Structure‐Based pKa Calculations Using Continuum Electrostatics Methods
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- Abstract
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Abstract
Electrostatic free energy is useful for correlating structure with function in proteins in which ionizable groups play essential functional roles. To this end, the pK a values of ionizable groups must be known and their molecular determinants must be understood. Structure?based calculations of electrostatic energies and pK a values are necessary for this purpose. This unit describes protocols for pK a calculations with continuum electrostatics methods based on the numerical solution of the linearized Poisson?Boltzmann equation by the method of finite differences. Critical discussion of key parameters, approximations, and shortcomings of these methods is included. Two protocols are described for calculations with methods modified empirically to maximize agreement between measured and calculated pK a values. Applied judiciously, these methods can contribute useful and novel insight into properties of surface ionizable groups in proteins.
Keywords: pKa calculations; continuum electrostatics; finite difference; Poisson?Boltzmann; UBHD
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- Basic Protocol 1: Calculating pKa Values Using the FDPB Method and the Single‐Site Charge Model (FDPB/SS)
- Alternate Protocol 1: Calculating pKa Values Using the FDPB Method and the Full Charge Model (FDPB/F)
- Guidelines for Understanding Results
- Commentary
- Literature Cited
- Figures
- Tables
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Figure 8.11.1 Thermodynamic cycle for p K a calculations. Thermodynamic cycle used in the FDPB/SS method for p K a calculations. p K a model represents the p K a of an ionizable group in a model compound. p K a prot is the p K a of the group in the protein. The transfer free energies, ΔG i tr , are the calculated electrostatic free energy changes for transferring the ionizable group from water to the protein environment in the neutral ( q = 0) and ionized ( q = 1) states. Larger circles denote ionizable groups in the protein; smaller circles denote the polar atoms of the protein, which are treated in these methods in terms of partial charges. View Image -
Figure 8.11.2 Model of the protein‐water system used for calculation of electrostatic potentials with FDPB methods. The solid line represents the van der Waal's envelope of the protein. The dashed line describes the water‐accessible surface that constitutes the boundary between the water phase with high dielectric constant and the protein phase with low dielectric constant ɛin . The dotted line represents the ion exclusion surface. A single Asp side chain is represented, with partial charges given for the atoms of the group. The grid is necessary for the solution of the Poisson‐Boltzmann equation by the method of finite differences. View Image -
Figure 8.11.3 H+ titrations of three acidic groups calculated with the FDPB/SS method. The curves were calculated with the 1stn.pdb structure with FDPB/SS method using ɛin = 20 and ionic strength = 100 mM. The p K a value [listed under p K a (app) in Table ] represents the pH where the extent of protonation is 0.5. View Image -
Figure 8.11.4 Overall H+ titration calculated by FDPB methods. Plot of the average charge ( Q ) of 1stn.pdb calculated with FDPB in 100 mM ionic strength: (solid line) FDPB/SS with ɛin = 20; (dashed‐dot) FDPB/F with ɛin = 4; (dashed) FDPB/SS‐HH with ɛin = 20; (dotted) calculated with the Henderson‐Hasselbalch equation using the p K a values of model compounds. View Image -
Figure 8.11.5 Comparison of p K a (app) values of an acidic residue calculated with different FDPB methods. The set of p K a values for a representative group in staphylococcal nuclease were calculated with nine different implementations of FDPB methods to illustrate the range of values and their sensitivity to different parameters. The effects of different values of ɛin (4 versus 20), different ionic strengths (100 mM versus 1 M), different charge distribution methods (FDPB/SS versus FDPB/F), different atomic charge sets (PARSE versus CHARMm), different tautomeric states, different structures (static versus MD relaxed), and different definition of the dielectric boundary (water accessible versus van der Waal's), are compared. View Image -
Figure 8.11.6 Energetic contributions to p K a (app) values calculated with different FDPB methods. These data illustrate how the calculated p K a values are parsed into Born (solid), background (gray), and Coulomb (white) energies by different implementations of FDPB methods. View Image
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| Key References | |
| Davis et al., 1991. See above. | |
| The above references contain a description of methodology for FDPB calculations with UHBD. | |
| Madura et al., 1995. See above. | |
| The above references contain reviews of PB and FDPB methods. | |
| Antosiewicz et al., 1996a. See above. | |
| The above references contain in depth discussions of problems of protein reorganization. | |
| Simonson, 2003. See above. | |
| Ullman and Knapp, 1999. See above. | |
| Garcia‐Moreno and Fitch, 2004. See above. | |
| Archontis and Simonson, 2005. See above. | |
| Sham et al., 1997. See above. | |
| Simonson et al., 1999. See above. | |
| Schutz and Warshel, 2001. See above. | |
| Simonson et al., 2004. See above. | |
| Internet Resources | |
| See Table . | |
| Prof. Jens Nielsen's website discusses many aspects of pKa calculations. Tools are available at this website for calculations and analysis of H+ titration curves. | |
| http://enzyme.ucd.ie/Science/pKa/pKa_introduction) | |
| Explanation of MCCE method | |
| http://honiglab.cpmc.columbia.edu/mcce/mcce.html |
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