QM/MM Studies of Light-responsive Biological Systems

350 Pages·2021·13.16 MB·English

by  Tadeusz Andruniów, Massimo Olivucci

Challenges and Advances
in Computational Chemistry and Physics 31
Series Editor: Jerzy Leszczynski
Tadeusz Andruniów
Massimo Olivucci   Editors
QM/MM Studies
of Light-responsive
Biological Systems
Challenges and Advances in Computational
Chemistry and Physics
Volume 31
Series Editor
Jerzy Leszczynski
Department of Chemistry and Biochemistry
Jackson State University, Jackson, MS, USA
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ó
Tadeusz Andruni w Massimo Olivucci
(cid:129)
Editors
QM/MM Studies
of Light-responsive
Biological Systems
123
Editors
Tadeusz Andruniów Massimo Olivucci
Faculty of Chemistry Department ofBiotech, Chemistry
Wrocław University of Science andPharma
andTechnology University of Siena
Wrocław,Poland Siena, Italy
ISSN 2542-4491 ISSN 2542-4483 (electronic)
ChallengesandAdvances inComputational Chemistry andPhysics
ISBN978-3-030-57720-9 ISBN978-3-030-57721-6 (eBook)
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Preface
Theunderstandingofthemechanismanddynamicsofchemical processes requires
the use of quantum mechanical calculations. In fact, quantum mechanics (QM) is
necessaryforthedescriptionofbasiceventssuchasthecovalentbond-breakingand
bond-makinginthermalchemistryortheproductionofelectronicallyexcitedstates
in photochemical, as well as in thermally induced chemiluminescent reactions [1].
In contrast with bonding-conserving conformational changes, these processes are
characterized by large electronic structure variations that accompany the nuclei
motion effectively driving the chemical transformation of the system. These elec-
tronic and nuclear changes are only observed indirectly and in too long timescale
throughexperimentalinvestigations.Accordingly,QMcalculations(alsoknownas
quantum chemical or electronic structure calculations) provide, even when applied
withintheBorn-Oppenheimerapproximation,informationstillnotaccessibleatthe
experimental level.
In spite of their high value, the application of QM calculations to chemical
reactionsoccurringinbiologicalmacromoleculesistroublesome.Thisisindeedthe
caseforproteinsandDNAstrandsthatcontainatoolargenumberofelectronstobe
treatable with the past, and regrettably, present QM technologies. However, more
than30yearsago,akeytechnicaladvancementmadepossible,forthefirsttime,the
modeling of chemical events in large molecules (e.g., proteins) and molecular
assemblies (e.g., molecules in solution and supramolecular materials). Such key
advancement is called the quantum mechanics/molecular mechanics (QM/MM)
hybrid method and it was first reported by Arieh Warshel and Michael Levitt in
1976[2],ultimatelyyieldingtheir2013,Nobelprizeforchemistry.Thestoryofthe
discovery made at the Medical Research Council (MRC) in the UK, is recounted
impressively well in a paragraph of the biography of Arieh Warshel (see https://
www.nobelprize.org/prizes/chemistry/2013/warshel/biographical/):
“...I arrived in the fall of 1974 at the MRC, with Tami, Merav and our second
daughter,Yael,andstartedtofocusonmyeffortsonmodelingenzymaticreactions.
Mytrialanderrorattemptsledtotherealizationthattheonlywaytoprogressisto
introduce the explicit effect of the charges and dipoles of the environment into the
quantummechanicalHamiltonian.Thisledtothebreakthroughdevelopmentofthe
v
vi Preface
QM/MMapproach,wheretheQMandMMwhereconsistentlycoupledincontrast
to the previous QM+MM attempts. Our advances also included the development
of the first consistent models for electrostatic effects in proteins. This model, that
was later called the protein-dipole Langevin-dipoles model, represented explicitly
(although in a simplified way) all the electrostatic elements of the protein plus the
surrounding water system and thus evaded all the traps that eluded the subsequent
macroscopic electrostatic models…”
Warshel and Levitt [2] proposed the simple, but at that time, original and
ingenious idea of dividing the model of a biological macromolecule into two
interacting regions: (i) a subsystem where the electronically driven chemical pro-
cess takes place which is treated at the QM level of theory, and (ii) the subsystem
formed by the surroundings described by a classical molecular mechanics force
field where the electrons are not explicitly treated and the only transformation
processescorrespondtoconformationalchangesoraredrivenbyweakinteractions.
The first version of such QM/MM technology was applied to the study of the
thermalreactionmechanismcharacterizingthelysozymecatalyticaction.Almostat
the same time, its effectiveness was demonstrated for conjugated (i.e.,
light-absorbing) molecules such as the retinal chromophore of visual photorecep-
tors,forwhichthechromophorephotochemicallyrelevantp-electronsweretreated
at the QM level of theory, whereas the r-bonds at the MM level [3]. Since then
both the development and the application of QM/MM technologies have become
common research activities when studying the reactivity of biological macro-
molecules, with special emphasis on enzymatic reactions.
Nowadays the original QM/MM method is seen as part of a larger array of
technologies called multi-scale methods [4–5]. Multi-scale methods can include
morethantwosubsystemswhichcanbetreatedatdifferentMMandQMlevels.For
instance,itispossibletohavetwoQMsubsystems,onetreatedattheabinitiolevel
andtheotheratthefastersemiempiricalordensityfunctionaltheory(DFT)level.It
is also possible to have, again in the same multi-scale molecular model, two MM
subsystems with one treated using atomistic MM force fields and the other using
coarse-grain force fields. The term multi-scale refers to the size of these subsys-
tems,andtherefore,totheirspatialscale.Forinstance,typically,thesubsystemwith
the smaller scale is the one treated with the most accurate but also most compu-
tationally “expensive” QM level. Then comes the larger subsystem treated at the
semiempirical level, which is much smaller than the one treatable at the atomistic
force field level to get finally to the largest portion of the molecule treated at the
coarse-grain level. Notice that such division in different subsystem (also called
“layers”) also allows, within certain limits, for running molecular dynamics
(MD)simulations(i.e.,trajectorycalculations)atdesiredtimescales.Thesmalleris
theexpensiveQMlevelcalculation,thelongeristhesimulationthattheresearcher
canafford.Thespatialmulti-scaletechnologydoes,therefore,allowmulti-timescale
studies. In other words, one can perform shorter time scale MD simulations using
multi-scale models with large QM subsystems and these calculations may then be
Preface vii
followed by longer timescale MD simulations calculations using QM/MM models
with smaller QM subsystems. In the limit, the longest MD simulations can be
performedwithatomisticandcoarse-grainMMforcefieldsandnoQMsubsystem.
As Arieh Warshel stresses in his biography (see above), even at the basic
two-layers model, the essence of the QM/MM technology, as well as the quality
ofthesimulation,dependsnotonlyontheselectedQMandMMmethods,butmost
relevantly,ontheaccuracyofthetreatmentoftheinteractionbetweentheQMand
MM subsystems. A brute-force attempt for overcoming the problem of correctly
describing such interaction is that of extending as much as possible the size of the
QM subsystem also including part of the environment surrounding the reactive
part. In this way the most important pair interactions (i.e., the interaction between
pairs of “reactive or electronically active” and “spectator” atoms) are treated
quantum mechanically, and substantially, at full accuracy. In the case of a protein
hosting a reactive (e.g., a catalytic or light-absorbing) site, this is equivalent to
including clusters of amino acids surrounding the activated-complex or chro-
mophore in the QM subsystem. Of course, this treatment could be extended up to
the point of treating the entire macromolecule at the QM level. While the latter
strategy would make the application of QM/MM modeling of lesser importance, it
would require an exceptional computing power not currently provided by con-
ventional computing machines. However, one must reckon that hardware devel-
opmentshaverecentlymade suchtypeofcalculationsmore accessible whenusing
workstations equipped with graphical processing units (GPUs) [6]. On the other
hand,suchatechnologyisstillimpractical,ifnotimpossible,whenhighlyaccurate
multi-configurational QM methods needed for studying, for instance, photochem-
ical reactions have to be used. In these cases, one has to rely on small QM sub-
systems and the rest of the macromolecule has to be treated at the MM level. In
these cases the accuracy can only be increased by introducing less approximate
ways of treating the interaction between the QM and MM subsystems.
Asalreadystressedabove,theinteractionbetweentheQMandMMsubsystems
represents, arguably, the most important technical challenge that the QM/MM
computational investigation of biological macromolecules faces. Primarily, this
calls for the development of more realistic MM force fields to describe the protein
and its interaction with the QM subsystem. The importance of polarizable
embedding has been pointed out in several pilot studies applied to the calculation
of the excitation energies in photoreceptor proteins. However, while several
polarizable embedding implementations exist and have been used to study spec-
troscopic properties, there is little experience in mechanistic or dynamics studies
using polarizable embedding yet. The same can be said for DFT embedding
schemes, which are also powerful and accurate but need to be further developed
before they can beusedinmechanistic/dynamicstudies of,for instance,biological
or synthetic photoreceptors. Finally, another promising approach for an uncon-
ventional QM/MM description is the Effective Fragment Potential (EFP) method
[7]. In this approach, a potential for solvent molecules is generated by calculating
several parameters from ab initio QM calculations.
viii Preface
Sophisticated and accurate QM/MM technologies have been applied to the
investigationoflight-drivenprocessesinbiologicalphotoreceptors(i.e.,specialized
proteins) and nucleic acids. One example, is the description of their spectroscopy
and light-induced ultrafast dynamics in condensed phase. This requires, in princi-
ple, the accurate computation of both the ground and electronically excited
Born-Oppenheimer potential energy surfacesand of theirinteraction. A case-study
by Filippi and Rothlisberger groups [8], illustrates this type of QM/MM treatment
when looking at the absorption spectroscopy of the dim-light visual pigment rho-
dopsin. The study reveals the ingredients affecting the accuracy of the simulation
of the absorption band: (i) size of the QM subsystem, including not just the
light-absorbingretinalchromophorebutalsothenearbyresidueswithatotalofover
250atoms,(ii)extensivethermalsampling,and(iii)mutualpolarizationoftheQM
chromophoreandtheMMproteinenvironmenthostingitbyusingpolarizableMM
forcefields[9].Someauthors[10],evenpostulatethatmultipolesuptoquadrupoles
andanisotropicpolarizabilitiesarerequiredintheMMforcefieldtoobtainaccurate
values for excitation energies at the QM/MM level. Unfortunately, such compu-
tationally demanding protocols preclude their systematic usage especially when
highly-correlated post-Hartree-Fock (post-HF) ab initio electronic structure meth-
ods are employed. In order, to make the study more practical, time-dependent
density functional theory (TDDFT) QM methods are used in practice. In fact,
highly-correlated post-HF multireference configuration interaction and multirefer-
ence second order perturbation theory methods, are often used in QM/MM tech-
niquebutatthepriceofaseverelyreducedsizeoftheQMsubsystemandlimiting
the description of the QM and MM subsystem interaction to electrostatic embed-
ding based on point charges only, and thus, not accounting for the environment
polarizability.
The aim of the present book QM/MM Studies of Light-responsive Biological
Systems is to review, on the basis of diverse methodological and applicative case
studies,inwhichwayQM/MMmodelsofbiologicalmoleculesarebeingcurrently
employed in mechanistic and dynamical studies involving electronic excitations.
Firstly, the different book Chapters will expose the characteristics of the models
selected as the best compromise between accuracy and computational cost; a “se-
lection” process depending on the specific information sought by the researcher.
For instance, if the researcher is looking for the simulation or prediction of prop-
erties trends rather than property values, the QM/MM model employed may have
differentfeatures.Secondly,asthebooktitlesuggests,anotherfeatureoftherevised
models is that these must be suitable for dealing with electronic excitations. As
anticipatedabove,thisimposesstrictconstraintstothetypeofQMmethodusedfor
describing the QM subsystem. Thirdly, the applications will not only regard the
calculationofstaticfeatureslikeexcitationenergies,computationofthestructureof
elusive reactive intermediates and fluorescent species but also the calculations of
excited state and nonadiabatic trajectories describing the transition from excited to
ground state. In conclusion, the reader will be guided through a wealth of diverse
examples of the design, setup, and application of QM/MM models to the mecha-
nistic and dynamics study of processes involving electronically excited states.
Preface ix
The three initial Chapters deal, at a certain extent, with QM/MM method and
protocol development. The chapter “On the Automatic Construction of QM/MM
Models for Biological Photoreceptors: Rhodopsins as Model Systems” by Laura
Pedraza-González, Maria del Carmen Marín, Luca de Vico, Xuchun Yang, and
MassimoOlivucci,discussesthepossibilitytoautomatetheparallelconstructionof
QM/MM models of entire sets of rhodopsin photoreceptors and of their mutants
mainly for predicting the trends of their spectroscopic properties. The models
generated for a set of wild-type and rhodopsin mutants, reveal that the corre-
sponding automated protocol, based on an ab initio multi-configurational QM
method, is capable of reproducing the trends in the wavelength of the absorption
maximum.Theproposedprotocolexemplifiesanefforttowardthestandardization,
reproducibility,andtransferabilityofrhodopsinQM/MMmodelswiththetargetof
reducing the consequences of human-errors during the QM/MM model building.
The authors also show the applicability of their technique in studies relevant to
optogenetics such as the engineering of microbal rhodopsins with enhanced
fluorescence. Throughout the chapter the QM/MM methodology used is the
Complete Active Space Self-Consistent Field (CASSCF) and Complete Active
SpaceSecondOrderPerturbationTheory(CASPT2)QMmethodscoupledwiththe
Amber MM force field and interacting via an electrostatic embedding scheme.
In the second chapter “Photo-Active Biological Molecular Materials: From
Photoinduced Dynamics to Transient Electronic Spectroscopies”, Irene Conti,
Matteo Bonfanti, Artur Nenov, Ivan Rivalta, and Marco Garavelli review a com-
putational strategy for characterizing transient spectra constructed on the basis of
static and dynamic exploration of the potential energy surfaces. It is shown that in
all discussed systems, the applied QM/MM model can successfully reproduce and
study the spectral signatures measured by (two-dimensional) steady state and
transient optical spectroscopy in rhodopsin pigments and DNA-related systems in
their native environments. The authors also mention the possibility to alleviate the
QMsizeproblempresentinmulti-chromophoricsystemsbyintroducinganexciton
modeleffectivelyintegratedintostaticanddynamicQM/MMengines.Throughout
the chapter the QM/MM methodology used is DFT, TDDFT, CASSCF, CASPT2,
Restricted Active Space Self-Consistent Field (RASSCF), and Restricted Active
SpaceSecondOrderPerturbationTheory(RASPT2)QMmethodscoupledwiththe
Amber MM force field and interacting via an electrostatic embedding scheme.
Finally, in the chapter “Polarizable Embedding as a Tool to Address Light-
Responsive Biological Systems” Peter Hartmann, Peter Reinholdt, and Jacob
Kongsted discuss the theoretical background and derivation of a polarizable
embedding scheme and how the latter can be formulated within QM response
theory to account for environmental effects using both discrete and polarizable
models.TheauthorsillustratetheirmethodologyonaNileRedchromophoremodel
incorporating local fields effects and structural dynamics (sampling). They show
that these effects are both crucial when the target is to simulate/predict in an
unbiased fashion one- and two-photon absorption spectra of the chromophore in
condensed phase.