Related papers: Intramolecular Structure of Proteins as driven by …
Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…
While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
Mapping between sequence and structure is currently an open problem in structural biology. Despite many experimental and computational efforts it is not clear yet how the structure is encoded in the sequence. Answering this question may…
The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial…
The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
Understanding complex biological macromolecules, especially proteins, is vital for grasping their diverse chemical functions with direct impact in biology and pharmacology. While techniques like X-ray crystallography and cryo-electron…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
We propose a general multiscale approach for the mechanical behavior of three-dimensional networks of macromolecules undergoing strain-induced unfolding. Starting from a (statistically based) energetic analysis of the macromolecule…
Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring…
The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…
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…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
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…
Biological membranes constitute boundaries of cells and cell organelles. Physico-chemical mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the…
Many models of genome rearrangement involve operations (e.g. inversions and translocations) that are self-inverse, and hence generate a group acting on the space of genomes. This gives a correspondence between genome arrangements and the…
Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show…
Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…