DI
DIPARTIMENTO DI BIOTECNOLOGIE, CHIMICA E FARMACIA DOTTORATO DI RICERCA IN SCIENZE CHIMICHE E FARMACEUTICHE
CICLO XXXIII
COORDINATORE: PROF. Maurizio TADDEI
Blueprinting, implementation, and application of fully automatic protocols for the QM/MM modeling of photo-excited states of rhodopsin
variants
SETTORE SCIENTIFICO-DISCIPLINARE: CHIM/06
Laura Milena PEDRAZA GONZÁLEZ Dottorando
Chiar.mo Prof. Massimo OLIVUCCI Supervisore
Chiar.mo Prof. Luca DE VICO Co-supervisore
ANNO ACCADEMICO 2017/2020
Digitally signed by: PEDRAZA GONZALEZ LAURA MILENA
Reason: Ph.D. Thesis, dottorato di ricerca in Scienze chimiche e farmaceutiche Ciclo XXXIII (Matricola N. 076319).
Location: Dipartimento Biotecnologie, Chimica e Farmacia. Università degli Studi di Siena. Siena, Italia.
Date: 16/04/2021 16:45:53
.
Dedicado con todo mi amor a mis padres, Martha y Roberto z
“Cuando encuentras un diamante que no es de nadie, es tuyo.
Cuando encuentras una isla que no es de nadie, es tuya.
Cuando eres el primero en tener una idea, la haces patentar:
es tuya. Yo poseo las estrellas porque jamás nadie antes que yo soñó con poseerlas”
“Quando trovi un diamante che non è di nessuno, è tuo.
Quando trovi un’isola che non è di nessuno, è tua. Quando tu hai un’idea per primo, la fai brevettare, ed è tua. E io possiedo le stelle, perchè mai nessuno prima di me si è sognato di possederle”
“When you find a diamond that belongs to nobody, it is yours. When you discover an island that belongs to nobody, it is yours. When you get an idea before any one else, you take out a patent on it: it is yours. So with me: I own the stars, because nobody else before me ever thought of owning them”
− Antoine de Saint-Exupéry, Le Petit Prince.
ACKNOWLEDGMENTS
“Es el tiempo que has dedicado a tu rosa el que la ha hecho tan importante”
−
Antoine de Saint-Exupéry, Le Petit Prince
I decided to start this section by sharing a quote from one of my favorites books: “It’s the time that you spent on your rose that makes your rose so important” (Antoine de Saint-Exupéry, Le Petit Prince). Those who have gone through the process of doing a Ph.D., know the importance of dedicating time and intellectual effort to take their ideas to another, more tangible level. From my experience, I can tell you that it is not just a matter of investing time, but achieving something that yourself can consider an “extraordinary job” requires making a compromise between your brain and your heart to dream high and work hard. That is what makes “my rose” so important...
I want to thank all those who made this process an extraordinary experience. To be fair, I will start with the person who, without hearing my name before, trusted me and gave me the “go-ahead” to pack my bags and start this adventure in Italy, my supervisor Prof. Massimo Olivucci. «Dear Prof., thank you very much for all your efforts aimed at my scientific training, for transmitting your love for science, and for giving me encouragement and support always I needed it. I know how important the work we do in the LCPP is to you, therefore, infinite thanks for allowing me to express and perform my ideas of “automating everything” (I did not write an automatic code for generating this text... sorry, it is the only thing about this thesis that is not still implemented into the ARM package). I also want to thank you for guiding me during the writing of this dissertation, and teaching me how to improve my different skills to become a better researcher. I am very fortunate of having the opportunity of working as a part of your team».
I would also like to thank my co-supervisor, Prof. Luca De Vico, for all his help, advice, support, and teaching during these three years. «I really appreciate our scientific conversations and the resulting ideas, as well as your technical support and actual lessons.
It has been a good aspect to know a person who shares my same OCD in terms of form and content for figures, slides, and this kind of things. I consider thanks to your “let’s stay positive” influence, I am pickier now».
I also want to express my sincere thanks to all the past and present members of the Laboratory of Photochemistry and Computational Biology: Jacopo Barbetti, Luca De Vico, María del Carmen Marín (Mari), Freja Storm, Salvatore Prioli, Filippo Sacchetta, Emanuele Marsili, Laleh Allahkaram, Martina Nucci, Riccardo Palombo, Daniele Padula, Michał Marszałek, Simone Bonfrate, and Leonardo Barneschi. «All of you were an impor- tant piece to complete this puzzle. Thanks for our scientific conversations and for respect- ing “my rule” of not talking about work during coffee time. I am kidding! Thank you for
vii
your friendship and your invaluable help.» I want to especially thank Michał, Simone, and Leonardo, who trusted me to help them as their co-supervisor. I learned a lot from the experience of working with you. Talking about learning processes... thanks to Dr. Alessio Valentini, who literally in three hours of Python lessons taught me the basis of what I needed for coding during three years. Also, my sincere thanks to Dr. Daniele Padula for his advice about Python and science, «it is being a pleasure working with you».
I would also like to thank Prof. Nicolas Ferré at the Université Aix-Marseille for our scientific conversations and also for doing his best for trying to make possible my “actually impossible” internship. I hope to have the opportunity to visit your laboratory soon. Many thanks to Prof. Hideki Kandori and Dr. Keichi Inoue at the Nagoya Institute of Technology for our scientific conversations and your advice during our collaboration.
Sorry for the language change, but it is necessary. . .
Vorrei ringraziare tutti i miei amici italiani, quelli che da quando sono arrivata in Italia mi hanno fatta sentire a casa. Ai miei primi coinquilini, Oreste, Stefano e Maria Chiara,
«grazie per fare del vostro meglio per insegnarmi a parlare in italiano e per farmi parte del vostro gruppo di amici, siete veramente importante per me>. Grazie anche ai miei amici dell’Università, Maher Al Khatib, Marco Valentini, Leire Iralde, Mari Marín, Nésar Viera, Federico Rossi, e Jessica Costa, per tanti aperitivi e risate insieme.
Nonostante di questa brutta situazione in cui non è più possibile passare il tempo (in presenza) insieme agli amici, ho avuto la fortuna di avere il supporto virtuale di Fede, «Non scherzavo quando ti ho detto che sei il mio contatto preferito su WhasApp... Grazie mille per essere sempre disponibile e per farmi ridere con l’aiuto di Pepe, voi due avete reso più amichevole le lunghe giornate in cui dovevo scrivere la Tesi».
Grazie mille al mio migliore amico italiano, Leonardo Barneschi, che a entrambi i livelli lavorativo e personale mi ha dato il suo sostegno e abbraccio sempre quando ho avuto bisogno. Ringrazio anche Daniele Padula, per la sua compagnia e disponibilità, per tanti pranzi e aperitivi insieme e quelle lunghe camminate in centro.
Vorrei esprimere un ringraziamento molto speciale a Daniele M., che durante questo periodo mi ha insegnato tante cose carine e interessanti. «Non sei consapevole di quanto mi hai aiutato e quanto mi hai resa felice. Grazie per essere paziente e darmi supporto durante la scrittura di questa Tesi ». Grazie anche a Marica M. per tutto quanto. «Voi e la vostra famiglia mi avete fatta sentire a casa e lo apprezzo molto. Spero sia possibile rimanere in contatto con voi...»
Grazie mille alla mia amica e vicina di casa Maria Grazia, che si è presa cura di me e mi ha accompagnata durante l’ultimo anno del mio dottorato.
Mi dispiace, ma devo nuovamente cambiare la lingua...
Quiero expresar un agradecimiento muy especial a dos queridas amigas y compañeras de viii
aventura, Andrea Robles y Mayra Avelar. «Andre, muchas gracias por estos tres años de locuras y risas, con tu corazón de oro me hiciste conocer otra perspectiva de la vida, te auguro lo mejor en esta nueva etapa como que inicias siendo la Dr. Robles». «Mayra, la mejor roomie, compañera de viajes y “compañera de celda” durante la pandemia. No tengo palabras para expresarte la inmensa gratitud que siento hacia tí; con paciencia me ayudaste a crecer en muchos aspectos personales y laborales. Te admiro y te deseo lo mejor.»
Ahora es el turno para mis queridos Amigos de toda la vida, aquellos que aparecen en los agradecimientos de las tres tesis que he escrito (espero que esta sea la última). A Juan, que siendo consciente de las inevitables consecuencias, fue la primera persona en apoyarme para iniciar este viaje y que, además de eso, siempre ha tenido una palabra y un gesto alentador para hacerme sentir mejor. «Tú sabes que no elegimos una vida fácil, pero estaremos más o menos cerquita para apoyarnos cuando sea necesario». A Diana, con quien también hemos vivido contemporaneamente el proceso de pregrado, maestría y doctorado,
«gracias por todo tu apoyo y sobre todo por tomar ese avión a Roma en el momento en que más lo necesitaba». Agradezco también a Paula Luna, Jessica Mune (Wii), Camilo Navarro, Félix Moncada, Jorge Charry, William Quintero, Ismael Ortíz, Sergio González, Ignacio y Nachito Uribe, May Gómez y a los demás que me han acompañado desde Colombia con sus llamadas.
También quiero agradecer a los miembros de mi antiguo grupo de investigación, el
<QCC>, donde aprendí todo lo necesario para cursar este doctorado. Gracias al Professor Andrés Reyes, quién siempre ha creído en mi y ha contribuído a mi formación científica y personal.
El agradecimiento más especial va dirigido a las personas que me dieron la vida y me enseñaron cómo vivirla con amor y compromiso. «Queridos padres y hermano (Alejandro), este es el fruto de todos los esfuerzos y sacrificios que durante lo largo de mi vida han hecho pensando en mi. A ustedes debo mi perseverancia, persistencia y deseos por sobresalir.
Saben que todo lo que he hecho ha sido con el objetivo de hacerlos muy orgullosos de lo que con su apoyo he logrado. Gracias por escucharme hablar de ciencia, trabajo y demás y, no obstante no entender nada, buscar la forma de ayudarme a resolver mis problemas. A mi papá, Roberto Pedraza, por brindarme su apoyo y amor desde la distancia y no dejar de llamarme ni un sólo día para verificar que todo estuviera bien. A mi mamá, Martha González, por tener el valor de cruzar el mundo dos veces para venir a visitarme, además de acompañarme todos los días por videollamada y tener siempre una palabra de aliento y de amor. Todos mis triunfos los debo a ustedes.»
Last but not least, I want to express, again, my special gratitude to Luca. You took care of each detail during the process of my formation as a researcher and also during the writing of this document. Thank you for not let me give up, for working remotely with me until late in
ix
the night, and for identifying details and mistakes that I was not able to see. Thank you also for being my friend and giving me advice and support during these difficult times. The final result of this thesis would not have been possible without your support and compromise.
To conclude, I promise that the rest of this document will sound more scientific...
x
ABSTRACT
The semi-automatic building of Quantum Mechanics/Molecular Mechanics (QM/MM) mod- els of rhodopsins has been recently proposed, by means of a new technology called Automatic Rhodopsin Model protocol. In its original version, here called original ARM protocol, pub- lished in 2016, the constructed QM/MM models were found to be useful for biophysical studies and for protein engineering, but had the disadvantage of being time-consuming to prepare, error prone and, also, difficult to replicate when the same model was independently constructed by different investigators. These issues were a consequence of the «semiauto- matic» (i.e., not fully automated) nature of the protocol, since (i) the generation of its input was achieved through «manual manipulation» of the template structure and (ii) the code (i.e., the computer program) for the construction of the QM/MM model was written as a non homogeneous collection of bash scripts, not driven by a parent program. Such methodolog- ical and computational pitfalls impaired the possibility of comparatively studying hundreds of rhodopsins (i.e., light-sensitive proteins belonging to the same superfamily), as well as hoping that, in the future, a similar protocol could be generalized to other families of light- responsive proteins (e.g., Xanthorhodopsin, phytochromes or synthetic rhodopsin mimics) of interest for biological or biotechnological applications.
In order to overcome the above drawbacks, this doctoral Thesis is devoted to the de- sign of a substantially improved ARM methodological framework, characterized by a fully automated, rather than manual, construction of QM/MM models. Accordingly, I intro- duce below the blueprinting of four different ARM-based fully automatic protocols for the QM/MM modeling of rhodopsin electronically excited states. Furthermore, I present their implementation into a new, user-friendly, Python-based software package, called ARM package, conceived for allowing the use of each protocol via a “one-click” command given either at the command-line or, in certain cases, Web-interface levels. Finally, I report on the performance of the four ARM-based protocols, highlighting both their methodological and scientific capabilities as well as their current limitations. To do so, I have constructed and employed a benchmark set of about 150 wild-type and mutant rhodopsins, as well as carried out selected applications, directed to the prediction of trends in light-induced properties, including absorption and emission spectra, as well as excited state molecular dynamics. Such trends unveil different mechanistic aspects of color tuning and fluorescence emission, as well as, more in perspective, the systematic prediction of photoisomerization quantum yields.
In conclusion, the research carried out during my doctoral Thesis has generated and ex- plored novel, automated, ARM-based research tools and, most importantly, a programming
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framework called the ARM package. I believe that these tools and package have the potential to be generalized, thanks to their characteristics that I will thoroughly describe. In other words, my hope is that the research line started with my thesis will not only be useful for achieving better performing QM/MM models of rhodopsins, but be expanded to deal with other sets of light-responsive proteins useful, for instance, in optogenetic studies.
xii
Contents
Title i
Certificate iii
Dedication v
Acknowledgments vii
Abstract xi
Contents xiii
List of Figures xvii
List of Tables xxi
Acronyms & Abbreviations xxiii
List of Publications xxix
1 Introduction 1
1.1 Rhodopsins: A family of biological photoreceptors . . . . 4
1.1.1 Structure and diversity . . . . 4
1.1.2 Biological functions . . . . 5
1.1.3 Photoreactivity and applications . . . . 6
1.1.3.1 Optogenetics . . . 10
1.1.4 Computational tools for rhodopsin modeling: The ARM protocol . . . 11
1.2 Motivation of this research work . . . 13
1.3 Aims and organization of the Thesis . . . 13
2 On the Construction of QM/MM Models for Rhodopsin-like Photore- ceptors 17 2.1 State-of-the-art for QM/MM modeling of rhodopsins . . . 18
2.2 The original version of the ARM protocol . . . 22
2.2.1 Definition of a ARM QM/MM model . . . 23
2.2.2 QM/MM model generator . . . 24
2.2.2.1 Initial setup . . . 24 xiii
2.2.2.2 QM/MM calculations . . . 26
2.2.3 Automation issues . . . 27
3 a-ARM: Achieving an Automatic QM/MM modeling technology 31 3.1 A protocol for the generation of ground-state QM/MM models . . . 33
3.1.1 a-ARM: Automatic Rhodopsin Modeling with Chromophore Cav- ity Generation, Ionization State Selection, and External Counterion Placement . . . 33
3.1.1.1 Methodological aspects . . . 34
3.1.1.2 Software implementation aspects . . . 37
3.1.1.3 Benchmark, validation and application aspects . . . 37
3.1.1.4 Limitations and pitfalls of a-ARM . . . 39
3.1.2 Web-ARM: a Web-Based Interface for the Automatic Construction of QM/MM Models of Rhodopsins . . . 40
3.1.2.1 Limitations and pitfalls of Web-ARM . . . 42
3.1.3 A standard protocol for the analysis of color tuning . . . 42
3.1.3.1 Steric effects. . . 44
3.1.3.2 Electrostatic effects. . . 45
3.1.3.3 Limitations and pitfalls of the protocol for color-tuning analysis 45 3.1.4 A strategy for the prediction of side-chain conformations in mutants . 46 3.1.4.1 Benchmarking of side-chain predictor . . . 48
3.1.4.2 Limitations and pitfalls of side-chain predictor . . . 51
4 Automated QM/MM Model Screening of Rhodopsin Variants Display- ing Enhanced Fluorescence 53 4.1 Methodological framework . . . 57
4.1.1 Phase I): Location of the first excited state (S1) minimum . . . 58
4.1.2 Phase II): Computation of Quantum-Classical Franck-Condon (FC) trajectories . . . 60
4.1.3 Phase III): Calculation of the excited state reaction path along the photoisomerization coordinate . . . 62
4.1.4 Protocol Automation . . . 65
4.2 Benchmarking and application of the protocol . . . 68
4.2.1 Benchmark Set Results . . . 70
4.2.2 Application Set Results . . . 73
4.2.2.1 Phase I: application set . . . 74
4.2.2.2 Phase II: application set . . . 77
4.2.2.3 Phase III: application set . . . 80
4.2.3 Search Set Results . . . 84
4.2.3.1 Phase I: search set . . . 84 xiv
4.2.3.2 Phase II: search set . . . 86
4.2.3.3 Phase III: search set . . . 88
4.3 Final remarks about the fluorescence screening protocol . . . 92
4.3.1 Software implementation aspects . . . 92
4.3.2 General aspects about the location of the PLA structure . . . 93
4.3.3 General aspects about the calculation of quantum-classical FC trajec- tories . . . 94
4.3.4 General aspects about the calculation of the isomerization RS . . . 95
5 Applications: Modeling ground- and excited-state properties 99 5.1 Mutants generation and color tuning analysis . . . 101
5.1.1 Screening Mouse Melanopsin Color-Tuning mutations . . . 101
5.1.2 Towards a Comparative Computational Photobiology: Invertebrate Rhodopsin Pigments . . . 103
5.1.3 Role of Pro219 as an Electrostatic Color Determinant in the Light- driven Sodium Pump KR2: Combined spectroscopic and QM/MM modelling studies . . . 105
5.2 Absorption bands and photodynamics simulations . . . 109
5.2.1 Analysis of Absorption Bands and light-induced Dynamics of Rhodopsins through a QM/MM-based Automatic Protocol . . . 110
5.2.2 Multi-State Multi-Configuration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin. . . 112
5.2.3 Non-adiabatic dynamics reveal coexisting reactive and non-reactive bicycle-pedal isomerization channels in heliorhodopsins . . . 114
5.3 Emission properties simulation and engineering of fluorescent rhodopsins . . . 117
5.3.1 Refining QM/MM methodologies to study the mechanism of fluores- cence in microbial rhodopsins . . . 117
5.3.2 «Paper [VI]» Automated QM/MM Model Screening of Rhodopsin Variants Displaying Enhanced Fluorescence . . . 119
6 Concluding remarks and future directions 121 6.1 Summary of the Thesis work, and conclusions . . . 121
6.1.1 Developing the ARM package . . . 122
6.1.2 Developing protocols to compute ground-state properties . . . 124
6.1.3 Developing protocols to compute excited-state properties, and screen- ing for fluorescent rhodopsin variants . . . 125
6.1.4 Applications of a-ARM to predict photophysical and photochemical properties . . . 127
6.2 Scope for future study . . . 127
Bibliography 129
xv
Appendices 145
A The ARM software package 147
A.1 Structure . . . 148
A.2 Drivers . . . 150
A.2.1 a-ARM rhodopsin model building . . . 150
A.2.1.1 Preparing a ARM input . . . 150
A.2.1.2 Preparing a QM/MM ARM model . . . 159
A.2.1.3 a-ARM Output files . . . 160
A.2.2 a-ARM rhodopsin fluorescence screening . . . 161
A.2.2.1 Computational details for geometry optimizations and en- ergy re-evaluation . . . 161
A.2.2.2 The a_arm_emission module . . . 163
A.2.2.3 The a_arm_fc module . . . 168
A.2.2.4 The a_arm_relaxed_scan module . . . 174
B Publications 181 B.1 Paper [I]: a-ARM: Automatic Rhodopsin Modeling with Chromophore Cavity Generation, Ionization State Selection, and External Counterion Placement . 181 B.2 Paper [II]: Web-ARM: a Web-Based Interface for the Automatic Construc- tion of QM/MM Models of Rhodopsins . . . 201
B.3 Paper [III]: Chapter 1: On the Automatic Construction of QM/MM Models for Biological Photoreceptors: Rhodopsins as Model Systems . . . 215
B.4 Paper [IV]: Multi-State Multi-Configuration Quantum Chemical Computa- tion of the Two-Photon Absorption Spectra of Bovine Rhodopsin. . . 291
B.5 Paper [V]: Role of Pro219 as an Electrostatic Color Determinant in the Light- driven Sodium Pump KR2: Combined spectroscopic and QM/MM modelling studies . . . 300
xvi
List of Figures
1.1 Rhodopsin types: structural similarities and differences. . . . 5 1.2 Primary photoreaction in animal (type-II), microbial (type-I) and helio-
rhodopsins. . . . 6 1.3 Light-induced and light-emission properties of rhodopsin proteins, investi-
gated using computational modeling. . . . 7 1.4 Methodological and computational developments of this doctoral Thesis. . . . 14 2.1 General structure of a monomeric, gas-phase and globally uncharged ARM
QM/MM model. . . . 19 2.2 External counterion positions relative to ionizable residues, according to the
“No Surface Charge” (NSC) scheme employed for the ARM QM/MM models. . . 24 2.3 General workflow of the QM/MM model generator , developed in the original
version of ARM. . . . 25 3.1 General workflow of the two phases, i.e., input file generator and QM/MM
model generator , of the a-ARM rhodopsin model building protocol. . . 34 3.2 Overview of the most relevant features of the input file generator introduced
in the a-ARM version of the protocol. . . 35 3.3 Default and customized a-ARM models for KR2 (PDB ID 3X3C). . . . 36 3.4 Benchmarking of the a-ARM version of the protocol, in terms of reproduction
of experimental trends in λamax. Comparison whit the original version that features manual input file generation. . . 38 3.5 General overview of the Web-ARM interface. . . 41 3.6 Schematic representation of color tuning mechanism in rhodopsins. . . 43 3.7 Scheme of the excitation energy analysis for the elucidation of its electrostatic
and steric contributions, that modulate color tuning mechanisms in rhodopsins. 44 3.8 Proposed approach for the modelling and choice of side-chain conformations,
included as the mutant generation routine in the input file generator . . . 49 3.9 Schematic representation of the procedure employed for the selection of the
side-chain conformation in mutants generation. . . 50 3.10 Benchmarking of the mutants generator routine based on Modeller . . . 50 4.1 Photoreaction scheme of two potential fluorescence mechanisms for microbial
rhodopsins. . . 55 xvii
4.2 Cavity residues of the S0 QM/MM models of ASRAT and two of its mutants,
studied in Ref. 49 with the original ARM protocol . . . 57
4.3 Phase I of the a-ARM rhodopsin fluorescence screening. Location of the first excited state minima. . . 59
4.4 Phase II of the a-ARM rhodopsin fluorescence screening. Computation of semiclassical Franck-Condon (FC) trajectories. . . . 61
4.5 Franck-Condon (FC) trajectory computation on S1for L83QASRAT , WTASRAT and W76S/Y179FASRAT , respectively, computed in Ref. 49 with the original ARM. 62 4.6 Phase III of the a-ARM rhodopsin fluorescence screening. Calculation of the excited state reaction path along the photoisomerization coordinate. . . 64
4.7 Relaxed scan (RS) C13=C14photoisomerization paths along S1for L83QASRAT , WTASRAT and W76S/Y179FASRAT , respectively, computed in Ref. 49 with the original ARM. . . . 65
4.8 General worflow of th three-phases a-ARM rhodopsin fluorescence screening protocol. . . 66
4.9 Input file required for the a-ARM rhodopsin fluorescence screening protocol. . 67
4.10 Extended benchmark of the a-ARM protocol, in terms of reproduction of experimental trends in λamax (benchmark set, application set and search set). . 72
4.11 Trends in vertical absorption (∆EaS1−S0) and emission (∆EfS1−S0) energies for the rhodopsins of the application set. . . 75
4.12 Franck-Condon (FC) trajectory computations on S1 for rhodopsins of the application set. . . 78
4.13 Franck-Condon (FC) trajectory computations on S1 for Arch7 . . . 79
4.14 Relaxed scan (RS) computation on S1 for the application set. . . 82
4.15 Correlation between computed Isomerization barrier and experimental Fluo- rescence quantum yield (φf) for the application set . . . 83
4.16 Franck-Condon (FC) trajectory computation on S1 for two rhodopsins of the search set, which do not exhibit S1-S2 mixing. . . 86
4.17 Franck-Condon (FC) trajectory computation on S1 for rhodopsins of the search set, which exhibit S1-S2 mixing. . . 88
4.18 Relaxed scan (RS) for members of the search set, without mixing S1-S2. . . . 89
4.19 Relaxed scan (RS) for members of the search set, that exhibit mixing S1-S2. . 90
4.20 Effects of the on the RS of the step size, relative to the constrained isomer- ization torsional angle variation. . . . 96
5.1 Overview of the master’s Thesis of Sacchetta et. al. . . 102
5.2 Overview of the master’s Thesis of Allahkaram . . . 104
5.3 Overview of the main results reported in paper [V] . . . 106
5.4 KR2 (PDB ID 6REW) model customization. . . . 107 xviii
5.5 Schematic representation of the selection of side-chain conformations for the
19 P219X mutants of KR2. . . 108
5.6 Preliminary screening of the KR2 cavity. . . 110
5.7 General workflow of the a_arm_opa driver. . . 111
5.8 Overview of the main results presented in paper [IV]. . . 113
5.9 Overview of the main results of the master’s thesis of Palombo et. al. . . . . 115
A.1 Representation of the contents of the ARM package . . . 148
A.2 ARM software requirements . . . 149
A.3 Command line interface for the a_arm_fluorescence_searcher module. . . 162
A.4 Specific methodological workflow of the a_arm_emission module. . . 163
A.5 Command line interface for the a_arm_emission module. . . 164
A.6 Specific methodological workflow of the a_arm_fc module. . . 169
A.7 Command line interface for the a_arm_fc module. . . 170
A.8 Specific methodological workflow of the a_arm_relaxed_scan module. . . 175
A.9 Command line interface for the a_arm_relaxed_scan module. . . 176
xix
List of Tables
2.1 QM/MM model setups reported in the literature for bovine rhodopsin (Rh) . 21 3.1 Overview of structural features and both experimental and computational
data for the ARM QM/MM model models of Anabaena sensory rhodopsin (ASR). 51 4.1 Experimental fluorescent properties for the Archaerhodopsin-3-based variants
of the application set.a . . . 54 4.2 Benchmark, application and search sets including wild-type and mutant
rhodopsins. . . 69 4.3 Ground-state Vertical Excitation energy (∆EaS1−S0), kcal mol−1 and eV in
italic and parenthesis), Maximum absorption wavelength (λamax), nm), and oscillator strength (fOsc), calculated using the a-ARMdefault and the a- ARMcustomized approaches. Differences between calculated and experimental data (∆∆ES1-S0Exp , ∆λa,Expmax ) are also presented. . . . 71 4.4 Setup of the protonation states for a-ARMdefaultand a-ARMcustomizedmodels.
The residues with different protonation states are highlighted. Asp, Glu are deprotonated while Ash and Glh are protonated. . . 73 4.5 First excited-state vertical excitation energies (∆ES1-S0, kcal mol−1 and eV
in italic and parenthesis), maximum emission wavelengths (λfmax, nm), and oscillator strength (fOsc), calculated using the a_arm_emission module. Dif- ferences between calculated and experimental data (∆∆Ef,ExpS1-S0, ∆λf,Expmax ) are also presented. . . . 76 4.6 Experimental fluorescence quantum yield, QYf, unit-less, along with calcu-
lated energy barrier, EfS1, kcal mol−1, for the rhodopsins of the application set. . . 83 4.7 Summary of the analysis performed in Phases I-III for the 10 rhodopsins of
the application set. . . . 84 4.8 Maximum emission wavelength (λfmax) computed with the a_arm_emission
module, for the rhodopsins in the search set, using two-state-averaged roots (n) for the evaluation of the S1 wave function. . . . 85 4.9 Summary of the analysis performed in Phases I-III for the rhodopsins of the
search set. . . . 91 A.1 Different instances of the a-ARM framework. . . 149
xxi
Acronyms & Abbreviations
∆∆EELE(d)S1−S0 Direct component of the electrostatic contribution to the total vertical Excitation energy 44
∆∆EELE(i)S1−S0 Indirect component of the electrostatic contribution to the total ver- tical Excitation energy 44
∆∆EELES1−S0 Electrostatic contribution to the total vertical Excitation energy 43, 44
∆∆EST RS1−S0 Steric contribution to the total vertical Excitation energy 43, 44
∆∆ET OTS1−S0 Total vertical Excitation energy 43, 44
∆ERETS1−S0 Vertical Excitation energy for retinal in vacuum 43
∆ET P AS1−S0 Vertical Excitation energy for two-photon absorption 7, 112
∆EaS1−S0 Vertical Excitation energy xviii, xxi, 7, 35, 37, 43, 45, 47, 48, 68, 70, 74, 91, 101–104, 106–108, 118
∆EfS1−S0 Vertical Emission energy xviii, 7, 8, 54, 66, 74, 76, 84, 85, 91, 94, 125
∆Expcalc∆EaS1−S0 Difference between experimental and calculated Vertical Excitation energy 48, 70, 73, 74, 76, 91, 106, 108
∆Expcalc∆EfS1−S0 Difference between experimental and calculated Vertical Emission en- ergy 74
∆Expcalcλamax Difference between experimental and calculated maximum absorption wavelength 20
λa,calcmax Calculated maximum absorption wavelength 20, 115
λamax Maximum absorption wavelength xvii, xviii, xxi, 6, 7, 9, 10, 15, 18, 20, 24, 28, 34, 37, 42, 43, 45, 48, 58, 61, 65, 68, 70, 72–74, 76, 77, 81, 84, 101–106, 108, 109, 112–116, 118, 119, 123, 126, 162, 166, 291 λfmax Maximum emission wavelength xxi, 7, 8, 15, 54, 58, 59, 61, 65, 66, 68,
74, 76, 77, 80, 81, 83–85, 94, 119, 120, 125, 126, 162, 167
φf Fluorescence quantum yield xviii, 8, 54, 57, 62, 68, 75, 80, 81, 91, 114, 117, 126
τS1F S fluorescent state lifetime 118
EfS1 Isomerization barrier xviii, xxi, 7, 8, 57, 62, 63, 65, 66, 80, 81, 83, 89–91, 96, 118, 119, 125, 126
S0 Ground-state xvii, 6–9, 13–15, 24, 27, 33, 34, 39, 40, 43, 45, 53, 55–63, 65, 66, 68, 70, 73–77, 81, 84–88, 92–95, 99, 101, 105, 111, 112, 114, 116, 118, 119, 124–127, 160–163, 165–169, 171, 172, 174
xxiii
S1 First excited-state xviii, xxi, 6–9, 15, 27, 43, 55–60, 62–64, 66, 68, 70, 74, 77, 80, 81, 83–91, 94–96, 104, 112–114, 116, 118, 119, 124, 125, 127, 161, 162, 166–168, 174, 177, 178
S2 Second excited-state xviii, 6, 7, 27, 57, 66, 77, 80, 81, 84–88, 90, 91, 96, 161
a-ARM Updated version of the Automatic Rhodopsin Modeling protocol xv, xvii, xviii, xxi, 14, 15, 17, 31–35, 37, 39, 40, 43, 45–48, 51, 53, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72–74, 76, 77, 81, 84, 92, 93, 95, 100–102, 104, 106, 109, 112, 114–117, 119, 122–128, 147, 149, 150, 160–163, 165, 168, 169, 171, 174, 215
rPSB Retinal protonated Schiff base 4, 6, 10, 11, 13, 16, 18, 22, 26, 28, 35, 43, 44, 46, 55, 57, 60, 62, 63, 68, 72, 74, 77, 81, 86, 87, 102–104, 106, 109, 118, 121, 123, 124, 178
rSB Retinal Schiff base 4, 7
ARM QM/MM model Final equilibrated structure composed of 10 replicas xvii, xxi, 18, 23, 24, 26, 28, 29, 31–34, 36, 39, 40, 42, 43, 48, 53, 70, 73, 74, 93–95, 99, 101, 103, 104, 106, 107, 109, 111, 112, 114–116, 118, 126, 128, 291 ARM input PDBARM + cavity file 33–35, 40, 150, 158, 159
11-cis 11-cis configuration of the retinal 5, 18, 28, 123 13-cis 11-cis configuration of the retinal 4, 5, 9, 28, 48, 95 AARh Ancestral archosaur rhodopsin 37
all-trans all-trans configuration of the retinal 4, 5, 9, 28, 48, 68, 123, 152 Arch1 Archaerhodopsin-1 37
Arch2 Archaerhodopsin-2 37
Arch3 Archaerhodopsin-3 xxi, 54–56, 68, 73–77, 80, 81, 94, 126
Arch5 Archaerhodopsin-5 (=Arch3 D95E/T99C/V59A/P60L/P196S) 68, 74–77, 81, 83, 126
Arch7 Archaerhodopsin-7 (=Arch3 D95E/T99C/V59A/P60L/P196S/
D222S/A225C) xviii, 68, 74–77, 80, 81, 83, 96, 126
Archon2 Archon2 (=Arch3 T56P/P60S/T80P/D95H/T99S/T116I/F161V/
T183I/L197I/A225C) 68, 74–77, 81, 83, 126
ARM original Automatic Rhodopsin Modeling protocol xi, xvii, xviii, 12–
14, 16, 17, 21–24, 27–29, 31–34, 37, 46, 57, 62, 64, 74, 84, 99, 101, 121, 122, 127, 215
ASR Anabaena sensory rhodopsin xvii, 26, 37, 46, 48, 56–59, 63, 68, 70, 80, 84, 93, 95, 126
BCone Human blue cone 37
BPR Blue light-absorbing proteorhodopsin from Med12 37, 68, 93
bR Bacteriorhodopsin from Halobacterium salinarum NRC-1 37, 46, 68
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CASPT2 Complete Active-Space second-order perturbation 77, 81, 88, 93, 94, 96
CASSCF Complete Active Space Self-Consistent field 74, 77, 80, 81, 83, 88, 93, 94, 96
CC computational chemistry 1, 2
ChRC1C2 Channelrhodopsin C1C2 chimaera between ChR1 and ChR2 from Chlamydomonas reinhardtii 37
ChR2 Channelrhodopsin 2 from Chlamydomonas reinhardtii 37, 68 CI Conical intersection 8, 9, 60, 62, 63, 75, 80, 87, 89, 91, 168 DA dark adapted state 4, 5, 9, 56, 65, 74, 75, 123, 150
DOPE Discrete optimized protein energy 47
ESL Excited state lifetime 7, 57, 58, 62, 65, 68, 74, 80, 87, 94, 95, 104, 105, 117
fOsc Transition oscillator strength 68, 77, 80, 84, 86–88
FC Franck-Condon xv, xviii, 7, 8, 15, 55, 58–62, 66, 74, 75, 77, 80, 81, 84–87, 89, 94, 95, 104, 105, 114, 119, 125, 166–169, 172, 173
GCone Human green cone 37
GEVI Genetically Encodable Voltage Indicator 53, 54, 56, 117 GLR sodium pumping rhodopsin from Gillisia limnaea 56 GPCR G-protein-coupled receptor 4, 103
GR Gloeobacter rhodopsin from Gloeobacter violaceus 56
GVirus DTS-motif rhodopsin from Phaeocystis globosa virus 12T 68 HBN Hydrogen-bond networks 24, 26, 44, 45, 124
HeR-48C12 Bacterial heliorhodopsin 48C12 68 hMeOp Human melanopsin 37, 101–103
HwBR bacteriorhodopsin from Haloquadratum walsbyi 56
IaNaR Sodium pumping rhodopsin from Indibacter alkaliphilus 56 IS intracellular surface 23, 24, 29, 35
IUPAC International Union of Pure and Applied Chemistry 1 JSiR1 Jumping spider iso-rhodopsin-1 68
JSR1 Jumping spider rhodopsin-1 68, 103
KR2 Krokinobacter rhodopsin 2 from Krokinobacter eikastus xviii, 35, 37, 45, 46, 56, 68, 72, 93, 105, 106, 109, 111
LA light adapted state 9
MCQC Multi-configurational quantum chemistry 11, 13, 93 MD Molecular Dynamics 2, 19, 26, 40, 46, 47, 51, 111
MM Molecular Mechanics 2, 11, 12, 17–19, 23, 26, 40, 77, 121, 161 mMeOp Mouse melanopsin 37, 101, 102
MNaR Sodium pumping rhodopsin from Micromonospora sp. CNB394 56
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MR middle rhodopsin from Haloquadratum walsbyi 56
NM-R3 Light-driven chloride ion-pumping rhodopsin, ClP, from Nonlabens marinus 37
NpHR Halorhodopsin from Natronomonas pharaonis 56
NpSRII Sensory rhodopsin II from Natronomonas pharaonis 37, 56 OLPVRII Organic Lake Phycodnavirus rhodopsin II 68, 93
OPA One-Photon Absorption 7, 15, 109–113, 124 OS extracellular surface 23, 24, 29, 35
PDBARM Input PDB file. Contains information on monomeric chain struc- ture (chromophore, crystallographic/comparative waters), protona- tion states for all ionizable amino acid residues; and external coun- terions (Cl−/Na+) xxiii, 150, 151, 158
PES Potential Energy Surface 6, 8, 58–60, 62, 74, 77, 85, 87
PLA excited state planar minimum xv, 7, 8, 58, 59, 63, 65, 66, 74–77, 80, 81, 83–91, 93–95, 125
PoXeR Parvularcula oceani Xenorhodopsin 37, 68
QC Quantum Chemistry 1, 2
QM Quantum Mechanics 1, 2, 11, 12, 17–19, 23, 26, 121, 161
QM/MM Quantum Mechanics/Molecular Mechanics xi, xiv, xvii, xxi, 2, 3, 7, 11–15, 17–24, 26–29, 31–35, 37, 39–42, 45, 48, 51, 53, 55–58, 61–63, 65, 66, 68, 73, 74, 77, 81, 84, 92–95, 99–101, 103, 105, 106, 108, 109, 114–116, 118–122, 124, 125, 127, 147, 150, 160–163, 165, 168, 169, 171, 174, 181, 215, 300
QuasAr1 QuasAr1 (=Arch3 P60S/T80S/D95H/D106H/F161V) 68, 74–77, 81, 126
QuasAr2 QuasAr2 (=QuasAr1 H95Q) 68, 74–77, 81, 126 QY Photoisomerization quantum yield 105, 110, 111, 124 RCone Human red cone 37
RESP Restrained Electrostatic Potential 26
Rh Bovine rhodopsin from Bos taurus xxi, 18, 20, 23, 26, 37, 46, 68, 103, 104
RMSD Root-mean square-deviation 47
RmXeR Xenorhodopsin from Rubricoccus marinus 56
RS Relaxed scan xv, xviii, 7, 64, 66, 80, 81, 84, 88, 91, 95, 96, 125 RxR Thermophilic rhodopsin from Rubrobacter xylanophilus 56, 68, 93 SqRh Squid rhodopsin from Todarodes pacificus 26, 37, 101
SyHR Synechocystis halorhodopsin from Synechocystis sp. PCC 7509 56 TaHeR Heliorhodopsin from an uncultured Thermoplasmatales archaeon SG8-
52-1 68, 114
xxvi
TC theoretical chemistry 1
TPA Two-Photon Absorption 7, 16, 109, 112–114
TR Thermophilic rhodopsin from Thermus thermophilus JL-18 56 Web-ARM Web-Based Interface for the Automatic Construction of QM/MM
Models of Rhodopsins xvii, 32, 39–42, 103, 104, 128, 201
WT Wild-type 10, 12, 13, 15, 16, 18, 31, 34, 43–45, 47, 48, 54, 56, 68, 70, 73, 75, 76, 81, 84, 93, 101–103, 105, 106, 116, 117, 122, 123, 125, 126, 300
xxvii
List of Publications
This thesis is based on the following publications:
Published:
[I] a-ARM: Automatic Rhodopsin Modeling with Chromophore Cavity Generation, Ion- ization State Selection, and External Counterion Placement.
Laura Pedraza-González, Luca De Vico, María del Carmen Marín, Francesca Fanelli and Massimo Olivucci.
J. Chem. Theory Comput., 2019, 15 , pp 3134–3152
[II] Web-ARM: a Web-Based Interface for the Automatic Construction of QM/MM Models of Rhodopsins.
Laura Pedraza-González, Marıa del Carmen Marín, Alejandro Nicolas Jorge, Tyler Douglas Ruck, Xuchun Yang, Alessio Valentini, Massimo Olivucci and Luca De Vico.
J. Chem. Inf. Model., 2020, 60 , (3), pp 1481–1493
[III] Chapter 1: On the Automatic Construction of QM/MM Models for Biological Pho- toreceptors: Rhodopsins as Model Systems. In QM/MM Studies of Light-responsive Biological Systems.
Laura Pedraza-González, María del Carmen Marín, Luca De Vico, Xuchun Yang and Massimo Olivucci. Springer International Publishing Editors Tadeusz Andruniów and Massimo Olivucci. Edition 1, Volume 31, 2020. eBook ISBN 978-3-030-57721-6, Hardcover ISBN 978-3-030-57720-9. DOI 10.1007/978-3-030-57721-6.
[IV] Multi-State Multi-Configuration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin.
Samira Gholami, Laura Pedraza-González, Xuchun Yang, Alexander Granovsky, Ilya N. Ioffe and Massimo Olivucci.
J. Phys. Chem. Lett., 2019, 10 , (20), pp 6293–6300
Submitted:
[V] Role of Pro219 as an Electrostatic Color Determinant in the Light-driven Sodium Pump KR2: Combined spectroscopic and QM/MM modelling studies
Yuta Nakajima†, Laura Pedraza-González†, Leonardo Barneschi, Keiichi Inoue, Mas- simo Olivucci, and Hideki Kandori. †Authors contributed equally.
In preparation:
[VI] Automated QM/MM Model Screening of Rhodopsin Variants Displaying Enhanced Flu- orescence.
Laura Pedraza-González, Leonardo Barneschi, Michał Marszałek, Alessio Valentini, xxix
Daniele Padula, Luca De Vico, and Massimo Olivucci.
I will refer to these publications by the numbers in the order they appear in the list above. Papers [I] to [VI] are appended at the end of this thesis.
Publications that are related to the Ph.D. topic, but not included in the thesis:
Published:
[VII] Modern Quantum Chemistry with [Open]Molcas.
Francesco Aquilante, Jochen Autschbach, Alberto Baiardi, Stefano Battaglia, Veni- amin Borin, Liviu Chibotaru, Irene Conti, Luca De Vico, Mikael Delcey, Ignacio Fdez. Galván, Nicolas Ferré, Leon Freitag, Marco Garavelli, Xuejun Gong, Ste- fan Knecht, Ernst Larsson, Roland Lindh, Marcus Lundberg, Per-Ake Malmqvist, Artur Nenov, Jesper Norell, Michael Odelius, Massimo Olivucci, Thomas Peder- sen, Laura Pedraza-González, Quan Phung, Kristine Pierloot, Markus Reiher, Igor Schapiro, Javier Segarra-Martí, Francesco Segatta, Luis Seijo, Saumik Sen, Dumitru- Claudiu Sergentu, Christopher Stein, Liviu Ungur, Morgane Vacher, Alessio Valentini, and Valera Veryazov.
All authors contributed equally.
J. Chem. Phys., 2020, 152 , pp 214117.
[VIII] Frontiers in Multiscale Modelling of Photoreceptor Proteins.
Maria-Andrea Mroginski, Suliman Adam, Gil S. Amoyal, Avishai Barnoy, AnaNicoleta Bondar, Veniamin Borin, Jonathan R. Church, Tatiana Domratcheva, Bernd Ens- ing, Francesca Fanelli, Nicolas Ferré, Ofer Filiba, Laura Pedraza-González, Ronald González, Cristina E. González-Espinoza, Rajiv K. Kar, Lukas Kemmler, Seung Soo Kim, Jacob Kongsted, Anna I. Krylov, Yigal Lahav, Michalis Lazaratos, Qays NasserEddin, Isabelle Navizet, Alexander Nemukhin, Massimo Olivucci, Jógvan Mag- nus Haugaard Olsen, Alberto Pérez de Alba Ortíz, Elisa Pieri, Aditya G. Rao, Young Min Rhee, Niccolò Ricardi, Saumik Sen, Ilia A. Solov’yov, Luca De Vico, Tomasz A.
Wesolowski, Christian Wiebeler, Xuchun Yang, Igor Schapiro.
Photochem. Photobiol., 2021, 97, 243–269.
In preparation:
[IX] Quantum Mechanics Derived Force Fields for Retinals: Validation and Applications through the Automatic Rhodopsin Modeling Protocol.
Daniele Padula, Giacomo Prampolini, Laura Pedraza-González, Javier Cerezo, Xuchun Yang, Samira Gholami, Leonardo Barneschi, Simone Bonfrate, Luca De Vico,
xxx
and Massimo Olivucci.
[X] Non-adiabatic dynamics reveals coexisting reactive and non-reactive bicycle-pedal iso- merization paths in heliorhodopsins.
Riccardo Palombo, Leonardo Barneschi, Laura Pedraza-González, Xuchun Yang, Luca De Vico and Massimo Olivucci.
xxxi
Chapter 1
Introduction
Ideally, the title of any scientific report (i.e., thesis, article, book, review) must provide enough insights into the content of the announced work. The title of this Ph.D. Thesis,
“Blueprinting, implementation and application of fully automatic protocols for the QM/MM modeling of photo-excited states of rhodopsin variants”, intends to indicate the basic key- words that the reader needs to get familiar with (notice the underlined terms), in order to get a sufficient background that allows her/him to fully understand this research work.
In this Chapter, I briefly introduce each of the above-underlined concepts, independently, and explain how they might be connected. Notice that for many concepts of photochemistry, I directly provide (as a footnote) the definition recommended by the IUPAC in the “Glos- sary of terms used in photochemistry”[1]. Afterward, the motivation and objectives of the present research work are also specified. Finally, I highlight the organization of the Thesis and summarize the main research products obtained.
Initial personal remarks
I would like to introduce my Ph.D. Thesis as a compilation of the main results obtained dur- ing three years of research work carried out in the fields of photochemistry and photobiology as well as in computational sciences (e.g., code development and implementation). In this context, I stress that my contribution might be considered as the blueprinting, validation, and application of novel fully automated computational tools (e.g., protocols, software pack- ages, and web interfaces), rather than as a standard investigation in applied computational chemistrya. Indeed, it is my hope that this research will reveal itself as a solid advancement towards the design of a general photobiological automated computational tool, applicable to biologically or technologically important photoresponsive proteins.
aConcept introduced by the Nobel prize Roald Hoffmann[2] (who I had the pleasure to meet in 2014): “To the chemistry community at large, to my fellow scientists, I have tried to teach “applied theoretical chemistry”: a special blend of computations stimulated by experiment and coupled to the construction of general models – frameworks for understanding” [3]
The term “Quantum Mechanics” (QM) refers to the proper mathematical description of the behavior of elemental particles, such as electrons.[4] The application of specialized QM approaches to deal with problems of chemical interest (e.g., understanding electronic structure of molecular systems) gives rise to a second compelling term, “Quantum Chem- istry” (QC).[4, 5] Nowadays, QC encompasses a series of disciplines that, used together in a wise fashion, facilitate the interpretation of chemical phenomena even at an atomistic level.
1
Chapter 1
Here, I am mostly interested on two of them: “theoretical chemistry” (TC) and “computa- tional chemistry” (CC). The former may be roughly defined as the mathematical description of chemistry, while the latter may be defined as the implementation, in a computer, of a mathematical method that is sufficiently developed as to be automatized. Along this The- sis, we will see how these two disciplines are complementary and must be simultaneously developed in order to generate suitable computational tools of QC. In doing so, I would like to stress that the knowledge (or at least the partial understanding) of the theories behind each computational implementation is crucial to avoid that scientists made use of QC tools as a «“black-box” that magically produce desired results».
Recent years have witnessed an increasing interest in scientists of different fields for the use of QC for many diverse applications and targets.[3–5] In this context, I highlight two general scenarios in which the use of QC tools has nowadays entered into the toolkit of many scientists. The first one is to model a molecular system before synthesizing it in the laboratory, consequently, saving months of labor and raw materials and avoiding the generation of toxic waste. The second one is to give insights into the nature of a chemical phenomenon that could not be experimentally elucidated (e.g., reaction mechanisms) as well as to predict specific properties that can be more easily calculated computationally than experimentally. I anticipate that the research problems on photochemistry and photobiology posed in this Thesis require the complementary use of both strategies.
As mentioned above, countless chemical problems might require diverse theoretical ap- proaches of QC to be studied (see for instance Refs. 3, 4). Hence, I consider that it is not worth reviewing all the available QC theories and methods without having in mind a target chemical problem to be solved. For instance, to select a suitable QC method one might consider different factors regarding the nature of the system to be studied. Such in- formation might be related to the type of atoms to be described, the intra- or intermolecular interactions to be modeled (i.e., bond-breaking and bond-forming), the size of the molecular system, etc. It is well-known that the latest represents one of the current biggest challenges for QM in QC modeling. Actually, despite the increasing computational capability currently available (i.e., either software and hardware), molecular modeling, and simulation of large, complex reactive systems (e.g., proteins that have hundreds if not thousands of atoms) at the atomic level remain a challenge to computational chemists. This issue can be handled with the use of Molecular Dynamics (MD)[6] simulations, that are widely employed for the study of proteins and materials.[7, 8] MD employs classical mechanical constructs such as Molecular Mechanical (MM) force fields, that are based on empirical potentials describing small-amplitude vibrations, torsions, van der Waals interactions, and electrostatic interac- tions. However, the main pitfall of MM force fields is that they are unable to describe the changes in the electronic structure of a system undergoing a chemical reaction (i.e., bond-breaking and bond-forming, charge transfer, electronic excitation). These phenomena require, without any doubt, the use of QM for a proper treatment.
2
