Recoverable One-dimensional Encoding of Three-dimensional Protein Structures

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of a protein whose sequence is known. Using insight obtained from simple model simulations of the folding of proteins, in particular of the fact that this phenomenon is essentially controlled by conserved (native) contacts among (few) strongly...

Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of protein structure. This representation can eliminate implausible neighbors not in physical contact, and can avoid spurious contact between two residues when a third residue is between them. We develop statistical alpha contact potential. A...

The primary structure of proteins, that is their sequence, represents one of the most abundant set of experimental data concerning biomolecules. The study of correlations in families of co--evolving proteins by means of an inverse Ising--model approach allows to obtain information on their native conformation. Following up on a recent development along this line, we optimize the algorithm to calculate effective energies between the residues, validating the approach both back-...

Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence information remains very challenging. Recently evolutionary coupling (EC) analysis, which predicts contacts by detecting co-evolved residues (or columns) in a multiple sequence alignment (MSA), has made good progress due to better statistical assessment techniques and high-throughput sequencing. Existing EC analysis methods predict only a single cont...

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapp...

A reliable prediction of 3D protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed b...

The simplest approximation of interaction potential between amino-acids in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact...

We present a novel technique of sampling the configurations of helical proteins. Assuming knowledge of native secondary structure, we employ assembly rules gathered from a database of existing structures to enumerate the geometrically possible three-dimensional arrangements of the constituent helices. We produce a library of possible folds for twenty-five helical protein cores. In each case, our method finds significant numbers of conformations close to the native structure. ...

The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps to better understand proteins' properties. Here, we investigate the emergent behaviour of contact maps for different geometrically constrained mode...

We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition for the native structure achieving the lower bound leads to the contact energy matrix that is a scalar multiple of the native contact matrix, i.e., the so-called Go potential. We also derive spectral relations between contact matrix and en...