Recoverable One-dimensional Encoding of Three-dimensional Protein Structures

Motivation. Protein contact map describes the pairwise spatial and functional relationship of residues in a protein and contains key information for protein 3D structure prediction. Although studied extensively, it remains very challenging to predict contact map using only sequence information. Most existing methods predict the contact map matrix element-by-element, ignoring correlation among contacts and physical feasibility of the whole contact map. A couple of recent metho...

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 attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We em...

Protein-protein interactions are fundamental to many biological processes. Experimental screens have identified tens of thousands of interactions and structural biology has provided detailed functional insight for select 3D protein complexes. An alternative rich source of information about protein interactions is the evolutionary sequence record. Building on earlier work, we show that analysis of correlated evolutionary sequence changes across proteins identifies residues tha...

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. This motivates predicting the structure of a protein from its sequence of amino acids, a fundamental problem in computational biology. In this work, we demonstrate state-of-the-art protein structure prediction (PSP) results using embedding...

Proteins are essential for life, and their structure determines their function. The protein secondary structure is formed by the folding of the protein primary structure, and the protein tertiary structure is formed by the bending and folding of the secondary structure. Therefore, the study of protein secondary structure is very helpful to the overall understanding of protein structure. Although the accuracy of protein secondary structure prediction has continuously improved ...

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 to give an introduction into Structural Bioinformatics, which is where the previous topics meet to explore three dimensional protein structures through computational analysis. We provide an overview of existing computational techniques, to v...

We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also uncovers the shortcomings of any optimization procedure. The strategy can be applied on any data set of native structures such as those available from the Protein Data Bank (PDB). In this work, however, we explain and test our approach on simp...

Protein secondary structure (SS) prediction is important for studying protein structure and function. When only the sequence (profile) information is used as input feature, currently the best predictors can obtain ~80% Q3 accuracy, which has not been improved in the past decade. Here we present DeepCNF (Deep Convolutional Neural Fields) for protein SS prediction. DeepCNF is a Deep Learning extension of Conditional Neural Fields (CNF), which is an integration of Conditional Ra...

A novel scheme is introduced to capture the spatial correlations of consecutive amino acids in naturally occurring proteins. This knowledge-based strategy is able to carry out optimally automated subdivisions of protein fragments into classes of similarity. The goal is to provide the minimal set of protein oligomers (termed ``oligons'' for brevity) that is able to represent any other fragment. At variance with previous studies where recurrent local motifs were classified, our...

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with th...