Recoverable One-dimensional Encoding of Three-dimensional Protein Structures

We present a sequence-based probabilistic formalism that directly addresses co-operative effects in networks of interacting positions in proteins, providing significantly improved contact prediction, as well as accurate quantitative prediction of free energy changes due to non-additive effects of multiple mutations. In addition to these practical considerations, the agreement of our sequence-based calculations with experimental data for both structure and stability demonstrat...

The three dimensional structure of a protein is an outcome of the interactions of its constituent amino acids in 3D space. Considering the amino acids as nodes and the interactions among them as edges we have constructed and analyzed protein contact networks at different length scales, long and short-range. While long and short-range interactions are determined by the positions of amino acids in primary chain, the contact networks are constructed based on the 3D spatial dista...

Exploring and understanding the protein-folding problem has been a long-standing challenge in molecular biology. Here, using molecular dynamics simulation, we reveal how parallel distributed adjacent planar peptide groups of unfolded proteins fold reproducibly following explicit physical folding codes in aqueous environments due to electrostatic attractions. Superfast folding of protein is found to be powered by the contribution of the formation of hydrogen bonds. Temperature...

An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only $C_\alpha$ atoms need to be specified, an accurate potential function is important. Such a simplified model is essential for efficient search of conformational space. In this work, we present a formulation of potential function for simplified representations of protein structures. It is based on the combination of des...

Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to the lowest structrally dissimilar conformation), aside from leading to fast folding, are highly designable (in the sense that many sequences target onto it in the folding process). These results are quite general, do not depend on the parti...

Recently exciting progress has been made on protein contact prediction, but the predicted contacts for proteins without many sequence homologs is still of low quality and not very useful for de novo structure prediction. This paper presents a new deep learning method that predicts contacts by integrating both evolutionary coupling (EC) and sequence conservation information through an ultra-deep neural network formed by two deep residual networks. This deep neural network allo...

We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that unique...

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the fol...

We discuss a stochastic approach for reconstructing the native structures of proteins from the knowledge of the "effective connectivity", which is a one-dimensional structural profile constructed as a linear combination of the eigenvectors of the contact map of the target structure. The structural profile is used to bias a search of the conformational space towards the target structure in a Monte Carlo scheme operating on a C_alpha-chain of uniform, finite thickness. Structur...

Residue-residue interactions that fold a protein into a unique three-dimensional structure and make it play a specific function impose structural and functional constraints on each residue site. Selective constraints on residue sites are recorded in amino acid orders in homologous sequences and also in the evolutionary trace of amino acid substitutions. A challenge is to extract direct dependences between residue sites by removing indirect dependences through other residues w...