Molecular Dynamics ofBiological Macromolecules:A Brief History andPerspective

Martin KarplusDepartment of Chemistry and

Chemical Biology,Cambridge, MA 02138, USA

and Laboratoire de ChimieBiophysique, ISIS,

Universite Louis Pasteur,67000 Strasbourg, France

Received 30 May 2002;accepted 30 July 2002

Abstract: A description of the origin of my interest in and the development of molecular dynamicssimulations of biomolecules is presented with a historical overview, including the role of myinteractions with Shneior Lifson and his group in Israel. Some early applications of the methodologyby members of my group are summarized, followed by a description of examples of recentapplications and some discussion of possible future directions. © 2003 Wiley Periodicals, Inc.Biopolymers 68: 350–358, 2003

Keywords: NMR; molecular dynamics simulations; trajectory calculations; proteins; conforma-tional change; channels

PROLOGUE

Since I was very young, I had been interested inbiology and progressed from being passionate about“birdwatching”1 to a desire to understand biologicalprocesses at the level of chemistry and physics. How-ever, for many years after my thesis research withLinus Pauling, I concentrated on chemical physicsand biological applications remained in the back-ground. After moving to Harvard in the late 1960s, Iconcluded that if I was ever to return to biology I hadto make a break with a very busy research program.For this purpose, I decided to take a six-month leavefrom Harvard and go somewhere with a good libraryand people to talk to about my biological interests. Idecided that the Weizmann Institute in Rehovotwould be a good place, in part because I had always

wanted to visit Israel and friends had told me theWeizmann had an excellent library. So the questionsarose as to what group I should join.

I was aware of Shneior Lifson’s work on polymertheory and his reputation for being an open-mindedscientist, as well as a wonderful storyteller. So I wroteShneior in 1968 asking whether I could come for asemester. He kindly invited me to join his group andI was able to obtain a one-semester research leavefrom Harvard, not always an easy thing to do. Thestay in Rehovot was a great success from my point ofview. I had the time I needed to read and was able tofind a number of areas where I thought I might be ableto do constructive research by applying my expertisein theoretical chemistry to biological problems.Among others, they included vision and particularlythe application of semiempirical quantum mechanics

Correspondence to: Martin Karplus; email: marci@tammy.harvard.edu

Contract grant sponsor: National Science Foundation and theNational Institutes of HealthBiopolymers, Vol. 68, 350–358 (2003)© 2003 Wiley Periodicals, Inc.

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to the visual chromophore, retinal.2 This is an area inwhich I had been interested since my undergraduatedays at Harvard when I had many discussions of theproblem with George Wald and Ruth Hubbard.3 An-other question that appeared ready for investigationwas the origin of hemoglobin cooperativity. Althoughthe phenomenological model of Monod, Wyman, andChangeux4 had provided many insights, it did notmake contact with the detailed structure of the mole-cule. The needed information was being obtained byx-ray diffraction in the laboratory of Max Perutz,5 andI was hopeful that it soon would be possible to con-nect the plethora of available thermodynamic datawith the atomic interactions involved.6,7 A focus onthe mechanism of protein folding arose from a visit ofChris Anfinsen to the Lifson’s group. Anfinsen was aregular visitor to the Weizmann and we had manydiscussions of his experiments8 on protein folding insolution. What most impressed me was that heshowed a film of the folding of a protein with “flick-ering helices forming and dissolving and coming to-gether to form stable substructures.” Of course, thefilm was purely imaginary, but it led to my asking himwhether he had thought of taking the ideas in the filmand translating them into a quantitative model. Hesaid that he did not really know how he would do this,but to me it seemed clear that such a model could bebased on straightforward physical concepts. WhenDavid Weaver joined my group at Harvard while hewas on a sabbatical leave from Tufts, we developedwhat is now known as the diffusion-collision modelfor protein folding.9,10 Although it is a simplifieddescription of the folding process, it was the firstmodel that made possible the calculation of foldingrates based on meaningful physical parameters.

In Shneior’s group at the time there was consider-able excitement about developing empirical potentialenergy functions for small molecules. The important“new” idea was to use a functional form that couldserve not only for calculating vibrational frequencies,as did the expansions of the potential about a knownor assumed minimum energy structure, but also fordetermining that structure. The so-called consistentforce field (CCF) of Lifson and his co-workers, par-ticularly Arieh Warshel, included nonbonded interac-tion terms so that the minimum energy structure couldbe found after the energy terms had been appropri-ately calibrated.10 The possibility of using such en-ergy functions for larger systems, such as proteins,struck me as very exciting, though I did not beginworking on this for a while. However, I did inviteArieh Warshel to join my group as a postdoctoralfellow.

When I returned to Harvard, biologically relatedresearch began in earnest. The first two systems to beinvestigated were the visual pigment retinal and thecooperative mechanism in hemoglobin, both of whichI had thought about in Rehovot, as I already men-tioned. An initial study of retinal, which presagedquantum mechanical/molecular mechanical (QM/MM)calculations with a Huckel �-electron energy and apairwise nonbonded energy2 was made by BarryHonig, who continued to do fundamental research onthe problem of vision for many years. Barry’s calcu-lation predicted a 12-s-cis geometry for 11-cis retinal,the active chromophore of rhodopsin; this predictionwas subsequently confirmed by experiment. In a re-view of this work,12 I noted, “Theoretical chemiststend to use the word ’prediction’ rather loosely torefer to any calculation that agrees with experiment,even when the latter was done before the former.”This is as true today as it was then. When AriehWarshel came to Harvard, he worked on improvingthe methodology for the calculation of the structureand spectra of �-electron systems, particularly poly-enes, including retinal.13 The �-electrons were treatedby molecular mechanics, essentially as in the CFFprogram, and the �-electrons by a refined version ofthe Pariser–Parr–Pople method. Useful results cameout of applications of this methodology,12 althoughthe rhodopsin structure was not known, so that thespecific effect of the protein on the conformation andspectrum could not be calculated at that time.

The next step was the investigation of hemoglobin.Attila Szabo had just finished a statistical mechanicalmodel of hemoglobin cooperativity6 that was basedon crystallographic studies and their interpretation byMax Perutz.5 This work raised a number of questionsconcerning the energetics of ligand binding in hemo-globin and its coupling to protein structural changesinvolved in the transition from the unliganded to theliganded state (the T to R transition). The best meansto study such a problem was to have available a wayof calculating the energy of the protein as a functionof the atomic positions, but we did not have such aprogram.

Bruce Gelin had begun theoretical research in mygroup in 1967 and started by studying the applicationof the random phase approximation to two-electronproblems. He was collaborating with Neal Ostlund,who was a postdoctoral fellow at Harvard at the time.However, after two years Bruce was drafted andended up in a laboratory as an MP concerned withdrug usage (LSD, etc.) in the U.S. Army. This arousedhis interest in living systems and when he returned tofinish his degree, he wanted to change his area ofresearch to biologically related problems. Bruce and I

Molecular Dynamics of Biological Macromolecules 351

decided it was time to try to develop a program thatwould make it possible to take a given amino acidsequence (e.g., that of the hemoglobin � chain) and aset of coordinates (e.g., those obtained from the x-raystructure of deoxy hemoglobin), and to use this infor-mation to calculate the energy of the system and itsderivatives as a function of the atomic positions. Thiswas a major task, but Bruce had just the right com-bination of abilities to carry it out.14

The result was Pre-CHARMM (it did not have aname at that time). Although not trivial to use, theprogram was applied to a variety of problems, includ-ing Bruce’s pioneering study of aromatic ring flips inthe bovine pancreatic trypsin inhibitor (BPTI),15 aswell as Bruce’s primary project to introduce the effectof ligand binding on the heme group as a perturbation(undoming of the heme) and to use energy minimiza-tion to determine the response of the protein.7 To dosuch a calculation on the available computers (an IBM7090 at Columbia University was our workhorse atthe time) required considerable courage. Another ap-plication was Dave Case’s analysis of ligand escapeafter photodissociation from myoglobin.16

Bruce would have had a very difficult time con-structing such a program if there had not been priorwork by other groups on protein energy calculations.Although many persons have contributed to the de-velopment of empirical potentials, the two major in-puts to our work came from Schneior’s group inRehovot and Harold Scheraga’s group at Cornell Uni-versity.17 As I already mentioned, Arieh Warshel wasat Harvard and had brought his CFF program withhim. His presence and the availability of the CFFprogram was an important resource for Bruce, whowas also aware of Michael Levitt’s and Shneior Lif-son’s pioneering energy calculations for proteins.18

Unfortunately, Bruce did not have access to Michael’sprogram; in fact, the present-day version, calledENCAD, is still is not generally available, although ithas been used by some Levitt’s co-workers, perhapsmost effectively in the recent simulations of proteinunfolding by Valerie Daggett.19

THE BEGINNING OF MOLECULARDYNAMICS OF BIOMOLECULES

Given a program that could calculate the forces on theatoms of a protein for minimization of the energy, thenext step was to use these forces in Newton’s equationto calculate the dynamics. This important develop-ment was introduced by Andy McCammon when hejoined my group. An essential element that encour-aged us in this attempt was the existence of molecular

dynamics simulation methods for simpler systems.Molecular dynamics had followed two pathways thatcome together in the study of biomolecule dynamics.One of these, usually referred to as trajectory calcu-lations, has an ancient history that goes back to two-body scattering problems for which analytic solutionscan be achieved. However, as is well known, even foronly three particles with realistic interactions, diffi-culties arise. An example is provided by the simplestchemical reaction, H � H2 3 H2 � H, for which aprototype calculation was attempted by Hirschfelder,Eyring, and Topley in 193620; they were able tocalculate a few steps along one trajectory. It wasnearly thirty years later that the availability of com-puters made it possible to complete the calculation.21

Much has been done since then in applying classicaltrajectory methods to a wide range of chemical reac-tions.22,23 These classical studies have been supple-mented by semiclassical and quantum-mechanicalcalculations in areas where quantum effects can playan important role.24,25 The focus at present is on morecomplex molecules, the redistribution of their internalenergy, and the effect of this on reactivity.26 The otherpathway in molecular dynamics has been concernedwith physical rather than chemical interactions andwith the thermodynamics and dynamic properties oflarge numbers of particles, rather than detailed trajec-tories of a few particles. Although the basic ideas goback to van der Waals and Boltzmann, the modern erabegan with the work of Alder and Wainright on hard-sphere liquids in the late 1950s.27 The paper by Rah-man28 in 1964 on a molecular dynamics simulation ofliquid argon with a soft sphere (Lennard–Jones) po-tential represented an important next step. Simula-tions of complex fluids followed; the original study ofliquid water by Stillinger and Rahman was publishedin 1971.29 Since then there have been many studies onthe equilibrium and nonequilibrium behavior of awide range of homogeneous systems.30,31

The background I have outlined set the stage forthe development of molecular dynamics of biomol-ecules.32 The size of an individual molecule, com-posed of 500 or more atoms for even a small protein,is such that its simulation in isolation can serve toobtain approximate equilibrium properties, as in themolecular dynamics of fluids, although detailed as-pects of the atomic motions are of considerable inter-est, as in trajectory calculations. A basic assumptionin initiating such studies was that potential functionscould be constructed that were sufficiently accurate togive meaningful results for systems as complex asproteins or nucleic acids. In addition, it was necessaryto assume that for these inhomogeneous systems, incontrast to the homogeneous character of even “com-

352 Karplus

plex” liquids such as water, simulations of an attain-able time scale (approximately 10–100 ps in initialstudies) could provide a useful sample of the phasespace in the neighborhood of the native structure.Although for neither of these assumptions was therestrong supporting evidence in 1975, the results ob-tained for BPTI32 have clearly stood the test of time,and perhaps more importantly, have served to open anew field that has become the research focus of a largenumber of scientists.

It is now twenty-five years since the first moleculardynamics simulation of a macromolecule of biologi-cal interest was published.32 The simulation con-cerned BPTI, which has served as the “hydrogenmolecule” of protein dynamics because of its smallsize, high stability, and relatively accurate x-ray struc-ture, available in 197533; interestingly, the physiolog-ical function of BPTI remains unknown. Althoughthis simulation was done in vacuum with a crudemolecular mechanics potential and lasted for only 9.2ps, the results were instrumental in replacing our viewof proteins as relatively rigid structures (In 1981, SirD. L. Phillips commented: “Brass models of DNA anda variety of proteins dominated the scene and much ofthe thinking.”34) with the realization that they weredynamic systems, whose internal motions play a func-tional role. Of course, there were already experimen-tal data, such as the hydrogen exchange experimentsof Linderstrom–Lang and his co-workers),35,36 point-ing in this direction. It is now recognized that thex-ray structure of a protein provides the averageatomic positions, but that the atoms exhibit fluid-likemotions of sizable amplitudes about these averages.The new understanding of protein dynamics sub-sumed the static picture in that the average positionsare still useful for the discussion of many aspects ofbiomolecular function in the language of structuralchemistry. However, the recognition of the impor-tance of fluctuations opened the way for more sophis-ticated and accurate interpretations of functional prop-erties.

The conceptual changes resulting from the earlystudies make one marvel at how much of great interestcould be learned with so little—such poor potentials,such small systems, so little computer time. This is, ofcourse, one of the great benefits of taking the initial,somewhat faltering steps in a new field where thequestions are qualitative rather than quantitative, andany insights, even if crude, are better than none at all.Subsequent applications have been concerned withmore detailed interpretations and predictions of phe-nomena that require the use of improved methods.Simulations based on more refined potentials, and thelonger runs required for improved statistics, are be-

coming possible for increasingly complex systems asa result of the progress in the available computers,which continue to increase in speed by a factor of twoor so every eighteen months, in accord with Moore’sLaw.

Molecular dynamics simulations of proteins, as ofmany other systems (e.g., liquids), can, in principle,provide the ultimate details of motional phenomena.The primary limitation of simulation methods is thatthey are approximate. It is here that experiment playsan essential role in validating the simulation meth-ods—that is, comparisons with experimental dataserve to test the accuracy of the calculated results andprovide criteria for improving the methodology. How-ever, the experimental approaches to bimolecular dy-namics are limited as to the information that can beobtained from them; e.g., if one is concerned with thetime scale of motions, the frequency spectrum cov-ered by experiments such as NMR is limited,37 so thatmotional models that are able to rationalize the datacan be inaccurate. When experimental comparisonsindicate that the simulations are meaningful, theircapacity for providing detailed results often makes itpossible to examine specific aspects of the atomicmotions far more easily than by making measure-ments.

EARLY APPLICATIONS

Two years after the BPTI simulation, it was recog-nized38,39 that thermal (B) factors determined in x-raycrystallographic refinement could be used to obtaininformation about the internal motions of proteins andplots of estimated mean-square fluctuations vs residuenumber (introduced in Ref. 32) became a standardpart of papers on high-resolution crystal structures,even though the contribution to the B factors of over-all translation and rotation, as well as crystal disorder,continues to be a concern in their interpretation.40

During the subsequent ten years, a wide range ofphenomena were investigated by molecular dynamicssimulations of proteins and nucleic acids. Most ofthese studies focused on the physical aspects of theinternal motions and the interpretation of experi-ments. They include the analysis of fluorescence de-polarization of tryptophan residues,41 the role of dy-namics in measured NMR parameters,42–44 and in-elastic neutron scattering,45,46 the effect of solventand temperature on protein structure and dynam-ics,47–49 as well as the now widely used simulatedannealing methods for x-ray structure refinement50,51

and NMR structure determination.52,53 Simulta-neously, there were a number of applications that

Molecular Dynamics of Biological Macromolecules 353

demonstrated the importance of internal motions inbiomolecular function, including the hinge bendingmodes for opening and closing active sites,54,55 theflexibility of tRNA,56 the induced conformationchange in the activation of trypsin,57 the fluctuationsrequired for ligand entrance and exit in heme pro-teins,16 and the role of configurational entropy inproteins and nucleic acids.58,59

Two attributes of molecular dynamics simulationshave played an essential part in the explosive growthin the number of studies based on such simulationsand the very wide range of applications that have beenmade. Simulations provide the ultimate detail con-cerning individual particle motions as a function oftime, so they can be used to answer specific questionsabout the properties of a system, often more easilythan experiments. For many aspects of biomoleculefunction, these are the details of interest (e.g., by whatpathways does oxygen enter into and exit from theheme pocket in myoglobin). Of course, experimentsplay an essential role in validating the simulationmethods—that is, comparisons with experimentaldata can serve to test the accuracy of the calculatedresults and to provide criteria for improving the meth-odology. This is particularly important because theo-retical estimates of the systematic errors inherent inthe simulations are still lacking; i.e., the errors intro-duced by the use of empirical potentials are difficult toquantify. Another important aspect of simulations isthat, although the potentials employed in simulationsare approximate, they are completely under the user’scontrol, so that by removing or altering specific con-tributions their role in determining a given propertycan be examined. This is most graphically demon-strated by the use of “computer alchemy”—transmut-ing the potential from that representing one system toanother during a simulation—in calculating free en-ergy differences.60–62

There are three types of applications of simulationmethods in the macromolecular area, as well as inother areas involving mesoscopic systems. The firstuses the simulation simply as a means of samplingconfiguration space. This is involved in the utilizationof molecular dynamics, often with simulated anneal-ing protocols, to determine or refine structures withdata obtained from experiments. The second usessimulations to determine equilibrium averages, in-cluding structural and motional properties (e.g.,atomic mean-square fluctuation amplitudes) and thethermodynamics of the system. For such applications,it is necessary that the simulations adequately sampleconfiguration space, as in the first application, withthe additional condition that each point be weightedby the appropriate Boltzmann factor. The third area

employs simulations to examine the actual dynamics.Here not only is adequate sampling of configurationspace with appropriate Boltzmann weighting re-quired, but it must be done so as to properly representthe time development of the system. For the first twoareas, Monte Carlo simulations can be utilized, aswell as molecular dynamics. By contrast, in the thirdarea where the motions and their time developmentsare of primary interest, only molecular dynamics canprovide the necessary information. The three sets ofapplications make increasing demands on the simula-tion method in terms of the required accuracy.

CURRENT APPLICATIONS

Most of the motional phenomena examined during thefirst ten years after the BPTI simulation paper waspublished32 continue to be studied both experimen-tally and theoretically. Every year more papers ap-pear, stimulated in part by improvement in the meth-odology for the former and in the increase in com-puter power for the latter. Moreover, the increasingscope of molecular dynamics is making possible thestudy of systems of increasing complexity with moreaccurate methods (e.g., improved potentials) on ever-increasing time scales. There are many recent exam-ples of the use of molecular dynamics to obtain func-tionally important information that is difficult or im-possible to obtain experimentally.

NMR-Related Studies

One area where there has been and continues to be asymbiotic relation between simulations and experi-ment is NMR, which in addition to its use for struc-ture determinations51,52,63 is a powerful technique forthe study of the dynamics and thermodynamics ofmacromolecules. Interpretations of relaxation rates(T1 and T2) and NOE measurement by moleculardynamics, initiated in the early 1980s,42–44 are nowwidespread.63–65 Yet, in a recent paper66 on the use ofNMR to study motional properties, Lee and Wandstate, “Despite its importance, the precise nature ofthe internal motions of protein molecules remains amystery.” The papers by Lee and Wand66 and byWand37 focus on internal protein motions (particularlyside-chain librations) and the correlation of the mea-sured flexibility based on order parameters with theentropy. In fact, molecular dynamics simulations overthe last 25 years have taught us much about thesemotions,67,68 and have been used successfully to cal-culate and interpret order parameters measured byNMR.42,44,63–65 It is interesting to note also that al-

354 Karplus

ready in 198358 (see also Ref. 69) normal mode cal-culations demonstrated that vibrational contributionsto the internal entropy of BPTI are equal to about 600kcal/mol (including quantum corrections, which so farhave been neglected in NMR analyses) and that thevalue per residue of a protein is very similar to that foran isolated peptide.70 More recent simulations haveshown the importance of the residual motion to theentropy of binding of internal waters, using BPTI asthe model system,71 and of antiviral drugs to thecapsid of rhinovirus72; for an experimental verifica-tion of the latter, see Ref. 73. A recent moleculardynamics analysis65 of the relation between NMRorder parameters and protein entropy suggests thatalthough there is a correlation, the NMR results cor-respond to only a fraction (25%) of the total entropy.

The Role of Solvent in Protein Dynamics

Molecular dynamics has been used to resolve thecontentious question concerning the role of the sol-vent in determining the internal motions of proteins,particularly at temperatures below the so-called glasstransition74,75; low-temperature studies have beenvery important in elucidating the fundamental role ofinternal motions—for example, in bacteriorhodop-sin.76 It has not been possible to determine experi-mentally whether or not the solvent fluctuations“drive” the internal motion of a protein, but this wasaccomplished by employing an attribute of the simu-lation methodology to create a physical system notaccessible in nature.77 Simulations can be performedwith one part of the system (e.g., the protein) at onetemperature and another part of the system (e.g., thesurrounding solvent) at a different temperature. Theamplitudes of the atomic fluctuations (correspondingto the B factors) in carbonmonoxymyoglobin werecalculated77 from simulations with the temperature ofthe protein and the solvent at either 300K or 180 K(i.e., above and below the protein glass transitionaround at 220 K). The results of the four possibletemperature combinations are given in Table I. It isstriking that the magnitude of the fluctuations is onlyweakly dependent on the protein temperature; thefluctuations are large when the solvent is at 300 K andsmall when the solvent is 180 K, independent of theprotein temperature. This demonstrates unequivocallythat the temperature of the solvent and its resultantmobility is the dominant factor in determining thefunctionally important protein fluctuations in this tem-perature range. Additional simulations have shownthat at still lower temperatures (around 80 K), theprotein “freezes” (i.e., has only small fluctuations),

even if the solvent is at 300 K, because the internalmotional barriers become dominant.

Conformational Change in theMechanism of GroEL

Chaperones are essential for the correct folding ofmany proteins in the highly concentrated milieu of thecell.78 One of the best characterized chaperonins isGroEL, which consists of two rings of seven identicalsubunits, stacked back-to-back.79 GroEL is requiredfor growth of Escherchia coli; it has been estimatedthat 10% of its proteins are assisted in folding byGroEL.80 During the functional cycle, GroEL under-goes large conformational changes that are regulatedby the binding and hydrolysis of ATP and involve thecochaperonin GroES, as demonstrated by x-ray crys-tallography.79 Each of the seven-membered rings hasbeen shown to have a “closed” structure in the ab-sence of ATP and GroES and an open structure intheir presence. Molecular dynamics simulations81

have been used to find the pathway between these twostructures, which it is impossible to determine byexperimental techniques. Since the actual transitionbetween the open and closed structure is believed tobe on the millisecond time scale (The full GroELcycle takes about 15 s), a direct simulation of theopening and closing motion in the presence and ab-sence of ATP by molecular dynamics is not possibleas yet. However, a number of methods have beendeveloped to follow the transition between two knownstates on the nanoseconds time scale accessible tosimulations. One of these, targeted molecular dynam-ics,82 was used to determine a transition pathway ofGroEL. It was shown that there is an intermediateform, which exists with ATP bound in the absence ofGroEL, and it was demonstrated that the early down-ward motion of the small intermediate domain in-duced by nucleotide binding is the trigger for thelarger movement of the apical and equatorial do-mains. Moreover, the results demonstrated that steric

Table I Average Mean Square Fluctuationsa

Temperature Backbone All Heavy Atoms

P300/S300b 0.23 0.36P180/S300 0.18 0.28P300/S180 0.09 0.13

P180/S180 0.09 0.13

a Temperatures in degrees Kelvin and mean square fluctuationsin Ångstroms.

b P refers to the protein and S to solvent.

Molecular Dynamics of Biological Macromolecules 355

interactions and salt bridges between different sub-units are the source of the measured positive cooper-ativity of ATP binding and hydrolysis within a ringand the negative cooperativity between the two rings.Recent cryo-electron microscopy results (Ref. 83; H.Saibil and A. L. Horwich, private communication)support the prediction from molecular dynamics ofthe mechanism by which the intermediate domainplays a key role in the allosteric transition of GroEL.There is still some uncertainty about the motion of theapical domain in this intermediate structure becausethe cryo–electron microscopy model83 and the simu-lations81 appear to disagree.

A PERSPECTIVE ON FUTUREAPPLICATIONS

One of the very exciting recent developments in mo-lecular dynamics simulations is that the time scalesbecoming available with modern computers (100 ns to�s) are making it possible to study phenomena ofbiological interest in real time. This is analogous, inan inverse sense, to the fact that while experiments onthe picosecond time scale were an important devel-opment, it is when the resolution was extended tofemtoseconds that the actual events involved in chem-ical reactions could be observed in real time.84,85 Byrunning multiple simulations of 10 ns duration, “realtime” visualization of water molecule migrationthrough models of the aquaporin channel has beenachieved.86,87 Although statistically significant stud-ies of the entire process of protein folding are stillbeyond the reach of present day simulations,88 (theexperimental time scale is tens of microseconds orlonger, and the potentials may not yet be good enoughto identify the native state in many cases), the foldingand unfolding of model peptides, such as a three-stranded �-sheet, with a simplified solvent model hasbeen possible.89

Systems containing more than 100,000 atoms havebeen studied by molecular dynamics simulation since1997.90 Current simulations include models of thenicotinic acetylcholine receptor91 and ATP syn-thase.92,93 The simulation of such complex systemsfor increasing periods of time is expected to provideunique insights into the specificity of binding in li-gand-gated channels, the mechanisms of receptor ac-tivation and desensitization, and the action and regu-lation of molecular motors.

It has always been my hope that when the meth-odology for molecular dynamics simulation had beencodified in available programs, experimentalists (e.g.,those doing x-ray crystallography, NMR spectros-

copy, and enzyme kinetics) would use them as astandard tool in their research. This is now beginningto happen. A beautiful example of such a study is theanalysis of the role of the dynamic coupling betweenSH2 and SH3 domains in the control of their func-tion.94

Another stage is the evolution of molecular dy-namics simulations from the molecular to the su-pramolecular to the cellular scale. The transition tothe supramolecular scale is already evident in thesome of the studies mentioned above. These currentlyrely on crystallographic or other models of the mo-lecular assemblages, and mainly consider structuralchanges of relatively modest amplitudes that are re-lated to function. Studies of the formation of suchassemblages will be more demanding. An interestingrecent example of structure formation studied in realtime by molecular dynamics concerns the formationof phospholipid bilayers.95,96 The simulation of suchcellular activities as synaptic transmission,97 and howthe nuclear membrane is dismantled on cell divisionby the motor protein cytoplasmic dynein,98 will even-tually follow, building upon the detailed knowledgeof the structure and dynamics of the channels, en-zymes and other components. (A recent simulationthat addressed a medical protein—the destruction offibrous caps and their relation to heart attacks— isalso indicative of what the future holds.99) Moreglobal simulations are likely to be initiated with lessdetailed models than the atomistic (Newtonian) onesconsidered in this review, but the ultimate descrip-tions, which will necessarily include such details asthe possible effects of mechanical stress upon thechannels and other components of a contracting neu-romuscular synapse, will require studies by atomisticmolecular dynamics simulations. Fortunately, thecontinued increase in computer power is (almost)keeping up with the demands made by such calcula-tions.

SUMMARY

Molecular dynamics simulations of macromoleculeshave provided many insights concerning the internalmotions of these systems since the first protein wasstudied over 25 years ago. With continuing advancesin the methodology and the speed of computers mo-lecular dynamics studies are being extended to largersystems, greater conformational changes, and longertime scales. This is making possible the investigationof motions that have particular biological functionsand to obtain information that is not accessible fromexperiment. The results available today make clear

356 Karplus

that the applications of molecular dynamics will playan even more important role in our understanding ofbiology in the future.

Much of the research described here was supported in partby grants from the National Science Foundation and theNational Institutes of Health. As is evident from the refer-ences, many of my co-workers have contributed to theresearch. The opportunity of working with them has beenone of the major rewards of my scientific career. Parts ofthis review are based on reference 100.

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