5.5 Correlation of the Protonation Behavior
5.5.1 Correlation between Asp85 and the Retinal Schiff Base
The retinal Schiff base is located in the center of BR and Asp85 close to the Schiff base on its extracellular side. In the [bR] protonation state, the retinal Schiff base is protonated and Asp85 is deprotonated. In the [M1] protonation state, the proton has been transferred from the Schiff base to Asp85. In both the [M1] and [M2] protonation state, the retinal Schiff base is deprotonated. In the [N] and [O] protonation state, the Schiff base is again protonated. Asp85 remains protonated, too, and only deprotonates when BR returns to the [bR] state. The photocycle and its proton transfer steps are depicted in Figure 5.2 and the intermediate protonation states are listed in Table 5.1.
In Figure 5.18, the protonation behavior of Asp85 and the retinal Schiff base is depicted for six BR structures. As can be seen, the protonation behavior of Asp85 and the retinal Schiff base is strongly negatively correlated in bR:1c3w, bR:1f50, M:1f4z and M:1kg8.
In L:1vjm.b, the behavior of Asp85 and the retinal Schiff base is uncorrelated in the pH range from 0 to 11. At pH>11, the correlation coefficient fluctuates between 0 and approximately -1,i.e., perfect negative correlation. In N:1p8u, the behavior of Asp85 and the retinal Schiff base is uncorrelated in the pH range from 0 to 13.5. At pH>13.5, a very slight negative correlation can be observed. In the following subsections, the correlation behavior is discussed in detail for the individual structures.
5.5. Correlation of the Protonation Behavior 103
0 2 4 6 8 10 12 14
pH
-1 -0.5 0 0.5 1
c ij
bR:1c3w bR:1f50 L:1vjm.b M:1f4z M:1kg8 N:1p8u
Figure 5.18.Correlation between Asp85 and the retinal Schiff base.The coefficient of the correlation between Asp85 and the retinal Schiff base is plotted against pH for six BR structures.
BR STRUCTURES
For bR:1c3w and bR:1f50, the correlation coefficient reaches its minimum value of -1 at pH = 5 and the correlation remains close to -1 in the pH range from 5 to 12. The protonation probability of the retinal Schiff base is close to 1 over the complete pH range from 0 to 14 for both bR:1c3w and bR:1f50 (cf. Figure 5.11 a). At pH>4, the protonation probability of Asp85 is close to 0 for both bR:1c3w and bR:1f50 (cf. Figure 5.12 a). This protonation behavior and the negative correlation indicate that Asp85 is deprotonated in all protonation states, where the retinal Schiff base is protonated and vice versa. As specified in Table 5.1, the [bR] protonation state, for which bR:1c3w and bR:1f50 have an almost exclusive probability as shown in Figure 5.3 a and c, respectively, has a protonated Schiff base and a deprotonated Asp85.
L STRUCTURE
For L:1vjm.b the correlation coefficient is 0 in the pH range from 0 to 11. However, at pH>13.5, a significant negative correlation can be observed at several pH values. As shown in Figure 5.11 c, at pH<2 the protonation probability of the retinal Schiff base is close to 1. In the pH range from 2 to 8, the Schiff base deprotonates. At pH>8, the protonation probability is close to 0. The protonation probability of Asp85 is 1 in the pH range from 0 to 11 (cf. Figure 5.12 c). At pH>11, probability values of 0.99 are observed several times: at pH = 11.1, 11.7, 11.8, 12.3, 12.5 to 12.7, 12.9 to 13.5, 13.7, 13.9 and 14. At each of these 17 pH values, the correlation is significantly negative,i.e., the coefficient takes values between -0.85 and -1.
This case illustrates one important characteristic of the correlation coefficient: when one of the variables does not show any variance, the covariance between this variable and another equals 0. Consequently, the correlation coefficient will be 0, too. That is, without variance the occurrence of positively or negatively correlated behavior cannot be assessed. In the case of L:1vjm.b, Asp85 does not show any variance, i.e., is fully protonated, at all pH values except at the 17 values mentioned above. As a result, the covariance and the correlation between Asp85 and the retinal Schiff base (or any other
protonatable group) are 0 at all pH values except those 17 values listed above. Thus, although the difference between the behavior of the two residues for example at pH = 12.2 and pH = 12.3 is very small, in terms of the correlation coefficient it is amplified to a difference between uncorrelated and perfectly negatively correlated behavior.
M STRUCTURES
For M:1f4z, the correlation coefficient is close to -1 in the pH range from 8 to 14. For M:1kg8, the correlation decreases from 0 to -1 in the pH range from 5 to 14. The negative correlation between Asp85 and the retinal Schiff base is more pronounced in M:1f4z than in M:1kg8. The protonation curves of Asp85 and the retinal Schiff base are, however, similar in M:1f4z and M:1kg8. As depicted in Figure 5.11 d, at pH<4 the protonation probability of the retinal Schiff base is close to 1. In the pH range from 4 to 8, the Schiff base deprotonates. In M:1f4z, the minimum protonation probability is approximately 0.15. At ph = 10, the protonation probability increases up to approximately 0.5 at pH = 14.
In M:1kg8, the protonation probability is close to 0 in the pH range from 8 to 14. As shown in Figure 5.12 d, at pH<3.5 the protonation probability of Asp85 is 1. At pH>3.5, Asp85 deprotonates. In M:1kg8, the protonation probability remains above 0.8, while in M:1f4z, the protonation probability decreases to about 0.5 at pH = 14. In the [M1] or [M2] protonation state Asp85 is protonated and the retinal Schiff base is deprotonated as characterized in Table 5.1. As depicted in Figure 5.6, for M:1f4z and M:1kg8 the [M1] and [M2] protonation state are the primary states. Additionally at high pH values, M:1f4z has a probability for the [bR] protonation state, where Asp85 is deprotonated and the Schiff base deprotonated. This is in accordance with the protonation behavior of Asp85 and the Schiff base in M:1f4z and also with the perfect negative correlation. In M:1f4z, when Asp85 is protonated, the Schiff base is deprotonated and vice versa. In the first case either a probability for the [M1] or the [M2] protonation state is observed and in the latter for the [bR] state. In M:1kg8, the negative correlation between Asp85 and the retinal Schiff base is not as strong. This indicates that M:1kg8 has a slight probability for protonation states, where Asp85 and the retinal Schiff base are both either protonated or deprotonated. In general, however, their behavior is converse.
N STRUCTURE
For N:1p8u the correlation coefficient is 0 in the pH range from 0 to 13.4. In the pH range from 13.5 to 14 a small negative correlation can be observed. As shown in Figure 5.11 e, at pH<3 the retinal Schiff base is protonated. In the pH range from 3 to 8, the Schiff base deprotonates. At pH = 8, the protonation probability is close to 0. In the pH range from 8 to 14, the probability increases slightly to approximately 0.2. In the pH range from 0 to 13.4, Asp85 is fully protonated (cf. Figure 5.12 e). Since Asp85 does not show any variance, the covariance and the correlation between Asp85 and the Schiff base are 0. In the pH range from 13.5 to 14, probability values of 0.99 are observed. Only at these pH values can the covariance and correlation be assessed, which is negative but not very strong. As can be seen, a correlation coefficient of 0 does not necessarily indicate that two variable are not correlated. It can also indicate that one or both of the variable does not show any variance.
5.5. Correlation of the Protonation Behavior 105
0 2 4 6 8 10 12 14
pH
-1 -0.5 0 0.5 1
c ij
bR:1c3w bR:1f50 L:1vjm.b M:1f4z M:1kg8 N:1p8u
Figure 5.19.Correlation between Asp96 and the retinal Schiff base.The coefficient of the correlation between Asp96 and the retinal Schiff base is plotted against pH for six BR structures.