Login Register Cart 0
Generic placeholder image

Current Drug Metabolism

Editor-in-Chief

ISSN (Print): 1389-2002
ISSN (Online): 1875-5453

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Mini-Review Article

Classical and Machine Learning Methods for Protein - Ligand Binding Free Energy Estimation

Author(s): Dakshinamurthy Sivakumar and Sangwook Wu*

Volume 23, Issue 4, 2022

Published on: 17 May, 2022

Page: [252 - 259] Pages: 8

DOI: 10.2174/1389200223666220315160835

Price: $65

Abstract

Binding free energy estimation of drug candidates to their biomolecular target is one of the best quantitative estimators in computer-aided drug discovery. Accurate binding free energy estimation is still a challengeable task even after decades of research, along with the complexity of the algorithm, time-consuming procedures, and reproducibility issues. In this review, we have discussed the advantages and disadvantages of diverse free energy methods like Thermodynamic Integration (TI), Bennett's Acceptance Ratio (BAR), Free Energy Perturbation (FEP), and alchemical methods. Moreover, we discussed the possible application of the machine learning method in proteinligand binding free energy estimation.

Keywords: Free energy, Bennett's acceptance ratio (BAR), alchemical methods, machine learning, computer-aided drug discovery, thermodynamic integration (TI).

« Previous Next »
Graphical Abstract

[1]
Damian, L. Isothermal titration calorimetry for studying protein-ligand interactions. Methods Mol. Biol., 2013, 1008, 103-118.
[http://dx.doi.org/10.1007/978-1-62703-398-5_4] [PMID: 23729250]
[2]
Jaquillard, L.; Saab, F.; Schoentgen, F.; Cadene, M. Improved accuracy of low affinity protein-ligand equilibrium dissociation constants directly determined by electrospray ionization mass spectrometry. J. Am. Soc. Mass Spectrom., 2012, 23(5), 908-922.
[http://dx.doi.org/10.1007/s13361-011-0305-7] [PMID: 22430390]
[3]
Viegas, A.; Manso, J.; Nobrega, F.L.; Cabrita, E.J. Saturation-transfer difference (STD) NMR: A simple and fast method for ligand screen-ing and characterization of protein binding. J. Chem. Educ., 2011, 88(7), 990-994.
[http://dx.doi.org/10.1021/ed101169t]
[4]
Jorgensen, W.L. Free energy calculations: A breakthrough for modeling organic chemistry in solution. Acc. Chem. Res., 1989, 22(5), 184-189.
[http://dx.doi.org/10.1021/ar00161a004]
[5]
Kollman, P. Free energy calculations: applications to chemical and biochemical phenomena. Chem. Rev., 1993, 93(7), 2395-2417.
[http://dx.doi.org/10.1021/cr00023a004]
[6]
Straatsma, T.P.; Berendsen, H.J.C. Free energy of ionic hydration: Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations. J. Chem. Phys., 1988, 89(9), 5876-5886.
[http://dx.doi.org/10.1063/1.455539]
[7]
Zwanzig, R.W. High‐temperature equation of state by a perturbation method. I. Nonpolar gases. J. Chem. Phys., 1954, 22(8), 1420-1426.
[http://dx.doi.org/10.1063/1.1740409]
[8]
Bennett, C.H. Efficient estimation of free energy differences from Monte Carlo data. J. Comput. Phys., 1976, 22(2), 245-268.
[http://dx.doi.org/10.1016/0021-9991(76)90078-4]
[9]
Shirts, M.R.; Chodera, J.D. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys., 2008, 129(12), 124105.
[http://dx.doi.org/10.1063/1.2978177] [PMID: 19045004]
[10]
Singh, N.; Warshel, A. Absolute binding free energy calculations: On the accuracy of computational scoring of protein-ligand interactions. Proteins, 2010, 78(7), 1705-1723.
[http://dx.doi.org/10.1002/prot.22687] [PMID: 20186976]
[11]
Kästner, J. Umbrella sampling. WIREs Computational Molecular Science, 2011, 1(6), 932-942.
[http://dx.doi.org/10.1002/wcms.66]
[12]
Rastelli, G.; Del Rio, A.; Degliesposti, G.; Sgobba, M. Fast and accurate predictions of binding free energies using MM-PBSA and MM-GBSA. J. Comput. Chem., 2010, 31(4), 797-810.
[http://dx.doi.org/10.1002/jcc.21372] [PMID: 19569205]
[13]
Mobley, D.L.; Klimovich, P.V. Perspective: Alchemical free energy calculations for drug discovery. J. Chem. Phys., 2012, 137(23), 230901.
[http://dx.doi.org/10.1063/1.4769292] [PMID: 23267463]
[14]
Mobley, D.L.; Chodera, J.D.; Dill, K.A. On the use of orientational restraints and symmetry corrections in alchemical free energy calcula-tions. J. Chem. Phys., 2006, 125(8), 084902.
[http://dx.doi.org/10.1063/1.2221683] [PMID: 16965052]
[15]
Wirnsberger, P.; Ballard, A.J.; Papamakarios, G.; Abercrombie, S.; Racanière, S.; Pritzel, A.; Jimenez Rezende, D.; Blundell, C. Targeted free energy estimation via learned mappings. J. Chem. Phys., 2020, 153(14), 144112.
[http://dx.doi.org/10.1063/5.0018903] [PMID: 33086827]
[16]
Åqvist, J.; Medina, C.; Samuelsson, J-E. A new method for predicting binding affinity in computer-aided drug design. Protein Eng., 1994, 7(3), 385-391.
[http://dx.doi.org/10.1093/protein/7.3.385] [PMID: 8177887]
[17]
Lee, F.S.; Chu, Z-T.; Bolger, M.B.; Warshel, A. Calculations of antibody-antigen interactions: Microscopic and semi-microscopic evalua-tion of the free energies of binding of phosphorylcholine analogs to McPC603. Protein Eng., 1992, 5(3), 215-228.
[http://dx.doi.org/10.1093/protein/5.3.215] [PMID: 1409541]
[18]
Gilson, M.K.; Zhou, H-X. Calculation of protein-ligand binding affinities. Annu. Rev. Biophys. Biomol. Struct., 2007, 36, 21-42.
[http://dx.doi.org/10.1146/annurev.biophys.36.040306.132550] [PMID: 17201676]
[19]
Uciechowska, U.; Schemies, J.; Scharfe, M.; Lawson, M.; Wichapong, K.; Jung, M.; Sippl, W. Binding free energy calculations and biologi-cal testing of novel thiobarbiturates as inhibitors of the human NAD+ dependent histone deacetylase Sirt2. MedChemComm, 2012, 3(2), 167-173.
[http://dx.doi.org/10.1039/C1MD00214G]
[20]
Ngo, S.T.; Tam, N.M.; Pham, M.Q.; Nguyen, T.H. Benchmark of popular free energy approaches revealing the inhibitors binding to SARS-CoV-2 Mpro. J. Chem. Inf. Model., 2021, 61(5), 2302-2312.
[http://dx.doi.org/10.1021/acs.jcim.1c00159] [PMID: 33829781]
[21]
Jeon, S.; Ko, M.; Lee, J.; Choi, I.; Byun, S.Y.; Park, S.; Shum, D.; Kim, S. Identification of antiviral drug candidates against SARS-CoV-2 from FDA-approved drugs. Antimicrob. Agents Chemother., 2020, 64(7), e00819-e00820.
[http://dx.doi.org/10.1128/AAC.00819-20] [PMID: 32366720]
[22]
Ngo, S.T.; Nguyen, M.T.; Nguyen, M.T. Determination of the absolute binding free energies of HIV-1 protease inhibitors using non-equilibrium molecular dynamics simulations. Chem. Phys. Lett., 2017, 676, 12-17.
[http://dx.doi.org/10.1016/j.cplett.2017.03.034]
[23]
van Dijk, M.; Ter Laak, A.M.; Wichard, J.D.; Capoferri, L.; Vermeulen, N.P.E.; Geerke, D.P. Comprehensive and automated linear interac-tion energy based binding-affinity prediction for multifarious cytochrome P450 aromatase inhibitors. J. Chem. Inf. Model., 2017, 57(9), 2294-2308.
[http://dx.doi.org/10.1021/acs.jcim.7b00222] [PMID: 28776988]
[24]
Srinivasan, J.; Cheatham, T.E.; Cieplak, P.; Kollman, P.A.; Case, D.A. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate−DNA helices. J. Am. Chem. Soc., 1998, 120(37), 9401-9409.
[http://dx.doi.org/10.1021/ja981844+]
[25]
Kollman, P.A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srini-vasan, J.; Case, D.A.; Cheatham, T.E. III. Calculating structures and free energies of complex molecules: Combining molecular mechanics and continuum models. Acc. Chem. Res., 2000, 33(12), 889-897.
[http://dx.doi.org/10.1021/ar000033j] [PMID: 11123888]
[26]
Lee, M.S.; Olson, M.A. Calculation of absolute protein-ligand binding affinity using path and endpoint approaches. Biophys. J., 2006, 90(3), 864-877.
[http://dx.doi.org/10.1529/biophysj.105.071589] [PMID: 16284269]
[27]
Stoica, I.; Sadiq, S.K.; Coveney, P.V. Rapid and accurate prediction of binding free energies for saquinavir-bound HIV-1 proteases. J. Am. Chem. Soc., 2008, 130(8), 2639-2648.
[http://dx.doi.org/10.1021/ja0779250] [PMID: 18225901]
[28]
Wang, E.; Sun, H.; Wang, J.; Wang, Z.; Liu, H.; Zhang, J.Z.H.; Hou, T. End-point binding free energy calculation with MM/PBSA and MM/GBSA: Strategies and applications in drug design. Chem. Rev., 2019, 119(16), 9478-9508.
[http://dx.doi.org/10.1021/acs.chemrev.9b00055] [PMID: 31244000]
[29]
Sun, H.; Li, Y.; Tian, S.; Xu, L.; Hou, T. Assessing the performance of MM/PBSA and MM/GBSA methods. 4. Accuracies of MM/PBSA and MM/GBSA methodologies evaluated by various simulation protocols using PDBbind data set. Phys. Chem. Chem. Phys., 2014, 16(31), 16719-16729.
[http://dx.doi.org/10.1039/C4CP01388C] [PMID: 24999761]
[30]
Sivakumar, D.; Mudedla, S.; Jang, S.; Kim, H.; Park, H.; Choi, Y.; Oh, J.; Wu, S. Computational study on selective PDE9 inhibitors on PDE9-Mg/Mg, PDE9-Zn/Mg, and PDE9-Zn/Zn Systems. Biomolecules, 2021, 11(5), 709.
[http://dx.doi.org/10.3390/biom11050709] [PMID: 34068780]
[31]
Zhao, R-N.; Fan, S.; Han, J-G.; Liu, G. Molecular dynamics study of segment peptides of Bax, Bim, and Mcl-1 BH3 domain of the apop-tosis-regulating proteins bound to the anti-apoptotic Mcl-1 protein. J. Biomol. Struct. Dyn., 2015, 33(5), 1067-1081.
[http://dx.doi.org/10.1080/07391102.2014.929028] [PMID: 24865469]
[32]
Torrie, G.M.; Valleau, J.P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys., 1977, 23, 187-199.
[http://dx.doi.org/10.1016/0021-9991(77)90121-8]
[33]
Kumar, S.; Rosenberg, J.M.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A. The weighted histogram analysis method for free-energy calcula-tions on biomolecules. I. The method. J. Comput. Chem., 1992, 13(8), 1011-1021.
[http://dx.doi.org/10.1002/jcc.540130812]
[34]
Kästner, J.; Thiel, W. Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: “Umbrella integration”. J. Chem. Phys., 2005, 123(14), 144104.
[http://dx.doi.org/10.1063/1.2052648] [PMID: 16238371]
[35]
Grubmüller, H.; Heymann, B.; Tavan, P. Ligand binding: Molecular mechanics calculation of the streptavidin-biotin rupture force. Science, 1996, 271(5251), 997-999.
[http://dx.doi.org/10.1126/science.271.5251.997] [PMID: 8584939]
[36]
You, W.; Tang, Z.; Chang, C.A. Evaluating the accuracy of the umbrella sampling plots with different dissociation paths, conformational changes, and structure preparation. bioRxiv, 2017, 169532.
[http://dx.doi.org/10.1101/169532]
[37]
You, W.; Tang, Z.; Chang, C.A. Potential mean force from umbrella sampling simulations: What can we learn and what is missed? J. Chem. Theory Comput., 2019, 15(4), 2433-2443.
[http://dx.doi.org/10.1021/acs.jctc.8b01142] [PMID: 30811931]
[38]
Kirkwood, J.G. Statistical mechanics of fluid mixtures. J. Chem. Phys., 1935, 3(5), 300-313.
[http://dx.doi.org/10.1063/1.1749657]
[39]
Zwanzig, R.W.; Kirkwood, J.G.; Oppenheim, I.; Alder, B.J. Statistical mechanical theory of transport processes. VII. The coefficient of thermal conductivity of monatomic liquids. J. Chem. Phys., 1954, 22(5), 783-790.
[http://dx.doi.org/10.1063/1.1740193]
[40]
Singh, N.; Li, W. Absolute binding free energy calculations for highly flexible protein MDM2 and its inhibitors. Int. J. Mol. Sci., 2020, 21(13), 4765.
[http://dx.doi.org/10.3390/ijms21134765] [PMID: 32635537]
[41]
Vaupel, A.; Holzer, P.; Ferretti, S.; Guagnano, V.; Kallen, J.; Mah, R.; Masuya, K.; Ruetz, S.; Rynn, C.; Schlapbach, A.; Stachyra, T.; Stutz, S.; Todorov, M.; Jeay, S.; Furet, P. In vitro and in vivo characterization of a novel, highly potent p53-MDM2 inhibitor. Bioorg. Med. Chem. Lett., 2018, 28(20), 3404-3408.
[http://dx.doi.org/10.1016/j.bmcl.2018.08.027] [PMID: 30217415]
[42]
Popowicz, G.M.; Czarna, A.; Wolf, S.; Wang, K.; Wang, W.; Dömling, A.; Holak, T.A. Structures of low molecular weight inhibitors bound to MDMX and MDM2 reveal new approaches for p53-MDMX/MDM2 antagonist drug discovery. Cell Cycle, 2010, 9(6), 1104-1111.
[http://dx.doi.org/10.4161/cc.9.6.10956] [PMID: 20237429]
[43]
Grace, C.R.; Ban, D.; Min, J.; Mayasundari, A.; Min, L.; Finch, K.E.; Griffiths, L.; Bharatham, N.; Bashford, D.; Kiplin Guy, R.; Dyer, M.A.; Kriwacki, R.W. Monitoring ligand-induced protein ordering in drug discovery. J. Mol. Biol., 2016, 428(6), 1290-1303.
[http://dx.doi.org/10.1016/j.jmb.2016.01.016] [PMID: 26812210]
[44]
Merz, K.M.; Kollman, P.A. Free energy perturbation simulations of the inhibition of thermolysin: Prediction of the free energy of binding of a new inhibitor. J. Am. Chem. Soc., 1989, 111(15), 5649-5658.
[http://dx.doi.org/10.1021/ja00197a022]
[45]
Pearlman, D.A.; Connelly, P.R. Determination of the differential effects of hydrogen bonding and water release on the binding of FK506 to native and Tyr82-->Phe82 FKBP-12 proteins using free energy simulations. J. Mol. Biol., 1995, 248(3), 696-717.
[http://dx.doi.org/10.1006/jmbi.1995.0252] [PMID: 7538591]
[46]
Fidelak, J.; Juraszek, J.; Branduardi, D.; Bianciotto, M.; Gervasio, F.L. Free-energy-based methods for binding profile determination in a congeneric series of CDK2 inhibitors. J. Phys. Chem. B, 2010, 114(29), 9516-9524.
[http://dx.doi.org/10.1021/jp911689r] [PMID: 20593892]
[47]
Clark, A.J.; Gindin, T.; Zhang, B.; Wang, L.; Abel, R.; Murret, C.S.; Xu, F.; Bao, A.; Lu, N.J.; Zhou, T.; Kwong, P.D.; Shapiro, L.; Honig, B.; Friesner, R.A. Free energy perturbation calculation of relative binding free energy between broadly neutralizing antibodies and the gp120 glycoprotein of HIV-1. J. Mol. Biol., 2017, 429(7), 930-947.
[http://dx.doi.org/10.1016/j.jmb.2016.11.021] [PMID: 27908641]
[48]
Mondal, D.; Florian, J.; Warshel, A. Exploring the effectiveness of binding free energy calculations. J. Phys. Chem. B, 2019, 123(42), 8910-8915.
[http://dx.doi.org/10.1021/acs.jpcb.9b07593] [PMID: 31560539]
[49]
Eastman, P.; Swails, J.; Chodera, J.D.; McGibbon, R.T.; Zhao, Y.; Beauchamp, K.A.; Wang, L-P.; Simmonett, A.C.; Harrigan, M.P.; Stern, C.D.; Wiewiora, R.P.; Brooks, B.R.; Pande, V.S. OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLOS Comput. Biol., 2017, 13(7), e1005659.
[http://dx.doi.org/10.1371/journal.pcbi.1005659] [PMID: 28746339]
[50]
Abraham, M.J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J.C.; Hess, B.; Lindahl, E. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX, 2015, 1-2, 19-25.
[http://dx.doi.org/10.1016/j.softx.2015.06.001]
[51]
Jespers, W.; Esguerra, M.; Åqvist, J.; Gutiérrez-de-Terán, H. QligFEP: An automated workflow for small molecule free energy calculations in Q. J. Cheminform., 2019, 11(1), 26.
[http://dx.doi.org/10.1186/s13321-019-0348-5] [PMID: 30941533]
[52]
Loeffler, H.H.; Michel, J.; Woods, C. FESetup: Automating setup for alchemical free energy simulations. J. Chem. Inf. Model., 2015, 55(12), 2485-2490.
[http://dx.doi.org/10.1021/acs.jcim.5b00368] [PMID: 26544598]
[53]
Riniker, S. Molecular Dynamics Fingerprints (MDFP): Machine learning from MD data to predict free-energy differences. J. Chem. Inf. Model., 2017, 57(4), 726-741.
[http://dx.doi.org/10.1021/acs.jcim.6b00778] [PMID: 28368113]
[54]
Scheen, J.; Wu, W.; Mey, A.S.J.S.; Tosco, P.; Mackey, M.; Michel, J. Hybrid alchemical free energy/machine-learning methodology for the computation of hydration free energies. J. Chem. Inf. Model., 2020, 60(11), 5331-5339.
[http://dx.doi.org/10.1021/acs.jcim.0c00600] [PMID: 32639733]
[55]
Lamim Ribeiro, J.M.; Tiwary, P. Toward achieving efficient and accurate ligand-protein unbinding with deep learning and molecular dy-namics through RAVE. J. Chem. Theory Comput., 2019, 15(1), 708-719.
[http://dx.doi.org/10.1021/acs.jctc.8b00869] [PMID: 30525598]
[56]
Lee, J.; Miller, B.T. Damjanović, A.; Brooks, B.R.; Constant, P.H. Constant pH molecular dynamics in explicit solvent with enveloping distribution sampling and hamiltonian exchange. J. Chem. Theory Comput., 2014, 10(7), 2738-2750.
[http://dx.doi.org/10.1021/ct500175m] [PMID: 25061443]
[57]
Sidler, D.; Schwaninger, A.; Riniker, S. Replica exchange enveloping distribution sampling (RE-EDS): A robust method to estimate multi-ple free-energy differences from a single simulation. J. Chem. Phys., 2016, 145(15), 154114.
[http://dx.doi.org/10.1063/1.4964781] [PMID: 27782485]
[58]
Wang, D.D.; Zhu, M.; Yan, H. Computationally predicting binding affinity in protein-ligand complexes: Free energy-based simulations and machine learning-based scoring functions. Brief. Bioinform., 2021, 22(3), bbaa107.
[http://dx.doi.org/10.1093/bib/bbaa107] [PMID: 32591817]
[59]
Ding, X.; Zhang, B. Computing absolute free energy with deep generative models. J. Phys. Chem. B, 2020, 124(45), 10166-10172.
[http://dx.doi.org/10.1021/acs.jpcb.0c08645] [PMID: 33143418]
[60]
Ding, X.; Zhang, B. DeepBAR: A fast and exact method for binding free energy computation. J. Phys. Chem. Lett., 2021, 12(10), 2509-2515.
[http://dx.doi.org/10.1021/acs.jpclett.1c00189] [PMID: 33719449]
[61]
Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M.K.; Greenwood, J.; Romero, D.L.; Masse, C.; Knight, J.L.; Steinbrecher, T.; Beuming, T.; Damm, W.; Harder, E.; Sherman, W.; Brewer, M.; Wester, R.; Murcko, M.; Frye, L.; Farid, R.; Lin, T.; Mobley, D.L.; Jorgensen, W.L.; Berne, B.J.; Friesner, R.A.; Abel, R. Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. J. Am. Chem. Soc., 2015, 137(7), 2695-2703.
[http://dx.doi.org/10.1021/ja512751q] [PMID: 25625324]
[62]
Homeyer, N.; Gohlke, H. FEW: A workflow tool for free energy calculations of ligand binding. J. Comput. Chem., 2013, 34(11), 965-973.
[http://dx.doi.org/10.1002/jcc.23218] [PMID: 23288722]
[63]
Kuhn, M.; Firth-Clark, S.; Tosco, P.; Mey, A.S.J.S.; Mackey, M.; Michel, J. Assessment of binding affinity via alchemical free-energy calculations. J. Chem. Inf. Model., 2020, 60(6), 3120-3130.
[http://dx.doi.org/10.1021/acs.jcim.0c00165] [PMID: 32437145]
[64]
Molecular Operating Environment (MOE); Chemical Computing Group ULC: 1010 Sherbooke St West, Suite #910, Montreal, QC, Canada, H3A 2R7.,
[65]
Brooks, B.R.; Brooks, C.L., III; Mackerell, A.D., Jr; Nilsson, L.; Petrella, R.J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A.R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M. Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R.W.; Post, C.B.; Pu, J.Z.; Schaefer, M.; Tidor, B.; Venable, R.M.; Woodcock, H.L.; Wu, X.; Yang, W.; York, D.M.; Karplus, M. CHARMM: The biomolecular simulation program. J. Comput. Chem., 2009, 30(10), 1545-1614.
[http://dx.doi.org/10.1002/jcc.21287] [PMID: 19444816]

Rights & Permissions Print Cite
Article Metrics
29
1
© 2024 Bentham Science Publishers | Privacy Policy