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PEPCAT—A New Tool for ConformationalAnalysis of Peptides

M. F. O’DONOHUE,1 E. MINASIAN,2 S. J. LEACH,2 A. W. BURGESS,1

H. R. TREUTLEIN1

1Ludwig Institute for Cancer Research and Cooperative Research Center for Cellular Growth Factors,P.O. Royal Melbourne Hospital, Parkville, Victoria 3050, Australia2Department of Biochemistry & Molecular Biology, Melbourne University, Parkville, Victoria 3052,Australia

Received 9 August 1999; accepted 15 November 1999

ABSTRACT: We report a new technique for the efficient analysis andvisualization of peptide and protein conformations and conformationalrelationships, which we have implemented in a computer program calledPEPCAT. PEPCAT (an abbreviation for Peptide Conformational Analysis Tool)provides a simple, graphical, and flexible framework that allows the user todefine a specific structural feature or juxtaposition of amino acids and to followthe fate of the motif during a molecular dynamics simulation. Here we describethe PEPCAT analysis of the effects of environmental and chemical modificationson conformational preferences of a regulator of hemopoiesis, namely thepentapeptide pyro-EEDCK, and of a conformational transition in theimmunosuppressant drug cyclosporin A. PEPCAT, however, can be applied tothe conformational analysis of peptides and proteins in general. c© 2000 JohnWiley & Sons, Inc. J Comput Chem 21: 446–461, 2000

Keywords: cyclosporin A; molecular modeling; transitions; dynamics;conformational search; conformational analysis; hemopoietic peptides

Introduction

C onformations of biological macromoleculesare determined by the properties of their

molecular building blocks and by their surround-ing environment.1, 2 Macromolecular systems, suchas peptides and proteins, often display multiple

Correspondence to: H. R. Treutlein; e-mail: [email protected]

conformations dependent on temperature and envi-ronment. A description and classification of possibleconformations is important for the understandingof molecular properties. Methods for the analysisand display of conformational types and energieshave been developed for small molecules,3 but untilnow simple methods have not been readily avail-able for macromolecules. In this work we describePEPCAT, a new method for evaluation, comparisonof conformational properties, and conformational

Journal of Computational Chemistry, Vol. 21, No. 6, 446–461 (2000)c© 2000 John Wiley & Sons, Inc.

PEPCAT—A NEW TOOL FOR CONFORMATIONAL ANALYSIS OF PEPTIDES

interrelationships, which can be applied to macro-molecules.

This article is organized as follows: the remain-der of the Introduction section will discuss prob-lems with current conformational analysis tools.The Method section describes our PEPCAT methodin detail, and this is followed in the Results sec-tion by a description of two examples of a PEP-CAT analysis. Finally, in the Discussion section, ourmethod is summarized, and possible extensions arediscussed.

CONFORMATION IDENTIFICATION

Some of the crucial questions for peptide struc-tural analysis are how to describe peptide structuresand how to determine when they are similar enoughthat they can be considered to share the same iden-tity or conformation. The most popular method forpeptide conformational analysis calculates a sim-ilarity measure between each pair of structures,using a root-mean-square difference (RMSD) tech-nique (see below). The structures are then groupedinto distinct conformations based on the relativedeviation to other observed structures.4 There areproblems with these techniques that can be illus-trated by their inability to generate classificationhierarchies similar to the three-dimensional folddatabases CATH5 and SCOP6 without manual in-spection as an essential contribution.

TRAJECTORY FILES

Molecular dynamics simulations provide an ex-cellent source of information about the details ofpathways between different molecular conforma-tions. The results of molecular dynamics simula-tions are often saved in a “trajectory file,” whichcontains coordinate sets (or “frames”) of the peptidestructure saved at regular intervals during the sim-ulation. Each frame consists of the set of all atomicCartesian coordinates in the peptide at that time-step in the simulation. Because of the large size oftrajectory files, and the fact that many separate cal-culations are needed to ensure statistically relevantresults, the data used for conformational analysiscan easily occupy large amounts of storage space.

Although automated trajectory analysis tech-niques exist,4, 7 – 10 direct viewing of the trajectoryfile in the form of a playback movie of molecularmovement still remains the most common analy-sis technique for the visualization of conformationalchanges. However, more elaborate and automatedtools are necessary to analyze and represent the

more subtle conformational features and changesthat occur during a dynamics simulation.

CARTESIAN RMSD MEASUREMENT

Peptide conformational analysis relies heavily onthe comparison between structures, and this placesa great responsibility on the comparison operator tocorrectly discriminate between structures. The mostpopular method to calculate a measure of structuralsimilarity is to overlay the structures using a least-squares fit algorithm, and to compare the Cartesiancoordinates of the backbone Cα atoms only. Thesimilarity can be expressed in terms of an averagedeviation of Cα atoms from their average position,the root mean square deviation (RMSD).4

The RMSD value often gives a good measureof similarity, and is insensitive to small changes inatomic Cartesian coordinates. However, the changeof a single backbone dihedral value can lead to alarge overall RMSD value. Consider, for example,a backbone dihedral angle change in a residue inthe middle of a peptide with an extended β-strandconformation. Under these circumstances, the singleRMSD value correctly identifies the quite signifi-cant change in the shape of the peptide and thevast number of atoms that have suffered dramaticchanges in their Cartesian coordinates. However, itgives no clue that a comparatively simple structuralchange (rotation of a single dihedral bond angle) isresponsible for the difference, and that the two sub-structures on either side of the changed residue arestill identical to the original peptide structure.

Calculation of the RMSD value requires the com-putation of the optimal overlay of the two peptidestructures. This is computationally expensive whencompared to other equivalent low level operationssuch as comparing two numerical values. The highcosts of the Cartesian RMSD operation make it anundesirable candidate for comparing large numbersof structures.

DIHEDRAL RMSD MEASUREMENT

A peptide structure can also be represented asa sequence of dihedral bond angle values ratherthan as a set of Cartesian coordinates. This “inter-nal” coordinate system better represents the localconformations and the degrees of movements thatare available to the molecule. Bond length and an-gle stretching are ignored, as they usually does notsignificantly contribute to the overall peptide con-formation. A backbone dihedral RMSD value canthen be calculated between two structures using the

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difference in peptide backbone dihedral angle val-ues. This has the advantage of not requiring theexpensive overlay operation necessary for Carte-sian RMSD comparisons. Structures that differ inonly one dihedral angle (such as our previouslymentioned example) will, when compared to theoriginal structure, generate a relatively small back-bone dihedral RMSD value.

RMSD AVERAGING EFFECT

The RMSD comparison measures the average dif-ference over all coordinate values (this applies inboth Cartesian and backbone dihedral angle com-parisons). Unfortunately, this destroys the ability todistinguish between large changes in a small num-ber of coordinates, which can be observed in someconformational transitions, from small changes in alarge number of coordinate values.

This problem is often accentuated in molecu-lar dynamics simulations (particularly those at el-evated temperatures) where the thermal motioninduces all coordinate values to undergo small fluc-tuations and produce a large number of structuralvariations of each peptide conformation. A struc-tural change, for example, the radical change of asingle amide peptide dihedral from cis to a trans,may go unnoticed against the background struc-tural fluctuations. This averaging effect obviouslyreduces the effectiveness of an RMSD-based classi-fication scheme to discriminate between groups ofstructures based on large changes in a small numberof residues.

GROUPING STRUCTURES USING RMSD

One popular method for grouping related pep-tide structures used in the analysis of trajectoryfiles is the calculation of a difference measure be-tween all possible pairs of structures. A clusteringalgorithm can then sort the structures into a hier-archy of groups and subgroups. A cutoff value canbe used to partition the structures into conforma-tional families.4 This clustering method does notscale up well for the processing of large volumesof data because the number of RMSD comparisonoperations required increases quadratically with in-creasing numbers of structures.

This restricts the application of this type ofanalysis to conformational data sets with hundredsor thousands of frames. However, current mole-cular dynamics calculations often produce muchlarger conformational data sets where the use ofRMSD-based techniques become computationallyprohibitive.

It is also difficult to extend an already concludedanalysis with the current method because the addi-tion of new conformational data to an existing set ofpreviously analyzed data set requires the reassess-ment of all existing data.

Much work has been done in applying cluster-ing techniques to dynamics simulations, and themethod is a subject of current research interest.11 – 15

GROUPING STRUCTURES USING ACLASSIFICATION SCHEME

An alternative method for grouping peptidestructures is the use of a classification scheme inwhich an abstract set of rules is applied to iden-tify similar peptide structures. A commonly usedclassification scheme is a residue–residue contactmap.16, 17 Two residues are considered to be in con-tact if any atom of one residue comes within apredetermined cutoff radius of an atom of the otherresidue. Different conformations of peptide struc-tures will have different patterns of residue–residuecontacts. This classification scheme does not use acontinuous solution space, as the peptide Cartesiancoordinates does, but instead, maps these structuresinto a discrete solution space. This new coordinatesystem has a number of advantages. A conforma-tion can be simply represented as a K × K matrix,where K is the number of residues in the peptide,with cell values containing a Boolean true or falsevalue for contact between residues. The size of thesolution space, which is infinite in atomic Cartesiancoordinate space and is still infinite (but with lessdimensions) in dihedral angle space, is reduced to2K×K possible contact matrices. A comparison be-tween two different contact maps can be calculatedeasily by comparing the two matrices. And finally,classification is computationally less expensive, as itdoes not require a comparison between all possiblepairs of structures, but only a calculation performedonce on each structure. The identification of a dis-crete conformational “state” in this manner opensthe way for use of traditional state space searchand analysis techniques commonly used in artificialintelligence applications.18 Contact map representa-tions have been used, for example, to analyze resultsfrom the series of CASP experimental predictiontrials.19

More general classification schemes not basedon a contact matrix, but on the application of anumber of independent descriptors can be used toidentify a conformation. Lambert et al.20 have useddescriptors based on regions in φ–ψ maps to ana-lyze and predict the conformation of small peptide

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sequences. The φ–ψ map for a peptide was di-vided into four regions, and a peptide conformationwas classified as the sequence of residue descrip-tor values. Bravi et al.21 used a mixture of distanceand dihedral descriptor measurements, each withan individual cutoff comparison threshold value todevelop a procedure to define and compare mole-cular conformations. A nonhierarchical clusteringtechnique is then employed to group the observedconformations.

SUBJECTIVE NATURE OF CLASSIFICATION

The definition of a peptide conformation de-pends upon the needs of the investigator and thequestion being asked. What constitutes a confor-mation in a ligand docking problem may differsubstantially from that required for evaluating pro-tein flexibility. This subjective nature of classifica-tion makes it difficult to devise a single structuralclassification scheme. However, it does allow forthe development of a “tool kit” that can be used todefine the structural criteria that will allow the re-searcher to discriminate between different proteinor peptide conformations. For instance, in a ligand-docking problem, only residues near the bindingpocket need to be considered in detail; changes inother residues can either be ignored or monitored ata lower level of accuracy.

It is worth noting that grouping of structuresusing only the three dimensional coordinates asthe basis for similarity, may also be misleading insome cases. Two conformations, which may be clus-tered together based on their structural similarity,may have significantly different potential energies,and/or be separated by great energy barriers on thepotential energy surface of the molecule.

THE PEPCAT METHOD

To address many of the problems encounteredin conventional conformational analysis methodswe have developed a method that allows a flexi-ble definition of conformational states and an effi-cient comparison of a large set of structures. Ourmethod is called PEPCAT (for Peptide Conforma-tional Analysis Tool), and consists of five steps:conformation definition, classification, comparison,trajectory analysis, and visualization of the results.Emphasis was also put on an intuitive display of theresults, which facilitates the recognition of impor-tant conformational features present in moleculardynamics trajectory files. The PEPCAT methodol-ogy is first defined in the next section. This is fol-

lowed by a detailed description of two applicationsof PEPCAT in the Results section.

Methods

There are five steps in the PEPCAT analysis tech-nique: first, the user defines the geometric proper-ties of the peptide relevant to the particular prob-lem; second, structures are processed using theclassification scheme; third, the similarities betweenstructures are calculated using a generalized dis-tance measure; forth, trajectory files are reexpressedas a compact sequence of conformational statesrather than coordinates; and the last step uses thenew trajectory files and a database of the knownconformations built during the previous steps toanalyze as well as visualize conformational prop-erties and conformational transitions. Each step isdescribed in detail below. The terminology specificto the PEPCAT methodology is italicized in the text,and is described in Table I. A visual guide to thePEPCAT methodology is also shown in Figure 1.

CONFORMATION DEFINITION

A classification scheme is devised by the user toidentify conformations of a peptide, and is codedinto an input file for the PEPCAT program.

A descriptor, such as the φ–ψ values for a par-ticular residue can be selected from the supporteddescriptor types for monitoring in the peptide. A mapis constructed for each descriptor to map all valuesof the generalized peptide property to a discrete nu-meric descriptor state. This allows the user to specifythe level of accuracy for monitoring a particular de-scriptor. PEPCAT currently supports three descriptortypes: φ–ψ regions (see Fig. 2a), angle range values(see Fig. 2b), and atomic distances (see Fig. 2c). Eachdescriptor maps a generalized peptide property to adiscrete numeric descriptor state.

A set of descriptors, called a classification scheme, ischosen to distinguish different conformations of thepeptide. Each distinct set of descriptor values result-ing from the application of the classification schemeto a peptide structure is defined as a unique peptideconformation or conformational state.

CLASSIFICATION

The PEPCAT program applies the constructedclassification scheme to peptide structures resultingin a set of descriptor values that identify each in-put structure. PEPCAT also uses this information to


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TABLE I.PEPCAT Terminology.

Descriptor type A generic type of measurement such as an angle, distance or φ–ψ map value thatcan be made of a peptide property.

Descriptor A specific property of a peptide to be monitored. The precise residue or angle tobe monitored is identified, the descriptor type, and an appropriate map isdesignated to map all values of the descriptor type to a discrete numericalvalue.

Descriptor value or The discrete numerical value returned from the application of a specific descriptordescriptor state to a peptide structure.

Classification scheme An ordered set of descriptors that are to be applied to a peptide structure todiscriminate between different conformations.

Descriptor value set An ordered set of descriptor values containing the results, of application of eachdescriptor described in the classification scheme to a peptide structure.

Conformational state A peptide conformational state is identified by a distinct set of descriptor values.State identification number or A unique numeric identifier assigned to each conformational state. Each new state

state id observed is given a unique numeric identifier.Known states database A database that contains a set of previously observed set of conformations. Each

identified by a unique state id, descriptor value set, and containing arepresentative structure for each chemical system investigated.

Conformational difference A measure of the difference between two conformational states.Chemical system A distinct environment or peptide chemical modification used in the analysis.

Many different chemical systems can share the same set of known statesdatabase.

FIGURE 1. Methodology: this diagram shows the classification of a pyro-EEDCK trajectory in vacuo using the PEPCATmethodology. A trajectory consists of a time sequenced set of peptide coordinates (bottom right). Each frame isclassified using a set of user specified descriptors (top right), and the set of values is looked up in a database of knownstates (left). If the set of descriptor values is not found in the database, a new entry is created. The conformational stateidentifier is returned (left) and stored with the frame. See text for more detail.

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FIGURE 2. Descriptor types: the currently supporteddescriptor types are: (a) a φ–ψ map region; (b) adihedral angle; and (c) a distance between two atoms.Each of the descriptors map every possible value to adiscrete, numerically identified state. The number ofstates and map structure are not limited to the rangesshown here, and can be altered by the user. Theexamples shown here can be used to: distinguishbetween four φ–ψ conformations of a residue (a);identify the cis or trans state of a peptide bond (b); andidentify contact, close or no contact between twoatoms (c).

maintain a database of all observed peptide confor-mations.

The known conformation database is initiallyempty, but as new conformational states are identifiedin the classification procedure, entries are appendedto the database to describe these new states. Eachnew state is assigned a unique state identificationtag (state id), and a new database entry is written.A conformational state database entry contains theunique state id, the distinct descriptor value set de-scribing the state, and the coordinates of a referencepeptide structure occupying the state.

As PEPCAT classifies each peptide structure us-ing the classification scheme the resulting descriptorvalue set is searched for in the database of knownconformations. If the descriptor value set (i.e., a par-ticular conformation) does not already exist in thedatabase, a new state id is generated and a new data-base entry is written, with the state id, the definingdescriptor value set, and the coordinates of the currentstructure, stored as the reference structure. The newstate id is then returned from the classification proce-dure. Otherwise, if the descriptor value set was foundin the database then the database entry matchingthe found descriptor value set is examined. If the en-

ergy value of the current structure is less than theenergy value of the reference structure, then the ref-erence structure in the database is replaced by thecurrent structure. The state id of the found databaseentry is then returned from the classification proce-dure.

The comparison of the energy values ensures thatthe reference structure for each state has the lowestenergy for all structures in this state, that have beenexamined to date.

As peptide structures are classified under a va-riety of conditions, for example, different environ-ments, etc., the data in the known conformationdatabase is held at two levels. The first level iden-tifies the conformational state, and contains the stateid and the descriptor values set that describes thestate. At the second level, each chemical system hasstored its own separate and distinct minimum en-ergy value and representative structure for each ofthe known conformational states. In this way theconformational state identifiers and descriptors can beshared among any number of investigated chemicalsystems and comparisons between different chemicalsystems are simplified.

For each chemical system a database of mini-mized conformational structures is maintained inaddition to the database of reference structure, anda link is maintained from the reference structure tothe minimized reference structure. After classifyinga large number of structures, the database of knownstates is subjected to a clean-up step. Every new orchanged chemical system reference structure is sub-jected to an energy minimization, and the databaseof minimized conformations is updated. These min-imized structures are then reevaluated using theclassification procedure, and the resulting state id isstored with the minimized reference structure. Thisreprocessing of reference structures helps ensurethat low-energy values are used for the referencestructures. Sometimes a high energy conformationalstate will, after minimization and classification, re-sult in a state different from the original structure.Where this occurs, the stored link from the originalclassification to the new classification can be used toidentify the new state achieved upon minimizationof the reference structure. In this way both the orig-inal state and the minimized state are available forreference in further analysis.

COMPARISON

The conformational difference1 between two statesA and B is determined by the differences in their


O’DONOHUE ET AL.

descriptor value sets and is calculated as follows:

1 =√√√√ n∑

i= 1

δ(A[i], B[i]

)2 (1)

where

δ(a, b) ={

0, if a = b1, else.

where A = (A[1], . . . , A[n]), B = (B[1], . . . , B[n])are descriptor value sets; A[i], B[i] are descriptorvalues of the descriptor i; and n is the number ofdescriptors in the classification scheme. The square ofthe result of the comparison function δ is actuallyredundant for the current choice in eq. (1), but is rel-evant if modifications are made to the function δ.

TRAJECTORY ANALYSIS

PEPCAT processes molecular dynamics trajecto-ries to produce a new much smaller trajectory file.Each frame of the original trajectory is classifiedusing the classification procedure, and an entry isappended to the new trajectory file containing twoidentifiers the state id, and the original frame energyvalue.

VISUALIZATION

The new trajectory file format can easily be sub-jected to further analysis techniques. Two reportsare currently available within PEPCAT.

The conformational population distribution re-port (see Fig. 3) displays the percentage of the

trajectory frames occupying each conformation state.The conformational state value of each frame in oneor more new format trajectories is counted, and thedistribution of occupation of each conformation inthe database of known states is displayed in bargraph form.

The conformation transition map (Figs. 4, 5, and9) is a visual map of the conformational changesthat occur during the course of a dynamics trajec-tory. The new PEPCAT formatted trajectories con-tain a time sequenced set of states id numbers andtheir energies. These are used to build a directedgraph of conformational states, which connects twoconformational states between which a transitionwas observed. This graph is then mapped ontoa two-dimensional surface.22 The resulting layoutprovides a simple picture of the often complex rela-tionships between the different conformational states.

COMPUTATIONAL DEMANDS

The CPU time demands for the classification of asingle frame depends upon the number of descrip-tors that are being monitored. A typical analysisrequires one descriptor per protein residue, and isconstant for any given classification scheme. Thetime taken to classify a single frame does increaseslinearly with the length of the peptide being ana-lyzed. However, even for proteins of several hun-dred residues length, classification takes less than asecond of CPU time, and this is still much less thanthe time required to perform the overlay operationrequired by RMSD-based techniques.

FIGURE 3. Conformation distribution: the occupancy of all conformational states for the trajectory can be calculated(although only four are shown). The report displays for each state, the number of frames occupying each conformation,as a percentage of the total trajectory frames (on left) and in a bar graph form (on right). The mean energy and standarddeviation for each state is printed along with a small graphical display of the energy distribution (on right).

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FIGURE 4. Pyro-EEDCK in vacuo transition map: a conformational transition map analysis for a simulated moleculardynamics trajectory of pyro-EEDCK performed in vacuum. Each state visited during the trajectory is represented by acircle, with an area proportional to the number of occurrences of the state in the trajectory. The state is identified by itsstate id, in bold type, and in a slightly smaller font, the defining set of descriptor values is also shown. The state’s graycolor shade identifies the minimum energy value. The lines between conformations show the conformational transitionsthat occurred in the trajectory. The arrowhead identifies the direction of the transition and its width proportional to thenumber of transitions that occurred.

The use of a more finely graded grid size for thedescriptors has no effect on the CPU time required.Because the time taken to classify a single frame isconstant, the time required analyzing a dynamicstrajectory grows linearly with the number of framesin the trajectory.

However, although there is no detrimental ef-fect on CPU time, the use of finer graded grids andthe analysis of larger molecules with more descrip-tors does have an exponential effect on the potentialsize of the known states database. The exact choiceof descriptor grid size and simulation temperatureare important factors in determining the numberof states visited in molecular dynamics trajecto-ries and, consequently, the size of the known statesdatabase. The size of the database is important indetermining the CPU times required for some of theanalysis procedures.

The CPU time required to produce the displaysgenerally has two components: the generation of acomparison matrix, which grows quadratically withthe number of distinct states (which is much less

than the number of trajectory frames, and hopefully,much less than the potential number of states), andthe creation of the displays and reports, which growlinearly with the number of frames analyzed.

For example, using a Pentium II 400 MHz run-ning the Linux operating system on data sets thathave less than 10 descriptors and less than 1000states (i.e., data sets of a similar size to those usedin this article), trajectories of 200 frames are classi-fied in minutes, and the analysis procedures takeless than 10 min CPU time. Increasing the num-ber of descriptors to 2000 increased the CPU timeto process a 200 frame trajectory to approximately10 min. The time taken to perform the analysis rou-tines is independent of the number of descriptors,but is dependent upon the size of the database ofknown states. The largest database we have builtso far contains 7300 states, and the calculation ofa combined transition map for 336,000 frames in atrajectory takes approximately half an hour of CPUtime.


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FIGURE 5. Pyro-EEDCK in solution transition map:a conformational transition map analysis for a simulatedmolecular dynamics trajectory of pyro-EEDCKperformed in explicit simulated water. See Figure 4 tocompare with a similar analysis performed for an invacuo simulation, and also see the Figure 4 caption for adescription of the diagram components.

Results

In this section the use of the PEPCAT methodis demonstrated with two examples: an analysis ofthe conformational space for pyro-EEDCK, and aconformational transition in cyclosporin A. WherePEPCAT specific terminology has been used, it hasbeen italicized in the text and is described in Table I.For a description of these terms and further detailsof the PEPCAT method, please consult the methodssection of this article.

PEPCAT ANALYSIS OF PENTAPEPTIDEPYRO-EEDCK

The pyro-EEDCK monomer inhibits hematopoi-etic stem cell proliferation of colony stimulationunits in the S state (CFU-S) by maintaining themin a quiescent state while they are exposed to theradiation or cytotoxic drugs used during cancertherapy. The acute and chronic bone marrow tox-icities are the major limiting factors in oncology.The acute effects include neutropenia and throm-bopenia by increasing patient susceptibility to in-fections and hemorrhage. They interfere with thetreatment and limit its therapeutic effects.23 – 25 Pyro-EEDCK appears to be a candidate drug for cancertreatment having a physiologic role for the pro-

tection of the hematopoietic system. Conservativechanges to the chemical sequence as in: EEDCK,pyro-EDDCK, pyro-EEDMK, and pyro-EEDSK, re-duce or destroy the inhibitory properties of thispeptide.24 Pyro-EEDCK-like sequences have beenidentified in the Giα chains of GTP-binding proteinsat position 63–67, proximal to the major phospho-rylation site.24, 26 Oxidation of the cysteine thiolgroups of pyro-EEDCK can lead to formation ofa disulphide-bridged homodimer (pyro-EEDCK)2

which, unlike the monomer, is a potent stimulatorof hematopoiesis.27

Molecular Dynamics Calculations

A number of molecular dynamics simulations ofpyro-EEDCK were performed. A 400-ps simulationwas carried out at a temperature of 300 K in vacuo,with a dielectric constant of 10 using the programDiscover (Molecular Simulations Inc., San Diego,CA). The CFF91 force field28 was used with a sim-ulation timestep of 1 fs and interatomic interactionswere reduced to zero using a switching algorithmfor atom pair distances between 8.5 and 13.0 Å andinteractions over 13 Å were ignored. At 2-ps inter-vals the coordinates were written to a trajectory file.Additional dynamics simulations of pyro-EEDCKwere calculated at a variety of temperatures from300 to 1000 K, for time periods ranging from 200 psto 2 ns. These calculations used the same proto-col except that at 2-ps intervals a 300-cycle energyminimization was performed before the frame waswritten to the trajectory file.

Molecular dynamics simulations of pyro-EEDCKwere also performed in explicit water. A singlemolecule of pyro-EEDCK was placed at the centerof a cubic box with side length of 27 Å, which wasthen filled with CFF9128 (Molecular SimulationsInc.) water molecules using the Insight II package(Molecular Simulations Inc.). Simulations were thenperformed using the Discover program as with thein vacuo calculations described above, except that adielectric of 1 was used and periodic boundary con-ditions were applied.

Using the same set of protocols, the confor-mational properties of peptides closely related topyro-EEDCK were also investigated using molec-ular dynamics in both in vacuo and solvated en-vironments. Modifications included simple residuesubstitutions and deletions, namely EEDCK, pyro-EDDCK, pyro-EEDMK, pyro-EEDSK, and extendedpeptides SEEDCKN and YSEEDCKNY as found inthe Giα protein sequence.

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Classification

Classification of the pyro-EEDCK and relatedpeptides makes use of the φ–ψ map descriptor type(see Fig. 2a). The descriptor used maps the φ–ψregion into four different numerical values, corre-sponding to the four quadrants of the φ–ψ plane.This partition scheme was suggested by an analysisof the distribution of φ–ψ dihedrals during initialcalculations.

The classification scheme for identifying pyro-EEDCK conformations (see Fig. 1) is based on φ–ψmap regions for the three central residues of pyro-EEDCK, namely Glu2, Asp3, and Cys4. These threeresidues form the descriptor set that defines the clas-sification scheme. For example, the notation, or de-scriptor set (2,3,1) would describe a conformationwhere the Glu2 (φ,ψ) conformation would be foundin the upper left quadrant of the Ramachandranplot, Asp3 in the upper right and Cys4 in the lowerleft quadrant.

Analysis

To illustrate the main steps of a PEPCAT analy-sis, we will discuss the analysis of a pyro-EEDCKdynamics simulation trajectory data file in detail.We assume that other trajectories for pyro-EEDCKhave been processed previously, and a database hasbeen populated with the states found in these tra-jectories. Before processing this particular dynamicstrajectory the database is loaded (see table on the leftof Fig. 1). Each entry in the known states databasecontains the states identification number (state id),with their classification descriptor set and a represen-tative coordinate structure. The input trajectory isthen processed one frame at a time (bottom right ofFig. 1). In Figure 1 the processing of frame 5 from thetrajectory is depicted. Prior to this, frames 1 to 4 willhave already been processed. The fifth frame in thetrajectory (see bottom right of Fig. 1) is categorizedaccording to the classification scheme (see top rightof Fig. 1), which results in a descriptor set of (1,1,2)(see center right of Fig. 1). This set (1,1,2) is thenused to search through the database of known statesand it is identified as conformational state 32 (seebottom left of Fig. 1). Frame 5 has, therefore, beenidentified as conformational state “32.” Because thestate already exists, the peptide structure in frame 5is compared to the reference structure for the state32, and replaces the database reference structure forstate 32 if it has a lower energy value. This com-pletes the processing of frame 5.

Alternatively if we assume that state 32:(1,1,2)does not yet exist in the database and the known

states database only contains states 0–31 [whichwould occur if this is the first time that the (1,1,2)structure has been observed], then the databasesearch using the frame 5 descriptor set (1,1,2) wouldnot have found a match. Thus, a new pyro-EEDCKconformational state would have been identifiedand new database entry would be created to de-scribe this new conformation. The new entry wouldbe assigned the next state id number (32), have thedescriptor set (1,1,2) and a reference structure takenfrom frame 5. The entry would be appended to thedatabase of known states effectively creating thestate 32 as observed in Figure 1.

Processing then continues through the rest ofthe frames in the trajectory (not shown here). Atthe completion of a trajectory analysis the updateddatabase of known pyro-EEDCK states is saved anda simplified trajectory containing only the state idand energy value for each frame are written to a file.The database of known states is then subjected toa minimization clean-up step (see the Methods sec-tion). The cleaned up database and the new trajec-tory file can now be used as input for the standardPEPCAT reporting routines. Figure 3 shows the con-formational distribution report that was producedfor all observed states; however, only the four mostpopulous states are shown here.

Comparison

The comparison procedure is described in theMethods section above, and makes use of a math-ematical function δ(x, y) which yields 0, if x = y andotherwise 1. For example, the “conformational dif-ference” 1 between state 0:(2,2,2) = (a1, b1, c1) andstate 1:(2,1,2)= (a2, b2, c2) is calculated as follows:

1 =√δ(a1, a2)2 + δ(b1, b2)2 + δ(c1, c2)2

= √0+ 1+ 0= 1 (2)

Similarly, for the states 0:(2,2,2) and 5:(1,1,2)1 = 2,quantifying the concept that states 0 and 1 are moresimilar to each other than states 0 and 5. A table canbe built up by applying the comparison procedureto all the known states, and these data can be usedfor further analyses.

Results

The analyzed trajectory file used in our exam-ple of pyro-EEDCK in vacuo at 300 K contained 14distinct pyro-EEDCK conformational states out ofthe 64 possible descriptor set conformations. State 0,


O’DONOHUE ET AL.

with an extended beta structure (2,2,2), was by farthe most preferred conformation (34%), and thisstate, together with the next three most populousstates 20:(2,1,2), 32:(1,1,2), and 33:(2,1,1), accountedfor almost 90% of the frames in this trajectory (seeFig. 3).

PEPCAT can also be used to visualize the path-ways traversed between the conformations ob-served during the dynamics simulation. Figure 4shows such a transition map display. The area ofeach circle represents the frequency of occupationof the state. The large circles representing the states0, 20, 32, and 33 easily identify them as the fourmajor conformations. Transitions between states areshown as arrows where the width of the arrowhead is proportional to the number of transitionsobserved. For example, there is a high fluctuationbetween states 0 and 30. Both states have a similarenergy, as indicated by the color of the circles. Stateswith lower energy are colored dark gray, states withhigher energy are shown in light gray. Not sur-prisingly, states with highest energy (white) are notvisited very often. Some of the remaining 11 statesreached during the molecular dynamics are inter-mediates on a pathway between two major states(see states 16, 24, and 47 in Fig. 4). Other states arehigher energy variants of one of the major states,which were occupied for brief periods of time be-fore returning to one of the major states (see states4, 45, 28, etc., in Fig. 4).

When simulations were performed in vacuo atincreasingly elevated temperatures the populationsof the major states declined as the temperatureincreased, and small populations of additional con-formational states were observed. Eventually, at1000 K transient populations of all 64 possible stateswere observed during 20-ns simulation runs. Evenat these greatly increased temperatures the low-energy conformations preferred at lower tempera-tures were still among the most populated (Table II).

Modification of the sequence or side chains andextension of the N- or C-terminus did not signif-icantly alter the conformational preferences of thecentral residues from those preferred for the wild-type pyro-EEDCK molecule. This was also true withsimulations at a variety of temperatures between300 and1000 K.

When the simulations were performed in a boxof water, with periodic boundaries, there was adramatic effect on the conformational preferencesof pyro-EEDCK (see Fig. 5). A new preferred con-formational state, 24:(2,3,2) was observed and thisoccupied 47% of the frames in the trajectory. Again,a large percentage (91.5%) of the trajectory was oc-

TABLE II.The Four Most Populated States for VacuumSimulations of pyro-EEDCK at DifferentTemperatures.

Occupancy (%)

State Description At 300 K At 1000 K

0 (2,2,2) 34 13.732 (1,1,2) 26.4 4.420 (2,1,2) 21.3 8.033 (2,1,1) 8.5 3.8

cupied by the top four states, 24:(2,3,2), 47:(2,4,2),25:(2,3,1), and 16:(1,2,2) (Table III), but these weredifferent conformational states from those preferredin the previous in vacuo calculations (see Fig. 6).Visual inspections of the conformations preferredin water (see bottom of Fig. 6) shows an orienta-tion that maximizes the exposure of the significantlycharged atoms found in the backbone side chain tothe solvent water, with a small cluster formed by theweakly charged atoms in the pyro-Glu1 and Cys4residues.

PEPCAT ANALYSIS OF CYCLOSPORIN

Cyclosporin A (CsA) is an 11-residue cyclic pep-tide used as an important therapeutic agent for theprevention of graft rejection in clinical organ trans-plantation. Its amino acid sequence MeBmt-Abu-MeGly-MeLeu-Val-MeLeu-Ala-(D-Ala)-MeLeu-MeLeu-MeVal, contains two uncommon aminoacids: (4R)-4-((E)-2butenyl)-4, N-dimethyl-L-thre-onine (Bmt) and L-α-aminobutyric acid (Abu). Ithas several N-methylated residues (residues 1, 3, 4,6, 9, 10, and 11)29 indicated by the “Me” prefix in thesequence above. CsA binds to a receptor cyclophilin(Cp) and induces an interaction between the CsA–Cp complex and the phosphatase calcineurin.30 The

TABLE III.The Four Most Populated States for Simulation ofpyro-EEDCK with Explicit Water.

State Description Occupancy (%)

24 (2,3,2) 4747 (2,4,2) 1725 (2,3,1) 1516 (1,2,2) 12.5

456 VOL. 21, NO. 6


FIGURE 6. pyro-EEDCK conformations: twopyro-EEDCK conformations with atoms shadedaccording to their atomic partial charge between −0.5and +0.5. The top figure is the reference structure forstate 0:(2,2,2) which forms an extended structure and isthe preferred conformation (with 37%) in the in vacuosimulations. The bottom conformation is the referencestructure for state 24:(2,3,2), which is the preferredconformation for the peptide in water. It adopts aconformation that maximizes the exposure of thesignificantly charged atoms of both the backbone andside chains to the solvent.

complex inhibits the signal transduction pathwaysthat lead to T lymphocyte activation.31

The conformation of unbound (“free”) CsA in anonpolar solvent (Fig. 7a) varies considerably fromthe conformation of CsA that is bound to its recep-tor Cyclophilin (Fig. 7c). The dominant hydrophobiccluster formed by the side chains of four residuesMeBmt-1, MeLeu-4, MeLeu-6, and MeLeu-10 is nowlocated on the opposite side of the molecular ringplane. In addition, the peptide bond at residue Leu9changes from cis in the free conformation to trans inthe bound conformation. In short, the molecule hasbeen turned inside out.32

Molecular Dynamics Calculations

The coordinates of free CsA in CCl4 solutionwere obtained from the NMR structure deposited inthe Cambridge Crystallographic Databank33 (access

FIGURE 7. CsA conformations: conformations of CsAfound in the dynamics calculation. From top to bottom,(a) the unbound (“free”) conformation of CsA, (b) oneintermediate conformation observed in a moleculardynamics simulation, and (c) the “bound” conformationof CsA. These conformations have been classified (seethe text for details) as states 0:(1,1,1,1,0,1),29:(2,1,0,2,0,0), and 36:(2,2,2,2,0,0), respectively.

code: DEKSAN34). The coordinates for the boundconformation were obtained from the X-ray struc-ture of the CsA-Cp complex35, 36 (Brookhaven Pro-tein Databank37 access code: 1CWA).

The molecular dynamics trajectory that is usedas the basis for the PEPCAT analysis describedhere was reported by O’Donohue et al.38 for an in-vestigation of conformational changes in CsA. Thetrajectory monitors the transition from a free CsAconformation in vacuo at 600 K through a num-ber of conformational changes to a structure nearlyidentical to the bound conformation (backbone RMSdeviation of 0.53 Å). The simulation was performedusing the program XPLOR10 with the CHARMM22force field.39

Classification

The classification scheme employed here for CsAconformational analysis makes use of an angle de-scriptor type (see Fig. 2b) to monitor the angle thata side chain makes relative to the plane defined by


O’DONOHUE ET AL.

FIGURE 8. CsA classification: the PEPCAT classification scheme used for CsA monitors the orientation of thesidechain relative to the backbone ring plane of the four resides that form the dominant hydrophobic cluster. The twopeptide bonds MeGly-3 and MeLeu-9 are also monitored, as they are known to have been observed in both cis andtrans orientations. See text for details.

the ring of backbone atoms in the cyclic molecule.This angle is monitored for all four side chains ofthe dominant hydrophobic cluster (see above), andis approximated by a dihedral angle defined by thefollowing four atoms: the Cβ and Cα atom positionsof the residue whose side chain we wish to monitor;the Cα atom position in the residue of the dominantcluster that is closest in the ring plane; and a Cα

atom position in a residue of the cluster on the otherside of the ring plane. The angle map value is classi-fied into three regions: region 0, parallel to the plane(value between −30◦ and +30◦); region 1, above theplane (value > 30◦); and region 2, below the plane(value < −30◦) (see Fig. 8a). Four descriptors are re-quired to monitor the relative side chain positionsfor each residue in the hydrophobic cluster. The de-tailed definition of the descriptors, i.e., the atomsthat make up the angle descriptors are: Descriptor 1:Bmt1 (Cβ1, Cα1, Cα10, Cα6); Descriptor 2: MeLeu4(Cβ4, Cα4, Cα6, Cα10); Descriptor 3: MeLeu6 (Cβ6,Cα6, Cα4, Cα1); and Descriptor 4: MeLeu10 (Cβ10,Cα10, Cα1, Cα4).

In addition to the four side chain orientations,ω-dihedral angles of two peptide bonds are alsomonitored using a angle descriptor type. Here, the an-gle map value is divided into two regions: region 0(value between−90 and+90) identifies a cis confor-mation and region 1 (value larger than +90 or lessthan −90), which corresponds to the trans confor-mation (see Fig. 8b). The MeLeu-9 peptide bond ismonitored, as it differs in the bound and free con-formations. The MeGly-3 peptide bond is monitoredas it has been found in a cis conformation in a CsAanalogue.40 The two peptide bonds descriptors are:Descriptor 5: Gly3 ω dihedral angle (Cα3, C3, N4,

Cα4); and Descriptor 6: Leu9 ω dihedral angle (Cα9,C9, N10, Cα10).

These six descriptors make up the classificationscheme used for the analysis of CsA conformations(see Fig. 8c).

Results

The free CsA conformation, which correspondsto conformational state “0,” has a descriptor valueset of (1,1,1,1,0,1). This conformation has all fourdominant hydrophobic side chains sitting abovethe molecular ring plane, a trans peptide bondfor MeGly-3, and a cis peptide bond for MeLeu-9.The bound CsA conformation corresponds to state36:(2,2,2,2,0,0), where all four side chains sit be-low the backbone ring plane, and MeLeu-9 has atrans peptide bond. Figure 9 shows the transitionmap diagram produced by PEPCAT. We can clearlysee transition pathways from the free conforma-tion (state 0) to the bound conformation (state 36),through a highly populated intermediate conforma-tion (state 29).

The lowest energy pathway from the free to thebound conformation of CsA is (see Fig. 9): state0:(1,1,1,1,0,1)—“free” conformation; state 2:(1,1,1,1,0,0); state 21:(1,1,1,0,0,0); state 29:(2,1,0,2,0,0)—“in-termediate” two side chains flipped and one inthe ring plane; state 35:(2,0,2,2,0,0); state 36:(2,2,2,2,0,0)—“bound” conformation.

The first major change in the free conformation(state 0) is the transition to state 2:(1,1,1,1,0,0) wherethe MeLeu-9 cis peptide bond has been lost. Inthe move to state 21:(1,1,1,0,0,0), the MeLeu-10 sidechain repositions itself parallel to the backbone ringplane. Then the transition to the highly populated

458 VOL. 21, NO. 6


FIGURE 9. CsA conformational transition map: this diagram displays the transitions between the conformations ofCyclosporin A found during the trajectory analysis. Several pathways can be seen from the “free” conformation (state 0)to the “bound” conformation (state 36). A stable intermediate conformation (state 29) was also found (see text for moredetails).

intermediate state 29:(2,1,0,2,0,0) involves the rota-tion of both MeBmt-1 and MeLeu-10 side chainsaround the outside of the ring plane to a positionbelow the backbone ring plane and the MeLeu-6side chain moving to an orientation parallel to thering plane. In the move to state 35:(2,0,2,2,0,0), theMeLeu-6 side chain now occupies a position belowthe ring plane, and the LEU-4 side chain is nowparallel to the ring plane. In the final transition tostate 36:(2,2,2,2,0,0) the MeLeu-4 side chain joins theother three dominant hydrophobic side chains be-low the backbone ring plane.

An alternative higher energy pathway for thetransition from state 0 to the highly populatedstate 29 can also be observed (see Fig. 9) via state23:(0,1,0,1,0,0), where the cis peptide bond is lostand the BMT-1 and LEU-10 side chains are paral-lel to the ring plane. The next steps along the pathare state 24:(0,1,0,0,0,0), where the LEU-6 side chain

has also moved into the ring plane, and then state29:(2,1,0,2,0,0). CsA can be divided into two regions(Leu10–Abu2, and Gly3–Leu9) roughly comprisingthe two halves of the molecular ring with flexiblehinge regions at Gly3 and Leu9.38 The intermedi-ate state 29 (see Fig. 9) has one region Leu10–Abu2that has flipped into a backbone conformation simi-lar to that of the bound conformation, while the tworemaining monitored hydrophobic residues Leu10and Bmt1 have remained in the configuration foundin the free conformation (see Fig. 7b). The high pop-ulation in Figure 9 is an indication of the stability ofthis state, as identified earlier.38

Interestingly, no pathway could be observedwhere one side chain alone flipped to the other ringplane to initiate the transition from the free to thebound CsA conformation. A cooperative change ofat least two side chains seems to be required.


O’DONOHUE ET AL.

Discussion

As demonstrated by the two examples, the PEP-CAT method is simple and allows the user to relateconformational states to changes in real conforma-tional properties of the molecule. It is computation-ally economical to perform, and the results of theconformational trajectory analysis can be displayedin a succinct, visual, and informative manner.

CLASSIFICATION

The classification step provides a powerful andflexible tool kit to identify related structures. Con-formational analysis is performed in a relativelysmall discrete solution space compared to thevery large atomic coordinate space. Conformationalstates can be defined in accordance with the user’srequirements based on (generalized) dihedral an-gles, φ–ψ regions or interatomic distances (seeFig. 2). Residue–residue distance measurements(Fig. 2c) for example, could be used to define a con-formational state based on a residue contact map.Other classification features can easily be includedin future versions of PEPCAT.

The choice of grid size used for the descriptorsin the classification scheme play an important partin determining the potential and actual sizes of thedatabase of known states. A finer grid size will im-ply a larger potential number of known states, andparticularly for the analysis of flexible molecules atelevated temperatures, more of these states will befound in the trajectory data files. The exact choice ofdata grid size used for each descriptor should, there-fore, be made with some consideration.

The conformational identity is not necessarily re-stricted to structures that share the same aminoacid sequence, as indicated in the analysis of thefamily of peptides related to pyro-EEDCK. The abil-ity to specify separate descriptors for each differentchemical composition and to map them to a shareddatabase of known states is helpful in this process.

COMPARISON

The comparison method returns a value thatreflects a generalized distance between conforma-tions, and gives meaningful results even for struc-tures that are not very similar. The simple compari-son procedure described here makes three assump-tions: (i) that all possible changes in a measurementvalue have the same level of significance, i.e., a de-scriptor is either the same or different; (ii) that eachdescriptor is independent from other descriptors;

and (iii) that all descriptors have the same rank-ing of importance. It is easy to incorporate mod-ifications such as returning a range of values formeasurement differences, or scaling a particular de-scriptor to emphasize a particular feature.

TRAJECTORY ANALYSIS

The PEPCAT trajectory analysis provides a com-pact representation of the trajectory data file, andextracts information about conformational stateconnectivity directly from the trajectory. It does notrequire N2 comparisons for N frames, and easily al-lows the incorporation of additional data from newtrajectory profiles.

If the dynamics of conformational transitionsneed to be analyzed, it is important that the con-formational state of the system does not undergomore than one change per frame in the trajectory. Ifthe time step with which frames are stored is longerthan the time taken for a single transition, multipleconformational changes can occur within one timestep, resulting in a distorted conformational transi-tion map. The data obtained from such trajectoriescan still be processed, for example, in a popula-tion analysis (see Fig. 3). Analysis of time sequencedevents, however, has been compromised. This prob-lem could also be solved by the inclusion of certainfeatures into the dynamics calculations. A first fea-ture is to record the highest energy value foundbetween two frames that are stored in a trajectory.A second more radical change would be the inclu-sion of the classification procedure into the molecu-lar dynamics program, so that structures could beanalyzed and classified within the dynamics pro-gram at the much finer scale of each calculation timestep.

OTHER APPLICATIONS

In addition to the analysis of molecular dy-namics simulations, our technique could also beapplied to other analytical procedures. Conforma-tional search procedures using simulated annealing,Monte Carlo, genetic algorithms, and ligand dock-ing methods could benefit from application of ourtechnique. In the construction and assessment ofprotein prediction procedures there is often a needto compare a large number of predicted structuresagainst a standard target structure. PEPCAT canbe used to measure the structural diversity of theprediction coverage and to assessing the closenessof each predicted structure to the standard struc-ture. QSAR methodologies designed to incorporate

460 VOL. 21, NO. 6


conformational properties could also employ ourmethodology, because QSAR descriptors could beincorporated in a PEPCAT classification scheme.

Further information, program source code, andaccess to on-line analysis using the PEPCAT serverare available from the PEPCAT web site at: http://www.ludwig.edu.au/pepcat/index.html.

Acknowledgments

We would like to thank Nicos A Nicola (fromthe Walter and Eliza Hall Institute of Medical Re-search) for suggesting the studies based on thepyro-EEDCK peptides and ongoing discussion. Inaddition, we would like to thank Leo Groenen, TranTrung Tran, David Smith, Robert Jorissen, NathanHall, and Jun Zeng for many helpful discussions inthe development of PEPCAT.

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