Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 2001 Oct;81(4):1841–1853. doi: 10.1016/S0006-3495(01)75836-5

Calculations of free-energy contributions to protein-RNA complex stabilization.

M A Olson 1
PMCID: PMC1301660  PMID: 11566759

Abstract

The problem of calculating binding affinities of protein-RNA complexes is addressed by analyzing a computational strategy of modeling electrostatic free energies based on a nonlinear Poisson-Boltzmann (NLPB) model and linear response approximation (LRA). The underlying idea is to treat binding as a two-step process. Solutions to the NLPB equation calculate free energies arising from electronic polarizability and the LRA is constructed from molecular dynamics simulations to model reorganization free energies due to conformational transitions. By implementing a consistency condition of requiring the NLPB model to reproduce the solute-solvent free-energy transitions determined by the LRA, a "macromolecule dielectric constant" (epsilon(m)) for treating reorganization is obtained. The applicability of this hybrid approach was evaluated by calculating the absolute free energy of binding and free-energy changes for amino acid substitutions in the complex between the U1A spliceosomal protein and its cognate RNA hairpin. Depending on the residue substitution, epsilon(m) varied from 3 to 18, and reflected dipolar reorientation not included in the polarization modeled by epsilon(m) = 2. Although the changes in binding affinities from substitutions modeled strictly at the implicit level by the NLPB equation with epsilon(m) = 4 reproduced the experimental values with good overall agreement, substitutions problematic to this simple treatment showed significant improvement when solved by the NLPB-LRA approach.

Full Text

The Full Text of this article is available as a PDF (802.2 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Aqvist J., Medina C., Samuelsson J. E. A new method for predicting binding affinity in computer-aided drug design. Protein Eng. 1994 Mar;7(3):385–391. doi: 10.1093/protein/7.3.385. [DOI] [PubMed] [Google Scholar]
  2. Ben-Naim A. Solvent effects on protein association and protein folding. Biopolymers. 1990 Feb 15;29(3):567–596. doi: 10.1002/bip.360290312. [DOI] [PubMed] [Google Scholar]
  3. Del Buono G. S., Figueirido F. E., Levy R. M. Intrinsic pKas of ionizable residues in proteins: an explicit solvent calculation for lysozyme. Proteins. 1994 Sep;20(1):85–97. doi: 10.1002/prot.340200109. [DOI] [PubMed] [Google Scholar]
  4. Freire E. The propagation of binding interactions to remote sites in proteins: analysis of the binding of the monoclonal antibody D1.3 to lysozyme. Proc Natl Acad Sci U S A. 1999 Aug 31;96(18):10118–10122. doi: 10.1073/pnas.96.18.10118. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Gilson M. K., Given J. A., Bush B. L., McCammon J. A. The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys J. 1997 Mar;72(3):1047–1069. doi: 10.1016/S0006-3495(97)78756-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Gilson M. K., Honig B. Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis. Proteins. 1988;4(1):7–18. doi: 10.1002/prot.340040104. [DOI] [PubMed] [Google Scholar]
  7. Jackson R. M., Sternberg M. J. A continuum model for protein-protein interactions: application to the docking problem. J Mol Biol. 1995 Jul 7;250(2):258–275. doi: 10.1006/jmbi.1995.0375. [DOI] [PubMed] [Google Scholar]
  8. Jackson R. M., Sternberg M. J. Application of scaled particle theory to model the hydrophobic effect: implications for molecular association and protein stability. Protein Eng. 1994 Mar;7(3):371–383. doi: 10.1093/protein/7.3.371. [DOI] [PubMed] [Google Scholar]
  9. Jessen T. H., Oubridge C., Teo C. H., Pritchard C., Nagai K. Identification of molecular contacts between the U1 A small nuclear ribonucleoprotein and U1 RNA. EMBO J. 1991 Nov;10(11):3447–3456. doi: 10.1002/j.1460-2075.1991.tb04909.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Jones-Hertzog D. K., Jorgensen W. L. Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method. J Med Chem. 1997 May 9;40(10):1539–1549. doi: 10.1021/jm960684e. [DOI] [PubMed] [Google Scholar]
  11. Karplus M., Janin J. Comment on: 'The entropy cost of protein association'. Protein Eng. 1999 Mar;12(3):185–187. doi: 10.1093/protein/12.3.185. [DOI] [PubMed] [Google Scholar]
  12. Kranz J. K., Hall K. B. RNA binding mediates the local cooperativity between the beta-sheet and the C-terminal tail of the human U1A RBD1 protein. J Mol Biol. 1998 Jan 23;275(3):465–481. doi: 10.1006/jmbi.1997.1441. [DOI] [PubMed] [Google Scholar]
  13. Kranz J. K., Hall K. B. RNA recognition by the human U1A protein is mediated by a network of local cooperative interactions that create the optimal binding surface. J Mol Biol. 1999 Jan 8;285(1):215–231. doi: 10.1006/jmbi.1998.2296. [DOI] [PubMed] [Google Scholar]
  14. Kranz J. K., Lu J., Hall K. B. Contribution of the tyrosines to the structure and function of the human U1A N-terminal RNA binding domain. Protein Sci. 1996 Aug;5(8):1567–1583. doi: 10.1002/pro.5560050812. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Lee F. S., Chu Z. T., Bolger M. B., Warshel A. Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603. Protein Eng. 1992 Apr;5(3):215–228. doi: 10.1093/protein/5.3.215. [DOI] [PubMed] [Google Scholar]
  16. Lu J., Hall K. B. Thermal unfolding of the N-terminal RNA binding domain of the human U1A protein studied by differential scanning calorimetry. Biophys Chem. 1997 Feb 28;64(1-3):111–119. doi: 10.1016/s0301-4622(96)02212-0. [DOI] [PubMed] [Google Scholar]
  17. Misra V. K., Hecht J. L., Yang A. S., Honig B. Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA. Biophys J. 1998 Nov;75(5):2262–2273. doi: 10.1016/S0006-3495(98)77671-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Misra V. K., Honig B. On the magnitude of the electrostatic contribution to ligand-DNA interactions. Proc Natl Acad Sci U S A. 1995 May 9;92(10):4691–4695. doi: 10.1073/pnas.92.10.4691. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Muegge I., Schweins T., Warshel A. Electrostatic contributions to protein-protein binding affinities: application to Rap/Raf interaction. Proteins. 1998 Mar 1;30(4):407–423. doi: 10.1002/(sici)1097-0134(19980301)30:4<407::aid-prot8>3.0.co;2-f. [DOI] [PubMed] [Google Scholar]
  20. Muegge I., Tao H., Warshel A. A fast estimate of electrostatic group contributions to the free energy of protein-inhibitor binding. Protein Eng. 1997 Dec;10(12):1363–1372. doi: 10.1093/protein/10.12.1363. [DOI] [PubMed] [Google Scholar]
  21. Nicholls A., Sharp K. A., Honig B. Protein folding and association: insights from the interfacial and thermodynamic properties of hydrocarbons. Proteins. 1991;11(4):281–296. doi: 10.1002/prot.340110407. [DOI] [PubMed] [Google Scholar]
  22. Novotny J., Bruccoleri R. E., Davis M., Sharp K. A. Empirical free energy calculations: a blind test and further improvements to the method. J Mol Biol. 1997 May 2;268(2):401–411. doi: 10.1006/jmbi.1997.0961. [DOI] [PubMed] [Google Scholar]
  23. Olson M. A., Cuff L. Free energy determinants of binding the rRNA substrate and small ligands to ricin A-chain. Biophys J. 1999 Jan;76(1 Pt 1):28–39. doi: 10.1016/S0006-3495(99)77175-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Olson M. A. Mean-field analysis of protein-protein interactions. Biophys Chem. 1998 Nov 16;75(2):115–128. doi: 10.1016/s0301-4622(98)00201-4. [DOI] [PubMed] [Google Scholar]
  25. Olson M. A., Reinke L. T. Modeling implicit reorganization in continuum descriptions of protein-protein interactions. Proteins. 2000 Jan 1;38(1):115–119. doi: 10.1002/(sici)1097-0134(20000101)38:1<115::aid-prot11>3.0.co;2-p. [DOI] [PubMed] [Google Scholar]
  26. Oubridge C., Ito N., Evans P. R., Teo C. H., Nagai K. Crystal structure at 1.92 A resolution of the RNA-binding domain of the U1A spliceosomal protein complexed with an RNA hairpin. Nature. 1994 Dec 1;372(6505):432–438. doi: 10.1038/372432a0. [DOI] [PubMed] [Google Scholar]
  27. Pellequer J. L., Chen S. W. Does conformational free energy distinguish loop conformations in proteins? Biophys J. 1997 Nov;73(5):2359–2375. doi: 10.1016/S0006-3495(97)78266-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Reyes C. M., Kollman P. A. Investigating the binding specificity of U1A-RNA by computational mutagenesis. J Mol Biol. 2000 Jan 7;295(1):1–6. doi: 10.1006/jmbi.1999.3319. [DOI] [PubMed] [Google Scholar]
  29. Reyes C. M., Kollman P. A. Structure and thermodynamics of RNA-protein binding: using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change. J Mol Biol. 2000 Apr 14;297(5):1145–1158. doi: 10.1006/jmbi.2000.3629. [DOI] [PubMed] [Google Scholar]
  30. Roux B., Simonson T. Implicit solvent models. Biophys Chem. 1999 Apr 5;78(1-2):1–20. doi: 10.1016/s0301-4622(98)00226-9. [DOI] [PubMed] [Google Scholar]
  31. Sham Y. Y., Chu Z. T., Tao H., Warshel A. Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease. Proteins. 2000 Jun 1;39(4):393–407. [PubMed] [Google Scholar]
  32. Sham Y. Y., Muegge I., Warshel A. The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins. Biophys J. 1998 Apr;74(4):1744–1753. doi: 10.1016/S0006-3495(98)77885-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Sharp K. A. Calculation of HyHel10-lysozyme binding free energy changes: effect of ten point mutations. Proteins. 1998 Oct 1;33(1):39–48. [PubMed] [Google Scholar]
  34. Tang Y., Nilsson L. Molecular dynamics simulations of the complex between human U1A protein and hairpin II of U1 small nuclear RNA and of free RNA in solution. Biophys J. 1999 Sep;77(3):1284–1305. doi: 10.1016/S0006-3495(99)76979-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Tsai C. J., Ma B., Nussinov R. Folding and binding cascades: shifts in energy landscapes. Proc Natl Acad Sci U S A. 1999 Aug 31;96(18):9970–9972. doi: 10.1073/pnas.96.18.9970. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Warshel A., Aqvist J. Electrostatic energy and macromolecular function. Annu Rev Biophys Biophys Chem. 1991;20:267–298. doi: 10.1146/annurev.bb.20.060191.001411. [DOI] [PubMed] [Google Scholar]
  37. Warshel A., Papazyan A. Electrostatic effects in macromolecules: fundamental concepts and practical modeling. Curr Opin Struct Biol. 1998 Apr;8(2):211–217. doi: 10.1016/s0959-440x(98)80041-9. [DOI] [PubMed] [Google Scholar]
  38. Williams D. J., Hall K. B. RNA hairpins with non-nucleotide spacers bind efficiently to the human U1A protein. J Mol Biol. 1996 Mar 29;257(2):265–275. doi: 10.1006/jmbi.1996.0161. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES