Streamlining NMR Chemical Shift Predictions for Intrinsically Disordered Proteins: Design of Ensembles with Dimensionality Reduction and Clustering
Language English Country United States Media print-electronic
Document type Journal Article
PubMed
39099394
PubMed Central
PMC11412307
DOI
10.1021/acs.jcim.4c00809
Knihovny.cz E-resources
- MeSH
- Algorithms * MeSH
- Protein Conformation MeSH
- Neural Networks, Computer MeSH
- Nuclear Magnetic Resonance, Biomolecular MeSH
- Cluster Analysis MeSH
- Intrinsically Disordered Proteins * chemistry MeSH
- Publication type
- Journal Article MeSH
- Names of Substances
- Intrinsically Disordered Proteins * MeSH
By merging advanced dimensionality reduction (DR) and clustering algorithm (CA) techniques, our study advances the sampling procedure for predicting NMR chemical shifts (CS) in intrinsically disordered proteins (IDPs), making a significant leap forward in the field of protein analysis/modeling. We enhance NMR CS sampling by generating clustered ensembles that accurately reflect the different properties and phenomena encapsulated by the IDP trajectories. This investigation critically assessed different rapid CS predictors, both neural network (e.g., Sparta+ and ShiftX2) and database-driven (ProCS-15), and highlighted the need for more advanced quantum calculations and the subsequent need for more tractable-sized conformational ensembles. Although neural network CS predictors outperformed ProCS-15 for all atoms, all tools showed poor agreement with HN CSs, and the neural network CS predictors were unable to capture the influence of phosphorylated residues, highly relevant for IDPs. This study also addressed the limitations of using direct clustering with collective variables, such as the widespread implementation of the GROMOS algorithm. Clustered ensembles (CEs) produced by this algorithm showed poor performance with chemical shifts compared to sequential ensembles (SEs) of similar size. Instead, we implement a multiscale DR and CA approach and explore the challenges and limitations of applying these algorithms to obtain more robust and tractable CEs. The novel feature of this investigation is the use of solvent-accessible surface area (SASA) as one of the fingerprints for DR alongside previously investigated α carbon distance/angles or ϕ/ψ dihedral angles. The ensembles produced with SASA tSNE DR produced CEs better aligned with the experimental CS of between 0.17 and 0.36 r2 (0.18-0.26 ppm) depending on the system and replicate. Furthermore, this technique produced CEs with better agreement than traditional SEs in 85.7% of all ensemble sizes. This study investigates the quality of ensembles produced based on different input features, comparing latent spaces produced by linear vs nonlinear DR techniques and a novel integrated silhouette score scanning protocol for tSNE DR.
Department of Chemistry Faculty of Science Masaryk University Kotlářská 2 611 37 Brno Czech Republic
School of Chemistry University of Bristol Cantock's Close BS8 1TS Bristol U K
See more in PubMed
Toto A.; Troilo F.; Visconti L.; Malagrinò F.; Bignon C.; Longhi S.; Gianni S. Binding Induced Folding: Lessons from the Kinetics of Interaction between NTAIL and XD. Arch. Biochem. Biophys. 2019, 671, 255–261. 10.1016/j.abb.2019.07.011. PubMed DOI
Kulkarni P.; Uversky V. N. Intrinsically Disordered Proteins: The Dark Horse of the Dark Proteome. Proteomics 2018, 18, 1800061.10.1002/pmic.201800061. PubMed DOI
Perdigão N.; Rosa A. Dark Proteome Database: Studies on Dark Proteins. High-Throughput 2019, 8, 8.10.3390/ht8020008. PubMed DOI PMC
Uversky V. N. Intrinsically Disordered Proteins and Their “Mysterious” (Meta)Physics. Front. Phys. 2019, 7, 10.10.3389/fphy.2019.00010. DOI
Lermyte F. Roles, Characteristics, and Analysis of Intrinsically Disordered Proteins: A Minireview. Life (Basel) 2020, 10, 320.10.3390/life10120320. PubMed DOI PMC
Uversky V. N. New Technologies to Analyse Protein Function: An Intrinsic Disorder Perspective. F1000Research 2020, 9, 101.10.12688/f1000research.20867.1. PubMed DOI PMC
Trivedi R.; Nagarajaram H. A. Intrinsically Disordered Proteins: An Overview. Int. J. Mol. Sci. 2022, 23, 14050.10.3390/ijms232214050. PubMed DOI PMC
Huang J.; MacKerell A. D. Force Field Development and Simulations of Intrinsically Disordered Proteins. Curr. Opin. Struct. Biol. 2018, 48, 40–48. 10.1016/j.sbi.2017.10.008. PubMed DOI PMC
Bencivenga D.; Stampone E.; Roberti D.; Della Ragione F.; Borriello A. p27Kip1, an Intrinsically Unstructured Protein with Scaffold Properties. Cells 2021, 10, 2254.10.3390/cells10092254. PubMed DOI PMC
Karlsson E.; Paissoni C.; Erkelens A. M.; Tehranizadeh Z. A.; Sorgenfrei F. A.; Andersson E.; Ye W.; Camilloni C.; Jemth P. Mapping the Transition State for a Binding Reaction between Ancient Intrinsically Disordered Proteins. J. Biol. Chem. 2020, 295, 17698–17712. 10.1074/jbc.RA120.015645. PubMed DOI PMC
Dyson H. J.; Wright P. E. Intrinsically Unstructured Proteins and Their Functions. Nat. Rev. Mol. Cell Biol. 2005, 6, 197–208. 10.1038/nrm1589. PubMed DOI
Brodsky S.; Jana T.; Mittelman K.; Chapal M.; Kumar D. K.; Carmi M.; Barkai N. Intrinsically Disordered Regions Direct Transcription Factor In Vivo Binding Specificity. Mol. Cell 2020, 79, 459–471.e4. 10.1016/j.molcel.2020.05.032. PubMed DOI
Kragelund B. B.; Schenstrøm S. M.; Rebula C. A.; Panse V. G.; Hartmann-Petersen R. DSS1/SEM1, a Multifunctional and Intrinsically Disordered Protein. Trends Biochem. Sci. 2016, 41, 446–459. 10.1016/j.tibs.2016.02.004. PubMed DOI
Kulkarni P. The Boscombe Valley Mystery: A Lesson in the Perils of Dogmatism in Science. J. Biosci 2021, 46, 59.10.1007/s12038-021-00179-x. PubMed DOI
Babu M. M.; van der Lee R.; de Groot N. S.; Gsponer J. Intrinsically Disordered Proteins: Regulation and Disease. Curr. Opin. Struct. Biol. 2011, 21, 432–440. 10.1016/j.sbi.2011.03.011. PubMed DOI
Bondos S. E.; Dunker A. K.; Uversky V. N. Intrinsically Disordered Proteins Play Diverse Roles in Cell Signaling. Cell Commun. Signal. 2022, 20, 20.10.1186/s12964-022-00821-7. PubMed DOI PMC
Dunker A. K.; Bondos S. E.; Huang F.; Oldfield C. J. Intrinsically Disordered Proteins and Multicellular Organisms. Semin. Cell Dev. Biol. 2015, 37, 44–55. 10.1016/j.semcdb.2014.09.025. PubMed DOI
Marín M.; Ott T. Phosphorylation of Intrinsically Disordered Regions in Remorin Proteins. Front. Plant Sci. 2012, 3, 86.10.3389/fpls.2012.00086. PubMed DOI PMC
Tompa P.; Schad E.; Tantos A.; Kalmar L. Intrinsically Disordered Proteins: Emerging Interaction Specialists. Curr. Opin. Struct. Biol. 2015, 35, 49–59. 10.1016/j.sbi.2015.08.009. PubMed DOI
Korsak M.; Kozyreva T. Beta Amyloid Hallmarks: From Intrinsically Disordered Proteins to Alzheimer’s Disease. Adv. Exp. Med. Biol. 2015, 870, 401–421. 10.1007/978-3-319-20164-1_14. PubMed DOI
Uversky V. N. Intrinsically Disordered Proteins and Their (Disordered) Proteomes in Neurodegenerative Disorders. Front. Aging Neurosci. 2015, 7, 18.10.3389/fnagi.2015.00018. PubMed DOI PMC
Phillips A. H.; Kriwacki R. W. Intrinsic Protein Disorder and Protein Modifications in the Processing of Biological Signals. Curr. Opin. Struct. Biol. 2020, 60, 1–6. 10.1016/j.sbi.2019.09.003. PubMed DOI
Ubersax J. A.; Ferrell Jr J. E. Mechanisms of Specificity in Protein Phosphorylation. Nat. Rev. Mol. Cell Biol. 2007, 8, 530–541. 10.1038/nrm2203. PubMed DOI
Iakoucheva L. M. The Importance of Intrinsic Disorder for Protein Phosphorylation. Nucleic Acids Res. 2004, 32, 1037–1049. 10.1093/nar/gkh253. PubMed DOI PMC
Beveridge R.; Calabrese A. N. Structural Proteomics Methods to Interrogate the Conformations and Dynamics of Intrinsically Disordered Proteins. Front. Chem. 2021, 9, 603639.10.3389/fchem.2021.603639. PubMed DOI PMC
Lermyte F. Roles, Characteristics, and Analysis of Intrinsically Disordered Proteins: A Minireview. Life 2020, 10, 320.10.3390/life10120320. PubMed DOI PMC
Mishra P. M.; Verma N. C.; Rao C.; Uversky V. N.; Nandi C. K. Intrinsically Disordered Proteins of Viruses: Involvement in the Mechanism of Cell Regulation and Pathogenesis. Prog. Mol. Biol. Transl. Sci. 2020, 174, 1–78. 10.1016/bs.pmbts.2020.03.001. PubMed DOI PMC
Bakker M. J.; Sørensen H. V.; Skepö M. Exploring the Role of Globular Domain Locations on an Intrinsically Disordered Region of p53: A Molecular Dynamics Investigation. J. Chem. Theory Comput. 2024, 20, 1423–1433. 10.1021/acs.jctc.3c00971. PubMed DOI PMC
Pauwels K.; Lebrun P.; Tompa P. To Be Disordered or Not To Be Disordered: Is That Still a Question for Proteins in the Cell?. Cell. Mol. Life Sci. 2017, 74, 3185–3204. 10.1007/s00018-017-2561-6. PubMed DOI PMC
Henriques J.; Arleth L.; Lindorff-Larsen K.; Skepö M. On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations. J. Mol. Biol. 2018, 430, 2521–2539. 10.1016/j.jmb.2018.03.002. PubMed DOI
Bakker M. J.; Mládek A.; Semrád H.; Zapletal V.; Pavlíková Přecechtělová J. Improving IDP Theoretical Chemical Shift Accuracy and Efficiency through a Combined MD/ADMA/DFT and Machine Learning Approach. Phys. Chem. Chem. Phys. 2022, 24, 27678–27692. 10.1039/D2CP01638A. PubMed DOI
Tremblay M.-L.; Banks A. W.; Rainey J. K. The Predictive Accuracy of Secondary Chemical Shifts is More Affected by Protein Secondary Structure than Solvent Environment. J. Biomol. NMR 2010, 46, 257–270. 10.1007/s10858-010-9400-5. PubMed DOI
Shen Y.; Bax A. Sparta+: A Modest Improvement in Empirical NMR Chemical Shift Prediction by Means of an Artificial Neural Network. J. Biomol. NMR 2010, 48, 13–22. 10.1007/s10858-010-9433-9. PubMed DOI PMC
Han B.; Liu Y.; Ginzinger S. W.; Wishart D. S. Shiftx2: Significantly Improved Protein Chemical Shift Prediction. J. Biomol. NMR 2011, 50, 43–57. 10.1007/s10858-011-9478-4. PubMed DOI PMC
Larsen A. S.; Bratholm L. A.; Christensen A. S.; Maher C.; Jensen J. H. ProCS15: a DFT-Based Chemical Shift Predictor for Backbone and CB Atoms in Proteins. PeerJ. 2015, 3, e1344.10.7717/peerj.1344. PubMed DOI PMC
Pavlíková Přecechtělová J.; Mládek A.; Zapletal V.; Hritz J. Quantum Chemical Calculations of NMR Chemical Shifts in Phosphorylated Intrinsically Disordered Proteins. J. Chem. Theory Comput. 2019, 15, 5642–5658. 10.1021/acs.jctc.8b00257. PubMed DOI
Vícha J.; Babinský M.; Demo G.; Otrusinová O.; Jansen S.; Pekárová B.; Žídek L.; Munzarová M. L. The Influence of Mg2+ Coordination on 13C and 15N Chemical Shifts in CKI1RD Protein Domain from Experiment and Molecular Dynamics/Density Functional Theory Calculations. Proteins: Struct., Funct., Bioinf. 2016, 84, 686–699. 10.1002/prot.25019. PubMed DOI
Exner T. E.; Frank A.; Onila I.; Möller H. M. Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 3. Conformational Sampling and Explicit Solvents Model. J. Chem. Theory Comput. 2012, 8, 4818–4827. 10.1021/ct300701m. PubMed DOI
Fukal J.; Páv O.; Buděšínský M.; Šebera J.; Sychrovský V. The Benchmark of 31P NMR Parameters in Phosphate: a Case Study on Structurally Constrained and Flexible Phosphate. Phys. Chem. Chem. Phys. 2017, 19, 31830–31841. 10.1039/C7CP06969C. PubMed DOI
Dračínský M.; Möller H. M.; Exner T. E. Conformational Sampling by Ab Initio Molecular Dynamics Simulations Improves NMR Chemical Shift Predictions. J. Chem. Theory Comput. 2013, 9, 3806–3815. 10.1021/ct400282h. PubMed DOI
González-Alemán R.; Hernández-Castillo D.; Caballero J.; Montero-Cabrera L. A. Quality Threshold Clustering of Molecular Dynamics: A Word of Caution. J. Chem. Inf. Model. 2020, 60, 467–472. 10.1021/acs.jcim.9b00558. PubMed DOI
Ezerski J. C.; Cheung M. S. CATS: ATool for Clustering the Ensemble of Intrinsically Disordered Peptides on a Flat Energy Landscape. J. Phys. Chem. B 2018, 122, 11807–11816. 10.1021/acs.jpcb.8b08852. PubMed DOI PMC
Träger S.; Tamò G.; Aydin D.; Fonti G.; Audagnotto M.; Peraro M. D. CLoNe: Automated Clustering Based on Local Density Neighborhoods for Application to Biomolecular Structural Ensembles. Bioinformatics 2021, 37, 921–928. 10.1093/bioinformatics/btaa742. PubMed DOI PMC
Ezerski J. C.; Cheung M. S. CATS: ATool for Clustering the Ensemble of Intrinsically Disordered Peptides on a Flat Energy Landscape. J. Phys. Chem. B 2018, 122, 11807–11816. 10.1021/acs.jpcb.8b08852. PubMed DOI PMC
Appadurai R.; Koneru J. K.; Bonomi M.; Robustelli P.; Srivastava A. Clustering Heterogeneous Conformational Ensembles of Intrinsically Disordered Proteins with t-Distributed Stochastic Neighbor Embedding. J. Chem. Theory Comput. 2023, 19, 4711–4727. 10.1021/acs.jctc.3c00224. PubMed DOI PMC
Trozzi F.; Wang X.; Tao P. UMAP as a Dimensionality Reduction Tool for Molecular Dynamics Simulations of Biomacromolecules: A Comparison Study. J. Phys. Chem. B 2021, 125, 5022–5034. 10.1021/acs.jpcb.1c02081. PubMed DOI PMC
Tribello G. A.; Gasparotto P. Using Dimensionality Reduction to Analyze Protein Trajectories. Front. Mol. Biosci. 2019, 6, 46.10.3389/fmolb.2019.00046. PubMed DOI PMC
Kukharenko O.; Sawade K.; Steuer J.; Peter C. Using Dimensionality Reduction to Systematically Expand Conformational Sampling of Intrinsically Disordered Peptides. J. Chem. Theory Comput. 2016, 12, 4726–4734. 10.1021/acs.jctc.6b00503. PubMed DOI
McInnes L.; Healy J.; Saul N.; Großberger L. UMAP: Uniform Manifold Approximation and Projection. J. Open Source Softw. 2018, 3, 861.10.21105/joss.00861. DOI
van der Maaten L.; Hinton G. Visualizing Data using t-SNE. J. Mach. Learn. Res. 2008, 9, 2579–2605.
Zapletal V.; Mládek A.; Melková K.; Louša P.; Nomilner E.; Jaseňáková Z.; Kubáň V.; Makovická M.; Laníková A.; Žídek L.; et al. Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions. Biophys. J. 2020, 118, 1621–1633. 10.1016/j.bpj.2020.02.019. PubMed DOI PMC
Alexa A.; Schmidt G.; Tompa P.; Ogueta S.; Vázquez J.; Kulcsár P.; Kovács J.; Dombrádi V.; Friedrich P. The Phosphorylation State of Threonine-220, a Uniquely Phosphatase-Sensitive Protein Kinase A Site in Microtubule-Associated Protein MAP2c, Regulates Microtubule Binding and Stability. Biochemistry 2002, 41, 12427–12435. 10.1021/bi025916s. PubMed DOI
Daubner S. C.; Le T.; Wang S. Tyrosine Hydroxylase and Regulation of Dopamine Synthesis. Arch. Biochem. Biophys. 2011, 508, 1–12. 10.1016/j.abb.2010.12.017. PubMed DOI PMC
Nagatsu T.; Nakashima A.; Ichinose H.; Kobayashi K. Human Tyrosine Hydroxylase in Parkinson’s Disease and in Related Disorders. J. Neural Transm. 2019, 126, 397–409. 10.1007/s00702-018-1903-3. PubMed DOI
Louša P.; Nedozrálová H.; Župa E.; Nováček J.; Hritz J. Phosphorylation of the Regulatory Domain of Human Tyrosine Hydroxylase 1 Monitored using Non-Uniformly Sampled NMR. Biophys. Chem. 2017, 223, 25–29. 10.1016/j.bpc.2017.01.003. PubMed DOI
Dunkley P. R.; Dickson P. W. Tyrosine Hydroxylase Phosphorylation In Vivo. J. Neurochem. 2019, 149, 706–728. 10.1111/jnc.14675. PubMed DOI
Herrmann J.; Lerman L. O.; Lerman A. Ubiquitin and Ubiquitin-Like Proteins in Protein Regulation. Circ. Res. 2007, 100, 1276–1291. 10.1161/01.RES.0000264500.11888.f0. PubMed DOI
Vijay-Kumar S.; Bugg C. E.; Cook W. J. Structure of Ubiquitin Refined at 1.8 Å Resolution. J. Mol. Biol. 1987, 194, 531–544. 10.1016/0022-2836(87)90679-6. PubMed DOI
Pratihar S.; Sabo T. M.; Ban D.; Fenwick R. B.; Becker S.; Salvatella X.; Griesinger C.; Lee D. Kinetics of the Antibody Recognition Site in the Third IgG-Binding Domain of Protein G. Angew. Chem., Int. Ed. 2016, 55, 9567–9570. 10.1002/anie.201603501. PubMed DOI
Ulmer T. S.; Ramirez B. E.; Delaglio F.; Bax A. Evaluation of Backbone Proton Positions and Dynamics in a Small Protein by Liquid Crystal NMR Spectroscopy. J. Am. Chem. Soc. 2003, 125, 9179–9191. 10.1021/ja0350684. PubMed DOI
Berendsen H.; van der Spoel D.; van Drunen R. Gromacs: AMessage-Passing Parallel Molecular Dynamics Implementation. Comput. Phys. Commun. 1995, 91, 43–56. 10.1016/0010-4655(95)00042-E. DOI
Carballo-Pacheco M.; Strodel B. Comparison of Force Fields for Alzheimer’s A B42: A Case Study for Intrinsically Disordered Proteins. Protein Sci. 2017, 26, 174–185. 10.1002/pro.3064. PubMed DOI PMC
Mu J.; Liu H.; Zhang J.; Luo R.; Chen H.-F. Recent Force Field Strategies for Intrinsically Disordered Proteins. J. Chem. Inf. Model. 2021, 61, 1037–1047. 10.1021/acs.jcim.0c01175. PubMed DOI PMC
Koder Hamid M.; Månsson L. K.; Meklesh V.; Persson P.; Skepö M. Molecular Dynamics Simulations of the Adsorption of an Intrinsically Disordered Protein: Force Field and Water Model Evaluation in Comparison with Experiments. Front. Mol. Biosci. 2022, 9, 958175.10.3389/fmolb.2022.958175. PubMed DOI PMC
Henriques J.; Cragnell C.; Skepö M. Molecular Dynamics Simulations of Intrinsically Disordered Proteins: Force Field Evaluation and Comparison with Experiment. J. Chem. Theory Comput. 2015, 11, 3420–3431. 10.1021/ct501178z. PubMed DOI
Henriques J.; Skepö M. Molecular Dynamics Simulations of Intrinsically Disordered Proteins: On the Accuracy of the TIP4P-D Water Model and the Representativeness of Protein Disorder Models. J. Chem. Theory Comput. 2016, 12, 3407–3415. 10.1021/acs.jctc.6b00429. PubMed DOI
Ozenne V.; Bauer F.; Salmon L.; Huang J.-R.; Jensen M. R.; Segard S.; Bernadó P.; Charavay C.; Blackledge M. Flexible-Meccano: ATool for the Generation of Explicit Ensemble Descriptions of Intrinsically Disordered Proteins and Their Associated Experimental Observables. Bioinformatics 2012, 28, 1463–1470. 10.1093/bioinformatics/bts172. PubMed DOI
Salmon L.; Nodet G.; Ozenne V.; Yin G.; Jensen M. R.; Zweckstetter M.; Blackledge M. NMR Characterization of Long-Range Order in Intrinsically Disordered Proteins. J. Am. Chem. Soc. 2010, 132, 8407–8418. 10.1021/ja101645g. PubMed DOI
Shen Y.; Bax A. Protein Backbone Chemical Shifts Predicted from Searching a Database for Torsion Angle and Sequence Homology. J. Biomol. NMR 2007, 38, 289–302. 10.1007/s10858-007-9166-6. PubMed DOI
Li J.; Bennett K. C.; Liu Y.; Martin M. V.; Head-Gordon T. Accurate Prediction of Chemical Shifts for Aqueous Protein Structure on “Real World” Data. Chem. Sci. 2020, 11, 3180–3191. 10.1039/C9SC06561J. PubMed DOI PMC
Sanz-Hernández M.; De Simone A. The Prosecco Server for Chemical Shift Predictions in Ordered and Disordered Proteins. J. Biomol. NMR 2017, 69, 147–156. 10.1007/s10858-017-0145-2. PubMed DOI PMC
Parr R. G.; Yang W. Density-Functional Theory of Atoms and Molecules. Annu. Rev. Phys. Chem. 1995, 46, 701–728. 10.1146/annurev.pc.46.100195.003413. PubMed DOI
Christensen A. S.; Hamelryck T.; Jensen J. H. FragBuilder: an Efficient Python Library to Setup Quantum Chemistry Calculations on Peptides Models. PeerJ. 2014, 2, e277.10.7717/peerj.277. PubMed DOI PMC
Stewart J. J. P. Optimization of Parameters for Semiempirical Methods V: Modification of NDDO Approximations and Application to 70 Elements. J. Mol. Model. 2007, 13, 1173–1213. 10.1007/s00894-007-0233-4. PubMed DOI PMC
Handy N. C.; Cohen A. J. Left-Right Correlation Energy. Mol. Phys. 2001, 99, 403–412. 10.1080/00268970010018431. DOI
Hoe W.-M.; Cohen A. J.; Handy N. C. Assessment of a New Local Exchange Functional OPTX. Chem. Phys. Lett. 2001, 341, 319.10.1016/S0009-2614(01)00581-4. DOI
Perdew J. P.; Burke K.; Ernzerhoff M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. 10.1103/PhysRevLett.77.3865. PubMed DOI
Perdew J. P.; Burke K.; Ernzerhoff M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865.10.1103/PhysRevLett.77.3865. PubMed DOI
Ditchfield R.; Hehre W. J.; Pople J. A. Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971, 54, 724–728. 10.1063/1.1674902. DOI
Francl M. M.; Pietro W. J.; Hehre W. J.; Binkley J. S.; Gordon M. S.; DeFrees D. J.; Pople J. A. Self-Consistent Molecular-Orbital Methods. XXIII. A Polarization-Type Basis Set for Second-Row Elements. J. Chem. Phys. 1982, 77, 3654–3665. 10.1063/1.444267. DOI
Gordon M. S.; Binkley J. S.; Pople J. A.; Pietro W. J.; Hehre W. J. Self-Consistent Molecular-Orbital Methods. 22. Small Split-Valence Basis Sets for Second-Row Elements. J. Am. Chem. Soc. 1982, 104, 2797–2803. 10.1021/ja00374a017. DOI
Hariharan P. C.; Pople J. A. The Influence of Polarization Functions on Molecular Orbital Hydrogenation Energies. Theor. Chim. Acta 1973, 28, 213–222. 10.1007/BF00533485. DOI
Hehre W. J.; Ditchfield R.; Pople J. A. Self-Consistent Molecular-Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257–2261. 10.1063/1.1677527. DOI
Boomsma W.; et al. PHAISTOS: A Framework for Markov Chain Monte Carlo Simulation and Inference of Protein Structure. J. Comput. Chem. 2013, 34, 1697–1705. 10.1002/jcc.23292. PubMed DOI
Juhas M.https://github.com/martinj80/phaistos.
McGibbon R. T.; Beauchamp K. A.; Harrigan M. P.; Klein C.; Swails J. M.; Hernández C. X.; Schwantes C. R.; Wang L.-P.; Lane T. J.; Pande V. S. MDTraj: a Modern Open Library for the Analysis of Molecular Dynamics Trajectories. Biophys. J. 2015, 109, 1528–1532. 10.1016/j.bpj.2015.08.015. PubMed DOI PMC
Daura X.; Gademann K.; Jaun B.; Seebach D.; van Gunsteren W. F.; Mark A. E. Peptide Folding: When Simulation Meets Experiment. Angew. Chem., Int. Ed. 1999, 38, 236–240. 10.1002/(SICI)1521-3773(19990115)38:1/2<236::AID-ANIE236>3.0.CO;2-M. DOI
Lindahl E.; Hess B.; Van Der Spoel D. GROMACS 3.0: a Package for Molecular Simulation and Trajectory Analysis. Mol. Modeling Annual 2001, 7, 306–317. 10.1007/s008940100045. DOI
Adzhubei A. A.; Sternberg M. J.; Makarov A. A. Polyproline-II Helix in Proteins: Structure and Function. J. Mol. Biol. 2013, 425, 2100–2132. 10.1016/j.jmb.2013.03.018. PubMed DOI
Kjaergaard M.; Nørholm A.-B.; Hendus-Altenburger R.; Pedersen S. F.; Poulsen F. M.; Kragelund B. B. Temperature-Dependent Structural Changes in Intrinsically Disordered Proteins: Formation of α–Helices or Loss of Polyproline II?. Protein Sci. 2010, 19, 1555–1564. 10.1002/pro.435. PubMed DOI PMC
Tomasso M. E.; Tarver M. J.; Devarajan D.; Whitten S. T. Hydrodynamic Radii of Intrinsically Disordered Proteins Determined from Experimental Polyproline II Propensities. PLoS Comput. Biol. 2016, 12, e1004686.10.1371/journal.pcbi.1004686. PubMed DOI PMC
Rieloff E.; Skepö M. The Effect of Multisite Phosphorylation on the Conformational Properties of Intrinsically Disordered Proteins. Int. J. Mol. Sci. 2021, 22, 11058.10.3390/ijms222011058. PubMed DOI PMC
Felli I. C.; Bermel W.; Pierattelli R. Exclusively Heteronuclear NMR Experiments for the Investigation of Intrinsically Disordered Proteins: Focusing on Proline Residues. Magn. Reson. 2021, 2, 511–522. 10.5194/mr-2-511-2021. PubMed DOI PMC
Gopal S. M.; Wingbermühle S.; Schnatwinkel J.; Juber S.; Herrmann C.; Schäfer L. V. Conformational Preferences of an Intrinsically Disordered Protein Domain: A Case Study for Modern Force Fields. J. Phys. Chem. B 2021, 125, 24–35. 10.1021/acs.jpcb.0c08702. PubMed DOI
Jia M.; Yuan D. Y.; Lovelace T. C.; Hu M.; Benos P. V. Causal Discovery in High-Dimensional, Multicollinear Datasets. Front. Epidemiol. 2022, 2, 899655.10.3389/fepid.2022.899655. PubMed DOI PMC