Protein titration calculations

Tanford, C, Theory of Protein Titration Curves. 11. Calculations for Simple Models at Low Ionic Strength, Journal of the American Chemical Society 79, 5340, 1957. 

Theoretical titration curves for enzymes can be calculated from known crystal structures and first principles of electrostatics. Key amino acids at the active site have significantly perturbed pK values and unusual regions in which they are partially protonated over a wide pH region.3 In principle, such titration calculations can identify the active site of a protein whose structure is known, but whose function is not. 

Since pairwise electrostatic interaction energies can be calculated from protein structures using Poisson-Boltzmann Equation (PBE) solvers [71,72], we can attempt to forge a unique link between protein structure and protein titration curves... 

The application of numerical methods to the solution of Poisson-Boltzmann problems with dielectric boundaries determined by the atomic coordinates and radii of a protein made it possible to carry out much more detailed and complete titration calculations using a MEAD-type model. The idealization used is illustrated in Figure 2. These calculations start from a model compound pK for each of the titrating sites and assume that the difference in titration behavior between the model compound and the analogous site in the protein can be accounted for by three kinds of electrostatic terms (i) AAGBom, the interaction of the site with the reaction field as a result of the polarization of the protein/solvent (versus model compound/solvent) system by the site s own charges ... 

The procedure is computationally efficient. For example, for the catalytic subunit of the mammalian cAMP-dependent protein kinase and its inhibitor, with 370 residues and 131 titratable groups, an entire calculation requires 10 hours on an SGI 02 workstation with a 175 MHz MIPS RIOOOO processor. The bulk of the computer time is spent on the FDPB calculations. The speed of the procedure is important, because it makes it possible to collect results on many systems and with many different sets of parameters in a reasonable amount of time. Thus, improvements to the method can be made based on a broad sampling of systems. 

The presented algorithm was applied to 4 proteins (lysozyme, ribonuclease A, ovomucid and bovine pancreatic trypsin inhibitor) containing 51 titratable residues with experimentally known pKaS [32, 33]. Fig. 2 shows the correlation between the experimental and calculated pKaS. The linear correlation coefficient is r = 0.952 the slope of the line is A = 1.028 and the intercept is B = -0.104. This shows that the overall agreement between the experimental and predicted pKaS is good. 

It can be seen from Table 2 that the intrinsic values of the pK s are close to the model compound value that we use for Cys(8.3), and that interactions with surrounding titratable residues are responsible for the final apparent values of the ionization constants. It can also be seen that the best agreement with the experimental value is obtained for the YPT structure suplemented with the 27 N-terminal amino acids, although both the original YPT structure and the one with the crystal water molecule give values close to the experimentally determined one. Minimization, however, makes the agreement worse, probably because it w s done without the presence of any solvent molecules, which are important for the residues on the surface of the protein. For the YTS structure, which refers to the protein crystallized with an SO4 ion, the results with and without the ion included in the calculations, arc far from the experimental value. This may indicate that con-... 

Bashford, D., Karplus, M. Multiple-site titration curves of proteins an analysis of exact and approximate methods for their calculation. J. Phys. Chem. 95 (1991) 9556-9561. 

The accuracy of PHMD methods and their feasibility for studying pH-dependent conformational phenomena of proteins can be assessed by pKa calculations. In this case, PHMD simulations are performed with several pH values. The resulting occupancy values for deprotonated states (.S dc prot) are plotted against pH (Figure 10-3). A titration curve and pATa values (Figure 10-3) can be obtained by fitting the data to the generalized HH equation (Eq. 10-5). 

Titrate the solution in the receiving vessel with the standardized 0.01 N NaOH until there is a color change from pink to light yellow. Calculate the percent protein in the sample as follows. A factor (F) is used to convert the weight of nitrogen to the weight of protein. 

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