Table 1.
pKa values calculated for protein 2LZT (Lysozyme) with different MC runsa in comparison with the results obtained by a rigorous calculation of a partition function over all possible ionization micro states given by Eq.(11) - Eq.(13).
| residue | (pKo)b | pKac | pK_Zd | pK_MC5Ke | pK_MC20Ke | pK_MC80Ke | pK_MC320Ke | pKMC1Me |
|---|---|---|---|---|---|---|---|---|
| N-end | 7.5 | 7.9 | 7.44 | 7.38 (0.04) | 7.43 (0.01) | 7.40 (0.04) | 7.39 (0.05) | 7.38 (0.06) |
| Glu7 | 4.4 | 2.8 | 3.49 | 3.54 (0.05) | 3. 50 (0.06) | 3.54 (0.05) | 3.56 (0.07) | 3.55 (0.06) |
| His 15 | 6.6 | 5.5 | 7.15 | 7.16 (0.01) | 7.20 (0.07) | 7.18 (0.03) | 7.18 (0.03) | 7.17 (0.02) |
| Asp 18 | 4.0 | 2.7 | 2.87 | 2.84 (0.03) | 2.82 (0.05) | 2.84 (0.03) | 2.84 (0.03) | 2.86 (0.03) |
| Tyr20 | 9.6 | 10.3 | 9.74 | 9.49 (0.15) | 9.65 (0.05) | 9.78 (0.04) | 9.77 (0.03) | 9.73 (0.01) |
| Tyr23 | 9.6 | 9.8 | 9.01 | 9.10 (0.09) | 9.04 (0.03) | 8.97 (0.04) | 8.98 (0.03) | 8.98 (0.02) |
| Glu35 | 4.4 | 6.2 | 3.85 | 3.69 (0.16) | 3.86 (0.04) | 3.86 (0.01) | 3.84 (0.01) | 3.87 (0.01) |
| Asp48 | 4.0 | 1.6 | 3.37 | 3.35 (0.02) | 3.36 (0.01) | 3.36 (0.01) | 3.36 (0.01) | 3.36 (0.01) |
| Asp 52 | 4.0 | 3.7 | 3.29 | 3.21 (0.08) | 3.30 (0.05) | 3.30 (0.01) | 3.27 (0.02) | 3.28 (0.01) |
| Tyr53 | 9.6 | 12.1 | 11.13 | 11.33 (0.20) | 11.18(0.04) | 11.19 (0.06) | 11.20 (0.06) | 11.20 (0.06) |
| Asp66 | 4.0 | 0.9 | 3.44 | 3.43 (0.01) | 3.46 (0.02) | 3.42 (0.02) | 3.47 (0.03) | 3.45 (0.01) |
| Asp 87 | 4.0 | 2.1 | 2.95 | 3.00 (0.07) | 2.93 (0.03) | 2.97 (0.02) | 2.94 (0.01) | 2.93 (0.02) |
| Asp101 | 4.0 | 4.1 | 3.25 | 3.31 (0.06) | 3.18 (0.07) | 3.23 (0.02) | 3.24 (0.01) | 3.26 (0.01) |
| Asp119 | 4.0 | 3.2 | 2.84 | 2.85 (0.01) | 2.84 (0.01) | 2.82 (0.02) | 2.82 (0.02) | 2.82 (0.02) |
| C-end | 3.8 | 2.8 | 2.73 | 2.78 (0.05) | 2.68 (0.05) | 2.74 (0.01) | 2.75 (0.02) | 2.75 (0.02) |
| < Δ > | 0.96f | 0.08 g | 0.05g | 0.03g | 0.03g | 0.02g | ||
| Δmax | 2.54f | 0.20 g | 0.07g | 0.06g | 0.07g | 0.06g |
all calculations were carried out with DI =16.0 and D0 = 80.0.
experimental pKo values in 0.15 M NaCl at T= 300 K (Demchuk, Wade, 1996);
experimental values of pKa for residues in 0.15 M NaCl at T = 300 K (Song, Mao, Gunner, 2009; Kilambi, Gray, 2012);
pK_ZS are the pK values obtained by a rigorous computation of the ionization partition function and the average degree of ionization;
pK_MC5K, MC20K, MC80K, MC320K and MC1M, are the pKa values obtained by using different numbers of MC trials for the Markov chains, namely (0.005, 0.02, 0.08, 0.32 and 1.2) × 106 steps, respectively, for each pH during the calculation of the ionization equilibria, with a step of 0.25; in parentheses, Δ, the average absolute error (deviation) from the result listed in column 4, i.e., pK_Z obtained by rigorous computation of the ionization partition function;
average (<Δ>) and maximal (Δmax) absolute deviations between observed pKa (column 3) and computed from pK_Z (column 4) values; the larger Δmax deviation (2.3 and 2.5) pertains to Glu35 and Asp66, respectively;
average (<Δ>) and maximal (Δmax) absolute pKa deviations from pK_Z (column 4) values.