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Accurate physical modeling with 3D-printing techniques could lead to new approaches to study structure and dynamics of biological systems complementing computational methods. Computational biology has become an important part of research…

Recent advancements in machine learning techniques for protein folding motivate better results in its inverse problem -- protein design. In this work we introduce a new graph mimetic neural network, MimNet, and show that it is possible to…

The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction,…

Protein design has the potential to revolutionize biotechnology and medicine. While most efforts have focused on proteins with well-defined structures, increased recognition of the functional significance of intrinsically disordered…

This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…

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…

A concrete analysis of the general properties and numerical characteristics of different atomic and nuclear shell systems and subnuclear particles is carried out on the base of the solution scheme for an introduced in part I physical graph…

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…

In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…

Is there a foreign language describing protein sequences and structures simultaneously? Protein structures, represented by continuous 3D points, have long posed a challenge due to the contrasting modeling paradigms of discrete sequences. We…

In this work we propose a geometric view of the azeotropy problem, using some simplified models. We demonstrate that the occurrence of azeotropes in binary mixtures can be viewed-geometrically-as the intersection of curves in the plane (for…

Machine learning in drug discovery has been focused on virtual screening of molecular libraries using discriminative models. Generative models are an entirely different approach that learn to represent and optimize molecules in a continuous…

The internal dynamics of strongly interacting systems and that of biomolecules such as proteins display several important analogies, despite the huge difference in their characteristic energy and length scales. For example, in all such…

A protein's function depends critically on its conformational ensemble, a collection of energy weighted structures whose balance depends on temperature and environment. Though recent deep learning (DL) methods have substantially advanced…

The key finding in the DNA double helix model is the specific pairing or binding between nucleotides A-T and C-G, and the pairing rules are the molecule basis of genetic code. Unfortunately, no such rules have been discovered for proteins.…

Introduction: molecular geometry, the three-dimensional arrangement of atoms within a molecule, is fundamental to understanding chemical reactivity, physical properties, and biological activity. The prevailing models used to describe…

Proteins are the workhorse molecules of the cell and perform their biological functions by binding to other molecules through physical contact. Protein function is then regulated through coupling of bindings on the protein (allosteric…

An all-atom model of proteins is used to show that the same sequence of amino acids can have many alternative structures, that are very distant from, and that can be as stable as, the corresponding native structure. Such alternative…

When studying multi-body protein complexes, biochemists use computational tools that can suggest hundreds or thousands of their possible spatial configurations. However, it is not feasible to experimentally verify more than only a very…

A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the…