Related papers: Computation of protein geometry and its applicatio…
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…
Structure-based drug design (SBDD) leverages the three-dimensional geometry of proteins to identify potential drug candidates. Traditional approaches, rooted in physicochemical modeling and domain expertise, are often resource-intensive.…
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…
A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…
Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields including protein structural modeling. Protein structural modeling, such as predicting…
Theory of multi-dimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
We discuss the problem of proteasomal degradation of proteins. Though proteasomes are important for all aspects of the cellular metabolism, some details of the physical mechanism of the process remain unknown. We introduce a stochastic…
Protein nanoparticles play pivotal roles in many areas of bionanotechnology, including drug delivery, vaccination and diagnostics. These technologies require control over the distinct particle morphologies that protein nanocontainers can…
In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function…
Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion…
Geometric deep learning has recently achieved great success in non-Euclidean domains, and learning on 3D structures of large biomolecules is emerging as a distinct research area. However, its efficacy is largely constrained due to the…
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.…
Protein structure prediction is a challenging and unsolved problem in computer science. Proteins are the sequence of amino acids connected together by single peptide bond. The combinations of the twenty primary amino acids are the…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
A novel approach for structure alignment is presented, where the key ingredients are: (1) An error function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. (2)…
For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…
Numerous cellular functions rely on protein$\unicode{x2013}$protein interactions. Efforts to comprehensively characterize them remain challenged however by the diversity of molecular recognition mechanisms employed within the proteome. Deep…
Understanding protein structure-function relationships is a key challenge in computational biology, with applications across the biotechnology and pharmaceutical industries. While it is known that protein structure directly impacts protein…
We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the…