Related papers: Representing Rod-Shaped Protein 3D Structures in C…
Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper,…
Current AI-assisted protein design mainly utilizes protein sequential and structural information. Meanwhile, there exists tremendous knowledge curated by humans in the text format describing proteins' high-level functionalities. Yet,…
A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our…
Protein structures and functions are determined by a contiguous arrangement of amino acid sequences. Designing novel protein sequences and structures with desired geometry and functions is a complex task with large state spaces. Here we…
Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…
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…
Identification of critical residues of a protein is actively pursued, since such residues are essential for protein function. We present three ways of recognising critical residues of an example protein, the evolution of which is tracked…
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…
In protein structure analysis, the accurate characterization of secondary structure elements is crucial for understanding protein function and dynamics. This paper presents a software system designed for the comprehensive analysis of the…
Recently developed deep learning techniques have significantly improved the accuracy of various speech and image recognition systems. In this paper we adapt some of these techniques for protein secondary structure prediction. We first train…
The spike protein (SP) of SARS-CoV-2 is the major molecular target for making diagnostic tests, vaccines, and therapeutic development. We used a combination of transmission electron microscopy (TEM) and surface enhanced Raman microscopy…
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…
We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework.…
Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural…
Motivation: Human cancer is caused by the accumulation of somatic mutations in tumor suppressors and oncogenes within the genome. In the case of oncogenes, recent theory suggests that there are only a few key "driver" mutations responsible…
We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced…
In the first part of the book, we classify the automorphic representations of {\rm GSp}(2) which are invariant under tensor product with a given quadratic id\`ele class character, via the lifting of automorphic representations of twisted…
Structure determination is key to understanding protein function at a molecular level. Whilst significant advances have been made in predicting structure and function from amino acid sequence, researchers must still rely on expensive,…
By providing new insights into the distribution of a protein's torsion angles, recent statistical models for this data have pointed the way to more efficient methods for protein structure prediction. Most current approaches have…
Amino acid sequence portrays most intrinsic form of a protein and expresses primary structure of protein. The order of amino acids in a sequence enables a protein to acquire a particular stable conformation that is responsible for the…