrete differential geometry of triangle tiles a…
We introduce a new model of proteins, which extends and enhances the traditional graphical representation by associating a combinatorial object called a fatgraph to any protein based upon its intrinsic geometry. Fatgraphs can easily be…
Predicting protein structure from amino acid sequence is one of the most important unsolved problems of molecular biology and biophysics.Not only would a successful prediction algorithm be a tremendous advance in the understanding of the…
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.…
Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as $\alpha$-helices and $\beta$-sheets. Secondary structure is characterized by the local rotational state of the protein…
Predicting the structure of a protein from its sequence is a cornerstone task of molecular biology. Established methods in the field, such as homology modeling and fragment assembly, appeared to have reached their limit. However, this year…
Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…
The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…
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 chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable…
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…
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…
We introduce a pipeline for representing a protein, or protein complex, as the union of signed distance functions (SDFs) by representing each atom as a sphere with the appropriate radius. While this idea has been used previously as a way to…
This chapter gives a graceful introduction to problem of protein three- dimensional structure prediction, and focuses on how to make structural sense out of a single input sequence with unknown structure, the 'query' or 'target' sequence.…
Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein function or structure. Existing approaches usually pretrain protein language models on a large number of unlabeled amino acid…
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…
Protein structure tokenization converts 3D structures into discrete or vectorized representations, enabling the integration of structural and sequence data. Despite many recent works on structure tokenization, the properties of the…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
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…
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
Deep Learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in…