Molecular ModelingDOI: 10.1002/anie.201403689

Multiscale Modeling of Biological Functions: FromEnzymes to Molecular Machines (Nobel Lecture)**Arieh Warshel*

biomolecules · computational chemistry ·free energy calculations · molecular modeling ·multiscale models

Introduction

The ability to model complex molecular systems is crucialfor advances in understanding biological systems and inrational progress in molecular medicine, as well as in therational design of new materials and devices. However,progress in this direction was hindered by the fact thatrigorous modeling of complex systems requires enormouscomputational power. That is, a reliable quantum mechanical

description[1] of more than a few atomswas practically impossible for a verylong time. Even now, it is still toocomputationally expensive to use high-level quantum calculations to obtainconvergent sampling on the manyconfigurations needed to reliably de-scribe the free energies of evenmedium sized systems. The solutionto this challenge (and related prob-lems) has emerged from the realizationthat a description of the properties ofcomplex systems does not require therepresentation of all parts of thesystem at the same level of detail. Forexample, the interactions of a watermolecule with a charge center that is10 � away can be treated classicallyinstead of quantum mechanically. Sim-ilarly, a bond that does not participatein a chemical reaction can be repre-sented as a classical spring. Thus, it ispossible to decompose the system toparts where the quantum mechanicaldescription is essential (e.g. partswhere bonds are being broken), andother parts that can be represented ona simpler level with empirical force

fields. This idea, that may seem obvious in retrospect, led tothe development of the combined quantum mechanics/molecular mechanics (QM/MM) model.[2] Here, the coupling

[*] Prof. A. WarshelDepartment of Chemistry, University of Southern CaliforniaLos Angeles, CA (USA)

[**] Copyright� The Nobel Foundation 2013. We thank the NobelFoundation, Stockholm, for permission to print this lecture.

A detailed understanding of the action of biological molecules isa pre-requisite for rational advances in health sciences and relatedfields. Here, the challenge is to move from available structural infor-mation to a clear understanding of the underlying function of thesystem. In light of the complexity of macromolecular complexes, it isessential to use computer simulations to describe how the molecularforces are related to a given function. However, using a full and reli-able quantum mechanical representation of large molecular systemshas been practically impossible. The solution to this (and related)problems has emerged from the realization that large systems can bespatially divided into a region where the quantum mechanicaldescription is essential (e.g. a region where bonds are being broken),with the remainder of the system being represented on a simpler levelby empirical force fields. This idea has been particularly effective in thedevelopment of the combined quantum mechanics/molecularmechanics (QM/MM) models. Here, the coupling between the elec-trostatic effects of the quantum and classical subsystems has been a keyto the advances in describing the functions of enzymes and otherbiological molecules. The same idea of representing complex systemsin different resolutions in both time and length scales has been found tobe very useful in modeling the action of complex systems. In suchcases, starting with coarse grained (CG) representations that wereoriginally found to be very useful in simulating protein folding, andaugmenting them with a focus on electrostatic energies, has led tomodels that are particularly effective in probing the action of molec-ular machines. The same multiscale idea is likely to play a major role inmodeling of even more complex systems, including cells and collec-tions of cells.

.AngewandteNobel Lectures A. Warshel

10020 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

between the electrostatic effects of the quantum and classicalsubsystems has eventually become a key to advances indescribing the function of enzymes and other biologicalmolecules.

The emergence of the QM/MM approach allowed one tofor the first time ask, in a well-defined and logical way, whatthe origin of the catalytic power of enzymes actually is. Thatis, although landmark works (see discussion in Ref. [3–5])suggested various ways by which enzymes can acceleratereactions, none of these could directly relate the structure ofthe enzyme to its catalytic effect, nor could any approachreliably predict the rate constants of enzymatic reactions.Here, the QM/MM approach (and, in particular its empiricalvalence bond (EVB) version) has provided what is probablythe best solution to this long-standing fundamental puzzle.The idea of dealing with complex systems by treating differentparts of the system on different scales is very general, and hasfound applications in many areas, and, in particular, in studiesof complex biological systems. An early example of this hasbeen our simplified coarse-grained (CG) model for proteinfolding.[6] Subsequent focus on electrostatic models has led toCG models that are particularly effective in probing theaction of molecular machines.

Overall, the philosophy that has emerged from our studiesis that the description of complex molecular systems requirescomputers to bridge between structural and functionalinformation, and that computational scientists should care-fully consider the resources available when choosing optimalmodels for describing the simulated systems. Here, usingmultiscale strategies is almost always a powerful way toexplore different systems with different time and lengthscales. In describing the emergence of multiscale modeling, Iwill start by some recollections of the early developments inthe field, and then move to specific examples, starting withenzyme action all the way through to the action of molecularmachines.

Early Journeys in Multiscale Computer Modeling

Growing up in a Kibbutz in Israel, I did not have muchscientific experience, but I liked to experiment with hot airballoons and building handguns, as well as in other subjectsthat have no relationship to chemistry. Nevertheless, afterbeing accepted to the Technion (Israel Institute of Technol-ogy), I rather randomly chose to study chemistry. Eventually

in 1964–1965, during my third year, I became interested inunderstanding how enzymes can accelerate chemical reac-tions, sometimes by up to twenty orders of magnitude. Istarted an experimental project that resulted in perhaps thefirst NMR measurement of a very fast step in the catalyticreaction of chymotrypsin, but this experiment did not provideany reasonable clues about the origin of the catalytic effect. Infact, although I did suspect that electrostatic effects aremaking the reaction go faster, my experiments showed thatchanging the ionic strength does not influence catalysis ina major way.[7] This result (incorrectly) indicated that electro-static effects do not contribute significantly to catalysis.

After the Technion, I joined Shneior Lifson, who was thescientific director of the Weizmann Institute, and was startingto move from statistical mechanics of helix coil transitions, tomodeling molecules with digital computers. In the fall of 1966,I started my PhD trying to develop what became known as theconsistent force field (CFF).[8, 9] My general suggested direc-tion was to represent molecules as balls and springs (whichbecame known as molecular mechanics (MM) or a “forcefield” approach) and to reproduce energies, structures, andperhaps vibrations. This was supposed to be done bya consistent refinement of the MM parameters that willforce the calculated and observed properties to be as close aspossibly to each other. However, we had no clue how toactually do so. As a start, I attempted to treat cyclic amides, onthe way to parameterizing amino acids� potential functions, byextending the internal coordinate approach of MordechaiBixon,[10] who was the previous student of Lifson. Unfortu-nately, this approach, which involved analytical derivatives ofcomplex interdependent transformation matrices, becamebasically impossible to formulate and implement. The sameinternal coordinate treatment had been the key to practicalconformational analysis programs of that time (e.g.Ref. [11,12]), which incidentally could not obtain convergentminimization, because this required the first and secondderivatives. In desperation, I tried to abandon the commondescription of molecules in terms of bond lengths and angles,and to move to a Cartesian coordinate description, wheresuddenly all the problems with analytical derivatives seemedto disappear. For example, obtaining the analytical first andsecond derivatives needed for minimizing the energy ofa cyclic molecule in a converging way, which was close toimpossible in internal coordinates (because each internalcoordinate depends on all other coordinates), became trivialin Cartesian coordinates. Similarly, obtaining vibrationalmodes, which previously demanded spending half a year onreading Bright Wilson�s molecular vibrations book,[13] andthen almost (at least for cyclic molecules) hopeless program-ming, required only the use of one simple equation in terms ofthe Cartesian second derivatives.

Fortunately, the Weizmann Institute had a specializedcomputer called the Golem (named after the “robot” fromJewish legend that helps the famous Prague rabbi), which hada remarkable double precision. Thus, I was able to obtain veryaccurate first and second numerical derivatives, and to provethat I was on the right track in obtaining exact minima andmolecular vibrations in a general molecule. At that point Istarted to write a program with Cartesian analytical deriva-

Arieh Warshel was born in 1940 in KibbutzSde-Nahum, Israel. He received his Ph.D. in1969 from the Weizmann Institute of Sci-ence, Rehovot, and is currently DistinguishedProfessor and the Dana and David DornsifeChair in Chemistry at the University ofSouthern California, Los Angeles. Photo:Max S. Gerber.

Nobel LectureAngewandte

Chemie

10021Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

tives and a least squares force field refinement (using thenumerical derivatives in pinpointing errors), stopping fora while during the Six-Days war, and then moving back to theprogram. At the end of the war, I returned to the WeizmannInstitute, and around this time Michael Levitt appeared.Guided by Schneior�s insight on obtaining consistent forcefield parameters, and his insistence that these parameters candescribe reality regardless of whether they are derived fromexperiment or theory, we developed the general CFFCartesian force field programs[8, 14] , that allowed one to useMM to find exact local minima and vibrations of any mediumsized molecule. The program also allowed for a fully con-sistent refinement of the MM parameters, by fitting thecalculated and observed properties of molecules and molec-ular crystals. At any rate, our CFF program eventuallybecame the basis of all modern MM molecular simulationprograms.[14] The CFF parameter refinement turned out to bequite a demanding job (as it required automatic fitting tomany independent properties), including inventing automaticfrequency assignments and developing a general way ofrefining parameters that would reproduce known unit celldimension of molecular crystals.[9] During 1968, in whatturned out to be eventually significant, I also startedexperimenting with combining my newly developed CFFmethod (with the spring-like description of bonds withlocalized electrons) and a valence bond (VB) quantummodel.[15] This QM(VB) + MM model helped to describethe extremely large isotope effect in a chemical reactionbetween oxygen and a medium sized organic molecule, andindicated to me that such a combination can be useful.

While still keeping enzymes at the back of my mind, Istarted a postdoctoral position at Harvard with MartinKarplus at the beginning of 1970, hoping to make the QM +

MM CFF more general. Karplus and his postdoc Barry Honigwere at that time making important advances in the study ofretinal (the chromophore of the visual pigment),[16] whichinvolves a 12p-electron system. This seemed to be a goodrationale to start developing the CFF for p-electron systems.Indeed, I succeeded to connect the molecular orbital (MO)description of atoms with p-electrons with an MM descriptionof s-bonds with localized electrons,[17] and to consistentlyrefine the corresponding parameters for a unified CFFdescription. This QM(MO) + MM model included only thebonding between the QM and MM region, and thus ignoredall key (e.g. electrostatic) coupling between the MM and QMregions. Nevertheless, the model provided a very powerfuland general way to treat large conjugated molecules. Duringthis project, I also figured out how to get the exact analyticalforces from the QM treatment, by fixing the molecularorbitals and differentiating only the integrals. As usual, Imade this fundamental advance by guessing it, then (asbefore) I confirmed my idea by using numerical derivativesand then finding the exact mathematical proof.[18] Here againit was shown that the combination of intuition and numericalvalidation is a powerful tool.

At any rate, the QM + MM treatment of delocalizedelectron systems still did not help me to move towardsstudying enzymes. Thus, upon returning to the Weizmanninstitute in 1972, I started to develop a very effective hybrid

orbital quantum program (QCFF/ALL), that represented allatoms in a relatively small part of a molecular quantummechanically, while representing the rest classically. I felt thatthis should allow me to finally make a progress towards myold dream of studying enzymes. At that time, Mike returnedfrom his PhD at the Medical Research Council (MRC) to theWeizmann Institute, and I started to explore the possibility ofcombining my quantum mechanical model with his MMcalculations on lysozyme (see below). While still strugglingwith the development of my QCFF/ALL approach, I foundmyself one day in the computer center discussing the protein-folding problem with Mike. This discussion turned to a strangeidea of studying mechanical models of molecules on a grav-itation-less spacecraft, and we suddenly came out with theidea of simplified protein models where spheres wouldrepresent amino acid side chains, and started to work onthis project. This folding project started to move in a remark-able way, and it appeared that the drastic simplifications wehad suggested allowed us to fold the small protein BPTIwithout using an enormous number of minimization steps.This simplified CG model[6] appeared to resolve the so-called“Levinthal paradox”, where the observation that proteinsactually fold appeared to contradict the fact that they have anastronomical number of possible conformations so that theycould never find a path for folding in a reasonable timescale.In fact, our simulations showed that the number of relevantcoordinates is relatively small, and that the protein foldingprocess can be effectively simulated. The progress on thefolding problem helped me to obtain an EMBO fellowship sothat I could collaborate with Mike when he moved back to theMRC. My time at the MRC turned out to lead to theculmination of several key advances pushing the frontiers inthe understanding of biological function.

Enzymes, Electrostatics and QM/MM

The three-dimensional structures of the enzyme lysozyme,which were solved by Phillips and coworkers in 1967,[19]

provided the first glimpse of the structure of the enzyme-substrate complex. These breakthroughs offered enormoushope that enzyme catalysis would now be finally understood.For example, Phillips suggested that enzymes work byapplying steric strain that pushes the substrate to a structurethat is closer to the structure of the so-called “transitionstate”, where the crucial bond between the carbon andoxygen atom in the sugar substrate is broken. This idea wasdue in part to the observation of what looks a distorted sugarring and to the assumption that the protein can inducea significant strain. The strain was argued to reduce thebarrier for bond breaking, and thus the activation barrier forthe reaction. However, as Mike demonstrated, the strain ideawas problematic since enzymes are flexible,[20] and it seemedclear to me that any further progress would require actuallymodeling the chemical reaction in the enzyme. Therefore,upon my arrival to the MRC in the autumn of 1974, I startedto focus on modeling enzymatic reactions, still attempting tosomehow combine my QCFF/ALL program with Mike�senergy minimization of lysozyme.[21] The first attempt to

.AngewandteNobel Lectures

A. Warshel

10022 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

combine the programs resulted in ridiculously high activationenergies (so the reaction would never happen), and I realizedthat something must be completely wrong with my modelingdirection. Eventually, it became clear that the work ofbreaking the bond between the carbon and oxygen atoms inthe sugar substrate was being described incorrectly. Theproblem was that the bond is broken to a positive carbon anda negative oxygen (C+ O�), and that these charges must bestabilized by the electrostatic environment of the protein +

solvent system (see Figure 1).The introduction of the effect of external charges was not

so simple, since practically all earlier work that tried to addthe effect of the environment started from the complicatedconfiguration-interaction (CI) picture, that gave the overallmolecular dipole moment and then used unreliable contin-uum cavity models (where the cavity radius is basically a freeparameter) to describe the environment. Instead, I realizedthat one can start from the general expression of the quantummechanical self-consistent Hamiltonian (see e.g. [22]):

Fiimm � Umm þ

12

Pmmgmm �X

n 6¼m

Pnngmn �X

i0 6¼i

Qigii0 �X

j

Qjgij ð1Þ

where U is the core Hamiltonian, P is the quantummechanical bond order, Q is the net atomic charge, g is theelectronic repulsive integral, and m and n are atomic orbitalson atom i. Now, assigning atoms i to the part of the system thatshould be treated quantum mechanically indicated that theother atoms (denoted by j) can be treated classically, assumingthat their charge is constant. That is, replacing g by e2/r gives:

Fiimm � Fii

mm

� �0�X

B

e2QB

rAB¼ Fii

mm

� �0�UA ð2Þ

where m2A and Fiimm

� �0

designates the contributionfrom the quantum atoms (typically the “solute (S)”),and UA designates the total electrostatic potential fromthe classical atoms (typically the “solvent (s)” mole-cules), at the site of atom A. This equation can begeneralized to cases where the charge distribution ofthe classical atoms it not fixed and can be polarized bythe field of the quantum atoms.[23] Thus, the leadingterm in the solute–solvent coupling Hamiltonian isobtained by adding the potential from the solvent atomsto the solute Hamiltonian. The total potential energy isthen given by:

Vtotal ¼ ESðFSÞ þ E0Ss þ Ess ð3Þ

In this equation, ES(FS) is the energy that isquantum mechanically obtained with the F matrix thatincludes the given electrostatic potential from thesolvent (the vector of all the UA values). E’Ss is thenon-electrostatic solute–solvent interaction term, andEss is the solvent–solvent classical force field. At thislevel of approximation, the non-electrostatic term isevaluated by the standard classical van der Waalspotential function. In studies of very large solute

molecules, we sometimes divide the solute region inquantum and classical parts. The “connection” between thequantum and classical regions is treated by a classical forcefield (which is included in E’Ss), where the quantum atoms atthe boundaries are connected to dummy hydrogen-like atomsin order to balance the electrons in the quantum system. Themain problem we faced in 1975 was how to evaluate themagnitude and positions of the charges in the environment(e.g. water molecules). Eventually, after spending severalmonths in the library and talking to eminent experts onelectromagnetic theory, I realized that none of the textbooksor the experts could tell us much about how to computation-ally model electrostatic effects in proteins or solution. Thus, Iturned to what I learned from my experience with developingforce fields: forget about what is in the books that werewritten before the emergence of computers, and just go to thebasic molecular level, using simplified models of needed.

I concluded that we would be unable to progressconsistently as long as we thought in terms of the standardelectrostatic theory, where all the details of the protein or thesurrounding solvent are included with an elusive dielectricconstant. Obviously, the computer power of the time wasinsufficient for modeling a protein surrounded by atomisticmodels of water molecules, while obtaining meaningfulenergetics. Thus, after considering several options withMike, we decided to represent the water molecules as a gridof polarizable Langevin type dipoles (the LD model), andself-consistently evaluated the interaction of these dipoleswith the charges in the protein–substrate system and witheach other. Of course, the key to the success of this approachwas the calibration of the LD model to observed solvationfree energies. A similar self-consistent treatment was thenintroduced for the induced dipoles on the protein atoms.[2]

This LD water model led to the first microscopic descriptionof protein electrostatics, evading the conceptual traps of the

Figure 1. Showing the energetics of breaking a C�O bond in an uncoupledQM+ MM (upper diagram) and when the electrostatic and steric effects ofthe environment are included in a coupled QM/MM (lower diagram). Thedipoles designate the effect of the surrounding residual charges. As seenfrom the Figure it is very hard to break the bond without including thecoupling between the QM and MM regions.

Nobel LectureAngewandte

Chemie

10023Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org

past and future continuum dielectric descriptions. Apparently,this model looked problematic to those who were trained withthe idea that the special, highly symmetric structure of watermolecules must be very relevant to their enormous solvationeffects. However, the LD grid model eventually turned out tobe an excellent approximation for studying solvation effects,long before any other microscopic model, and also before thedevelopment of macroscopic models that tried to consider theprotein shape.

The introduction of a realistic electrostatic model for theenzyme and its surrounding water molecules, together withthe incorporation of this effect in a quantum Hamiltonian,finally for the first time yielded the energy of heterolytic bondbreaking processes in enzymes and in solution. This QM/MMapproach reflected the realization that we cannot treat largesystems quantum mechanically, and we cannot describe thechemistry without a quantum treatment. Thus, we usedEquations (2) and (3) and described only the reactingregion quantum mechanically, while treating the rest of theprotein and the solvent classically (Figure 2). This approach,along with related models that we subsequently introduced,has become known as “multiscale modeling”. The QM/MMmodel suggested that enzymes work by using electrostatic

fields to reduce the activation barriers for bond breaking (seebelow). At any rate, the use of our QM/MM approach inmodeling the catalytic reaction of lysozyme paved the way forthe current direction in modeling enzyme action,[24] and hasbecome a major direction in theoretical chemistry andbiophysics.

Our QM/MM studies also eventually led to what I believeis a true understanding of the origin of enzyme catalysis,which turned out to be associated with the electrostaticpreorganization effect.[25] More specifically, my subsequent(mainly EVB) studies led to the non-trivial finding thatenzyme catalysis is not due to the interaction between theenzyme and substrate (which is what was believed by most

people), but rather to a large free-energy penalty for thereorganization of the solvent in the reference reactionwithout the enzyme (the work of rotating the watermolecules towards the transition state charges). Asdescribed in Figure 3, the reorganization energyincreases the activation barrier in solution, whereas inthe enzyme, the polar groups that stabilize the transitionstate do not have to rotate, since they are already foldedwith correctly polarized dipoles. In subsequent years, Iwas also able to prove that the change in the electrostaticreorganization energy accounts for almost the entirecatalytic power of enzymes.[26] Although this elusiveorigin of catalysis was not envisioned during our studiesat the MRC, I had benefited from the general feelingthat it should be somehow associated with electrostaticeffects (see Max Perutz� insightful review[27]). Interest-ingly, while Max intuitively recognized the importanceof this effect, he originally felt that it was like theassumed stabilization of ion pairs in a low dielectricenvironment, while I found that enzyme active sites arein fact very polar, and pointed out to him that ion pairswould not be stable in oil surrounded by water. Thisexplanation eventually led to a paper that he commu-

nicated for me to PNAS.[25] The electrostatic models con-ceived in 1975 became the basis for consistent microscopictreatment of biological models, the understanding of the truenature of protein dielectric constants,[28, 29] and the simulationof key functional properties, including pKa values, redoxpotentials, binding free energies, ion and proton conduc-tance,[29] and protein stability.[30]

In subsequent years, my co-workers and I drasticallysimplified the QM/MM approach, using a valence bonddescription of the different steps of the reaction, in what Icalled the “empirical valence bond” (EVB) method.[31] Thisapproach, which exploits the clear physics of the diabaticreactant and product states, has allowed us to take a consid-

Figure 2. A QM/MM model of the lysozyme active site. The enzyme isdivided to a small reactive QM region, and to the rest of the system, which isdescribed by a classical MM model.

Figure 3. Schematic demonstration of the reorganization of the envi-ronment dipoles in an SN2 reaction, where the charges change frombeing on one atom in the reactant state (RS), to being delocalized inthe transition state (TS) in A) water and B) an enzyme active site.[26]

.AngewandteNobel Lectures

A. Warshel

10024 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

erable leap towards approaching my early vision, and tofinally quantitatively model enzyme catalysis and exploreenzyme design. This also helped me to explore (andfrequently to eliminate) popular suggestions of factors thatpresumably lead to enzyme catalysis, such as entropic effects,ground state destabilization by desolvation, dynamical effects,orbital steering and more (see discussions in Ref. [32] and[26]). The key to the ability to figure out the secret of enzymecatalysis has been the ability to model the actual chemicalreaction in the enzyme active site, and to dissect the differentcontributions to the rate constant, which is close to impossiblewhen one is just using experimental approaches. Overall, theQM/MM studies provided a solution to the long-standingpuzzle of the origin of the catalytic power of enzymes, andpaved the way for quantitative studies of enzymatic reac-tions.[26] This strategy also allowed one to start to explore theissue of enzyme design in a rational way.[33]

QM/MM approaches with an ab initio QM Hamiltonian(QM(ai)/MM calculations) have advanced in recent years toa level where they can be used with proper sampling to obtainreliable free energy surfaces in the condensed phase.[34]

Nevertheless, it seems to me that at the time of writing thispaper, it is still preferable to calibrate the EVB on QM(ai)/MM calculations in solution and then move to studies inproteins with the EVB approach.[35] However, it is clear thatin the future, one will be able to obtain convergent QM(ai)/MM surfaces also for reactions occurring in enzyme activesites. Finally, when talking about multiscale modeling in thecontext of QM/MM and related approaches, it is important toemphasize that the general idea can be described as an“embedding approach”, where one is looking for the best wayto incorporate the effect of the surrounding of the activesystem, that is the focus of the given study. Here, one of themost promising strategies is the use of the frozen DFT(FDFT) and constrained DFT (CDFT) approaches (e.g.Ref. [36]). These approaches treat the entire system on thequantum mechanical DFT level, with a formalism that is inprinciple rigorous.[37] However, the density around the mainregion is not subject to self-consistent optimization, and thecorresponding electron densities are determined by approx-imate considerations (including a freeze-and-thaw strategy).The CDFT approach can be described as a QM/QMapproach, but, again, the main idea is to have a less rigorousand less demanding description of part of the system in orderto save computational cost.

The Primary Event in Vision and the Dawn ofMolecular Dynamics Simulations in Biology

In 1971, I realized that the optimal way to study photo-chemical reactions of any medium size or large molecules wasto forget about the traditional description of crossing betweenenergy levels, and to adopt the surface-hopping semi-classicaltrajectory approach that was introduced for treating gas-phase reactions of very small molecules.[38] This advance,which turned out to be a conceptual breakthrough, was onlypublished in 1975,[39] using the photoisomerization of buteneas an example. Fortunately, my conviction that this was the

key to quantitative studies of photobiology gave me thecourage to look at the most important problem of biologicalphotochemistry, namely the primary photoisomerization ofretinal in the visual process. More specifically, I becameinterested in retinal during my postdoc time (see e.g.Ref. [40]), but this interest was focused on spectroscopicand geometric properties, and not on the most excitingproblem of what is happening during the first step of thevision process (a problem that seems to be completelyinaccessible to theoretical studies with the standard strat-egies). At that time, it was known that when light strikes theeye, it is absorbed in the Schiff base of retinal, which isembedded in a protein called rhodopsin. After absorption oflight, the retinal molecule isomerizes from its initial 11-cisstructure to an all-trans structure, forcing structural changesof the protein, where the new form of the protein (meta-rhodopsin) activates the transfer of the visual signal to thebrain. Later, it was found that the metarhodopsin activatesa G-protein called transducing, and that rhodopsin is in facta G protein-coupled receptors (GPCR).[41] It was also knownthat the primary absorption of light leads to a photoisomeri-zation of the retinal molecule in less than 6 picoseconds(which was the shortest time that could be measured in theearly 1970s). Furthermore, the absence of structural informa-tion seemed to introduce an even bigger challenge. AlthoughI considered binding retinal to chymotrypsin, I decided tomodel the protein�s effect by a steric cavity plus an assumedinternal counter ion, and used the semiclassical surfacehopping approach with a Schiff base of retinal, constrainedto be in the starting 11-cis conformation.[42] My MD simu-lations, depicted in Figure 4, predicted that the primaryprocess takes about 100 femtoseconds, with an enormousprobability of jumping from the excited state to the groundstate due to very large non-adiabatic coupling (a phenomenonthat was later identified as the effect of conical intersections).Remarkably, the results of these simulations, that representedthe first use of MD simulations in biology, have since beenconfirmed both experimentally[43] and theoretically.[44]

The molecular motion that emerged from these computersimulations resolved the problem of fast movement ina restricted protein cavity without strongly clashing with it.That is, it was found that the isomerization occurs witha concerted rotation of several bonds, which I called the“bicycle pedal” motion. To see if the bicycle pedal modelmade sense, I borrowed model building parts from MaxPerutz�s structural biology lab, and built a model thatappeared to reproduce the concerted motion without anylarge structural changes. Interestingly, about 30 years after myoriginal model, this motion has been confirmed by ab initiostudies.[44]

Over the following years, my long-time collaborator BillParson and our coworkers[45] used the structure of a bacterialreaction center (RC) and the same semi-classical approach tomodel the primary electron transfer event in photosynthesis,establishing that the observed 3 ps process involves a sequen-tial hopping from the primary chlorophyll dimer (P*) to onemonomer (B), and then to a second monomer (H). This wasagain done before the confirmation of our findings by decisiveexperimental studies (e.g. Ref. [46]), and at a time where most

Nobel LectureAngewandte

Chemie

10025Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org

workers assumed that the primary event cannot be a stepwiseand assumed that it is a single step super-exchange process.Here, the ability to determine the correct electrostatic energyof each intermediate has been a major advantage over relatedattempts that did not involve experience in the conversion ofprotein structures to model electrostatic energies and redoxpotentials. Instructively, in this case, the advantage of workingwith and developing tools for studies of biological functionshas been demonstrated in an effective way. That is, althoughwe waited four years to get the RC coordinates, all thecomputer programs were ready and tested for a long time, andit took us only two weeks at the end of 1987 to convert thestructure of the RC to a detailed (and correct) functionalmechanism.

Free Energy Calculations and ThermodynamicCycles

One of the most remarkable advances that resulted fromthe emergence of computer modeling of biological moleculeshas been the ability to evaluate the relevant free energies,and, in particular, the energetics of charged groups inproteins. Arguably, this started with the very rough attemptin the original 1976 paper (see Figure 8 of Ref. [2]), andcontinued with more quantitative free energy considerationsand the introduction of well-defined microscopic basedthermodynamic cycles, using the PDLD model that pavedthe way to evaluation of pKa values,[28] redox energies,[47] iontransfer energies[48] and drug binding free energies.[29] In 1977/78, after reading Valleau and Toerrie�s masterful review,[49] Istarted free energy perturbation (FEP) calculations of thecharging of an ion in my surface-constrained soft spheredipole (SCSSD) water model.[50] This was mainly in order toshow the referees of the SCSSD paper that the entropiccontribution to the solvation free energies of ions is small. Thecalculations gave a reasonable trend, but I was too busy tryingto fight the referees on other trivial issues that I did notpublish the preliminary entropy study. Eventually, theincrease in computer power allowed us to move into free

energy calculations of charges in all atom solution models in1982,[51] as well as starting free energy calculations of proteinsin 1983/84.[52] The microscopic free energy perturbationcalculations and the corresponding free energy cycles havebecome a major part of the field, in part due to the excitementfrom rather trivial changes of a few solute atoms in solution[53]

and then in proteins.[54] In light of my conviction in theimportance of electrostatic energies, I did not consider these“alchemical changes” to be a real challenge, and continued tofocus on evaluating the large absolute solvation free energy,providing the first FEP studies of the free energy of ionizingacids in proteins, and of redox process (for a review seeRef. [29]), as well as the free energies of countless enzymaticreactions.[26] My co-workers and I also tried to educate thecommunity about the enormous risks of looking at the so-called potential of mean force (PMF) in studies of biologicalcharge transport and related problems. Here, we pointed outthat looking at the PMF of say ion penetration in ion channelscan be extremely misleading, since it does not tell you muchabout the error in getting the absolute solvation free energy,and can lead to enormous problems. On the other hand,insisting on obtaining the absolute free energy is the best wayto know if the model captures the correct physics.[26, 29] Thisissue is strongly related to the tendency of confusing formalrigor with actual reliability. Here, the realization that theproper boundary conditions are key to the reliability of theresults and the speed of the convergence, took a rather longtime to reach the community.

Bridging Time and Length Scales: Coarse-grained(CG) Simplified Models of the Function of ComplexMolecular machines:

While the MD studies of ultrafast photobiological pro-cesses of the type discussed above have been very effective,[55]

the simulations of functional properties that involve longertime steps and larger systems have presented a much moreserious challenge. In fact, even today, despite the exponentialgrowth of MD simulations of proteins and related systems,

Figure 4. Snapshots from the simulated MD trajectory of the primary event in the vision process. The trajectory starts with 11-cis retinal in theground state, and, upon absorption of light, the system moves to the excited state where the 11–12 torsional angle rotates without a barrier to908, and the trajectory crosses to the ground state in the trans direction. The motion involves only a small change in the overall structure, sincethe other torsional angles move in the opposite direction to the 11–12 torsional angle. The snapshots are taken from a movie that used theoriginal trajectory presented in Ref. [42].

.AngewandteNobel Lectures

A. Warshel

10026 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

and the enormous progress in computer power (e.g.Ref. [56,57]), the ability to capture functional properties hasbeen limited. Here, one faces enormous sampling problemsthat, (as discussed in Ref. [58]), are not necessarily reduced byusing sophisticated formulations such as that of Ref. [59]. Ofcourse, running one very long trajectory to represent a func-tional property suffers from the problem of having a singleobservation, which might not correspond to the overallaction. Furthermore, having a single long trajectory can stillbe considered as an experiment that needs careful interpre-tation and an analysis by a general reduced model. Thus, ourpoint of view has been that in simulating complex systems, weclearly have the need to bridge the time and length scales bysimple models.

Here, we have reverted back to the CG idea of the proteinfolding days,[6] and asked how it can be used to study proteinfunctions. It was clear that this task requires an improvedtreatment of electrostatic energies (which appear to be thekey for structure-function correlations), and thus we under-took a major project, generating an improved electrostaticmodel and calibrating it on absolute protein stabilities.[30] Theresulting CG model appeared to provide what is arguably thebest current tool for moving from the structure to the functionof molecular machines (see below). Another challenge thatwe had to address has been the requirement that the longtime-scale behavior of the simplified model would reproducethe corresponding trend in the full model. The solution camewith our renormalization method,[60] where we apply strongexternal forces in MD simulations of the full model (thusinducing large conformational changes in short times), andalso apply the same forces in the reduced model, which issimulated by Langevin dynamics. We then chang the effectivefriction in the Langevin dynamics simulations until both thefull and the reduced model produced the same time-dependent response to the applied forces. The resulting

friction is then used as the optimal friction for long timescalesimulations with the reduced model, in the absence of theexternal force. This renormalization approach appeared toreliably reproduce the long timescale microscopic simula-tion,[61] and allowed us to explore the long timescale behaviorof complex molecular machines.[60, 62]

Significantly, in developing the above CG and multiscalemodels, one faces the question of how to relate the simplifiedfree energy surface to the corresponding results that would beobtained with the full explicit model. Here, we recruited theparadynamics (PD) philosophy, first evaluating the CG freeenergy, and then performing a perturbation between the CGand full surfaces at different key regions on the landscape.[60]

These developments allowed us to use our CG model insimulations of molecular machines and other complexbiological systems, and I will consider some of the mostinstructive recent examples below.

F1F0-ATPsynthase is a ubiquitous cellular engine com-posed of two rotational motors, the cytoplasmic F1 coupled tothe membrane embedded F0 units. The F0 rotor uses theenergy of the proton transport across the cellular membraneto rotate the membrane embedded c-ring, while the F1

couples the rotation of the c-ring with its central stalk (g

subunit) to generate ATP from ADP and Pi. In spite ofnumerous simulation and phenomenological studies (e.g.Ref. [63,64]), the origin of the coupling between chemicaland mechanical events in the F1F0-ATPsynthase has not beenelucidated or simulated in a consistent and unbiased way.More specifically, several single molecule experiments[65] havediscovered the amazing presence of the 808/408 stepwiserotation of the system and noticed that the chemical stepoccurs after the 808 step (the delay before the chemical stephas been called the “catalytic dwell”). Unfortunately, it hasbeen especially difficult to understand the origin and signifi-cance of the stepwise coupling from a structural perspective.

Figure 5. Exploring the coupling between the rotation of the g-stalk to ATP hydrolysis in F1-ATPase. The relevant system (namely F1-ATPase) isshown from the membrane side (A), and along the vertical direction parallel to the central g-stalk (B). The a catalytic subunits are shown in deepblue, deep green and orange, while the b units are shown in cyan, light green and yellow. The g-stalk is shown in magenta. The nucleotideoccupancies of the b subunits are depicted as T (ATP bound), D (ADP bound) or E (empty) states. (C) The CG electrostatic free energy surface ofthe rotation of the g-stalk coupled to the a/b conformational changes. This landscape reflects the stepwise 808/408 features discussed in themain text. The combination of the diagram of (C) with the energetic of the chemical steps (which is given in Ref. [62]) provides a structure-baseddescription of the action of F1-ATPase. This Figure is taken from Ref. [62].

Nobel LectureAngewandte

Chemie

10027Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org

This difficulty has been in part due to the large system size,and the very long timescale of the process, which extendsbeyond the millisecond regime. Remarkably, the CG electro-static free energy surface coupled to the ATP hydrolysis andproduct release free energies could successfully reproduce theobserved behavior of the system. This included generatingelectrostatic landscape that has a high energy region after the808 g-stalk rotation (see Figure 5) and then upon addition ofthe chemical landscape, reproduce (see Ref. [62]) a functionallandscape, where the 808 barrier is coupled zo thechemical coordinate of the ATP hydrolysis and generatethe catalytic dwell. This reproduced the experimentallyobserved catalytic dwell at 808/408. The details of ourCG modeling and the corresponding analysis are givenin Ref. [62].

An additional encouraging CG study[66] has for thefirst time reproduced the directionality of the couplingbetween the protomotive force and the rotation of the cring in F0-ATPase. Phenomenological models have beenused in attempts to understand the action of the c-ringrotation coupled to the proton transfer from the low tohigh pH reservoirs across the membrane.[67, 68] However,a quantitative structure-function relationship that elu-cidates the physical nature of the directional rotationhas been completely missing. Our CG model hasgenerated the electrostatic free energy surface of thec-ring rotation coupled to the proton transport from theP side (pH 5) to the N side (pH 8) of the membrane. Thegenerated landscape has shown that the CG surface, themolecular origin of the directional c-ring rotation ismostly due to the asymmetry of the proton transportpath on the N and P sides of the F0 unit, rather thanbeing driven by the energetics of the centrally placedsalt bridge between the c-ring and the stator subunita.[66]

Another interesting biological system that wasexplored with our CG model is the translocon complexthat controls the translocation of polypeptides acrossthe membrane. We used the CG model to addressseveral key questions about this system, starting withthe mechanism of membrane insertion of chargedresidues.[69] We then made significant advances inexploring the energetics of the translocon-assistedprotein insertion, where we challenged ourselves toobtain the complete free energy profile for the proteintranslocation through the translocon and the partitionto the water and membrane phases. By applying severalconstraints on the system, we were able to obtain a freeenergy profile[70] that was used to investigate the effectof different mutations and the ribosome binding.Comparison with experimental data led to the conclu-sion that the insertion process is most likely a non-equilibrium process, and that the insertion barrier intothe translocon controls the peptide topology. Theobtained free energy profile allowed us to approachextremely challenging and fundamental questionsregarding the nature of the coupling between twolarge biological systems: the translocon and ribosomes.That is, we investigated the origin of the experimentally

observed[71] biphasic pulling force from the translocon thatreleases the stalling of some elongated nascent peptide chainfrom the ribosome. By combining the estimates of thechemical barriers of peptide bond formation for the regularand stalled peptide sequences with the profile for thetranslocon-assisted protein membrane integration and per-forming Langevin dynamics simulations of the ribosome/translocon model, we were able to reproduce the experimen-tal effect ([72] and Figure 6). Our simulation of the action of

Figure 6. Simulations of the coupling between the ribosome and the trans-locon (TR). The simulation addresses the effect of the TR on stalled peptides,where for some lengths of the linker, L, the coupling to the TR helps torelease the stalled peptide. The time dependence of xistall and x1 for a peptidechain with 40 and 36 units is shown here, which corresponds to L = 31 (blue)and 27 (red), respectively. The x coordinate designates the insertion coor-dinate and is defined in Ref. [72]. The barriers used for the LD simulationswere obtained by scaling down the energy terms by 0.43. This allowed for thesimulation of the insertion process in a relatively short timescale, and thenestimating the relevant time for the actual barriers by using the correspond-ing Boltzmann probability. The snapshots on the top and bottom of the plotshow the configuration of the nascent peptide chain for L = 31 and L = 27,respectively. The ribosome and TR are shown schematically, the startingconfiguration of the nascent chain is in cyan, the leading particle (x1) is inred, and all other particles added to the growing chain are shown in magenta.The interpolated times (that should be obtained without scaling) for L =31and L = 27 are 6 min and 36 min, respectively. This Figure is taken fromRef. [72], which also gives a complete description of the problem and thesimulations performed.

.AngewandteNobel Lectures

A. Warshel

10028 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

voltage activation ion channels[73] provides another instructivecase study. The above examples highlight the importance ofobtaining the relevant free energy profiles for a thoroughunderstanding of the mechanisms underlying different bio-logical processes.

Future Directions

The enormous increase in computer power makes itvirtually certain that computer simulations will increasinglybecome the key tool in modeling complex systems. Althoughit is hard to predict the exact future trajectory of the field, itmay be useful to consider some promising directions. Oneclear direction is the field of fighting drug resistance. That is,at the turn of the 20th century, we had a short life-span due inpart to the effect of deadly diseases. The discovery ofpenicillin and other drugs helped to protect against majordiseases. However, in recent years, the phenomenon of drugresistance has started to reverse the picture. It appears thatthere is no magic bullet: key drugs become ineffective due inpart to excessive irresponsible use of antibiotics. In othercases, we have diseases like HIV that are hard to combat dueto the inherent fast mutations of the pathogen, or diseases likemalaria, where we also have drug resistance. Thus, it hasbecome essential to pursue new drug design strategies. Here,the challenge is to predict the moves of the pathogen inresponse to different drugs. Of course, one can try to explorethe actual experimental response of the pathogen to differentdrugs, but this is obviously not a predictive approach. Thus, itwould be tremendously helpful to use computational strat-egies for studies of drug resistance, but such a strategy mustdrastically reduce the options for effective mutations.

One such strategy is to exploit the fact that a virus fightingagainst a given drug must reduce the affinity to this drug,while still maintaining a reasonable catalytic efficiencytowards the native substrates. Thus, it would be useful tofind a way to out-maneuver the virus by designing inhibitors,whose binding to the target enzyme cannot be reduced bymutations without significantly reducing its kcat/KM value. Inother words, the drug resistant mutants must increase Ki forthe drug, while maintaining a reasonable kcat/KM value fortheir native substrate. Thus, an effective strategy can exploitthe ability to calculate the vitality value, g (g = Ki kcat/KM),and to determine the chance that the virus will mutate ina given way. Combining the vitality value and other con-straints (such as maintaining reasonable protein stability) willprovide the survival value, which is the chance that the givenmutant will survive in the presence of the specific drug. Ourability to evaluate the vitality value has already beendemonstrated in preliminary studies,[74, 75] and thus we areconfident that it will be possible to develop a robust ability topredict the survival of the virus mutants, and thus to designdrugs that would reduce the resistance problem. Otherconstraints such as mutation tendency and other factors canbe introduced by bioinformatics approaches. It is quite likelythat an aggressive use of computer simulations will providea way to beat the pathogens in their own game.

Another exciting direction can involve the design of drugsthat interfere with protein–protein interactions. Here, theidea is to learn about key interactions between partners insignal transduction networks (e.g. Ras/RAF[76]), and thendesigning molecules based on the regions with the strongestinteraction (see the strategy in Figure 49 of Ref. [77]). Yetanother direction that will gradually mature is the field oftruly rational enzyme design. Here, it seems obvious to methat the design approaches must involve actual modeling ofthe catalytic effect of different design options. It is unlikelythat unverified ideas of how enzymes may work (e.g. the ideathat enzyme catalysis is due to dynamical effects), or ideasthat are based on gas-phase modeling, would lead to artificialenzymes with large catalytic effects. On the other hand,approaches that can reproduce the catalytic effects of knownenzymes must eventually be very powerful in screeningdifferent design options. Multiscale modeling of the action ofmolecular complexes is likely to be used in describing signaltransduction, and allowing one to have a clearer and clearerunderstanding of cellular action. Finally, it should also bementioned that multiscale modeling provides a very powerfultool in modeling non-biological systems. Promising directionshere include the design of catalysts for a wide range ofapplications, the design of advanced materials, and theoptimization of nanotechnological devices. Overall, the useof computer modeling is likely to increase enormously in anybranch of molecule science, as well as in modeling very largesystems that can be considered as macroscopic systems.

I would like to express my gratitude to my wife Tamar, whofollowed me along my scientific life, and helped me both toendure difficulties and to enjoy successes.

Received: March 25, 2014Published online: July 24, 2014

[1] “Quantum Chemical Models (Nobel Lecture)”: J. A. Pople,Angew. Chem. 1999, 111, 2014 – 2023; Angew. Chem. Int. Ed.1999, 38, 1894 – 1902.

[2] “Theoretical Studies of Enzymic Reactions – Dielectric,Electrostatic and Steric Stabilization of Carbonium-Ion inReaction of Lysozyme”: A. Warshel, M. Levitt, J. Mol. Biol.1976, 103, 227 – 249.

[3] A. Fersht, Structure and Mechanism in Protein Science: A Guideto Enzyme Catalysis and Protein Folding, Freeman, New York,1999, p. 631.

[4] A. Warshel, Computer Modeling of Chemical Reactions inEnzymes and Solutions, Wiley-Interscience, Hoboken, 1997,p. 256.

[5] W. P. Jencks, Catalysis in Chemistry and Enzymology, McGraw-Hill, New York, 1969, p. 644.

[6] “Computer Simulation of Protein Folding”: M. Levitt, A.Warshel, Nature 1975, 253, 694 – 698.

[7] “Proceedings of the XXXVI Meeting of the Israel ChemicalSociety: On the interaction of Chymotrypsin with ionizedsubstrates”: A. Warshel, Y. Shalitin, Isr. J. Chem. 1966, 4, 85p.

[8] “Consistent Force Field for Calculations of ConformationsVibrational Spectra and Enthalpies of Cycloalkane and N-Alkane Molecules”: S. Lifson, A. Warshel, J. Chem. Phys. 1968,49, 5116 – 5129.

Nobel LectureAngewandte

Chemie

10029Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org

[9] “Consistent Force Field Calculations. 2. Crystal Structures,Sublimation Energies, Molecular and Lattice Vibrations, Molec-ular Conformations, and Enthalpies of Alkanes”: A. Warshel, S.Lifson, J. Chem. Phys. 1970, 53, 582 – 594.

[10] “Potential Functions and Conformations in Cycloalkanes”: M.Bixon, S. Lifson, Tetrahedron 1967, 23, 769.

[11] “Molecular Geometry.4. Medium Rings”: J. B. Hendrickson, J.Am. Chem. Soc. 1964, 86, 4854 – 4866.

[12] “Conformational-Analysis. 84. Study of Structures and Energiesof Some Alkenes and Cycloalkenes by Force Field Method”:N. L. Allinger, J. T. Sprague, J. Am. Chem. Soc. 1972, 94, 5734 –5747.

[13] E. B. Wilson, J. C. Decius, P. C. Cross, Molecular Vibrations. TheTheory of Infrared and Raman Vibrational Spectra, McGraw-Hill, New York 1955, p. 388.

[14] “The birth of computational structural biology”: M. Levitt, Nat.Struct. Biol. 2001, 8, 392 – 393.

[15] “Oxidation of 4a,4b-Dihydrophenanthrenes. 3. A TheoreticalStudy of Large Kinetic Isotope Effect of Deuterium in InitiationStep of Thermal Reaction with Oxygen”: A. Warshel, A.Bromberg, J. Chem. Phys. 1970, 52, 1262 – 1269.

[16] “Implications of Torsional Potential of Retinal Isomers forVisual Excitation”: B. Honig, M. Karplus, Nature 1971, 229, 558 –560.

[17] “Calculation of Ground and Excited-State Potential Surfaces ofConjugated Molecules. 1. Formulation and Parametrization”: A.Warshel, M. Karplus, J. Am. Chem. Soc. 1972, 94, 5612 – 5625.

[18] “Quantum-Mechanical Consistent Force-Field (Qcff/Pi) Method- Calculations of Energies, Conformations and Vibronic Inter-actions of Ground and Excited-States of Conjugated Mole-cules”: A. Warshel, Isr. J. Chem. 1973, 11, 709 – 717.

[19] “Hen Egg-White Lysozyme Molecule”: D. C. Phillips, Proc. Natl.Acad. Sci. USA 1967, 57, 483 – 495.

[20] “On the Nature of the Binding of Hexa-N-Acetyl GlucosamineSubstrate to Lysozyme”: M. Levitt, Pept. Polypept. Proteins1974, 99 – 113.

[21] “Energy Refinement of Hen Egg-White Lysozyme”: M. Levitt,J. Mol. Biol. 1974, 82, 393 – 420.

[22] J. A. Pople, D. L. Beveridge, Approximate Molecular OrbitalTheory, McGraw-Hill, New York, 1970, p. 214.

[23] “Microscopic Models for Quantum Mechanical Calculations ofChemical Processes in Solutions: LD/AMPAC and SCAAS/AMPAC Calculations of Solvation Energies”: V. Luzhkov, A.Warshel, J. Comput. Chem. 1992, 13, 199 – 213.

[24] “Progress in Ab Initio QM/MM Free-Energy Simulations ofElectrostatic Energies in Proteins: Accelerated QM/MM Stud-ies of pKa Redox Reactions and Solvation Free Energies”:S. C. L. Kamerlin, M. Haranczyk, A. Warshel, J. Phys. Chem. B2009, 113, 1253 – 1272.

[25] “Energetics of Enzyme Catalysis”: A. Warshel, Proc. Natl. Acad.Sci. USA 1978, 75, 5250 – 5254.

[26] “Electrostatic basis for enzyme catalysis”: A. Warshel, et al.,Chem. Rev. 2006, 106, 3210 – 3235.

[27] “Electrostatic Effects in Proteins”: M. F. Perutz, Science 1978,201, 1187 – 1191.

[28] “Calculations of Electrostatic Interactions in Biological Systemsand in Solutions”: A. Warshel, S. T. Russell, Q. Rev. Biophys.1984, 17, 283 – 421.

[29] “Modeling electrostatic effects in proteins”: A. Warshel, P. K.Sharma, M. Kato, W. W. Parson, Biochim. Biophys. ActaProteins Proteomics 2006, 1764, 1647 – 1676.

[30] “Effective approach for calculations of absolute stability ofproteins using focused dielectric constants”: S. Vicatos, M. Roca,A. Warshel, Proteins Struct. Funct. Bioinf. 2009, 77, 670 – 684.

[31] “An Empirical Valence Bond Approach for Comparing Reac-tions in Solutions and in Enzymes”: A. Warshel, R. M. Weiss, J.Am. Chem. Soc. 1980, 102, 6218 – 6226.

[32] “Computer simulations of enzyme catalysis: Methods, progress,and insights”: A. Warshel, Annu. Rev. Biophys. Biomol. Struct.2003, 32, 425 – 443.

[33] “Exploring challenges in rational enzyme design by simulatingthe catalysis in artificial kemp eliminase”: M. P. Frushicheva, J.Cao, Z. T. Chu, A. Warshel, Proc. Natl. Acad. Sci. USA 2010,107, 16869 – 16874.

[34] “Exploring, Refining, and Validating the Paradynamics QM/MM Sampling”: N. V. Plotnikov, A. Warshel, J. Phys. Chem. B2012, 116, 10342 – 10356.

[35] “Quantitative exploration of the molecular origin of theactivation of GTPase”: B. R. Prasad, N. V. Plotnikov, J. Lameira,A. Warshel, Proc. Natl. Acad. Sci. USA 2013, 110, 20509 – 20514.

[36] “Quantum chemistry �without orbitals�—An old idea and recentdevelopments”: T. A. Wesolowski, Chimia 2004, 58, 311 – 315.

[37] “Frozen Density-Functional Approach for Ab-Initio Calcula-tions of Solvated Molecules”: T. A. Wesolowski, A. Warshel, J.Phys. Chem. 1993, 97, 8050 – 8053.

[38] “Semiclassical Trajectory Surface Hopping Approach to Non-adiabatic Molecular Collisions: The reaction of H+ with D2”:J. C. Tully, R. M. Preston, J. Phys. Chem. 1971, 55, 562 – 572.

[39] “Semiclassical Trajectory Approach to Photoisomerization”: A.Warshel, M. Karplus, Chem. Phys. Lett. 1975, 32, 11 – 17.

[40] “Calculation of pp* Excited-State Conformations and VibronicStructure of Retinal and Related Molecules”: A. Warshel, M.Karplus, J. Am. Chem. Soc. 1974, 96, 5677 – 5689.

[41] “Nobel Prizes 2012: Cells and Sensitivity-GPCR Heroes Hon-ored”: B. K. Kobilka, R. J. Lefkowitz, Angew. Chem. 2012, 124,11361 – 11361; Angew. Chem. Int. Ed. 2012, 51, 11199 – 11199.

[42] “Bicycle-Pedal Model for 1st Step in Vision Process”: A.Warshel, Nature 1976, 260, 679 – 683.

[43] “Direct Observation of the Femtosecond Excited-State Cis-Trans. Isomerization in Bacteriorhodopsin”: R. A. Mathies,R. A. Mathies, C. H. Brito Cruz, W. T. Pollard, C. V. Shank,Science 1988, 240, 777 – 779.

[44] “Tracking the excited-state time evolution of the visual pigmentwith multiconfigurational quantum chemistry”: L. M. Frutos, T.Andruni�w, F. Santoro, N. Ferr�, M. Olivucci, Proc. Natl. Acad.Sci. USA 2007, 104, 7764 – 7769.

[45] “Simulating the Dynamics of the Primary Charge SeparationProcess in Bacterial Photosynthesis”: S. Creighton, J. K. Hwang,A. Warshel, W. W. Parson, J. Norris, Biochemistry 1988, 27, 774 –781.

[46] “Energetics and kinetics of radical pairs in reaction centers fromRhodobacter sphaeroides. A femtosecond transient absorptionstudy”: A. R. Holzwarth, M. G. Muller, Biochemistry 1996, 35,11820 – 11831.

[47] “Control of Redox Potential of Cytochrome c and MicroscopicDielectric Effects in Proteins”: A. K. Churg, A. Warshel,Biochemistry 1986, 25, 1675.

[48] “Energetics of Ion Permeation through Membrane Channels—Solvation of Na+ by Gramicidin-A”: J. Aqvist, A. Warshel,Biophys. J. 1989, 56, 171 – 182.

[49] “A Guide to Monte Carlo for Statistical Mechanics: 2. Byways”:J. P. Valleau, G. M. Torrie, Statistical Mechanics (Ed.: B. Berne),Springer, New York, 1977, pp. 169 – 194.

[50] “Calculations of Chemical Processes in Solutions”: A. Warshel,J. Phys. Chem. 1979, 83, 1640 – 1652.

[51] “Dynamics of reactions in polar solvents. Semiclassical trajec-tory studies of electron-transfer and proton-transfer reactions”:A. Warshel, J. Phys. Chem. 1982, 86, 2218 – 2224.

[52] “Simulating the Energetics and Dynamics of Enzymatic Reac-tions”: A. Warshel in Specificity in Biological Interactions (Eds.:C. Chagas, B. Pullman), Springer, Dordrecht, 1984, pp. 59 – 81.

[53] “Monte-Carlo Simulation of Differences in Free-Energies ofHydration”: W. L. Jorgensen, C. Ravimohan, J. Chem. Phys.1985, 83, 3050 – 3054.

.AngewandteNobel Lectures

A. Warshel

10030 www.angewandte.org � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031

[54] “Free Energy Perturbation Calculations on Binding and Catal-ysis after Mutating Asn 155 in Subtilisin”: S. N. Rao, U. C. Singh,P. A. Bash, P. A. Kollman, Nature 1987, 328, 551 – 554.

[55] “Molecular dynamics simulations of biological reactions”: A.Warshel, Acc. Chem. Res. 2002, 35, 385 – 395.

[56] “Millisecond-long molecular dynamics simulations of proteinson a special-purpose machine”: D. E. Shaw, Abstr. Pap. Am.Chem. Soc. 2012, 243, 0.

[57] “Molecular Simulation of ab Initio Protein Folding for a Milli-second Folder NTL9(1 – 39)”: V. A. Voelz, G. R. Bowman, K.Beauchamp, V. S. Pande, J. Am. Chem. Soc. 2010, 132, 1526 –1528.

[58] “Renormalizing SMD: The Renormalization Approach and ItsUse in Long Time Simulations and Accelerated PAU Calcu-lations of Macromolecules”: A. Dryga, A. Warshel, J. Phys.Chem. B 2010, 114, 12720 – 12728.

[59] “Nonequilibrium equality for free energy differences”: C.Jarzynski, Phys. Rev. Lett. 1997, 78, 2690 – 2693.

[60] “Coarse-grained (multiscale) simulations in studies of biophys-ical and chemical systems”: S. C. Kamerlin, S. Vicatos, A. Dryga,A. Warshel, Ann. Rev. Phys. Chem. 2011, 62, 41 – 64.

[61] “Renormalizing SMD: The Renormalization Approach and ItsUse in Long Time Simulations and Accelerated PMF Calcu-lations of Macromolecules”: A. Dryga, A. Warshel, J. Phys.Chem. B 2010, 114, 12720 – 12728.

[62] “Electrostatic origin of the mechanochemical rotary mechanismand the catalytic dwell of F1-ATPase”: S. Mukherjee, A.Warshel, Proc. Natl. Acad. Sci. USA 2011, 108, 20550 – 20555.

[63] “Energy transduction in the F-1 motor of ATP synthase”: H. Y.Wang, G. Oster, Nature 1998, 396, 279 – 282.

[64] “How subunit coupling produces the gamma-subunit rotarymotion in F-1-ATPase”: J. Z. Pu, M. Karplus, Proc. Natl. Acad.Sci. USA 2008, 105, 1192 – 1197.

[65] “Direct observation of the rotation of F-1-ATPase”: H. Noji, N.Yasuda, M. Yoshida, K. Kinosita, Jr., Nature 1997, 386, 299 – 302.

[66] “Realistic simulations of the coupling between the protomotiveforce and the mechanical rotation of the F0-ATPase”: S.

Mukherjee, A. Warshel, Proc. Natl. Acad. Sci. USA 2012, 109,14876 – 14881.

[67] “Catalytic and mechanical cycles in F-ATP synthases—Fourth inthe cycles review series”: P. Dimroth, C. von Ballmoos, T. Meier,EMBO Rep. 2006, 7, 276 – 282.

[68] “Torque generation and elastic power transmission in the rotaryF0F1-ATPase”: W. Junge, H. Sielaff, S. Engelbrecht, Nature2009, 459, 364 – 370.

[69] “On the energetics of translocon-assisted insertion of chargedtransmembrane helices into membranes”: A. Rychkova, S.Vicatos, A. Warshel, Proc. Natl. Acad. Sci. USA 2010, 107,17598 – 17603.

[70] “Exploring the nature of the translocon-assisted protein inser-tion”: A. Rychkova, A. Warshel, Proc. Natl. Acad. Sci. USA2013, 110, 495 – 500.

[71] “A biphasic pulling force acts on transmembrane helices duringtranslocon-mediated membrane integration”: N. Ismail, R.Hedman, N. Schiller, G. von Heijne, Nat. Struct. Mol. Biol.2012, 19, 1018-1022.

[72] “imulating the pulling of stalled elongated peptide from theribosome by the translocon S”: A. Rychkova, S. Mukherjee,R. B. Prasad, A. Warshel, Proc. Natl. Acad. Sci. USA 2013, 110,10195 – 10200.

[73] “Realistic simulation of the activation of voltage-gated ionchannels”: A. Dryga, S. Chakrabarty, S. Vicatos, A. Warshel,Proc. Natl. Acad. Sci. USA 2012, 109, 3335 – 3340.

[74] “Predicting drug-resistant mutations of HIV protease”: H.Ishikita, A. Warshel, Angew. Chem. 2008, 120, 709 – 712;Angew. Chem. Int. Ed. 2008, 47, 697 – 700.

[75] “Validating the vitality strategy for fighting drug resistance”: N.Singh, M. P. Frushicheva, A. Warshel, Proteins Struct. Funct.Bioinf. 2012, 80, 1110 – 1122.

[76] “Electrostatic contributions to protein-protein binding affinities:Application to Rap/Raf interaction”: I. Muegge, T. Schweins, A.Warshel, Proteins Struct. Funct. Genet. 1998, 30, 407 – 423.

[77] “Why nature really chose phosphate”: S. C. L. Kamerlin, P. K.Sharma, R. B. Prasad, A. Warshel, Q. Rev. Biophys. 2013, 46, 1 –132.

Nobel LectureAngewandte

Chemie

10031Angew. Chem. Int. Ed. 2014, 53, 10020 – 10031 � 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org