Accurate Calculation of Free Energy Changes upon Amino Acid Mutation

  • Matteo AldeghiEmail author
  • Bert L. de GrootEmail author
  • Vytautas GapsysEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1851)


Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally, we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well as large-scale mutational scans.

Key words

Molecular dynamics free energy calculations alchemistry amino acid mutation pmx hybrid structure hybrid topology non-equilibrium transitions 

Supplementary material (57 kb)
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  1. 1.
    Gapsys V,  Michielssens S,  Seeliger D, de Groot BL (2016) Accurate and rigorous prediction of the changes in protein free energies in a large-scale mutation scan. Angew Chem Int Ed Engl 55(26):7364–7368PubMedPubMedCentralGoogle Scholar
  2. 2.
    Griss R,  Schena A,  Reymond L,  Patiny L,  Werner D, Tinberg CE,  Baker D,  Johnsson K (2014) Bioluminescent sensor proteins for point-of-care therapeutic drug monitoring. Nat Chem Biol 10(7):598–603PubMedGoogle Scholar
  3. 3.
    Feng J, Jester BW, Tinberg CE, Mandell DJ, Antunes MS,  Chari R, Morey KJ,  Rios X, Medford JI, Church GM,  Fields S,  Baker D (2015) A general strategy to construct small molecule biosensors in eukaryotes. eLife 4:323–329Google Scholar
  4. 4.
    Zhou L,  Bosscher M,  Zhang C,  Özçubukçu S,  Zhang L,  Zhang W, Li CJ,  Liu J, Jensen MP,  Lai L,  He C (2014) A protein engineered to bind uranyl selectively and with femtomolar affinity. Nat Chem 6(3):236–241PubMedGoogle Scholar
  5. 5.
    Correia BE, Bates JT, Loomis RJ,  Baneyx G,  Carrico C, Jardine JG,  Rupert P,  Correnti C,  Kalyuzhniy O,  Vittal V, Connell MJ,  Stevens E,  Schroeter A,  Chen M,  MacPherson S, Serra AM,  Adachi Y, Holmes MA,  Li Y, Klevit RE, Graham BS, Wyatt RT,  Baker D, Strong RK, Crowe JE, Johnson PR, Schief WR (2014) Proof of principle for epitope-focused vaccine design. Nature 507(7491):201–206PubMedPubMedCentralGoogle Scholar
  6. 6.
    Koday MT,  Nelson J,  Chevalier A,  Koday M,  Kalinoski H,  Stewart L,  Carter L,  Nieusma T, Lee PS, Ward AB, Wilson IA,  Dagley A, Smee DF,  Baker D, Fuller DH (2016) A computationally designed hemagglutinin stem-binding protein provides in vivo protection from influenza independent of a host immune response. PLoS Pathog 12(2):e1005409PubMedPubMedCentralGoogle Scholar
  7. 7.
    Clark AJ,  Gindin T,  Zhang B,  Wang L,  Abel R, Murret CS,  Xu F,  Bao A, Lu NJ,  Zhou T, Kwong PD,  Shapiro L,  Honig B, Friesner RA (2017) Free energy perturbation calculation of relative binding free energy between broadly neutralizing antibodies and the gp120 glycoprotein of HIV-1. J Mol Biol 429(7):930–947PubMedPubMedCentralGoogle Scholar
  8. 8.
    Fowler PW,  Cole K, Gordon NC, Kearns AM, Llewelyn MJ, Peto TEA, Crook DW, Walker AS (2018) Robust prediction of resistance to trimethoprim in Staphylococcus aureus. Cell Chem Biol 25:339–349PubMedGoogle Scholar
  9. 9.
    Hauser K,  Negron C, Albanese SK,  Ray S,  Steinbrecher T,  Abel R, Chodera JD,  Wang L (2018) Predicting resistance of clinical Abl mutations to targeted kinase inhibitors using alchemical free-energy calculations. Commun Biol 1:70Google Scholar
  10. 10.
    Tinberg CE, Khare SD,  Dou J,  Doyle L, Nelson JW,  Schena A,  Jankowski W, Kalodimos CG,  Johnsson K, Stoddard BL,  Baker D (2013) Computational design of ligand-binding proteins with high affinity and selectivity. Nature 501(7466):212PubMedPubMedCentralGoogle Scholar
  11. 11.
    Yang W,  Lai L (2017) Computational design of ligand-binding proteins. Curr Opin Struct Biol 45:67–73PubMedGoogle Scholar
  12. 12.
    Brender JR, Zhang Y (2015) Predicting the effect of mutations on protein-protein binding interactions through structure-based interface profiles. PLoS Comput Biol 11(10):e1004494PubMedPubMedCentralGoogle Scholar
  13. 13.
    Pires DEV, Ascher DB, Blundell TL (2014) mCSM: predicting the effects of mutations in proteins using graph-based signatures. Bioinformatics 30(3):335–342PubMedGoogle Scholar
  14. 14.
    Schymkowitz J,  Borg J,  Stricher F,  Nys R,  Rousseau F,  Serrano L (2005) The FoldX web server: an online force field. Nucleic Acids Res 33(Suppl 2):W382–W388PubMedPubMedCentralGoogle Scholar
  15. 15.
    Kortemme T,  Baker D (2002) A simple physical model for binding energy hot spots in protein-protein complexes. Proc Natl Acad Sci USA 99(22):14116–14121PubMedGoogle Scholar
  16. 16.
    Leaver-Fay A,  Tyka M, Lewis SM, Lange OF,  Thompson J,  Jacak R,  Kaufman K, Renfrew PD, Smith CA,  Sheffler W, Davis IW,  Cooper S,  Treuille A, Mandell DJ,  Richter F, Ban YEA, Fleishman SJ, Corn JE, Kim DE,  Lyskov S,  Berrondo M,  Mentzer S,  Popović Z, Havranek JJ,  Karanicolas J,  Das R,  Meiler J,  Kortemme T, Gray JJ,  Kuhlman B,  Baker D,  Bradley P (2011) Rosetta3: an object-oriented software suite for the simulation and design of macromolecules. Methods Enzymol 487(C):545–574PubMedPubMedCentralGoogle Scholar
  17. 17.
    Petukh M,  Li M,  Alexov E (2015) Predicting binding free energy change caused by point mutations with knowledge-modified MM/PBSA method. PLoS Comput Biol 11(7):e1004276PubMedPubMedCentralGoogle Scholar
  18. 18.
    Beard H,  Cholleti A,  Pearlman D,  Sherman W, Loving KA (2013) Applying physics-based scoring to calculate free energies of binding for single amino acid mutations in protein-protein complexes. PLoS ONE 8(12):e82849PubMedPubMedCentralGoogle Scholar
  19. 19.
    Moreira IS, Fernandes PA, Ramos MJ (2007) Computational alanine scanning mutagenesis - An improved methodological approach. J Comput Chem 28(3):644–654PubMedGoogle Scholar
  20. 20.
    Seeliger D, de Groot BL (2010) Protein thermostability calculations using alchemical free energy simulations. Biophys J 98(10):2309–2316PubMedPubMedCentralGoogle Scholar
  21. 21.
    Chipot C,  Pohorille A (eds) (2007) Free energy calculations: theory and applications in chemistry and biology, vol  86. Springer, BerlinGoogle Scholar
  22. 22.
    Neidigh JW, Fesinmeyer RM, Andersen NH (2002) Designing a 20-residue protein. Nat Struct Mol Biol 9(6):425–430Google Scholar
  23. 23.
    Abraham MJ,  Murtola T,  Schulz R,  Páll S, Smith JC,  Hess B,  Lindahl E (2015) GROMACS: high performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 2:1–7Google Scholar
  24. 24.
    Gapsys V,  Michielssens S,  Seeliger D, de Groot BL (2015) pmx: automated protein structure and topology generation for alchemical perturbations. J Comput Chem 36(5):348–354PubMedGoogle Scholar
  25. 25.
    Chipot C (2014) Frontiers in free-energy calculations of biological systems. Wiley Interdiscip Rev Comput Mol Sci 4(1):71–89Google Scholar
  26. 26.
    Gapsys V,  Michielssens S, Peters JH, de Groot BL,  Leonov H (2015) Molecular modeling of proteins, vol 1215. Humana Press, New YorkGoogle Scholar
  27. 27.
    Pohorille A,  Jarzynski C,  Chipot C (2010) Good practices in free-energy calculations. J Phys Chem B 114(32):10235–10253PubMedGoogle Scholar
  28. 28.
    Hansen N, van Gunsteren WF (2014) Practical aspects of free-energy calculations: a review. J Chem Theory Comput 10(7):2632–2647PubMedGoogle Scholar
  29. 29.
    Goette M,  Grubmüller H (2009) Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes. J Comput Chem 30(3):447–456PubMedGoogle Scholar
  30. 30.
    Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78(14):2690–2693Google Scholar
  31. 31.
    Jarzynski C (1997) Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach. Phys Rev E 56:5018–5035Google Scholar
  32. 32.
    Crooks GE (1998) Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems. J Stat Phys 90(5/6):1481–1487Google Scholar
  33. 33.
    Crooks GE (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys Rev E 60(3):2721–2726Google Scholar
  34. 34.
    Crooks GE (2000) Path-ensemble averages in systems driven far from equilibrium. Phys Rev E 61(3):2361–2366Google Scholar
  35. 35.
    Hummer G,  Szabo A (2001) Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc Natl Acad Sci USA 98(7):3658–3661PubMedGoogle Scholar
  36. 36.
    Hummer G (2001) Fast-growth thermodynamic integration: error and efficiency analysis. J Chem Phys 114(17):7330–7337Google Scholar
  37. 37.
    Hummer G,  Szabo A (2005) Free energy surfaces from single-molecule force spectroscopy. Acc Chem Res 38(7):504–513PubMedGoogle Scholar
  38. 38.
    Zwanzig RW (1954) High-temperature equation of state by a perturbation method. I. nonpolar gases. J Chem Phys 22(8):1420–1426Google Scholar
  39. 39.
    Kirkwood JG (1935) Statistical mechanics of fluid mixtures. J Chem Phys 3(5):300–313Google Scholar
  40. 40.
    Cuendet MA (2006) The Jarzynski identity derived from general Hamiltonian or non-Hamiltonian dynamics reproducing NVT or NPT ensembles. J Chem Phys 125(14):144109PubMedGoogle Scholar
  41. 41.
    Wood RH, Mühlbauer WCF, Thompson PT (1991) Systematic errors in free energy perturbation calculations due to a finite sample of configuration space: sample-size hysteresis. J Phys Chem 95(17):6670–6675Google Scholar
  42. 42.
    Gore J,  Ritort F,  Bustamante C (2003) Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements. Proc Natl Acad Sci USA 100(22):12564–12569PubMedGoogle Scholar
  43. 43.
    Nanda H,  Lu N, Woolf TB (2005) Using non-Gaussian density functional fits to improve relative free energy calculations. J Chem Phys 122(13):134110PubMedGoogle Scholar
  44. 44.
    Massey FJ Jr (1951) Kolmogorov-Smirnov test for goodness of fit. Test 46(253):68– 78Google Scholar
  45. 45.
    Efron B, Tibshirani RJ (1994) An introduction to the bootstrap, vol 5, 1st edn. Chapman and Hall/CRC, London/West Palm BeachGoogle Scholar
  46. 46.
    Bennett CH (1976) Efficient estimation of free energy differences from Monte Carlo data. J Comput Phys 22(2):245–268Google Scholar
  47. 47.
    Shirts MR,  Bair E,  Hooker G, Pande VS (2003) Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods. Phys Rev Lett 91(14):140601PubMedGoogle Scholar
  48. 48.
    Nelder JA,  Mead R (1964) A simplex method for function minimization. Comput J 7(4):308–313Google Scholar
  49. 49.
    Hahn AM,  Then H (2010) Measuring the convergence of Monte Carlo free-energy calculations. Phys Rev E Stat Nonlinear Soft Matter Phys 81(4):041117Google Scholar
  50. 50.
    Lindorff-Larsen K,  Trbovic N,  Maragakis P,  Piana S, Shaw DE (2012) Structure and dynamics of an unfolded protein examined by molecular dynamics simulation. J Am Chem Soc 134(8):3787–3791PubMedGoogle Scholar
  51. 51.
    Rauscher S,  Gapsys V, Gajda MJ,  Zweckstetter M, de Groot BL,  Grubmüller H (2015) Structural ensembles of intrinsically disordered proteins depend strongly on force field: a comparison to experiment. J Chem Theory Comput 11(11):5513–5524PubMedGoogle Scholar
  52. 52.
    Prevost M, Wodak SJ,  Tidor B,  Karplus M (1991) Contribution of the hydrophobic effect to protein stability: analysis based on simulations of the Ile-96 → Ala mutation in barnase. Proc Natl Acad Sci USA 88(23):10880–10884PubMedGoogle Scholar
  53. 53.
    Sneddon SF, Tobias DJ (1992) The role of packing interactions in stabilizing folded proteins. Biochemistry 31(10):2842–2846PubMedGoogle Scholar
  54. 54.
    Pitera JW, Kollman PA (2000) Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides. Proteins Struct Funct Bioinf 41(3):385–397Google Scholar
  55. 55.
    Pearlman DA, Kollman PA (1991) The overlooked bond-stretching contribution in free energy perturbation calculations. J Chem Phys 94(6):4532Google Scholar
  56. 56.
    Pearlman DA (1994) A comparison of alternative approaches to free energy calculations. J Phys Chem 98(5):1487–1493Google Scholar
  57. 57.
    Boresch S,  Karplus M (1999) The role of bonded terms in free energy simulations: 1. Theoretical analysis. J Phys Chem A 103(1):103–118Google Scholar
  58. 58.
    Boresch S,  Karplus M (1996) The Jacobian factor in free energy simulations. J Chem Phys 105(12):5145–5154Google Scholar
  59. 59.
    Boresch S,  Karplus M (1999) The role of bonded terms in free energy simulations. 2. Calculation of their influence on free energy differences of solvation. J Phys Chem A 103(1):119–136Google Scholar
  60. 60.
    Beutler TC, Mark AE, van Schaik RC, Gerber PR, van Gunsteren WF (1994) Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations. Chem Phys Lett 222(6):529–539Google Scholar
  61. 61.
    Zacharias M, Straatsma TP, McCammon JA (1994) Separation-shifted scaling, a new scaling method for Lennard-Jones interactions in thermodynamic integration. J Chem Phys 100:9025–9031Google Scholar
  62. 62.
    Pham TT, Shirts MR (2011) Identifying low variance pathways for free energy calculations of molecular transformations in solution phase. J Chem Phys 135(3):034114PubMedGoogle Scholar
  63. 63.
    Gapsys V,  Seeliger D, de Groot BL (2012) New soft-core potential function for molecular dynamics based alchemical free energy calculations. J Chem Theory Comput 8(7):2373–2382PubMedGoogle Scholar
  64. 64.
    Buelens FP,  Grubmüller H (2012) Linear-scaling soft-core scheme for alchemical free energy calculations. J Comput Chem 33(1):25–33PubMedGoogle Scholar
  65. 65.
    Gapsys V, de Groot BL (2017) pmx Webserver: a user friendly interface for alchemistry. J Chem Inf Model 57(2):109–114PubMedGoogle Scholar
  66. 66.
    Šali A, Blundell TL (1993) Comparative protein modelling by satisfaction of spatial restraints. J Mol Biol 234(3):779–815PubMedGoogle Scholar
  67. 67.
    Schrödinger, LLC (2015) The PyMOL molecular graphics system, version 1.8, November 2015Google Scholar
  68. 68.
    Vriend G (1990) WHAT IF: a molecular modeling and drug design program. J Mol Graph 8(1):52–56PubMedGoogle Scholar
  69. 69.
    Hornak V,  Abel R,  Okur A,  Strockbine B,  Roitberg A,  Simmerling C (2006) Comparison of multiple amber force fields and development of improved protein backbone parameters. Proteins Struct Funct Bioinf 65(3):712–725Google Scholar
  70. 70.
    Best RB,  Hummer G (2009) Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides. J Phys Chem B 113(26):9004–9015PubMedPubMedCentralGoogle Scholar
  71. 71.
    Lindorff-Larsen K,  Piana S,  Palmo K,  Maragakis P, Klepeis JL, Dror RO, Shaw DE (2010) Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins Struct Funct Bioinf 78(8):1950–1958Google Scholar
  72. 72.
    Lindahl E (2015) Molecular dynamics simulations. In: Molecular modeling of proteins. Springer, Berlin, pp 3–26Google Scholar
  73. 73.
    Barua B, Andersen NH (2001) Determinants of miniprotein stability: can anything replace a buried H-bonded Trp sidechain? Lett Pept Sci 8(3–5):221–226Google Scholar
  74. 74.
    Barua B, Lin JC, Williams VD,  Kummler P, Neidigh JW, Andersen NH (2008) The Trp-cage: optimizing the stability of a globular miniprotein. Protein Eng Des Sel 21(3):171–185PubMedPubMedCentralGoogle Scholar
  75. 75.
    Darden T,  York D,  Pedersen L (1993) Particle mesh Ewald: an Nlog(N) method for Ewald sums in large systems. J Chem Phys 98(12):10089–10092Google Scholar
  76. 76.
    Essmann U,  Perera L, Berkowitz ML,  Darden T,  Lee H, Pedersen LG (1995) A smooth particle mesh Ewald method. J Chem Phys 103(19):8577–8593Google Scholar
  77. 77.
    Rocklin GJ, Mobley DL, Dill KA, Hünenberger PH (2013) Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects. J Chem Phys 139(18):184103PubMedPubMedCentralGoogle Scholar
  78. 78.
    Lin Y-L, Aleksandrov A, Simonson T, Roux B (2014) An overview of electrostatic free energy computations for solutions and proteins. J Chem Theory Comput 10(7):2690–2709PubMedGoogle Scholar
  79. 79.
    Hub JS, de Groot BL,  Grubmüller H,  Groenhof G (2014) Quantifying artifacts in Ewald simulations of inhomogeneous systems with a net charge. J Chem Theory Comput 10(1):381–390PubMedGoogle Scholar

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Authors and Affiliations

  1. 1.Max Planck Institute for Biophysical ChemistryComputational Biomolecular Dynamics GroupGöttingenGermany

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