Related papers: Geometrical comparison of two protein structures u…
This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the discrete curve namely the hop distance, the discrete…
Classification of proteins based on their structure provides a valuable resource for studying protein structure, function and evolutionary relationships. With the rapidly increasing number of known protein structures, manual and…
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…
Structural assessment of biomolecular complexes is vital for translating molecular models into functional insights, shaping our understanding of biology and aiding drug discovery. However, current structure-based scoring functions often…
This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a…
Recent developments in deep learning-based methods demonstrated its potential to predict the 3D protein structures using inputs such as protein sequences, Cryo-Electron microscopy (Cryo-EM) images of proteins, etc. However, these methods…
Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects, however, for most…
Protein-ligand scoring is a central component of structure-based drug design, underpinning molecular docking, virtual screening, and pose optimization. Conventional physics-based energy functions are often computationally expensive,…
The contributions of this thesis stem from technology developed to analyse large sets of volumetric images in terms of atom-like features extracted in 3D image space, following SIFT algorithm in 2D image space. New feature properties are…
We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be…
In this paper we address the problem of protein classification starting from a multi-view 2D representation of proteins. From each 3D protein structure, a large set of 2D projections is generated using the protein visualization software…
We show that the dimension of the geometric shape formed by the phenomenologically valid points inside a multi-dimensional parameter space can be used to characterise different new physics models and to define a quantitative measure for the…
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it…
The correct prediction of protein secondary structures is one of the key issues in predicting the correct protein folded shape, which is used for determining gene function. Existing methods make use of amino acids properties as indices to…
Proteins are biomolecules of life. They fold into a great variety of three-dimensional (3D) shapes. Underlying these folding patterns are many recurrent structural fragments or building blocks (analogous to `LEGO bricks'). This paper…
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 protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature $\kappa(s)$ and torsion $\tau(s)$ both expressed as a function of arc length s. It is shown that the…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer…
Experimental determination of protein function is resource-consuming. As an alternative, computational prediction of protein function has received attention. In this context, protein structural classification (PSC) can help, by allowing for…