Related papers: Reconstruction of protein structures from a vector…
The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different…
Much scientific enquiry across disciplines is founded upon a mechanistic treatment of dynamic systems that ties form to function. A highly visible instance of this is in molecular biology, where an important goal is to determine…
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.…
Crystal structure prediction is now playing an increasingly important role in discovery of new materials. Global optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) have been combined with first…
Determining protein structures at an atomic level remains a significant challenge in structural biology. We introduce $\texttt{RecCrysFormer}$, a hybrid model that exploits the strengths of transformers with the aim of integrating…
Protein structure representation is an important tool in structural biology. There exists different methods of representing the protein 3D structures and different biologists favor different methods based on the information they require.…
This work reports a new methodology aimed at describing characteristics of protein structural shapes, and suggests a framework in which to resolve or classify automatically such structures into known families. This new approach to protein…
Nucleic acid-based drugs like aptamers have recently demonstrated great therapeutic potential. However, experimental platforms for aptamer screening are costly, and the scarcity of labeled data presents a challenge for supervised methods to…
We introduce a new, simplified model of proteins, which we call protein metastructure. The metastructure of a protein carries information about its secondary structure and $\beta$-strand conformations. Furthermore, protein metastructure…
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…
We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three…
Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of…
We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition…
A unicellular map, or one-face map, is a graph embedded in an orientable surface such that its complement is a topological disk. In this paper, we give a new viewpoint to the structure of these objects, by describing a decomposition of any…
We introduce ProteinWorkshop, a comprehensive benchmark suite for representation learning on protein structures with Geometric Graph Neural Networks. We consider large-scale pre-training and downstream tasks on both experimental and…
Native contacts between residues could be predicted from the amino acid sequence of proteins, and the predicted contact information could assist the de novo protein structure prediction. Here, we present a novel pipeline of a residue…
Protein-protein interactions are fundamental to many biological processes. Experimental screens have identified tens of thousands of interactions and structural biology has provided detailed functional insight for select 3D protein…
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…
Combinatorial enumeration of various RNA secondary structures and protein contact maps, is of great interest for both combinatorists and computational biologists. Enumeration of protein contact maps has considerable difficulties due to the…
We present a novel technique of sampling the configurations of helical proteins. Assuming knowledge of native secondary structure, we employ assembly rules gathered from a database of existing structures to enumerate the geometrically…