In this chapter, the electrostatic potential at the retinal
π
-system was analyzed for three archaeal rhodopsins. As discussed in Section 4.1, electrostatic interactions of the retinal with the protein are likely to be the main reason for the different absorption behavior of these proteins. First, the electrostatic potential of the proteins at the retinalπ
-systemwas calculated. The potentials differ significantly between the archaeal rhodopsins. The potential of SRII shows a more pronounced difference between theβ-ionone ring and the Schiff base than the potentials of BR and HR. Compared to the experimental absorption maxima of BR and HR at about 570 nm, the experimental absorption maximum of SRII is considerably blue-shifted to about 500 nm,i.e., shifted to light of higher energy. Thus, the significantly higher potential difference between β-ionone ring and the Schiff base observed in SRII as compared to BR and HR is in accordance with their experimental ab-sorption maxima. However, this conclusion is intuitive. Therefore, a mathematical model was introduced to qualitatively calculate absorption maxima based on the electrostatic potential. To derive absorption maxima from the calculated electrostatic potential, the model of a quantum mechanical particle in a box was generalized by including a step po-tential. Thismodel of a particle in a box with step potentialallowed to relate the observed differences in the electrostatic potential of the archaeal rhodopsins to their different ab-sorption maxima.
To identify the origin of the difference between the archaeal rhodopsins, the potential was decomposed into the contribution of individual residues. The presented data showed that the counterion cannot explain the difference between the electrostatic potential of BR, HR and SRII. In agreement with mutational experiments, it could be shown that the retinal binding pocket contributes significantly to the difference between the electrostatic potentials at the retinal of BR, HR and SRII. Altogether, seven residues were identified
4.7. Concluding Remarks 75 that account for the difference between the electrostatic potential of the proteins. Three of these residues are located in the retinal binding pocket. Another residue is located close to the β-ionone ring, but outside of the binding pocket. Three residues are, however, located more than 8 ˚A away from the retinal. The four residues that are far from the retinal have not been discussed before as contributing to the absorption shift between BR, HR and SRII. The electrostatic potential of the three archaeal rhodopsins at the retinal omitting these seven residues is virtually identical.
One approximation of continuum electrostatics is the representation of atoms as point charges, neglecting the electron distribution. The behavior of electrons, therefore, cannot be explicitly analyzed by classical methods. Instead, quantum mechanical methods are required for an explicit description of the electron distribution and in general for excited state processes. These methods are, however, limited to relatively few atoms. There-fore, those residues that are located far from the retinal, but, nevertheless, significantly interact with the chromophore electrostatically, would not have been identified using a quantum mechanical approach. Classical methods in general and continuum elec-trostatics in particular offer, thus, meaningful insights also for excited state processes.
The analysis of an observed phenomenon can be greatly advanced by applying different methods and the interplay between these investigations may subsequently lead to a true understanding of this phenomenon.
C HAPTER 5
P ROTONATION P ROBABILITIES AND
C ORRELATIONS IN B ACTERIORHODOPSIN
I NTERMEDIATE S TRUCTURES
I didn’t discover curves, I only uncovered them.
Mae West
Proton gradients across membranes are the most important potential energy source in living organisms. Proton gradients are generated by transmembrane proteins, so-called proton pumps, which translocate protons across the membrane. The energy for proton pumping is, for example, provided by light energy. The resulting gradient is a potential energy form that can subsequently be utilized, for example, for solute transport across the membrane. In bacteria, proton gradients may also be used to drive flagellar move-ment. Most importantly, ATP synthases can convert the potential energy of a proton gradient into chemical energy in the form of ATP.
A proton moves through a protein according to a mechanism first outlined by Theodor von Grotthuß in 1806 [206]. As showcased in Figure 5.1 proton transfer occurs along a hydrogen-bonded chain of proton donors and acceptors. Effectively, a single positive charge is transported along this chain through a rearrangement of covalent and hydrogen bonds. However, no proton undergoes substantial movement. Due to this phenomenon, proton transfer is significantly faster than the diffusion of an ion of the same size. In pro-teins, the proton may be transferred along a hydrogen-bonded chain comprising internal water molecules and protein side-chains. Proton transfer is accompanied by a successive change of protonation states of the involved groups. Understanding the protonation of proton pumps is, thus, a fundamental precondition for an understanding of their proton transfer mechanism.
Bacteriorhodopsin (BR), the smallest proton pump known to date, has become the para-digm in the investigation of proton transfer across membranes. BR utilizes light energy to translocate a proton across the plasma membrane. The resulting proton gradient is converted into chemical energy by an ATP synthase. Together, BR and the ATP
syn-77
H+
Figure 5.1. The Grotthuß mechanism. Three water molecules are depicted that are connected through hydrogen bonds as indicated by the blue dotted lines. Grotthuß envisioned proton transfer as a chain reaction: each oxygen atom consecutively receives a proton and passes another proton to the next oxygen atom. The proton transfer events are indicated by red arrows. The hydrogen atoms that change their position and the positive charge that is transported along the chain of water molecules are shown in red.
thase constitute a photosynthetic pathway in halophilic archaea. In contrast to the photosynthesis in bacteria and plants, no carbon fixation occurs in the archaeal pho-tosynthesis. Furthermore, a retinal Schiff base and not chlorophyll is the light absorbing chromophore. Retinal-based photosynthesis occurs only in archaea. It is, moreover, the only photosynthetic process known to occur in the archaeal kingdom.
This chapter presents the results of Metropolis Monte Carlo calculations to determine the protonation behavior of multiple BR structures. The computational details of the per-formed calculations are outlined in Section 5.2. The protonation states relevant for the proton transfer in BR are examined and the results are presented in Section 5.3. In Sec-tion 5.4, the individual protonaSec-tion probabilities of funcSec-tionally important residues are analyzed. Thereafter, the pair-correlation of the protonation behavior is investigated in Section 5.5. The chapter concludes with a general discussion of the results (Section 5.6).
To begin with, the main events of the proton transfer of BR are summarized in the fol-lowing section. A more detailed discussion of the functional mechanism can be found in Chapter 1.