Mapping Conformational Space of All 8000 Tripeptides by Quantum Chemical Methods: What Strain Is Affordable within Folded Protein Chains?

Abstract

To gain more insight into the physicochemical aspects of a protein structure from the first principles, conformational space of all 8000 "capped" tripeptides (i.e., N-Ac-X 1 X 2 X 3 -NH-CH 3 , where X i is one of the 20 natural amino acids) was investigated computationally. An enormous dataset (denoted P-CONF_1.6M and containing close to 1 600 000 conformers in total) has been obtained by employing a composite protocol combining density functional theory, semiempirical quantum mechanics (SQM), and state-of-theart solvation methods with 1000 K molecular dynamics (MD) used to generate initial structures (200 snapshots for each tripeptide). This allowed us to present the first rigorous QM-based glimpse at the vast conformational space spanned by small protein fragments. The same computational procedure was repeated for tripeptide fragments taken from the SCOPe database of three-dimensional protein folds, by restraining them to their geometry in a protein. Such complementary data allowed us to compare the distribution of conformational strain energies of unrestrained tripeptidic fragments "in solvent" with those in existing protein chains. Besides providing a rigorous (ab initio) proof of a few wellknown concepts and hypotheses concerning protein structures, such as the distribution of (φ, ψ) angles in Ramachandran plots, we have made several observations that came as a certain surprise: (1) distribution of conformational energies does not significantly differ between the "unbiased/unrestrained" conformers obtained from MD sampling in solvent and the biased conformers, i.e., those of a given tripeptide obtained from protein structures; (2) conformational (strain) energy window up to ∼20 to 25 kcal•mol −1 is readily available to tripeptide fragments within the context of a protein chain; (3) overpopulation in certain regions of Ramachandran plot was observed for the unbiased conformers. Last but not least, the massive dataset of accurate (DFT-D3// COSMO-RS) conformational (free) energies of ∼1.6 M peptide conformers, P-CONF_1.6M, obtained throughout this work may serve as excellent dataset for calibrating and benchmarking of popular force fields.

Exhaustive Mapping of the Conformational Space of Natural Dipeptides by the DFT-D3//COSMO-RS Method

“…The accuracy of the used BP86 functional with DGauss-DZVP basis set and custom dispersion correction has been previously evaluated on the MPCONF196 data set against CCSD­(T) calculations. Some of us also previously showed that the SQM GFN2-xTB method can reproduce the important features of the DFT potential energy surface of di- and tripeptides . In the present work, we evaluated the accuracy of the SQM optimizations as opposed to full DFT optimizations and frequency calculations on a randomly chosen subset of 50 minima and 50 constrained structures for each amino acid or dipeptide (in total >50 000 structures; all results are available in the Supporting Information).…”

“…We found that the histograms of conformational energies (of a unique energy minima) obey the Poisson distribution, and most of the conformers lie within 30 kcal/mol of the global minimum. This is in line with our previous findings, , which showed that, to form their 3D structures, proteins select fragments from the large portion of the amino acid conformational space and that an internal strain of up to 5–7 kcal/mol per residue is affordable. Comparing the distribution of mean conformational energy, maximum energy, and the 15th and 95th percentiles for all dipeptides in all solvents, we obtained a surprising picture that these distributions are almost identical.…”

“…Final free energies of conformers were obtained via the following formula: where E COSMO is the BP86-D3/COSMO (ε = ∞) energy of the conformer, ΔE is the averaged correction for the dielectric energy, and μ is the chemical potential of the conformer. All these values were obtained from and added within the COSMOtherm program (version 21), in the same manner as in our previous work . In the subsequent chapters, we are working only with relative energies with respect to the global minimum.…”

“…All these values were obtained from and added within the COSMOtherm 27 program (version 21), in the same manner as in our previous work. 37 In the subsequent chapters, we are working only with relative energies with respect to the global minimum. Henceforth, we will denote these as conformational energies (E).…”

Residue Folding Degree—Relationship to Secondary Structure Categories and Use as Collective Variable

“…We would like to declare upfront that we do not intend/propose to use the residue folding degree as a substitute for SS defining algorithms. The dynamical aspects of stabilising effects of proteins SS are studied elsewhere [ 52 , 53 , 54 ].…”