Related papers: Fractal and Mathematical Morphology in Intricate C…
In this PhD thesis, a novel method to determine protein structures using chemical shifts is presented.
Learning meaningful protein representation is important for a variety of biological downstream tasks such as structure-based drug design. Having witnessed the success of protein sequence pretraining, pretraining for structural data which is…
To determine the 3D conformation of proteins is a necessity to understand their functions or interactions with other molecules. It is commonly admitted that, when proteins fold from their primary linear structures to their final 3D…
This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature…
Proteins are the basic building blocks of life. They usually perform functions by folding to a particular structure. Understanding the folding process could help the researchers to understand the functions of proteins and could also help to…
Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might…
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…
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 complete time-parameterized statistical model quantifying the divergent evolution of protein structures in terms of the patterns of conservation of their secondary structures is inferred from a large collection of protein 3D structure…
Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
We show that given $m$ proteins (or protein backbones, which are modeled as 3D polygonal chains each of length O(n)) the problem of protein local structure alignment under the discrete Fr\'{e}chet distance is as hard as Independent Set. So…
The paper presents a geometrical model for protein secondary structure analysis which uses only the positions of the $C_{\alpha}$-atoms. We construct a space curve connecting these positions by piecewise polynomial interpolation and…
Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
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…
In this paper we report on an algorithm for aligning multiple protein structures. The algorithm has been tested on a variety of inputs and it performs well in comparison to well-known algorithms for this problem.
As the number of solved protein structures increases, the opportunities for meta-analysis of this dataset increase too. Protein structures are known to be formed of domains; structural and functional subunits that are often repeated across…