Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 19Advanced Chemical Physics StudiesMass Spectrometry Techniques and ApplicationsProtein Structure and Dynamics

The DOI matches its Crossref record; 120 of the 120 references it cites were found in a registry or an index.

Surrogate Based Genetic Algorithm Method for Efficient Identification of Low-Energy Peptide Structures

Open access
Villard, Justin, Kılıç, Murat, Rothlisberger, Ursula·2023·Journal of Chemical Theory and Computation
DOI 10.1021/acs.jctc.2c01078PMC PMC9933449

Published version of a preprint

Open this paper in CoChat — free accountOpen PDF

Abstract

High Resolution Image Download MS PowerPoint Slide Identification of the most stable structure(s) of a system is a prerequisite for the calculation of any of its properties from first-principles. However, even for relatively small molecules, exhaustive explorations of the potential energy surface (PES) are severely hampered by the dimensionality bottleneck. In this work, we address the challenging task of efficiently sampling realistic low-lying peptide coordinates by resorting to a surrogate based genetic algorithm (GA)/density functional theory (DFT) approach (sGADFT) in which promising candidates provided by the GA are ultimately optimized with DFT. We provide a benchmark of several computational methods (GAFF, AMOEBApro13, PM6, PM7, DFTB3-D3(BJ)) as possible prescanning surrogates and apply sGADFT to two test case systems that are (i) two isomer families of the protonated Gly-Pro-Gly-Gly tetrapeptide ( Masson, A.; J. Am. Soc. Mass Spectrom. 2015, 26, 1444−1454) and (ii) the doubly protonated cyclic decapeptide gramicidin S ( Nagornova, N. S.; J. Am. Chem. Soc. 2010, 132, 4040−4041). We show that our GA procedure can correctly identify low-energy minima in as little as a few hours. Subsequent refinement of surrogate low-energy structures within a given energy threshold (≤10 kcal/mol (i), ≤5 kcal/mol (ii)) via DFT relaxation invariably led to the identification of the most stable structures as determined from high-resolution infrared (IR) spectroscopy at low temperature. The sGADFT method therefore constitutes a highly efficient route for the screening of realistic low-lying peptide structures in the gas phase as needed for instance for the interpretation and assignment of experimental IR spectra.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1021/acs.jctc.2c01078

Cites

120 of 120 references verified0 citation errors · 0 not checkable

Statistics

Figures

Figure 1 Schematic structure of the 39-atom protonated GPGG peptide in its cis (ω = 0) isomer, shown with the respective backbone dihedrals employed for GA optimization.
Figure 1 Schematic structure of the 39-atom protonated GPGG peptide in its cis (ω = 0) isomer, shown with the respective backbone dihedrals employed for GA optimization.CC BY-NC-ND · PubMed Central
Figure 2 Schematic structure of the 176-atom doubly protonated gramicidin S cyclic decapeptide, shown with respective backbone and side-chain dihedrals employed for optimization.
Figure 2 Schematic structure of the 176-atom doubly protonated gramicidin S cyclic decapeptide, shown with respective backbone and side-chain dihedrals employed for optimization.CC BY-NC-ND · PubMed Central
Figure 3 Schematic representation of the GA cycle as implemented in EVOLVE for this study.
Figure 3 Schematic representation of the GA cycle as implemented in EVOLVE for this study.CC BY-NC-ND · PubMed Central
Figure 4 Illustration of the local relaxation of test structures on the surrogate and reference PES projected along two arbitrary reaction coordinates. The LM resulting from the same initial points are not necessarily close in energy and/or geometry.
Figure 4 Illustration of the local relaxation of test structures on the surrogate and reference PES projected along two arbitrary reaction coordinates. The LM resulting from the same initial points are not necessarily close in energy and/or geometry.CC BY-NC-ND · PubMed Central
Figure 5 (a) MAE of relative energies between surrogate LM and their bb-RMSD closest B3LYP/6-31G(d,p) counterparts for the GPGG test set. (b) Average bb-RMSD between the surrogate LM and their closest B3LYP/6-31G(d,p) counterparts. Average values over max(S, 70) random subsets for each size S are plotted; standard deviations are of the order of 1 kcal/mol, respectively, 0.03 Å, and are provided in the Supporting Information (Figure S5a,b). The energies of the reference LM span 30 kcal/mol with two outliers around 40 and 60 kcal/mol.
Figure 5 (a) MAE of relative energies between surrogate LM and their bb-RMSD closest B3LYP/6-31G(d,p) counterparts for the GPGG test set. (b) Average bb-RMSD between the surrogate LM and their closest B3LYP/6-31G(d,p) counterparts. Average values over max(S, 70) random subsets for each size S are plotted; standard deviations are of the order of 1 kcal/mol, respectively, 0.03 Å, and are provided in the Supporting Information (Figure S5a,b). The energies of the reference LM span 30 kcal/mol with two outliers around 40 and 60 kcal/mol.CC BY-NC-ND · PubMed Central
Figure 6 GPGG: cumulative success of finding the surrogate GM at each generation, averaged over 10 GA optimizations per surrogate/isomer combination.
Figure 6 GPGG: cumulative success of finding the surrogate GM at each generation, averaged over 10 GA optimizations per surrogate/isomer combination.CC BY-NC-ND · PubMed Central
Figure 7 cis-GPGG: putative GM and closest LM found on surrogate PES after 10 GA runs for (a, b) AMOEBA and (c, d) GAFF. is the relative energy of the LM with respect to the putative GM. The B3LYP/6-31G(d,p) GM is depicted in green with respective backbone/heavy-atom RMSD. Similar structures are obtained with or without elitism.
Figure 7 cis-GPGG: putative GM and closest LM found on surrogate PES after 10 GA runs for (a, b) AMOEBA and (c, d) GAFF. is the relative energy of the LM with respect to the putative GM. The B3LYP/6-31G(d,p) GM is depicted in green with respective backbone/heavy-atom RMSD. Similar structures are obtained with or without elitism.CC BY-NC-ND · PubMed Central
Figure 8 trans-GPGG: putative GM and closest LM found on surrogate PES after 10 GA runs for (a, b) AMOEBA and (c, d) GAFF. is the relative energy of the LM with respect to the putative GM. The B3LYP/6-31G(d,p) GM is depicted in green with respective backbone/heavy-atom RMSD. Similar structures are obtained with or without elitism.
Figure 8 trans-GPGG: putative GM and closest LM found on surrogate PES after 10 GA runs for (a, b) AMOEBA and (c, d) GAFF. is the relative energy of the LM with respect to the putative GM. The B3LYP/6-31G(d,p) GM is depicted in green with respective backbone/heavy-atom RMSD. Similar structures are obtained with or without elitism.CC BY-NC-ND · PubMed Central
Figure 9 trans-GPGG: number of low-lying minima found on the AMOEBA PES within 15, 10, and 5 kcal/mol with respect to the putative GM. (a) Per GA generation, averaged over 10 GA runs. (b) By running independent GAs. Distinct LM are taken to be at least separated by 10–4 kcal/mol and 0.2 heavy-atom RMSD.
Figure 9 trans-GPGG: number of low-lying minima found on the AMOEBA PES within 15, 10, and 5 kcal/mol with respect to the putative GM. (a) Per GA generation, averaged over 10 GA runs. (b) By running independent GAs. Distinct LM are taken to be at least separated by 10–4 kcal/mol and 0.2 heavy-atom RMSD.CC BY-NC-ND · PubMed Central
Figure 10 GPGG: predictive performance of AMOEBA in reproducing geometries and relative energies of LM at the B3LYP/6-31G(d,p) level for (a) cis isomers and (b) trans isomers. Backbone (bb) and heavy-atom (no-H) RMSDs are reported. Also indicated are the median and 75% quantile of absolute errors on energies. The 75% quantile outliers are marked in green with their respective RMSD. Corresponding plots for the GAFF force field are given in the Supporting Information (Figure S10).
Figure 10 GPGG: predictive performance of AMOEBA in reproducing geometries and relative energies of LM at the B3LYP/6-31G(d,p) level for (a) cis isomers and (b) trans isomers. Backbone (bb) and heavy-atom (no-H) RMSDs are reported. Also indicated are the median and 75% quantile of absolute errors on energies. The 75% quantile outliers are marked in green with their respective RMSD. Corresponding plots for the GAFF force field are given in the Supporting Information (Figure S10).CC BY-NC-ND · PubMed Central
Figure 11 GPGG: zero point energy-corrected energies of B3LYP/6-31G(d,p) reoptimized structures obtained with ab initio simulated annealing (SA) at B3LYP/6-31G1 and GA with AMOEBA or GAFF force fields. The green and shorter red levels are respectively matches and misses compared to SA. The respective number of LM is indicated in parentheses.
Figure 11 GPGG: zero point energy-corrected energies of B3LYP/6-31G(d,p) reoptimized structures obtained with ab initio simulated annealing (SA) at B3LYP/6-31G1 and GA with AMOEBA or GAFF force fields. The green and shorter red levels are respectively matches and misses compared to SA. The respective number of LM is indicated in parentheses.CC BY-NC-ND · PubMed Central
Figure 12 Gramicidin: two views (a) and (b) of the AMOEBA putative GM that is also the closest LM found over 10 GA runs (with 10% elitism). The DFT B3LYP/6-31G(d,p) reference GM is depicted in green. Backbone/heavy-atom RMSDs are 0.2/0.4 Å.
Figure 12 Gramicidin: two views (a) and (b) of the AMOEBA putative GM that is also the closest LM found over 10 GA runs (with 10% elitism). The DFT B3LYP/6-31G(d,p) reference GM is depicted in green. Backbone/heavy-atom RMSDs are 0.2/0.4 Å.CC BY-NC-ND · PubMed Central
Figure 13 Gramicidin: predictive performance of AMOEBA and GAFF in reproducing geometries and relative energies of LM at the B3LYP/6-31G(d,p) level. Backbone (bb) and heavy-atom (no-H) RMSDs are reported. Also indicated are the median and 75% quantile of absolute errors on energies. The 75% quantile outliers are marked in green with their respective RMSD.
Figure 13 Gramicidin: predictive performance of AMOEBA and GAFF in reproducing geometries and relative energies of LM at the B3LYP/6-31G(d,p) level. Backbone (bb) and heavy-atom (no-H) RMSDs are reported. Also indicated are the median and 75% quantile of absolute errors on energies. The 75% quantile outliers are marked in green with their respective RMSD.CC BY-NC-ND · PubMed Central
Figure 14 Gramicidin: surrogate AMOEBA and GAFF LM candidates within 5 kcal/mol in the RG (radius of gyration) and NH (number of hydrogen bonds) space, connected by lines to their reoptimized structures at the B3LYP/6-31G(d,p) level of theory. are the respective energies of the putative GM for each PES, indicated by for the surrogates and GM for B3LYP.
Figure 14 Gramicidin: surrogate AMOEBA and GAFF LM candidates within 5 kcal/mol in the RG (radius of gyration) and NH (number of hydrogen bonds) space, connected by lines to their reoptimized structures at the B3LYP/6-31G(d,p) level of theory. are the respective energies of the putative GM for each PES, indicated by for the surrogates and GM for B3LYP.CC BY-NC-ND · PubMed Central
Figure 15 Gramicidin: zero point energy-corrected energies of B3LYP/6-31G(d,p) reoptimized structures obtained with SA based on classical force fields (SA/FF),30 and GAs with AMOEBA and GAFF force fields. The green and shorter red levels are respectively matches and misses compared to SA/FF. The respective number of LM is indicated in parentheses. A similar plot restricted to clearly distinct structures (only LM differing by at least two side chain dihedrals) is provided in Figure S18.
Figure 15 Gramicidin: zero point energy-corrected energies of B3LYP/6-31G(d,p) reoptimized structures obtained with SA based on classical force fields (SA/FF),30 and GAs with AMOEBA and GAFF force fields. The green and shorter red levels are respectively matches and misses compared to SA/FF. The respective number of LM is indicated in parentheses. A similar plot restricted to clearly distinct structures (only LM differing by at least two side chain dihedrals) is provided in Figure S18.CC BY-NC-ND · PubMed Central
Figure 16 Probability distributions (eq 6) of contracting and expanding SBX crossover to mimic binary single-point crossover distributions.
Figure 16 Probability distributions (eq 6) of contracting and expanding SBX crossover to mimic binary single-point crossover distributions.CC BY-NC-ND · PubMed Central

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Research works printed but not linked: 2

  1. 10.1002/(SICI)1097-0134(1997)1+<179::AID-PROT23>3.0.CO;2-K · DOI
  2. Deb K., 1995, Complex Syst., 9, 115

Metadata

Authors
Villard, J., Kılıç, M., & Rothlisberger, U.
Affiliations
  • École Polytechnique Fédérale de Lausanne (CH)
  • Laboratory of Computational Chemistry and Biochemistry, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015Lausanne, Switzerland
ORCID
Venue
Journal of Chemical Theory and Computation
Publisher
American Chemical Society (ACS)
Published
2023-01-24
Volume
19
Issue
3
Pages
1080-1097
ISSN
  • 1549-9618 (ISSN-L)
  • 1549-9626
DOI
10.1021/acs.jctc.2c01078
PMC
PMC9933449
OpenAlex
W4317867555
Cited by
19
References
120
Citations by year
2026: 12 · 2025: 2 · 2024: 3 · 2023: 2
FWCI
2.21
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Chemical Theory and Computation (publishedVersion, cc-by-nc-nd)
  • ChemRxiv (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
Funders
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (200020_185092)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Chemistry › Spectroscopy › Mass Spectrometry Techniques and Applications
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
Keywords
density functional theory, gramicidin S, infrared spectroscopy, GAFF, amoebae, PM6, PM7
MeSH terms
Algorithms, Gramicidin, Peptides

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.