Related papers: Computation of protein geometry and its applicatio…
Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here a novel protein model capable of simultaneously provide quantitative protein design and…
Folded proteins have a modular assembly. They are constructed from regular secondary structures like alpha-helices and beta-strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe…
Proteins are miniature machines whose function depends on their three-dimensional (3D) structure. Determining this structure computationally remains an unsolved grand challenge. A major bottleneck involves selecting the most accurate…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
A novel parallel simulation algorithm on the GPU, implemented in CUDA and C++, is presented for the simulation of Brownian particles that display excluded volume repulsion and interact with long and short range forces. When an explicit…
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how…
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…
An effective model for protein structures is important for the study of protein geometry, which, to a large extent, determine the functions of proteins. There are a number of approaches for modelling; one might focus on the conformation of…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…
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…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only $C_\alpha$ or backbone atoms are attractive because they enable efficient search of…
A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a…
We review algorithms for protein design in general. Although these algorithms have a rich combinatorial, geometric, and mathematical structure, they are almost never covered in computer science classes. Furthermore, many of these algorithms…
It is important that a spatial network's construction algorithm reproduces the structural properties of the original physical embedding. Here, we assess the Delaunay triangulation as a spatial network construction algorithm for seven…
Determining the absolute configuration of gas-phase molecules in position-space has long been a fundamental challenge in molecular physics. While strong-field-induced Coulomb explosion imaging (CEI) has emerged as a powerful tool for…
We combine a conventional harmonic analysis of vibrations in a one-atomic model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the structure. ``Structure potentials'' (tetragonality, sphericity or perfectness) are…
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…
The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein…