Related papers: Embedding protein 3D-structures in a cubic lattice…

In a recent paper by the same authors, we provided a theoretical foundation for the component-by-component (CBC) construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic…

Steric clashes pose a challenge when exploring dense protein systems using conventional explicit-chain methods. A minimal example is a single lattice protein confined on a minimal grid, with no free sites. Finding its minimum energy is a…

We present a 3D stylization algorithm that can turn an input shape into the style of a cube while maintaining the content of the original shape. The key insight is that cubic style sculptures can be captured by the as-rigid-as-possible…

Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible…

We explore the potential application of quantum annealing to address the protein structure problem. To this end, we compare several proposed ab initio protein folding models for quantum computers and analyze their scaling and performance…

Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design.…

Silicon is an excellent material for microelectronics and integrated photonics with untapped potential for mid-IR optics. Despite broad recognition of the importance of the third dimension, current lithography methods do not allow…

I propose a mathematical framework for embedding an unshaped discrete lattice $L$ on a smooth manifold $M$. This framework simplifies complex concepts in pure mathematics and physics by connecting discrete lattice structures with continuous…

We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…

An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger…

Learning from 3D protein structures has gained wide interest in protein modeling and structural bioinformatics. Unfortunately, the number of available structures is orders of magnitude lower than the training data sizes commonly used in…

Structural templates are 3D signatures representing protein functional sites, such as ligand binding cavities, metal coordination motifs or catalytic sites. Here we explore methods to generate template libraries and algorithms to query…

We present a new lattice model for proteins that incorporates a tube-like anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.

Prediction of ligand binding sites of proteins is a fundamental and important task for understanding the function of proteins and screening potential drugs. Most existing methods require experimentally determined protein holo-structures as…

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…

The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…

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…

Many quantum computing platforms are based on a two-dimensional physical layout. Here we explore a concept called looped pipelines which permits one to obtain many of the advantages of a 3D lattice while operating a strictly 2D device. The…

The functionality of proteins is related to their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube…

Deep Learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in…