Skip to main content
Log in

Comprehensive evaluation of end-point free energy techniques in carboxylated-pillar[6]arene host–guest binding: II. regression and dielectric constant

  • Published:
Journal of Computer-Aided Molecular Design Aims and scope Submit manuscript

Abstract

End-point free energy calculations as a powerful tool have been widely applied in protein–ligand and protein–protein interactions. It is often recognized that these end-point techniques serve as an option of intermediate accuracy and computational cost compared with more rigorous statistical mechanic models (e.g., alchemical transformation) and coarser molecular docking. However, it is observed that this intermediate level of accuracy does not hold in relatively simple and prototypical host–guest systems. Specifically, in our previous work investigating a set of carboxylated-pillar[6]arene host–guest complexes, end-point methods provide free energy estimates deviating significantly from the experimental reference, and the rank of binding affinities is also incorrectly computed. These observations suggest the unsuitability and inapplicability of standard end-point free energy techniques in host–guest systems, and alteration and development are required to make them practically usable. In this work, we consider two ways to improve the performance of end-point techniques. The first one is the PBSA_E regression that varies the weights of different free energy terms in the end-point calculation procedure, while the second one is considering the interior dielectric constant as an additional variable in the end-point equation. By detailed investigation of the calculation procedure and the simulation outcome, we prove that these two treatments (i.e., regression and dielectric constant) are manipulating the end-point equation in a somehow similar way, i.e., weakening the electrostatic contribution and strengthening the non-polar terms, although there are still many detailed differences between these two methods. With the trained end-point scheme, the RMSE of the computed affinities is improved from the standard ~ 12 kcal/mol to ~ 2.4 kcal/mol, which is comparable to another altered end-point method (ELIE) trained with system-specific data. By tuning PBSA_E weighting factors with the host-specific data, it is possible to further decrease the prediction error to ~ 2.1 kcal/mol. These observations along with the extremely efficient optimized-structure computation procedure suggest the regression (i.e., PBSA_E as well as its GBSA_E extension) as a practically applicable solution that brings end-point methods back into the library of usable tools for host–guest binding. However, the dielectric-constant-variable scheme cannot effectively minimize the experiment-calculation discrepancy for absolute binding affinities, but is able to improve the calculation of affinity ranks. This phenomenon is somehow different from the protein–ligand case and suggests the difference between host–guest and biomacromolecular (protein–ligand and protein–protein) systems. Therefore, the spectrum of tools usable for protein–ligand complexes could be unsuitable for host–guest binding, and numerical validations are necessary to screen out really workable solutions in these ‘prototypical’ situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

The atomic-charge files of all molecules and the docking-produced initial bound structures with the AD4 and Vina scoring functions are shared online at https://github.com/proszxppp/WP6-host-guest-binding. All free energy estimates obtained in this work are given in the supporting information.

References

  1. Zeng J, Huang Z (2019) From levinthal’s paradox to the effects of cell environmental perturbation on protein folding. Curr Med Chem 26:7537–7554

    CAS  PubMed  Google Scholar 

  2. Chen J, Zeng Q, Wang W, Hu Q, Bao H (2022) Q61 mutant-mediated dynamics changes of the GTP-KRAS complex probed by Gaussian accelerated molecular dynamics and free energy landscapes. RSC Adv 12:1742–1757

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Sotriffer, C. A.; Sanschagrin, P.; Matter, H.; Klebe, G., SFCscore: scoring functions for affinity prediction of protein–ligand complexes. Proteins: Structure, Function, and Bioinformatics 2008, 73, 395–419.

  4. Pecina A, Eyrilmez SM, Köprülüoğlu C, Miriyala VM, Lepšík M, Fanfrlík J, Řezáč J, Hobza P (2020) SQM/COSMO scoring function: reliable quantum-mechanical tool for sampling and ranking in structure-based drug design. ChemPlusChem 85:2362–2371

    CAS  PubMed  Google Scholar 

  5. Wang, X., Conformational Fluctuations in GTP-Bound K-Ras: A Metadynamics Perspective with Harmonic Linear Discriminant Analysis. J. Chem. Inf. Model. 2021.

  6. Goel H, Yu W, MacKerell AD (2022) hERG blockade prediction by combining site identification by ligand competitive saturation and physicochemical properties. Chemistry 4:630–646

    CAS  Google Scholar 

  7. Nicolaï A, Petiot N, Grassein P, Delarue P, Neiers F, Senet P (2022) Free-energy landscape analysis of protein-ligand binding: the case of human glutathione transferase A1. Appl Sci 12:8196

    Google Scholar 

  8. Giordano D, Biancaniello C, Argenio MA, Facchiano A (2022) Drug design by pharmacophore and virtual screening approach. Pharmaceuticals 15:646

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Homeyer N, Gohlke H (2012) Free energy calculations by the molecular mechanics poisson−boltzmann surface area method. Mol Inf 31:114–122

    CAS  Google Scholar 

  10. Lindstrom A, Edvinsson L, Johansson A, Andersson CD, Andersson IE, Raubacher F, Linusson A (2011) Postprocessing of docked protein− ligand complexes using implicit solvation models. J Chem Inf Model 51:267–282

    CAS  PubMed  Google Scholar 

  11. Yang T, Wu JC, Yan C, Wang Y, Luo R, Gonzales MB, Dalby KN, Ren P (2011) Virtual screening using molecular simulations. Proteins 79:1940–1951

    CAS  PubMed  PubMed Central  Google Scholar 

  12. Khalak, Y.; Tresadern, G.; de Groot, B. L.; Gapsys, V., Non-equilibrium approach for binding free energies in cyclodextrins in SAMPL7: force fields and software. J. Comput.-Aided Mol. Des. 2021, 35, 49–61.

  13. Sun Z, Wang X, Zhang JZH (2017) BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation. Phys Chem Chem Phys 19:15005–15020

    CAS  PubMed  Google Scholar 

  14. Sun, Z.; Wang, M.; He, Q.; Liu, Z., Molecular modelling of ionic liquids: force-field validation and thermodynamic perspective from large-scale fast-growth solvation free energy calculations. Adv. Theory Simul. 2022, 2200274.

  15. Sun Z, Gong Z, Zheng L, Payam K, Huai Z, Liu Z (2022) Molecular modelling of ionic liquids: general guidelines on fixed-charge force fields for balanced descriptions. Journal of Ionic Liquids 2:100043

    Google Scholar 

  16. Sun Z, Kayal A, Gong Z, Zheng L, He Q (2022) Molecular modelling of ionic liquids: physical properties of species with extremely long aliphatic chains from a near-optimal regime. J Mol Liq 367:120492

    CAS  Google Scholar 

  17. Ferrari AM, Degliesposti G, Sgobba M, Rastelli G (2007) Validation of an automated procedure for the prediction of relative free energies of binding on a set of aldose reductase inhibitors. Biorg Med Chem 15:7865–7877

    CAS  Google Scholar 

  18. Rapp C, Kalyanaraman C, Schiffmiller A, Schoenbrun EL, Jacobson MP (2011) A molecular mechanics approach to modeling protein-ligand interactions: relative binding affinities in congeneric series. J Chem Inf Model 51:2082–2089

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Miller BR, Mcgee TD, Swails JM, Homeyer N, Gohlke H, Roitberg AE (2012) MMPBSA.py: an efficient program for end-state free energy calculations. J Chem Theory Comput 8:3314–3321

    CAS  PubMed  Google Scholar 

  20. Wan S, Knapp B, Wright DW, Deane CM, Coveney PV (2015) Rapid, precise, and reproducible prediction of peptide–MHC binding affinities from molecular dynamics that correlate well with experiment. J Chem Theory Comput 11:3346–3356

    CAS  PubMed  Google Scholar 

  21. Panday SK, Alexov E (2022) Protein-protein binding free energy predictions with the MM/PBSA approach complemented with the gaussian-based method for entropy estimation. ACS Omega 7:11057–11067

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Tian S, Zeng J, Liu X, Chen J, Zhang JZ, Zhu T (2019) Understanding the selectivity of inhibitors toward PI4KIIIα and PI4KIIIβ based molecular modeling. Phys Chem Chem Phys 21:22103–22112

    CAS  PubMed  Google Scholar 

  23. Su PC, Tsai CC, Mehboob S, Hevener KE, Johnson ME (2015) Comparison of radii sets, entropy, QM methods, and sampling on MM-PBSA, MM-GBSA, and QM/MM-GBSA ligand binding energies of F. tularensis enoyl-ACP reductase (F abI). J Comput Chem 36:1859–1873

    CAS  PubMed  PubMed Central  Google Scholar 

  24. Sangpheak W, Khuntawee W, Wolschann P, Pongsawasdi P, Rungrotmongkol T (2014) Enhanced stability of a naringenin/2, 6-dimethyl β-cyclodextrin inclusion complex: Molecular dynamics and free energy calculations based on MM-and QM-PBSA/GBSA. J Mol Graph Model 50:10–15

    CAS  PubMed  Google Scholar 

  25. Tsitsanou KE, Hayes JM, Keramioti M, Mamais M, Oikonomakos NG, Kato A, Leonidas DD, Zographos SE (2013) Sourcing the affinity of flavonoids for the glycogen phosphorylase inhibitor site via crystallography, kinetics and QM/MM-PBSA binding studies: comparison of chrysin and flavopiridol. Food Chem Toxicol 61:14–27

    CAS  PubMed  Google Scholar 

  26. Huai Z, Yang H, Li X, Sun Z (2021) SAMPL7 TrimerTrip host-guest binding affinities from extensive alchemical and end-point free energy calculations. J Comput Aided Mol Des 35:117–129

    CAS  PubMed  Google Scholar 

  27. Van Zundert G, Rodrigues J, Trellet M, Schmitz C, Kastritis P, Karaca E, Melquiond A, van Dijk M, De Vries S, Bonvin A (2016) The HADDOCK2. 2 web server user-friendly integrative modeling of biomolecular complexes. J Mol Biol 428:720–725

    PubMed  Google Scholar 

  28. Krammer A, Kirchhoff PD, Jiang X, Venkatachalam C, Waldman M (2005) LigScore: a novel scoring function for predicting binding affinities. J Mol Graph Model 23:395–407

    CAS  PubMed  Google Scholar 

  29. Wang X, Chong B, Sun Z, Ruan H, Yang Y, Song P, Liu Z (2022) More is simpler: Decomposition of ligand-binding affinity for proteins being disordered. Protein Sci 31:e4375

    CAS  PubMed  Google Scholar 

  30. Ahmadian N, Mehrnejad F, Amininasab M (2020) Molecular insight into the interaction between camptothecin and acyclic cucurbit[4]urils as efficient nanocontainers in comparison with cucurbit[7]uril: molecular docking and molecular dynamics simulation. J Chem Inf Model 60:1791–1803

    CAS  PubMed  Google Scholar 

  31. Mitkina T, Naumov DY, Gerasko O, Dolgushin F, Vicent C, Llusar R, Sokolov M, Fedin V (2004) Inclusion of nickel (II) and copper (II) complexes with aliphatic polyamines in cucurbit [8] uril. Russ Chem Bull 53:2519–2524

    CAS  Google Scholar 

  32. Samsonenko, D.; Virovets, A.; Lipkowski, J.; Geras' ko, O.; Fedin, V., Distortion of the cucurbituril molecule by an included 4‐methylpyridinum cation. J. Struct. Chem. 2002, 43, 664–668.

  33. Sun Z, He Q, Li X, Zhu Z (2020) SAMPL6 host–guest binding affinities and binding poses from spherical-coordinates-biased simulations. J Comput Aided Mol Des 34:589–600

    CAS  PubMed  Google Scholar 

  34. Litim A, Belhocine Y, Benlecheb T, Ghoniem MG, Kabouche Z, Ali FAM, Abdulkhair BY, Seydou M, Rahali S (2021) DFT-D4 insight into the inclusion of amphetamine and methamphetamine in cucurbit[7]uril: energetic, structural and biosensing properties. Molecules 26:7479

    CAS  PubMed  PubMed Central  Google Scholar 

  35. Hsiao Y-W, Söderhjelm P (2014) Prediction of SAMPL4 host–guest binding affinities using funnel metadynamics. J Comput Aided Mol Des 28:443–454

    CAS  PubMed  Google Scholar 

  36. Jansook P, Ogawa N, Loftsson T (2018) Cyclodextrins: structure, physicochemical properties and pharmaceutical applications. Int J Pharm 535:272–284

    CAS  PubMed  Google Scholar 

  37. Gebhardt J, Kleist C, Jakobtorweihen S, Hansen N (2018) Validation and comparison of force fields for native cyclodextrins in aqueous solution. J Phys Chem B 122:1608–1626

    CAS  PubMed  Google Scholar 

  38. Peerannawar SR, Gejji SP (2013) Theoretical investigations on vibrational spectra of pillar [5] arene-bis (pyridinium) complexes. Spectrochim Acta Part A Mol Biomol Spectrosc 104:368–376

    CAS  Google Scholar 

  39. Li S-H, Zhang H-Y, Xu X, Liu Y (2015) Mechanically selflocked chiral gemini-catenanes. Nat Commun 6:1–7

    Google Scholar 

  40. Qin S, Xiong S, Han Y, Hu XY, Wang L (2015) Controllable fabrication of various supramolecular nanostructures based on nonamphiphilic azobenzene derivatives and pillar [6] arene. Chin J Chem 33:107–111

    CAS  Google Scholar 

  41. Liu L, Cao D, Jin Y, Tao H, Kou Y, Meier H (2011) Efficient synthesis of copillar [5] arenes and their host–guest properties with dibromoalkanes. Org Biomol Chem 9:7007–7010

    CAS  PubMed  Google Scholar 

  42. Zhang C-C, Li S-H, Zhang C-F, Liu Y (2016) Size switchable supramolecular nanoparticle based on azobenzene derivative within anionic pillar [5] arene. Sci Rep 6:1–9

    Google Scholar 

  43. Xia B, He J, Abliz Z, Yu Y, Huang F (2011) Synthesis of a pillar [5] arene dimer by co-oligomerization and its complexation with n-octyltrimethyl ammonium hexafluorophosphate. Tetrahedron Lett 52:4433–4436

    CAS  Google Scholar 

  44. Yu G, Han C, Zhang Z, Chen J, Yan X, Zheng B, Liu S, Huang F (2012) Pillar [6] arene-based photoresponsive host–guest complexation. J Am Chem Soc 134:8711–8717

    CAS  PubMed  Google Scholar 

  45. Ogoshi T, Yamafuji D, Akutsu T, Naito M, Yamagishi T-A (2013) Achiral guest-induced chiroptical changes of a planar-chiral pillar [5] arene containing one π-conjugated unit. Chem Commun 49:8782–8784

    CAS  Google Scholar 

  46. Strutt NL, Zhang H, Schneebeli ST, Stoddart JF (2014) Amino-functionalized pillar [5] arene. Chem Eur J 20:10996–11004

    CAS  PubMed  Google Scholar 

  47. Ma Y, Yang J, Li J, Chi X, Xue M (2013) A cationic water-soluble pillar [6] arene: synthesis, host–guest properties, and self-assembly with amphiphilic guests in water. RSC Adv 3:23953–23956

    CAS  Google Scholar 

  48. Yang K, Chang Y, Wen J, Lu Y, Pei Y, Cao S, Wang F, Pei Z (2016) Supramolecular vesicles based on complex of trp-modified pillar [5] arene and galactose derivative for synergistic and targeted drug delivery. Chem Mater 28:1990–1993

    CAS  Google Scholar 

  49. Strutt NL, Schneebeli ST, Stoddart JF (2013) Stereochemical inversion in difunctionalised pillar [5] arenes. Supramol Chem 25:596–608

    CAS  Google Scholar 

  50. Dasgupta S, Mukherjee PS (2017) Carboxylatopillar [n] arenes: a versatile class of water soluble synthetic receptors. Org Biomol Chem 15:762–772

    CAS  PubMed  Google Scholar 

  51. Gu A, Wheate NJ (2021) Macrocycles as drug-enhancing excipients in pharmaceutical formulations. J Incl Phenom Macrocycl Chem 100:55–69

    CAS  Google Scholar 

  52. Wheate NJ, Dickson K-A, Kim RR, Nematollahi A, Macquart RB, Kayser V, Yu G, Church WB, Marsh DJ (2016) Host-guest complexes of carboxylated pillar [n] arenes with drugs. J Pharm Sci 105:3615–3625

    CAS  PubMed  Google Scholar 

  53. Li Z, Yang J, Yu G, He J, Abliz Z, Huang F (2014) Water-soluble pillar [7] arene: synthesis, pH-controlled complexation with paraquat, and application in constructing supramolecular vesicles. Org Lett 16:2066–2069

    CAS  PubMed  Google Scholar 

  54. Liu, X.; Zheng, L.; Qin, C.; Zhang, J. Z. H.; Sun, Z., Comprehensive Evaluation of End-Point Free Energy Techniques in Carboxylated-Pillar[6]arene Host-guest Binding: I. Standard Procedure. J. Comput.-Aided Mol. Des. 2022.

  55. Liu X, Liu J, Zhu T, Zhang L, He X, Zhang JZ (2016) PBSA_E: A PBSA-based free energy estimator for protein-ligand binding affinity. J Chem Inf Model 56:854–861

    CAS  PubMed  Google Scholar 

  56. Xu L, Sun H, Li Y, Wang J, Hou T (2013) Assessing the performance of MM/PBSA and MM/GBSA methods. 3. The impact of force fields and ligand charge models. J Phys Chem B 117:8408–8421

    CAS  PubMed  Google Scholar 

  57. Wang E, Weng G, Sun H, Du H, Zhu F, Chen F, Wang Z, Hou T (2019) Assessing the performance of the MM/PBSA and MM/GBSA methods. 10. Impacts of enhanced sampling and variable dielectric model on protein–protein interactions. Phys Chem Chem Phys 21:18958–18969

    CAS  PubMed  Google Scholar 

  58. Wang E, Sun H, Wang J, Wang Z, Liu H, Zhang JZ, Hou T (2019) End-point binding free energy calculation with MM/PBSA and MM/GBSA: strategies and applications in drug design. Chem Rev 119:9478–9508

    CAS  PubMed  Google Scholar 

  59. https://github.com/samplchallenges/SAMPL9.

  60. Procacci P, Guarnieri G (2022) SAMPL9 blind predictions using nonequilibrium alchemical approaches. J Chem Phys 156:164104

    CAS  PubMed  Google Scholar 

  61. Jakalian A, Jack DB, Bayly CI (2002) Fast, efficient generation of high-quality atomic charges AM1-BCC model: II. Parameterization and validation. J Comput Chem 23:1623–1641

    CAS  PubMed  Google Scholar 

  62. Bayly CI, Cieplak P, Cornell W, Kollman PA (1992) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J Phys Chem 97:10269–10280

    Google Scholar 

  63. Mcweeny R, Diercksen G (1968) Self-consistent perturbation theory. II. Extension to open shells. J Chem Phys 49:4852–4856

    CAS  Google Scholar 

  64. Pople JA, Nesbet RK (1954) Self-consistent orbitals for radicals. J Chem Phys 22:571–572

    CAS  Google Scholar 

  65. Roothaan CCJ (1951) New developments in molecular orbital theory. Rev Mod Phys 23:69–89

    CAS  Google Scholar 

  66. Hertwig RH, Koch W (1997) On the parameterization of the local correlation functional. What is Becke-3-LYP? Chem Phys Lett 268:345–351

    CAS  Google Scholar 

  67. Becke AD (1996) Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing. J Chem Phys 104:1040–1046

    CAS  Google Scholar 

  68. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98:11623–11627

    CAS  Google Scholar 

  69. Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA (2004) Development and testing of a general amber force field. J Comput Chem 25:1157–1173

    CAS  PubMed  Google Scholar 

  70. Dong X, Yuan X, Song Z, Wang Q (2021) The development of an Amber-compatible organosilane force field for drug-like small molecules. Phys Chem Chem Phys 23:12582–12591

    CAS  PubMed  Google Scholar 

  71. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926–935

    CAS  Google Scholar 

  72. Price DJ, Brooks CL III (2004) A modified TIP3P water potential for simulation with ewald summation. J Chem Phys 121:10096–10103

    CAS  PubMed  Google Scholar 

  73. Berendsen HJC, Grigera JR, Straatsma TPJ (1987) The missing term in effective pair potentials. J Phys Chem 91:6269–6271

    CAS  Google Scholar 

  74. Su M, Yang Q, Du Y, Feng G, Liu Z, Li Y, Wang R (2019) Comparative assessment of scoring functions: the CASF-2016 update. J Chem Inf Model 59:895–913

    CAS  PubMed  Google Scholar 

  75. Eberhardt J, Santos-Martins D, Tillack AF, Forli S (2021) AutoDock Vina 1.2.0: New docking methods, expanded force field, and python bindings. J Chem Inf Model 61:3891–3898

    CAS  PubMed  Google Scholar 

  76. Morris GM, Huey R, Lindstrom W, Sanner MF, Belew RK, Goodsell DS, Olson AJ (2009) AutoDock4 and AutoDockTools4: sutomated docking with selective receptor flexibility. J Comput Chem 30:2785–2791

    CAS  PubMed  PubMed Central  Google Scholar 

  77. Nguyen NT, Nguyen TH, Pham TNH, Huy NT, Bay MV, Pham MQ, Nam PC, Vu VV, Ngo ST (2020) Autodock vina adopts more accurate binding poses but autodock4 forms better binding affinity. J Chem Inf Model 60:204–211

    CAS  PubMed  Google Scholar 

  78. Gaillard T (2018) Evaluation of AutoDock and AutoDock Vina on the CASF-2013 benchmark. J Chem Inf Model 58:1697–1706

    CAS  PubMed  Google Scholar 

  79. Joung IS, Cheatham TE III (2008) Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations. J Phys Chem B 112:9020–9041

    CAS  PubMed  PubMed Central  Google Scholar 

  80. Joung IS, Cheatham TE (2009) Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters. J Phys Chem B 113:13279–13290

    CAS  PubMed  PubMed Central  Google Scholar 

  81. Ryckaert JP, Ciccotti G, Berendsen HJC (1977) Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n -alkanes. J Comput Phys 23:327–341

    CAS  Google Scholar 

  82. Miyamoto S, Kollman PA (1992) Settle: an analytical version of the SHAKE and RATTLE Algorithm for rigid water models. J Comput Chem 13:952–962

    CAS  Google Scholar 

  83. Pastor RW, Brooks BR, Szabo A (1988) An analysis of the accuracy of Langevin and molecular dynamics algorithms. Mol Phys 65:1409–1419

    Google Scholar 

  84. Tuckerman ME, Berne BJ, Martyna GJ (1991) Molecular dynamics algorithm for multiple time scales: Systems with long range forces. J Chem Phys 94:6811–6815

    CAS  Google Scholar 

  85. Case DA, Cheatham TE, Tom D, Holger G, Luo R, Merz KM, Alexey O, Carlos S, Bing W, Woods RJ (2005) The amber biomolecular simulation programs. J Comput Chem 26:1668–1688

    CAS  PubMed  PubMed Central  Google Scholar 

  86. Massova I, Kollman PA (2000) Combined molecular mechanical and continuum solvent approach (MM-PBSA/GBSA) to predict ligand binding. Perspect Drug Discovery Des 18:113–135

    CAS  Google Scholar 

  87. Onufriev A, Bashford D, Case DA (2004) Exploring protein native states and large-scale conformational changes with a modified generalized born model. Proteins: Struct, Funct, Bioinf 55:383–394

    CAS  Google Scholar 

  88. Feig M, Onufriev A, Lee MS, Im W, Case DA (2004) Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures. J Comput Chem 25:265–284

    CAS  PubMed  Google Scholar 

  89. Weiser J, Shenkin PS, Still WC (1999) Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO). J Comput Chem 20:217–230

    CAS  Google Scholar 

  90. Case DA (2010) Normal mode analysis of protein dynamics. Curr Opin Struct Biol 4:285–290

    Google Scholar 

  91. Karplus M, Kushick JN (1981) Method for estimating the configurational entropy of macromolecules. Macromolecules 14:325–332

    CAS  Google Scholar 

  92. Sun Z, Yan YN, Yang M, Zhang JZ (2017) Interaction entropy for protein-protein binding. J Chem Phys 146:124124

    PubMed  Google Scholar 

  93. Chen J, Pang L, Wang W, Wang L, Zhang JZ, Zhu T (2019) Decoding molecular mechanism of inhibitor bindings to CDK2 using molecular dynamics simulations and binding free energy calculations. J Biomol Struct Dyn 38:985–996

    CAS  PubMed  Google Scholar 

  94. Zheng L, Yang Y, Bao J, He L, Qi Y, Zhang JZH (2022) Discovery of novel inhibitors of CDK2 using docking and physics-based binding free energy calculation. Chem Biol Drug Des 99:662–673

    CAS  PubMed  Google Scholar 

  95. Procacci P (2016) Reformulating the entropic contribution in molecular docking scoring functions. J Comput Chem 37:1819–1827

    CAS  PubMed  Google Scholar 

  96. Deng C-L, Cheng M, Zavalij PY, Isaacs L (2022) Thermodynamics of pillararene·guest complexation: blinded dataset for the SAMPL9 challenge. New J Chem 46:995–1002

    CAS  PubMed  Google Scholar 

  97. Kendall MG (1938) A new measure of rank correlation. Biometrika 30:81–93

    Google Scholar 

  98. Pearlman DA, Charifson PS (2001) Are free energy calculations useful in practice? A comparison with rapid scoring functions for the p38 MAP kinase protein system. J Med Chem 44:3417–3423

    CAS  PubMed  Google Scholar 

  99. He X, Man VH, Ji B, Xie X-Q, Wang J (2019) Calculate protein–ligand binding affinities with the extended linear interaction energy method: application on the Cathepsin S set in the D3R Grand Challenge 3. J Comput Aided Mol Des 33:105–117

    CAS  PubMed  Google Scholar 

  100. Hao D, He X, Ji B, Zhang S, Wang J (2020) How well does the extended linear interaction energy method perform in accurate binding free energy calculations? J Chem Inf Model 60:6624–6633

    CAS  PubMed  Google Scholar 

  101. Zhu K, Shirts MR, Friesner RA (2007) Improved methods for side chain and loop predictions via the protein local optimization program: variable dielectric model for implicitly improving the treatment of polarization effects. J Chem Theory Comput 3:2108–2119

    CAS  PubMed  Google Scholar 

  102. Yan Y, Yang M, Ji CG, Zhang JZ (2017) Interaction entropy for computational alanine scanning. J Chem Inf Model 57:1112–1122

    CAS  PubMed  Google Scholar 

  103. Wang E, Liu H, Wang J, Weng G, Sun H, Wang Z, Kang Y, Hou T (2020) Development and evaluation of MM/GBSA based on a variable dielectric GB model for predicting protein–ligand binding affinities. J Chem Inf Model 60:5353–5365

    CAS  PubMed  Google Scholar 

  104. Simões IC, Costa IP, Coimbra JT, Ramos MJ, Fernandes PA (2017) New parameters for higher accuracy in the computation of binding free energy differences upon alanine scanning mutagenesis on protein–protein interfaces. J Chem Inf Model 57:60–72

    PubMed  Google Scholar 

  105. Onufriev AV, Izadi S (2018) Water models for biomolecular simulations. Wiley Interdisip Rev Comput Mol Sci 8:e1347

    Google Scholar 

  106. Liu X, Peng L, Zhang JZ (2018) Accurate and efficient calculation of protein-protein binding free energy-interaction entropy with residue type-specific dielectric constants. J Chem Inf Model 59:272–281

    PubMed  Google Scholar 

  107. Genheden S, Ryde U (2012) Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies. Proteins Struct Function Bioinformatics 80:1326–1342

    CAS  Google Scholar 

  108. Wang C, Nguyen PH, Pham K, Huynh D, Le T-BN, Wang H, Ren P, Luo R (2016) Calculating protein–ligand binding affinities with MMPBSA: Method and error analysis. J Comput Chem 37:2436–2446

    CAS  PubMed  PubMed Central  Google Scholar 

  109. Sun Z, Zheng L, Kai W, Huai Z, Liu Z (2022) Primary vs Secondary: Directionalized Guest Coordination in β-Cyclodextrin Derivatives. Carbohydr Polym 297:120050

    CAS  PubMed  Google Scholar 

  110. Sun Z, Huai Z, He Q, Liu Z (2021) A general picture of cucurbit[8]uril host-guest binding. J Chem Inf Model 61:6107–6134

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 21633001), Beijing Natural Science Foundation (Grant No. 7224357), National Natural Science Foundation of China (Grant No. 22107063) and National Natural Science Foundation of China (Grant No. 62072296). Part of the simulation was performed on the high-performance computing platform of the Center for Life Science (Peking University). We thank Dr. Zhe Huai (XtalPi), Dr. Tong Zhu (ECNU) and the anonymous reviewers for valuable comments and critical reading.

Author information

Authors and Affiliations

Authors

Contributions

Xiao Liu and Zhaoxi Sun designed the research. Xiao Liu performed the simulation with the help of Yalong Cong, Zhaoxi Sun and John Z. H. Zhang. Lei Zheng and Zhaoxi Sun prepared figures and tables. Xiao Liu, Yalong Cong, Zhihao Gong, Zhixiang Yin, John Z. H. Zhang, Zhirong Liu and Zhaoxi Sun contributed to the explanation of observations obtained in the work. Zhaoxi Sun drafted the manuscript and the final version of the paper has been revised by all authors.

Corresponding authors

Correspondence to Xiao Liu, John Z. H. Zhang or Zhaoxi Sun.

Ethics declarations

Conflict of interest

There are no conflicts of interest to declare.

Supporting Information Description

The detailed values of PBSA_E and GBSA_E estimates of WP6 host–guest binding free energies obtained with three charge schemes, two water models, initial bound structures from AD4 and Vina docking, and the dielectric-constant-dependent MM/GBSA and MM/PBSA estimates for five combinations of modelling parameters are given in the supporting information.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 656 kb)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Zheng, L., Cong, Y. et al. Comprehensive evaluation of end-point free energy techniques in carboxylated-pillar[6]arene host–guest binding: II. regression and dielectric constant. J Comput Aided Mol Des 36, 879–894 (2022). https://doi.org/10.1007/s10822-022-00487-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10822-022-00487-w

Keywords

Navigation