Simple Model of Protein Energetics To Identify Ab Initio Folding Transitions from All-Atom MD Simulations of Proteins

Abstract

A fundamental requirement to predict the native conformation, address questions of sequence design and optimization, and gain insights into the folding mechanisms of proteins lies in the definition of an unbiased reaction coordinate that reports on the folding state without the need to compare it to reference values, which might be unavailable for new (designed) sequences. Here, we introduce such a reaction coordinate, which does not depend on previous structural knowledge of the native state but relies solely on the energy partition within the protein: the spectral gap of the pair nonbonded energy matrix (ENergy Gap, ENG). This quantity can be simply calculated along unbiased MD trajectories. We show that upon folding the gap increases significantly, while its fluctuations are reduced to a minimum. This is consistently observed for a diverse set of systems and trajectories. Our approach allows one to promptly identify residues that belong to the folding core as well as residues involved in non-native contacts that need to be disrupted to guide polypeptides to the folded state. The energy gap and fluctuations criteria are then used to develop an automatic detection system which allows us to extract and analyze folding transitions from a generic MD trajectory. We speculate that our method can be used to detect conformational ensembles in dynamic and intrinsically disordered proteins, revealing potential preorganization for binding.

Mechanism of collagen folding propagation studied by Molecular Dynamics simulations

“…In future studies it might also be possible to follow and identify folding nuclei directly from unrestraint simulations [ 27 ]. If propagation has started the conditions on how the nucleus has been formed are not relevant.…”

Conformational Dynamics, Energetics, and the Divergent Evolution of Allosteric Regulation: The Case of the Yeast MAPK Family

“…Such residues indeed correspond to the components of the vector with larger absolute values. [31,34,35] Here, in the considered eigenvector, the so-called principal component of energy (PRICE), we considered as significant the components with a value higher than t ¼ 1= p N which identify the residues with the highest contribution to the protein's conformational stabilization. The reference threshold value corresponds to a hypothetical situation where the contribution of each residue to stabilization is the same (flat eigenvector situation).…”

“…Eigenvalue decomposition of the resulting matrix returns eigenvectors with a number of components equal to N. As each eigenvector is associated with an eigenvalue, the N components of the eigenvector associated with the lowest eigenvalue (capturing only the stabilising interactions, as previously shown) can pinpoint the residues behaving as strong, stabilising interaction centres. Such residues indeed correspond to the components of the vector with larger absolute values [31,34,35] . Here, in the considered eigenvector, the so‐called principal component of energy (PRICE), we considered as significant the components with a value higher than $${t=1/\surd N}$$ which identify the residues with the highest contribution to the protein's conformational stabilization.…”

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

“…Understanding the contribution of the hydrophobic core to the overall stability of the Trp-cage is of significant interest in protein-folding studies and has implications in protein engineering. − This protein is known to fold spontaneously and cooperatively in ∼4 μs, whereas a variant thereof folds in ∼1 μs at room temperature . The Trp-cage is therefore highly appropriate for studying the folding processes of peptides, both experimentally ,, and theoretically, ,− and in combination. , The Trp-cage has also been used as a test system for various new methods. ,− Many studies have shown that the Trp-cage can also exist in the form of metastable non-native states, which makes it useful for studying complex folding processes. ,,,,− …”

“…The side chain of Trp6 is in contact with the side chain of Tyr3, ,,,, Leu7, Pro12, , Arg16, Pro18, and Pro19, ,, but not in contact with the side chain of Pro17. These side chains form the hydrophobic core of the Trp-cage, which plays a crucial role in maintaining its structural stability. − The rotamer of the Trp6 side chain is the rate-limiting factor that governs the folding rate. ,, In addition to the hydrophobic core, the formation of a salt bridge between Asp9 and Arg16 also contributes to the structural stability of the Trp-cage. − ,,,,,,,− The interaction responsible for the formation of the hydrophobic core is driven by the solvation entropy, which indicates a many-body interaction with the surrounding solvent. During the folding process, the side chains that form the salt bridge are dehydrated.…”