Characterizing Protein Protonation Microstates Using Monte Carlo Sampling

Abstract

Proteins are polyelectrolytes with acidic and basic amino acids Asp, Glu, Arg, Lys, and His, making up ≈25% of the residues. The protonation state of residues, cofactors, and ligands defines a "protonation microstate". In an ensemble of proteins some residues will be ionized and others neutral, leading to a mixture of protonation microstates rather than in a single one as is often assumed. The microstate distribution changes with pH. The protein environment also modifies residue proton affinity so microstate distributions change in different reaction intermediates or as ligands are bound. Particular protonation microstates may be required for function, while others exist simply because there are many states with similar energy. Here, the protonation microstates generated in Monte Carlo sampling in MCCE are characterized in HEW lysozyme as a function of pH and bacterial photosynthetic reaction centers (RCs) in different reaction intermediates. The lowest energy and highest probability microstates are compared. The ΔG, ΔH, and ΔS between the four protonation states of Glu35 and Asp52 in lysozyme are shown to be calculated with reasonable precision. At pH 7 the lysozyme charge ranges from 6 to 10, with 24 accepted protonation microstates, while RCs have ≈50,000. A weighted Pearson correlation analysis shows coupling between residue protonation states in RCs and how they change when the quinone in the Q_B site is reduced. Protonation microstates can be used to define input MD parameters and provide insight into the motion of protons coupled to reactions.

Figure 1

Microstate energy distribution for lysozyme (PDB ID: 4LZT) at pH 7. The density is the probability density, and each bin shows the number of times microstates in that energy window are accepted divided by the total number of accepted microstate and the bin width. Thus, the area under the histogram integrates to 1. The black line is the best fit to a skewed normal distribution curve with a skew of 2.86.

Figure 2

Unique tautomer charge distribution for lysozyme at pH (A) 5 and (B) 7. Each point in the scatter plot is a unique protonation microstate. The count gives its acceptance in MC sampling, with high count indicating higher probability. Color and size of points correspond to the range of microstate energies associated with all microstates found for that protonation microstate. Histogram at the top counts the number of tautomers at each charge.

Figure 3

Thermodynamic box for titration of Glu35 and Asp52 in lysozyme at pH 4 at 298.15 K. The full microstate ensemble is sorted into the four protonation states of these two residues, and these groups are independently characterized. Corner boxes: first row is charge of Glu35 and Asp52; second row is the average microstate energy (H); third row is the count of microstates in this protonation state. The boxes along the arrows give the ΔG, ΔH, and TΔS for the transition between different protonation states. The top right and bottom left states are tautomers. All energies are in kcal/mol.

Figure 4

Temperature dependence of thermodynamic parameters. (A) Change in ΔG for the reaction taking Glu35 and Asp52 with both neutral to both ionized with temperature. The line is the linear best fit and each dot represent the ΔG value for an independent MC sampling run using the same input conformer energies. The slope of the graph gives the −ΔS of 0.0045 kcal/(mol deg), and the intercept gives the ΔH of 0.387 kcal/mol; R² is 0.979. (B) Van’t Hoff plot for the same data set. The slope is ΔH/R and intercept ΔS/R, where R is the gas constant. ΔH is 0.377 kcal/mol, and −ΔS is 0.0045 kcal/mol.

Figure 5

Heat map of Pearson’s weighted correlation coefficient of residue ionization states in RCs at pH 7. Only residues with an absolute value for the correlation ≥0.1 with at least one other residue are shown. Each square in the heat map gives the correlation strength for the two residues obtained with eq 3. Residues are identified as chain (L, M, or H), one letter residue name, and then residue number. Ubiquinone is UQ. Dark blue, blue, sky blue, light gray, orange, red, and dark red correspond to the correlation values in the ranges 0.5 to 1.0, 0.3 to 0.5, 0.1 to 0.3, −0.1 to 0.1, −0.3 to −0.1, −0.5 to −0.3, and −1.0 to −0.5, respectively. (a) Neutral quinone, (b) 50:50 mixture of Q_B and Q_B^•−, and (c) anionic semiquinone Q_B^•–. The quinone is not seen in panel a or c as it is 100% in a single redox state.

Figure 6

Structure representation of residues that show correlations in the MC sampling with a 50:50 mixture of Q_B and Q_B^•–. Only those residues whose absolute correlation coefficient is ≥0.1 are shown. Residue names follow as chain (L, M, or H), one letter residue name, and then residue number. Ubiquinone is UQ. Blue and red two-sided arrows show the positive and negative correlation, respectively. The color code is the same as Figure 5. Wider arrows indicate a higher correlation.