is presented for only four bR state structures.
HALORHODOPSIN ANDSENSORYRHODOPSINII
In crystallized form HR is organized in trimers like BR, whereas the functional unit of SRII is a heterodimer formed together with its transducer HTRII. For the calculations presented in this thesis, the ground state structures of HR and SRII listed in Table 3.1 are used.
3.3 P REPARATION OF THE X-R AY S TRUCTURES
The X-ray structures listed in Table 3.1 have to be prepared for the electrostatic calcula-tions presented in this thesis. The resolution is for example not high enough to reveal the positions of hydrogen atoms. These can only be detected if the structure is resolved to a value below 1 ˚A. Care is taken to keep the modifications of the structures to a minimum to avoid biasing the results of the electrostatic calculations. For instance, the coordinates stored in the Protein Data Bank are in general not altered. A minimization of the coor-dinates is in most cases restricted to those added to the structure,i.e., hydrogen atom coordinates or the atom coordinates of unresolved residues.
MINIMIZATION OF THEPOTENTIAL ENERGY FUNCTION
All energy minimizations are done using CHARMM(Chemistry at Harvard Macromolecular Mechanics) [162]. In the CHARMM force field, atoms are represented as charged point masses. Its fundamental potential functionVis separated into bonded and non-bonded terms. The bonded terms Vbonded describe the bonds, angles and bond rotations in a molecule and the non-bonded terms Vnon−bonded account for interactions between non-bonded atoms,i.e., atoms separated by three or more covalent bonds:
Vtotal = Vbonded + Vnon−bonded
where
Vbonded = Vbond + Vangle + Vdihedral + Vimproper
and
Vnon−bonded = VvdW + Velec
whereVbond is the bond stretching energy term,Vangle is the angle bending energy term, Vdihedral accounts for the distortion around a bond, i.e., the dihedral or torsion angle, andVimproper is the distortion term, i.e., the energy of so-called improper torsions. The improper torsion angle can be observed for four connected atoms where the torsion angle is not defined by four angles connected sequentially. A schematic representation of the bonded atom interactions is given in Figure 3.2. VvdW is the van der Waals interaction
1
2 3
4
bond stretching
angle bending
torsion angle
improper angle
Figure 3.2. Schematic representation of the bonded terms. In the CHARMM force field, the bonded terms include the bond stretching between two covalently bound atoms, the angle bending between three covalently bound atoms and the torsion angle between four covalently bound atoms. Furthermore, the improper angle between four atoms is taken into consideration. The graphics are kindly provided by Torsten Becker.
energy modeled using a 6-12 Lennard-Jones potential, where the repulsive forces fall off with distance with the square of which the attractive forces decrease. Velec is the electrostatic energy between a pair of atoms represented by the Coulomb potential.
The potential function is optimized using the steepest descent and subsequently the adopted basis Newton-Raphson method. Steepest descent is the simplest way to opti-mize a function. In each step of steepest descent, the coordinates are adjusted in the negative direction of the gradient, i.e., in the direction opposite to its most significant increase. The adopted basis Newton-Raphson method in principle expands the function to the second order and attempts to find the point where the gradient of the second-order approximation is zero.
ATOMIC PAR TIALCHARGES
The atomic partial charges for the standard amino acids are taken from the CHARMM22 parameter set of the CHARMMforce field [163]. Since the CHARMM22 parameter set does not contain partial charges for the retinal Schiff base these are taken from Ref. [75].
MISSING COORDINATES
Coordinates for residue atoms that could not be determined from the electron den-sity map are generated from internal coordinates of the CHARMM22 topology using the ICBUILD routine of CHARMM. Coordinates generated from internal coordinates are min-imized with the steepest descent and subsequently the adopted basis Newton-Raphson
3.3. Preparation of the X-Ray Structures 49 method until a tolerance gradient criterion is fulfilled. Using the parameter TOLGRD, the minimization is stopped, if the gradient is less or equal to 10−7.
As indicated in Table 3.1, some BR structures miss coordinates for the residues 157–161.
These residues are part of the highly flexible cytoplasmic EF-loop. The coordinates for the missing residues of the EF-loop are taken from the 1qhj structure [41] after superposition of the backbone Cαatoms using the Kabsch algorithm [164]. The EF-loop and its flanking residues, i.e., residues 150–176, are then carefully relaxed, while all other heavy atom coordinates are kept fixed. During the minimization, harmonic constraints are used to limit coordinate changes. A force constant of 1 kcal/(mol ˚A2) restrained the residues 157–161 and the nearby Met163 residue. Higher restraints are applied to the residues flanking the EF-loop,i.e., residues 150–154, 162 and 164–176. Their backbone and side chain atoms are constrained by a force constant of 5 and 2 kcal/(mol ˚A2), respectively.
Only the side chains of Arg175 and Lys172 are restrained with a weaker force constant of 0.1 kcal/(mol ˚A2). The steepest descent subsequently followed by the adopted basis Newton-Raphson method is used for the minimization until a tolerance gradient criterion is fulfilled. Using the parameter TOLGRD, the minimization is stopped, if the gradient is less or equal to 10−7. The O-like structure of BR, 1jv7, is lacking coordinates for the BD-loop. These are generated in equivalence to the procedure described above for the EF-loop.
The N- and C-termini could not be resolved by X-ray crystallography due to their high flexibility. Their absence has, however, no significant influence on the electrostatic cal-culations performed during this thesis. This is due to the solvent exposure of the termini that screens their charges. Furthermore, they are relatively far from all functionally important regions that are analyzed here. Neutral blocking groups are added to the main-chain termini, i.e., an acetylated N-terminus and an N-methylamide C-terminus.
Mutants are converted back to the wild type by replacing the mutated with the respective wild type amino acid side chain and minimizing the new coordinates.
HYDROGENATOMS
For all structures, hydrogen atoms are constructed using the HBUILD routine of CHARMM and their positions are optimized with the steepest descent and subsequently with the adopted basis Newton-Raphson routine until a tolerance gradient criterion is fulfilled. Using the parameter TOLGRD, the minimization is stopped, if the gradient is less or equal to 10−7. All non-hydrogen atom coordinates are constraint during the min-imization. The hydrogen atom positions are minimized with all internal water molecules present. For the electrostatic calculations, the water molecules are deleted and repre-sented implicitly by a continuum that accounts for reorientation of the water dipoles in response to the electrostatic field.
IONS
The chloride ion which is resolved for the HR structure in the chloride binding site below the retinal Schiff base is included in all calculations. Additionally, the electron density of HR revealed a potassium ion which is not considered in the calculations. No biological
a)
b)
Figure 3.3. Membrane model. Depicted is the torus of tightly packed dummy atoms around BR. The dummy atoms are uncharged and have a radius of 1.5 ˚A.a)View from the cytoplasm. b)View along the membrane plane, the cytoplasm is at the top. These figures are kindly provided by Nicolas Calimet.
function can be attributed to this potassium ion. Furthermore, it is located relatively far from the retinal Schiff base. The presence of this ion is not discussed in the publication of this structure, possibly since it may in fact be a water molecule [46].
LIPIDS
HR binds a palmitic acid which is located approximately parallel to helix D. In its de-protonated form, the palmitic acid is negatively charged. It is, therefore, included in the electrostatic calculations as a protonatable site. Other lipids resolved for archaeal rhodopsin structures are neutral and are, therefore, not considered in the electrostatic calculations. The lipids surrounding the archaeal rhodopsins are represented by a mem-brane model as described in the next section.