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Structure-Function Relationship of Archaeal Rhodopsin Proteins Analyzed by Continuum Electrostatics

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Structure-Function Relationship of Archaeal Rhodopsin Proteins analyzed by Continuum Electrostatics DISSERTATION submitted to the Faculty of Biology, Chemistry and Geoscience of the University of Bayreuth, Germany for obtaining the degree of Doctor of Natural Sciences presented by Edda Kloppmann born in Luneburg,¨ Germany Bayreuth 2010 Vollstandiger¨ Abdruck der von der Fakultat¨ fur¨ Biologie, Chemie und Geowissenschaften der Universitat¨ Bayreuth genehmigten Disserta- tion zur Erlangung des akademischen Grades Doktor der Naturwis- ” senschaften (Dr. rer. nat.)“. Die vorliegende Arbeit wurde im Zeitraum von November 2002 bis November 2003 am IWR Heidelberg und von Dezember 2003 bis April 2007 am Lehrstuhl fur¨ Biopolymere an der Universitat¨ Bayreuth unter der Leitung von Professor G. Matthias Ullmann erstellt. Hiermit erklare¨ ich, dass ich die vorliegende Arbeit selbststandig¨ ver- fasst und keine anderen als die von mir angegebenen Quellen und Hilfsmittel verwendet habe. Ferner erklare¨ ich, dass ich nicht bereits anderweitig mit oder ohne Er- folg versucht habe, eine Dissertation einzureichen oder mich der Dok- torprufung¨ zu unterziehen. Bayreuth, den 13.01.2010 Prufungsausschuss:¨ 1. Gutachter: Prof. Dr. G. Matthias Ullmann 2. Gutachter: Prof. Dr. Franz X. Schmid Prufungsvorsitz:¨ Prof. Dr. Thomas Hellweg Prof. Dr. Benedikt Westermann Einreichung des Promotionsgesuchs: 13.01.2010 Kolloqium: 04.05.2010 Structure-Function Relationship of Archaeal Rhodopsin Proteins analyzed by Continuum Electrostatics ABSTRACT Rhodopsin proteins perform two cellular key functions: signaling of external stimuli and ion transport. Examples of both functional types are found in the family of archaeal rho- dopsins, namely the proton pump bacteriorhodopsin, the chloride pump halorhodopsin and the photoreceptor sensory rhodopsin II. For these three membrane proteins, high- resolution X-ray structures are available, allowing a theoretical investigation in atomic detail. In this thesis, calculations are presented based on a continuum electrostatics approach using a finite-difference discretization of the Poisson-Boltzmann equation. The results can be divided into three parts. One of the interesting features of rhodopsin proteins is the extreme range over which the absorption maximum of their chromophore retinal is tuned. This characteristic and the precision of the tuning mechanism is a fundamental requirement for color vision. Using the archaeal rhodopsins as model systems, this work aims at advancing the un- derstanding of the inter-protein absorption shift. The presented results demonstrate that the electrostatic interactions of the protein with the retinal are a major determinant of the inter-protein shift. The differences in electrostatic potential that the proteins cause at the retinal could be assigned to seven residues. A generalized model of a quantum mechanical particle in a box including the electrostatic potential as a parameter allows a qualitative description of the absorption maxima. Bacteriorhodopsin has become one of the most important model systems in the field of bioenergetics. This is due to its relative simplicity making it amenable to experimental and theoretical studies. Here, the probability of functionally relevant protonation states is calculated to characterize the available structures. The protonation behavior of the key residues of proton transfer and the correlation between the protonation of these residues is analyzed. The results show that with respect to the protonation the bR, K, L and M1 intermediate state are well represented by the available structures, while the M2, N and O intermediate state are less well represented. An algorithm is introduced that determines a gap-free list of the lowest energy states. Such a list allows to analyze the ensemble of states accessible to a system in a certain energy range and, thus, can provide useful insight into the functional mechanism. The newly developed algorithm, termed X-DEE, is based on the dead-end elimination theo- rem. The X-DEE algorithm is applicable to a wide range of problems, for instance in protein design attempts. Here, X-DEE is successfully applied to bacteriorhodopsin to obtain gap-free lists of the lowest energy protonation states. i ZUSAMMENFASSUNG Rhodopsine uben¨ zwei zellulare¨ Schlusselfunktionen¨ aus, die Weiterleitung externer Signale und den Transport von Ionen. Beispiele beider Funktionstypen finden sich in der Familie der archaealen Rhodopsine: die Protonenpumpe Bacteriorhodopsin, die Chloridionenpumpe Halorhodopsin und den Photorezeptor Sensorisches Rhodopsin II. Ihre hochaufgelosten¨ Rontgenkristall-Strukturen¨ ermoglichen¨ theoretische Untersuch- ungen auf atomarer Ebene. Die in der vorliegenden Arbeit durchgefuhrten¨ Berechnungen basieren auf einem Kontinuum-Elektrostatik-Modell, das durch die Poisson-Boltzmann Gleichung gegeben ist, die mit Finite-Differenzen diskretisiert wird. Die Ergebnisse kon-¨ nen in drei Abschnitte unterteilt werden. Ein Charakteristikum der Rhodopsine ist der extreme Bereich, uber¨ den diese das Ab- sorptionsmaximum ihres Chromophors Retinal einstellen. Diese Eigenschaft und die Prazision¨ dieses Mechanismus ist eine grundlegende Voraussetzung des Farbsehens. Die archaealen Rhodopsine werden in der vorliegenden Arbeit als Modellsysteme genutzt, um die Verschiebung der Absortion zwischen den Proteinen zu untersuchen. Die vor- liegenden Ergebnisse zeigen elektrostatische Wechselwirkungen des Proteins mit dem Retinal als entscheidenden Faktor fur¨ die Verschiebung der Absorption. Die Unterschie- de des elektrostatischen Potentials, das die Proteine am Retinal verursachen, kann sie- ben Aminosauren¨ zugeschrieben werden. Ein verallgemeinertes Modell eines quanten- mechanischen Teilchens in einer Box mit dem elektrostatischen Potential als Parameter ermoglicht¨ eine qualitative Beschreibung der Absorptionsmaxima. Bacteriorhodopsin ist eines der wichtigsten Modellsysteme der Bioenergetik. Da es ein re- lativ einfaches Protein ist, sind experimentelle und theoretische Studien gut durchfuhr-¨ bar. In dieser Arbeit wird die Wahrscheinlichkeit funktionell relevanter Protonierungs- zustande¨ berechnet, um die vorhandenen Strukturen genauer zu charakterisieren. Das Protonierungsverhalten der Schlusselgruppen¨ des Protonentransfers und die Korrelation der Protonierung dieser Gruppen wird analysiert. Die Ergebnisse zeigen, dass der bR-, K-, L- und M1-Zustand bezuglich¨ der Protonierung gut, wahrend¨ der M2-, N- und O-Zustand weniger gut durch die vorhandenen Strukturen reprasentiert¨ sind. Ein Algorithmus wird eingefuhrt,¨ der eine luckenlose¨ Liste der Zustande¨ niedrigster Ener- gie ermittelt. Eine solche Liste ermoglicht¨ die Untersuchung des gesamten Zustandsen- sembles, welches dem System in einem bestimmten Energiebereich zuganglich¨ ist. Da- durch konnen¨ hilfreiche Erkenntnisse uber¨ den funktionellen Mechanismus gewonnen werden. Der neu entwickelte Algorithmus, X-DEE genannt, basiert auf dem Theorem uber¨ die Dead-End-Eliminierung. Der X-DEE-Algorithmus ist in den unterschiedlichsten Gebieten verwendbar, unter anderem in Protein-Design-Ansatzen.¨ In dieser Arbeit wird X-DEE erfolgreich angewandt, um luckenlose¨ Listen der Protonierungszustande¨ niedrig- ster Energie fur¨ Bacteriorhodopsins zu erhalten. iii LIST OF PUBLICATIONS ‘When I use a word,’ Humpty Dumpty said in rather a scornful tone. ‘It means just what I choose it to mean – neither more or less.’ Lewis Carroll, Alice in Wonderland [ 1 ] Edda Kloppmann, Torsten Becker and G Matthias Ullmann. Electrostatic potential at the retinal of three archaeal rhodopsins: implications for their different absorption spectra. Proteins, 61: 953-965, 2005. [ 2 ] Edda Kloppmann, G Matthias Ullmann and Torsten Becker. An extended dead-end elimination algorithm to determine gap-free lists of low en- ergy states. J Comput Chem, 28: 2325-2335, 2007. [ 3 ] G Matthias Ullmann, Edda Kloppmann, Timm Essigke, Eva-Maria Krammer, Astrid R Klingen, Torsten Becker and Elisa Bombarda. Investigating the mechanisms of photosynthetic proteins using continuum electro- statics. Photosynth Res, 97: 33-53, 2008. [ 4 ] Edda Kloppmann and G Matthias Ullmann. Protonation states and correlation of the protonation behavior of the key residues of proton transfer in bacteriorhodopsin: a continuum electrostatic analysis of the photocycle intermediate structures. In preparation. v ACKNOWLEDGEMENTS For all that has been, thanks. For all that will be, yes. Dag Hammarskjold¨ This work would not have been possible without the support and encouragement of my colleagues, friends and family and I deeply value and appreciate the help of all who - directly or indirectly - contributed to this thesis. First and foremost, I would like to sincerely thank my supervisor Matthias Ullmann for giving me the opportunity to work on a topic I enjoyed, for guiding the progress of my work with countless helpful and inspiring discussions, and for his unequivocal support. Thanks to the whole BISB-group for making it a pleasure to work there. Special thanks go to Torsten Becker who collaborated on the solution for the generalized model of a particle in a box and on the development of the X-DEE algorithm. His ideas and his patience have greatly contributed to this work. Thanks to Timm Essigke, who installed and maintained our computer network, for his much appreciated technical help. Astrid Klingen and Elisa Bombarda have been splendid roommates and I thank both for all work-related and non- work-related discussions. Many, many
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