Journal of Structural Biology 173 (2011) 436–444

Contents lists available at ScienceDirect

Journal of Structural Biology

journal homepage: www.elsevier .com/ locate/y jsbi

Modeling pilus structures from sparse data

Manuel Campos a, Olivera Francetic a, Michael Nilges b,⇑a Institut Pasteur, Unité de Génétique moléculaire, CNRS URA 2172, Département de Microbiologie, 25 rue du docteur Roux, F-75015 Paris, Franceb Institut Pasteur, Unité de Bio-informatique structurale, CNRS URA 2185, Département de Biologie Structurale et Chimie, 25 rue du docteur Roux, F-75015 Paris, France

a r t i c l e i n f o a b s t r a c t

Article history:Available online 27 November 2010

Keywords:Molecular modelingPilus assemblyProtein secretionCysteine cross-linking

1047-8477/$ - see front matter � 2010 Elsevier Inc. Adoi:10.1016/j.jsb.2010.11.015

⇑ Corresponding author.E-mail address: michael.nilges@pasteur.fr (M. Nilg

Bacterial Type II secretion systems (T2SS) and type IV pili (T4P) biogenesis machineries share the abilityto assemble thin filaments from pilin protein subunits in the plasma membrane. Here we describe indetail the calculation strategy that served to determine a detailed atomic model of the T2SS pilus fromKlebsiella oxytoca (Campos et al., PNAS 2010). The strategy is based on molecular modeling with general-ized distance restraints and experimental validation (salt bridge charge inversion; double cysteine sub-stitution and crosslinking). It does not require directly fitting structures into an envelope obtained fromelectron microscopy, but relies on lower resolution information, in particular the symmetry parametersof the helix forming the pilus. We validate the strategy with T4P where either a higher resolution struc-ture is available (for the gonococcal (GC) pilus from Neisseria gonorrhoeae), or where we can compare ourresults to additional experimental data (for Vibrio cholerae TCP). The models are of sufficient precision tocompare the architecture of the different pili in detail.

� 2010 Elsevier Inc. All rights reserved.

1. Introduction

Type IV pili (T4P) and type II secretion systems (T2SS) are mem-bers of a superfamily of filament biogenesis machineries that sharea common origin with achaeal flagella and pili (Ng et al., 2006;Hansen and Forest, 2006). They assemble thin flexible filamentsusing a highly conserved basic machinery consisting of a polytopicinner membrane protein, a cytoplasmic ATPase and a prepilin pep-tidase enzyme involved in pilin maturation. T2SS and T4P pilinsubunits typically have a conserved N-terminal amino acidsequence in an extended a-helix that mediates filament assembly(Craig et al., 2003). The amino acid sequences of the C-terminalglobular domains are much less well conserved among T4P andT2SS pilins and are responsible for the pilus functions. The molec-ular structures of these filaments are of great interest due to theircentral role in bacterial pathogenesis and their attractiveness astargets for vaccines and therapeutics. However, they are difficultto study at atomic resolution, due to the insolubility of the pilinprotomers, and due to the fact that they readily assemble into het-erogeneous and flexible pilus filaments. The molecular structuresof these pili could provide important insights into the mechanismsof their assembly and function.

The method of choice to study the structure of the pili at atomicdetail would be high resolution determination of the protomers(the pilins) combined with cryo-electron microscopy of the assem-bly. Several high resolution structures of T4P or T2SS pilin subunits

ll rights reserved.

es).

or subunit fragments have been obtained by X-ray crystallographyand nuclear magnetic resonance spectroscopy (Audette et al.,2004; Craig et al., 2003, 2006; Hazes et al., 2000; Keizer et al.,2001; Parge et al., 1995; Ramboarina et al., 2005; Xu et al., 2004;Korotkov et al., 2009; Köhler et al., 2004). Only one structure ofan intact type IV pilus filament has been determined to date bycombined X-ray crystallography and cryo-electron microscopy(cryo-EM) reconstruction the gonococcal (GC) pilus from Neisseriagonorrhoeae (Craig et al., 2006).

The cryo-EM study of the GC pilus resulted in a 12.5 Å resolu-tion map of the pilus (Craig et al., 2006), a resolution much toolow to obtain atomic detail. However, by fitting an atomic modelof the individual components into the EM reconstruction, a pseu-do-atomic model can be obtained, thereby effectively bridgingthe different resolution ranges (Rossmann et al., 2005; Volkmannand Hanein, 2003). In the case of the GC pilus (Craig et al., 2006),symmetry reduced the number of possible arrangements withinthe EM surface sufficiently to obtain a unique arrangement of pro-tomers. The structure is based on a computational docking proce-dure using rigid body operations only, assuming that the pilinstructure is influenced neither by the packing in the crystal norin the pilus. Considering the overall nonglobular structure of thepilin (a globular head with a long N-terminal hydrophobic helix),this is a strong assumption.

We describe here an alternative strategy, which is not based ona cryo-EM map of the molecular complex, but on quantities thatcan be obtained with fairly high confidence from lower resolutionEM studies (the symmetry of the helix), on conformational re-straints and on molecular modeling. The restraints can either serve

M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444 437

to bias the conformational docking and to limit the conformationalspace, or to evaluate and select models from unbiased calculations.In the current study, the restraints are assumed to be derived frommutation experiments (salt bridge charge inversion; double cys-teine substitution and crosslinking), but distance restraints couldcome from a variety of other experiments that could be appliedto this non-soluble system (FRET, solid state NMR). The helical piliare highly symmetrical, and all distance data present an ambiguitysimilar to that observed for NMR data of symmetric systems inliquid or solid state (Nilges et al., 2010). That is, since it is unknownhow the subunits are arranged in the pilus before its assembly isdetermined, it is a priori impossible to assign an interaction specif-ically to two subunits.

For NOE derived distance restraints for small symmetric assem-blies, we developed a concept that allows the use of ambiguousdistance data, the ambiguous distance restraint (ADR) (Nilges,1993; Bardiaux et al., 2009). This restraint can be used in the sameway as standard distance restraints during a structure calculation.Its use circumvents the necessity to explicitly assign the restraintto two unique atoms. The principal use of ambiguous distance re-straints is automated structure determination from NMR data (seeNilges and O’Donoghue (1998), Altieri and Byrd (2004), and Günt-ert (2009) for reviews). Several software packages (Linge et al.,2001; Herrmann et al., 2002) use the concept of ambiguous dis-tance restraints for automated assignment of ambiguous distancedata in combination with an iterative assignment strategy, alter-nating structure calculation and assignment. The concept of ADRsis not limited to the treatment of ambiguities in NOEs but is usefulfor a variety of other interactions (Nilges, 1995; Bardiaux et al.,2009). In particular, data from NMR interface mapping experi-ments can be converted into ambiguous distance restraints (Nilgesand O’Donoghue, 1998; Dominguez et al., 2003), but also othercontact relationships are ambiguous (Alber et al., 2007).

In the present paper, we use it in particular for restraints de-rived from charge inversion and from double cysteine substitutionsand crosslinking experiments. In the Klebsciella oxytoca T2S pilusand the Vibrio cholerae Toxin-coregulated pilus (TCP), inter-molec-ular salt bridges could be demonstrated by single charge inversionsabolishing pilus assembly, and their combinations that restored it(Li et al., 2008; Campos et al., 2010). In addition, double cysteinesubstitutions in the hydrophobic segment of the major pilin PulGin the T2S pilus led to position-specific cross-linking of protomersin the assembled pili, providing evidence for interactions in thecore of the filament of the T2S pilus. For the GC pilus, we compareour models to the published structure (Craig et al., 2006) and dis-cuss differences due to the different computational strategies (rigiddocking versus flexible docking). For the V. cholerae toxin-coregu-lated pilus (TCP), we compare our model to the deuterium ex-change data obtained by mass spectrometry (Li et al., 2008). Thepresent study is a special case of using proteomics type data forintegrative from sparse conformational data, a field that has beenreviewed extensively recently (Lasker et al., 2010; Karaca et al.,2010; Das and Baker, 2008).

2. Materials and methods

2.1. Modeling of the pilins

Only for the GC pilus, a complete structure of the pilin includingits N-terminal a-helix is available (Craig et al., 2006) (PDB code2HIL). For the TcpA and the PulG pilins, the N-terminus is missingin the X-ray crystal structures (PDB codes 1OQV and 1T92, respec-tively). For PulG, we used the structure of the N-terminal helix ta-ken from the Pseudomonas aeruginosa T4 pilin PilA full-lengthstructure (Craig et al., 2003) (pdb 1OQW) to complete the struc-ture. In particular, a proline at position 22 conserved in the GC PilE,

K. oxytoca PulG and the P. aeruginosa PilA, all members of the groupa T4 pilins, induces a kink in the helix at this position in the 3Dstructures of PilA and PilE. A mutation of this proline in PulGstrongly reduces pilus generation in K. oxytoca, an indication thatthe kink or additional flexibility induced by the proline at this po-sition is important for the proper assembly of the pilus.

Despite the high overall sequence similarity between the N-ter-minal helices of different T2SS and T4P pilins, the TcpA pilin, amember of group b T4P pilins, lacks this proline residue at position22. In contrast to a preceding study on the TCP (Li et al., 2008), wetherefore extended the C-terminal helix as a straight continuationof the helix. For the PulG pilin, the 20 C-terminal residues weremodeled by exploiting the close homology to GspG from enter-ohaemorragic Escherichia coli (pdb 3G20), to include the calciumbinding site in the b2–b3 loop (Korotkov et al., 2009), which is ab-sent in the crystal structure of PulG (Köhler et al., 2004).

For the homology modeling, we used ad hoc scripts written forCNS (Brunger et al., 1998) to superpose structures and replace res-idues. The N-terminal methyl group was included in the model ofall three pilins (Strom and Lory, 1991).

2.2. Use of conformational restraints

The calculation strategy described in this paper relies in part onconformational restraints. We used different types of conforma-tional restraints in different stages of the calculation protocol de-scribed further below.

1. The initial structures of the pilins were maintained in a flexibleand adaptive way using log-harmonic distance restraintsand automated weighting (Nilges et al., 2008) on the alphacarbons, apart from the two N-terminal residues (and the twoC-terminal residues for the PulG pilin, for which no structuraltemplate was available). A log-harmonic distance restraintpotential is derived from the log-normal distribution (Riepinget al., 2005) and depends on the square of the difference ofthe logarithms of the distances (Nilges et al., 2008):

Elog ¼ k logdd0

� �� �2

; ð1Þ

where d is the instantaneous distance in the structure, d0 is thetarget distance (in this case, the distance in the original struc-ture), and k is a weighting factor. The method bears some simi-larity to methods based on the elastic network model recentlydescribed for X-ray crystal refinement of low resolution struc-tures (Schröder et al., 2007; Schröder et al., 2010), with impor-tant differences: (i) We use the log-harmonic potential whichdiffers from a harmonic potential that it is more tolerant to lar-ger deviations. It is an advantage to allow for changes in thestructure since there may be important changes between the astructure in the crystal and in the pilus. The external packingforces present in both situations may be different. (ii) Ratherthan updating the network, we combined the ‘‘log-elastic’’ net-work with an automatic reclassification of restraints dependingon their deviation from the initial distance (corresponding to aBayesian mixture model), and automated weighting. We used atotal of four classes of restraints, with limits between classesset to multiples of the overall logarithmic standard deviation.

2. In the first stage of modeling, a single linear restraint (i.e., theforce is independent of the distance to the pilus axis) was intro-duced between the center of mass of the helix and the origin, tomaintain the protomers close to the pilus axis. The origin isfixed in space and serves also as the center of the coordinatesystem for the symmetry operations. The center of mass ofthe helix is determined ‘‘on the fly’’ at each molecular dynamicsor minimization step.

438 M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444

3. The experimental distance information on salt bridges obtainedby double charge inversion (experimental for the T2S and TCP;predicted for GC) was introduced as a distance restraint in somecalculations. The symmetry of the pilus leads to an ambiguity inthis contact information: it is not known between which twoprotomers the saltbridge exists without knowing the arrange-ments of the protomers in the pilus. This type of ambiguitycan be readily treated by an ambiguous distance restraint. Aquantity with the dimension of a distance can be calculatedfor N distances:

D ¼XN

n

d�mn

!�1=m

; ð2Þ

where each of the N distances dn is calculated between the firstresidue of the saltbridge to the second residue on one of theN neighbors (in our case, N = 30 since there are a total of 30neighbors simulated), and where the exponent m determinesthe ‘‘selectivity’’ of the restraint: the higher the exponent, themore selective, with limm!1D ¼minðdn;n ¼ 1; . . . ;NÞ. For NOEderived distances, the natural choice for m is 6, because of thedistance dependency of the NOE. For the current applicationwe have chosen m = 20. The advantage of using an ambiguousdistance restraint rather than the minimum distance is thatthe restraint is differentiable everywhere, which makes minimi-zation and molecular dynamics more stable. The symmetry inthe distances is imposed using the symmetry operators directlyin the calculation of the non-bonded interaction of one monomerwith the images and in the calculation of the different contribu-tions in Eq. (2).

4. In some of the calculations (see below for a description of thedifferent calculations performed), a linear restraint (force inde-pendent on distance) was used to incorporate the (experimen-tal or predicted) cysteine crosslinking data, also usingambiguous restraints. This restraint was active in stages 1 and2 of the minimization protocol only. We preferred a linear dis-tance dependency for this restraint since it is difficult to convertthe crosslinking efficiency directly into an upper limit for thedistance. The ambiguity was treated as for the saltbridgerestraints.

5. To improve the interactions of the charged side chains, in par-ticular in the first two stages of the calculation where no or onlyapproximate electrostatic interactions were present, an adap-tive log-harmonic ambiguous restraint was used, as an attrac-tive intermolecular interaction between a charged residue andall residues of opposite charge on any protomer in the pilus.For example, for a Lysine residue, the restraint connects theLysine Nf to all Od atoms of Aspartates, all Oe of Glutamates,and the C-terminal oxygens, on any of the neighbors. Thisrestraint was motivated by the observation that charges arevery well compensated in the interior of the pilus. Theserestraints were checked, re-classified and weighted at regularintervals in a similar way as the conformational restraints onthe initial structures.

2.3. Search strategy for pilus modeling

The full-length structures of the pilins served to generate molec-ular models of the pili by a multi-stage minimization and moleculardynamics procedure, identical for all three pili. We ran calculationswith different combinations of conformational restraints. The bio-physical properties derived from electron microscopy measure-ments were always used, throughout the calculation: for the T2Spilus, rise per unit: 10.4 Å, rotation angle per unit: 84.71� (Köhleret al., 2004); for the GC pilus, rise per unit: 10.5 Å, rotation angleper unit: 104� (Craig et al., 2006); and for the TCP, rise per unit:

7.5 Å, rotation per unit: 140� (Li et al., 2008). The helical sense wasimposed to be right handed for T2S and GC, left handed for TCP,but we also tested the effect of using the wrong handedness (see Sec-tion 3).

The symmetry of the pili was imposed by modeling only one pri-mary protomer explicitly and by calculating the interactions of theprimary protomer with the rest of the pilus (force field and distancerestraints) by using symmetry operators. Ideal symmetry of the sys-tem is thus maintained throughout the whole calculation. We useda total of 31 protomers (15 neighbors of the primary protomer ineach direction of the helix axis). This may seem excessive, but add-ing protomer units in this way comes at a negligible computationalcost. Also, more partners need to be considered when longer cutoffsare used (up to 12 Å during the modeling for the electrostatic inter-action, and up to 25 Å in the analysis) than those that are in directcontact. All symmetry operators required to reconstruct the entiresystem were explicitly specified, using the ‘‘NCS strict’’ option inCNS (Brunger et al., 1998). These are rotations in multiples of therotation per unit (e.g., lefthanded rotation of 140� for the TCP),and multiples of the translation per unit along the helix axis (e.g.,7.5 Å for the TCP). The primary monomer is free to rotate and trans-late (i.e., the distance from the symmetry axis and the orientationwith respect to the symmetry axis can vary).

To include the symmetry-related ambiguity in the restraints,we modified the NOE distance routine in CNS to use the symmetryoperators and calculate summed distances over all images of theprimary protomer specified by the symmetry operators. A flag al-lows to either include or exclude the intra-protomer contribution.

In the beginning of the calculation, a monomer was placed closeto the pilus axis, with the a-helix approximately parallel to the pi-lus axis. The orientation around the N-terminal a-helix was chosenrandomly within 180� (for the GC and T2S pili) or 360� (for theTCP). The orientation around the two axes perpendicular to the pi-lus axis were randomized within 20�. The minimization proceededthen in a three-stage protocol. The scripts are available as supple-mentary material.

2.4. Stage 1: Rapid packing optimization

The first stage consisted in a fast optimization of the geometryand the packing, with a simplified non-bonded interaction (repul-sive van der Waals only, no electrostatics). A constant force (linear)restraint was used to attract the protomer to the pilus axis. Inaddition, a non-specific salt-bridge restraint favored interactionsbetween oppositely charged residues.

2.5. Stage 2: Vacuum refinement

In the second stage, the structures were refined in vacuo with afull force field (the CHARMM Param19 extended atom force field(Brooks et al., 1983)), with adapted non-bonded parameters simi-lar to previous work (a distance-dependent dielectric of 1.41, aswitching function between 2 and 9 Å, and a non-bonded cut-offof 10 Å (Blondel et al., 1999)). All the restraints from stage 1 re-mained active. This stage served to further optimize the packingbetween protomers.

2.6. Stage 3: Clustering and solvent refinement

After the second stage, the pilus structures were clusteredbased on the RMS difference of their Ca positions. To calculate amatrix of RMS distances, the pilins were not superimposed but ro-tated around and shifted along the pilus axis to an equivalent posi-tion within the pilus (i.e., the distance from the pilus axis and theorientation of the protomer remained unchanged). In this way, theRMS difference between different models still includes differences

M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444 439

due to rigid body translations and rotations in addition to differ-ences in the structure of the protomer. The clustering algorithm(Daura et al., 1999) counts the number of neighbors of a structureusing a user-defined cutoff (see Table 1) and takes the structurewith largest number of neighbors with all its neighbors as a cluster.It then eliminates all structures in the cluster from the pool ofstructures. We ran the algorithm in ‘‘full linkage’’ mode, whichadds a structure to a cluster when its distance to any element ofthe cluster is less than the cutoff. Two structures within a clustercan thus differ by more than the cut-off.

The third refinement stage, usually only performed on the firstcluster, consisted in a short refinement in explicit water of the maincluster, similar to the one used in NMR structure determination(Linge et al., 2003). We used a water layer of 10 Å thickness and anon-bonded cutoff of 12 Å, and the TIP3P water model, with theCHARMM Param19 extended atom force field and standard non-bonded parameters, with electrostatic force-shifting (Steinbachand Brooks, 1994). No conformational restraints were used duringthis stage.

2.7. Structure validation and energy evaluation

Structures of the pili were validated by calculating the overallenergy with the CHARMM19 force field and with PROCHECK(Laskowski et al., 1993). No bad non-bonded contacts were identi-fied. The final 10 ps of molecular dynamics of the 20 lowest energymodels were used for more detailed energetic analysis. The energyof the total structure and the energetic contributions of single res-idues were evaluated using the generalized Born electrostatic op-tions in CNS, modified for symmetric systems (Moulinier et al.,2003). We used the CHARMM Param19 force field with the ACEgeneralised Born implementation (Calimet et al., 2001), with aninternal dielectric constant of 4 and an external dielectric constantof 80. The energetic contribution of a residue to the pilus stabilitywas evaluated as the total non-bonded energy (vdW, electrostatic,

Table 1Overview over calculations.

Calculationa Pilus Handb Restraintc

PG-L0 T2S Left – –PG-LSB1C T2S Left Asp 48 Arg 87PG-R0 T2S Right – –PG-RSB1C T2S Right Asp 48 Arg 87PG-RSB1CC T2S Right Asp 48 Arg 87

GC-L0 GC Left – –GC-LSB4C GC Left Asp 113 Lys 74

Glu 49 Arg 30Asp 153 Lys 76

GC-R0 GC Right – –GC-RSB1C GC Right Glu 113 Lys 74GC-RSB2C GC Right Glu 49 Arg 30GC-RSB3C GC Right Asp 153 Lys 76GC-RSB4C GC Right Asp 113 Lys 74

Glu 49 Arg 30Asp 153 Lys 76

GC-RSB4CC GC Right Glu 113 Lys 74Glu 49 Arg 30Asp 153 Lys 76

TC-L0 TCP Left – –TC-LSB1 TCP Left Glu 83 Arg 26TC-R0 TCP Right – –TC-RSB1 TCP Right Glu 83 Arg 26

a Name of the calculation in the text and in the figure legends. PG: T2S pilus; GC: GCb Left-handed is correct for TCP and right-handed for PulG and GC.c Restraint applied in the calculation. 4 Å upper limit for salt bridges, linear restraintd Percentage of structures in the first (largest) cluster.e Cutoff distance applied in cluster calculation. Any member of a cluster is separated

generalized Born) between the residue and the rest of the system,evaluated once in the pilus, from which we subtracted the energyevaluated with the pilin protomer placed at 100 Å from the pilusaxis (no interaction between protomers). Entropic contributionswere neglected.

3. Results

3.1. Overview of the calculations

Between 400 and 1000 pilus structures were calculated for eachsystem and setup, and clustered with respect to structural differ-ences, position and orientation. We performed stage 1 (rapid pack-ing optimization) and stage 2 (molecular dynamics refinementwith distance-dependent dielectric) for all structures. In all threesystems, there were many more structures in the first cluster thanin any of the other clusters, and therefore only the first cluster wasrefined in water and analysed further. In contrast to the modelingprocedure used for the published models of the GC pilus and TCP,the sidechains and the entire two N-terminal residues were keptcompletely flexible, in addition to an overall flexibility of the back-bone, allowing the protomers to explore conformations that wouldbe missed in a procedure based on rigid body motions only.

For all systems, we ran a calculation with only the overall pack-ing restraint (see Table 1). For the T2S, we ran calculations withrestraints derived from cysteine crosslinking and salt bridge chargereversal experiments, for the TCP, with a restraint derived fromcharge reversal experiment only. For the GC pilus, we predictedclose distances from the cryo-EM derived model, for those chargepairs or CB–CB distances that could potentially be determinedexperimentally. For some calculations, we used the incorrect hand.Table 1 gives an overview over all calculations performed.

In the cryo EM structure (Craig et al., 2006), two inter-molecularsaltbridges are clearly present, with distances between the chargedatoms of less than 3 Å (Glu 49/Arg 30, and Asp 153/Lys 76). Two

1st clusterd Cutoff (Å)e

– – 17.7 1.75Val 10 Leu 16 37.8 1.75– – 23.5 1.75Ile 10 Leu 16 66.1 1.75Val 10 Leu 16 47.7 1.75Ile 6 Leu 13Val 9 Leu 16

– – 4.0 1.75Val 9 Leu 16 9.0 1.75

– – 35.6 1.75Val 9 Leu 16 65.8 1.75Val 9 Leu 16 46.5 1.75Val 9 Leu 16 57.3 1.75Val 9 Leu 16 71.8 1.75

Val 9 Leu 16 26.7 1.75Leu 6 Ile 12Leu 6 Leu 16

– – 12.7 2.5– – 16.5 2.5– – 8.9 2.5– – 9.9 2.5

pilus; and TC: TCP.

for crosslinks.

from another cluster member maximally by this distance.

440 M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444

more distances (between Glu 5 and the N-terminal nitrogen, andbetween Glu 113 and Lys 74), are between 5 and 6 Å. In the calcu-lations with restraints, we imposed a uniform upper limit of 4 Å onthe distance between the charged side-chains, using a restraintambiguous for the two oxygens in Glu and Asp, and the two nitro-gens in Arg, in addition to the ambiguity due to the symmetry ofthe pilus. Hence, in total, for a saltbridge between a Glu and anArg residue, there are 2 * 2 * 30 possibilities in the restraint.

Interestingly, the closest contacts between b carbons in theN-terminal helix in the GC pilus differ slightly from the experimen-tally established closest contacts in the PulG pilus (Campos et al., inpress). In the GC pilus, we observe the hierarchy 6–16 < 6–12 < 6–15 < 9–16 < 6–13 < 7–12 < 10–16, whereas in the PulG system, theprobability to form a disulfide bridge indicated a hierarchy9–16 < 6–13 < 11–16 < 11–17 � 10–17 (Campos et al., 2010). Forthe double cysteine mutants at position 11–17 and 10–17, virtuallyno crosslinking had been observed (Campos et al., 2010). The dis-tance range for Cb–Cb distances observed in disulfide bridges inX-ray crystal structures is between 2.9 and 4.6 Å (Hazes and Dijk-stra, 1988). Since it is difficult to establish an exact quantitativerelationship between the probability of forming a disulfide bridgeand the distance between the b carbons, we chose a linear restraintwhere the force is independent of the distance to incorporate thecrosslinking results in the calculations.

3.2. Convergence

The convergence is dominated by overall packing. In all threesystems, the pilin protomers readily rotate by up to 90� (for thePulG and GC pili) or 180� (in the case of the TCP) around the N-ter-minal a-helix to the same orientation. Table 1 indicates the frac-tion of calculations converging to the largest cluster. Without anyconformational restraints, the convergence is best for the GC pilus,followed by the T2S pilus and the TCP. The performance is compa-rable for TCP and T2S, since the rotation angle sampled in the start-ing structure is twice as large for TCP than for the T2S pilus (seeSection 2), albeit with a larger cluster cutoff for TCP.

Conformational restraints have a strong influence on the conver-gence to the largest cluster. In the GC pilus, it nearly doubles if onesalt bridge restraint (Glu 113–Lys 74) and one crosslink restraint(Val 9–Leu 16) are applied (calculation GC-RSB1C). Not all saltbridges have the same influence on convergence (compare calcula-tions GC-RSB1C, GC-RSB2C and GC-RSB3C), and, surprisingly, con-vergence deteriorates when more than one cysteine crosslinkrestraint is applied (calculation GC-RSB4C). The restraints have asimilar effect in the T2S pilus (cf. calculations PG-R0 and PG-SB1C).Surprisingly, also here the convergence is reduced if more thanone cysteine crosslink restraint is applied (calculation PG-RSB1CC).In the TCP, an application of the one experimentally validated salt

Fig. 1. Analysis of the unrestraint calculation GC-R0. Left: Atomic RMS differences to therestraint energy.

bridge (Glu 83–Arg 26) increases the convergence only little. Thisindicates the importance of the cysteine crosslink restraint for thecorrect organisation of the N-terminal helices in the center of thepilus.

Only for the GC pilus we can compare the results of the proce-dure with the structure of a pilus obtained with EM data of muchhigher resolution (Craig et al., 2006). It is therefore important tofind criteria to identify the most likely model without a referencestructure, in addition to the size of the cluster. The total energy(CHARMM19 force field with ACE generalized Born) is incapableto distinguish between incorrect models and the correct model,and does not show any correlation with the atomic RMS differenceto the cryo-EM model (Fig. 1, left). The restraint energy, in contrast,shows very good correlation with the similarity to the cryo-EMmodel. For the models from the unrestraint calculation, the re-straints identify structures between 1 and 5 Å away from thecryo-EM model, with an average of around 2.5 Å (Fig. 1, right). Asexplained in Section 2 (in the section on clustering and solventrefinement), this number is obtained by calculating the RMS differ-ence of atomic positions without superposition and contains con-tributions from differences in the structure, distance from thecenter of the pilus and orientation of the protomer. The averageRMS difference of the calculated structures is very similar to theestimated error in atomic position in the cryo-EM GC pilus model(around 2.5 Å) (Craig et al., 2006).

3.3. Calculations with the incorrect handedness

The fact that the original handedness of the T2S pilus had beenproposed incorrectly (Köhler et al., 2004) is indicative of the poten-tial difficulties to establish the handedness experimentally fromEM data. We therefore performed some calculations with theincorrect handedness, in order to see if the choice of the correcthandedness would be possible from the result of our calculations.

In terms of convergence to the largest cluster, there is a more orless marked difference: 17.7% vs. 23.5% in T2S; 4.0% vs. 35.6% forthe GC pilus, and 8.9% vs. 12.7% for the TCP (see Table 1). Hence,this criterion (number of structures in top cluster) alone would al-low a clear distinction between correct and incorrect handednessonly in the GC pilus.

The variation of non-bonded energy (van der Waals and electro-static with implicit solvent) is much bigger within the top clusterin each calculation than the difference between calculations withcorrect and incorrect handedness (not shown), and it is thereforenot possible to use this criterion either.

The situation changes if the experimentally established contactsare used in the analysis. The difference becomes clear-cut whenthe restraint energy is evaluated for structures calculated withoutrestraints (Fig. 2, red and green bars). There are structures without

cryo-EM model as a function of energy. Right: RMS to the cryo-EM structure against

Fig. 2. Histograms of restraint energy for the PilE and the PulG systems. Left: GC-R0 (red), GC-RSB1C (black), GC-L0 (green), and GC-LSB1C (blue). Right: PG-R0 (red),PG-RSB1C (black), PG-L0 (green), and PG-LSB1C (blue).

M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444 441

any restraint violations for the correct, right-handed pilus, for PilEand PulG. In contrast, there are no structures that can satisfy therestraints completely for the left-handed structures for these twosystems.

When we biased the calculation by the application of structuralrestraints, we found that structures with the wrong hand could beobtained that satisfied the restraints. The ratio of convergence tothe largest cluster remains roughly the same for the GC and T2S pili.However, comparing the results with left- and right-handed struc-tures allowed in both cases to clearly identify the correct handed-ness, since the right-handed structures satisfy the restraints better(Fig. 2, black and blue bars): the distribution becomes much sharperand its maximum shifts to the left (lower RMS difference torestraints).

3.4. Geometry of the pili and water accessibility

Despite differences in the structure of the pilins, in particularthe size of the globular head, and in the measured helical repeats,the structures of the T2SS and T4P pili modeled in this study havecommon features (Fig. 3). The outer diameter is similar; it variesbetween approximately 65 Å for the PulG and the GC pili and80 Å for the TCP. This outer diameter was not restraint directly inany of the calculations, it is a consequence of the packing of thepilin protomers in the pili. There is a very small or vanishing cen-tral cavity in all three pili.

Profound grooves separate the strands of the helices in the pili,making the N-terminal a-helices in the core of the pili accessible towater. For the TCP, this is shown in Fig. 4, which maps the accessi-bility measured by mass spectrometry (Li et al., 2008) onto the sur-face. It is difficult to make a strict quantitative correlation betweenthe mass spectrometry data and a three dimensional structure,since many factors influence hydrogen exchange (Best andVendruscolo, 2006). The regions showing fastest hydrogenexchange are clearly water accessible in our model. The interac-tions between protomers are similar in our model and in the modeldirectly based on the hydrogen exchange data (Li et al., 2008).However, the ‘‘hole’’ giving access to the central helix is less widein our model, and is more focussed on residues 13–23, which showthe fastest hydrogen exchange. Other parts of the N-terminal helixare very little accessible to water in our model, in agreement withthe mass spectrometry data.

3.5. Protomer packing

The tight packing within the pilus produces numerous specificinteractions between neighboring protomers in all pili, such thateach protomer (P) interacts directly with several neighboring sub-units. Whereas the packing is similar in the GC and PulG pilus, we

observed some differences for the TCP. In the PulG and the GC pi-lus, most interactions are with four upper (P+4, P+3, P+1, P+7) andfour lower (P�4, P�3, P�1, P�7) protomers in the filament; in theTCP, with four upper (P+3, P+5, P+2, P+8) and four lower (P�3, P�5,P�2, P�8) protomers. Some direct contacts extend to protomersP+10/P�10 for the TCP and protomer P+8/P�8 for the GC pilus.The P+7 interactions in PulG are electrostatic interactions betweenthe N-terminus and the side chain of Asp53.

Different models were proposed for the GC and the T2S pilusassembly (Craig et al., 2006; Campos et al., 2010). However, thepacking order and the assembly machinery between these systemsare similar (Sauvonnet et al., 2000) . For the PulG pilus, the interac-tions P�P+1 are crucial for assembly and secretion function – thereis a clear correlation between the formation of two conserved saltbridges at the P/P+1 interface and function (Campos et al., 2010).

We also analysed the number of protomers within a 25 Å rangeof the principal protomer in the pilus, the cutoff chosen for theelectrostatic interactions. We observed the maximum number ofinteracting protomers for the TCP, up to positions P+13/P�13, indi-cating that the 15 neighbors on each side included in the modelingwere indeed sufficient for calculating the electrostatic interactionsbut not excessive.

3.6. Role of charged and polar interactions

There are about twice as many charged residues in PulG than inPilE or TcpA (seven negatively charged and six positively chargedresidues in PulG, including the N-terminal Phe; three and four,respectively, in PilE, and two and four, respectively, in TcpA). Apartfrom the strictly conserved charged positions at the N-terminusand for Glu 5, there are other positions (approximately) conservedfor charged or polar residues: position 29/30; position 35; and posi-tion 44. Intra- or inter-subunit salt bridges neutralize each charge.Fig. 4 shows an close up view of the region around residues Arg26and Lys 35 in an ensemble of 20 structures for the TCP, which pro-vides a rather dynamic view of these polar interactions, similar towhat we had observed in the T2S pilus (Campos et al., 2010).

3.7. Energetic contributions of each residue

Fig. 5 shows the average energetic contribution of each residueto the stability of the pilus in all three systems, estimated byMMGBSA calculations. A few dominant residues are predicted toadd substantially to the stability of the pilus. The exact locationof the minima depends on the exact sequence. A common featureis that the predicted contributions to stability are scattered overthe whole sequence and not only concentrated in the N-terminalhelix.

Fig. 3. Ensembles of the 20 lowest energy structuress of the first cluster of calculations without restraints. Colouring ranges from blue (10 Å from the pilus axis) to red(maximum distance). Top row: side view. Bottom row: top view. Left: TCP. Middle: T2S pilus. Right: GC pilus.

Fig. 4. Left: Close-up of a ‘‘hole’’ in the TCP filament surface, which exposes part of the N-terminal a-helix (residues 13–23). One protomer is colored to representapproximately deuterium exchange as measured in Li et al. (2008) (blue: less than 20%, green: around 40%, and orange: more than 50%. A part of the N-terminal helix isclearly visible (red). To illustrate the accessibility of the helix to water through this channel some water molecules introduced during the modeling are shown. Right: Close-upof the interface between neighboring subunits in the TCP, formed between the ab-loop of one subunit and the N-terminal a-helix of a neighboring subunit. The interface isshown as if looking out from the interior of the filament. An ensemble of charged side-chains is shown involving residues Arg26, Lys35, Asp82 and Glu83 (in red and blue fornegatively and positively charged residues, respectively). Ensembles of other charged side chains in the neighborhood are also shown (in pink for acidic and in pale blue forbasic side chains). The coloring of the backbone is as in Fig. 3.

442 M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444

Fig. 5. By-residue energy contribution to the overall stability of the pili. Top: PulGpilus. Middle: GC pilus. Bottom: TCP.

M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444 443

In PulG, two pairs, Asp48–Arg87, and Asp44–Arg88, were con-sistently predicted to form intermolecular salt bridges. These inter-actions were validated by site-directed mutagenesis, viareplacement of residues Asp44, Glu48, Arg87 and Arg88 individu-ally and in pairs by residues of the opposite charge.

4. Discussion

In this paper, we describe a strategy to obtain models withpseudo-atomic detail from sparse distance data and low resolutionelectron microscopy data. We show that with this strategy we canobtain reliable models for pili of the T2SS, T4aP and T4bp (TCP)families. Electron microscopy data as used here is available forother pili in this family, and a more atomic picture of the pili couldbe obtained in a straightforward way. The strategy also permits to

test the influence of structural restraints that could be obtained bycrosslinking and mass spectrometry or by site-directed mutagene-sis. The strategy may be more generally applicable to structuresshowing helical symmetry.

We have deliberately not based our calculation protocol onusing very long molecular dynamics trajectories. The principaldriving force is derived from experimental data: from the helicalparameters of the pilus derived from EM data, from conformationalrestraints from mutation experiments, and from compactness con-siderations. The capabilities of CNS to handle many differentsources of experimental restraints and strict symmetry is thereforemost important, in addition to the possibility to write elaboraterefinement scripts. For generating the structures, the force field isin a way of secondary importance, and we can use a somewhat da-ted force field such as PARAM19.

To assess convergence, we have used the size of the cluster andenergetic criteria. The energetic criteria alone were not sufficient toidentify the correct structures. We are currently modifying ourscripts to use a more recent force field (than PARAM19) and a moreelaborate implicit solvent implementation (than ACE).

How sparse can the data be to still get meaningful structures?This is difficult to answer in general. The whole project started withcalculating structures without any restraints (Campos et al., inpress), in order to determine different arrangements of the pilinsin the pilus compatible with the overall symmetry, and to identifyinter-molecular contacts that distinguish the different conforma-tions that could be used for experimental validation. In this respect,the calculations are useful even without any restraints derived frommutation experiments. The only data necessary consist in an overalldescription of the helical symmetry (rise per protomer and rotationangle per protomer).

The use of a computational script allowed us to construct mod-els of the three pili in identical ways and to compare the obtainedmodels in detail. T2SS and T4aP are more closely related (shortN-terminal presequence, Pro22, right handed) to each other thanto TcpA (type IVb group pilin), consistent with the fact that theassembly machinery is different (Pelicic, 2008). There are differ-ences in the size of the pilin protomers, the exact helical parame-ters (from 7.5 Å rise along the axis in TCP to 10.5 Å in the GCpilus; and from 84.71� rotation per protomer in the T2S pilus to140� in TCP; left-handed helix for TCP and right-handed helicesfor GC and T2S pili). These differences in the overall parametersare likely due to the different sizes of the globular heads and thespacing of the charged residues that make inter-molecular salt-bridges. The organisation is dictated by the packing of the hydro-phobic N-terminal helices close to the pilus axis and the packingof the much larger globular C-terminal heads. In consequence, inspite of some similarities, there are also differences in the organi-sation of the protomers in the pili, making it important to havetools for the modeling of reliable models from data that is rela-tively easy to obtain.

Acknowledgement

This work was partially supported by the Institute Pasteurtransversal project Grant No. 339.

References

Alber, F., Dokudovskaya, S., Veenhoff, L.M., Zhang, W., Kipper, J., Devos, D., Suprapto,A., Karni-Schmidt, O., Williams, R., Chait, B.T., Rout, M.P., Sali, A., 2007.Determining the architectures of macromolecular assemblies. Nature 450,683–694.

Altieri, A.S., Byrd, R.A., 2004. Automation of NMR structure determination ofproteins. Curr. Opin. Struct. Biol. 14, 547–553.

Audette, G.F., Irvin, R.T., Hazes, B., 2004. Crystallographic analysis of thePseudomonas aeruginosa strain K122-4 monomeric pilin reveals a conservedreceptor-binding architecture. Biochemistry 43, 11427–11435.

444 M. Campos et al. / Journal of Structural Biology 173 (2011) 436–444

Bardiaux, B., Bernard, A., Rieping, W., Habeck, M., Malliavin, T.E., Nilges, M., 2009.Influence of different assignment conditions on the determination of symmetrichomodimeric structures with ARIA. Proteins 75, 569–585.

Best, R.B., Vendruscolo, M., 2006. Structural interpretation of hydrogen exchangeprotection factors in proteins: characterization of the native state fluctuationsof CI2. Structure 14, 97–106.

Blondel, A., Renaud, J.P., Fischer, S., Moras, D., Karplus, M., 1999. Retinoic acidreceptor: a simulation analysis of retinoic acid binding and the resultingconformational changes. J. Mol. Biol. 291, 101–115.

Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., Karplus, M.,1983. Charmm: a program for macromolecular energy and minimization anddynamics calculations. J. Comput. Chem. 4, 187–217.

Brunger, A.T., Adams, P.D., Clore, G.M., DeLano, W.L., Gros, P., Grosse-Kunstleve,R.W., Jiang, J.S., Kuszewski, J., Nilges, M., Pannu, N.S., Read, R.J., Rice, L.M.,Simonson, T., Warren, G.L., 1998. Crystallography & NMR system: a newsoftware suite for macromolecular structure determination. Acta Crystallogr. D:Biol. Crystallogr. 54, 905–921.

Calimet, N., Schaefer, M., Simonson, T., 2001. Protein molecular dynamics with theGeneralized Born/ACE solvent model. Proteins 45, 144–158.

Campos, M., Nilges, M., Cisneros, D.A., Francetic, O., 2010. Detailed structural andassembly model of the type II secretion pilus from sparse data. Proc. Natl. Acad.Sci. USA 107, 13081–13086.

Craig, L., Taylor, R.K., Pique, M.E., Adair, B.D., Arvai, A.S., Singh, M., Lloyd, S.J., Shin,D.S., Getzoff, E.D., Yeager, M., Forest, K.T., Tainer, J.A., 2003. Type IV pilinstructure and assembly: X-ray and EM analyses of Vibrio cholerae toxin-coregulated pilus and Pseudomonas aeruginosa PAK pilin. Mol. Cell 11, 1139–1150.

Craig, L., Volkmann, N., Arvai, A.S., Pique, M.E., Yeager, M., Egelman, E.H., Tainer, J.A.,2006. Type IV pilus structure by cryo-electron microscopy and crystallography:implications for pilus assembly and functions. Mol. Cell 23, 651–662.

Das, R., Baker, D., 2008. Macromolecular modeling with Rosetta. Annu. Rev.Biochem. 77, 363–382.

Daura, X., Gademann, K., Jaun, B., Seebach, D., van Gunsteren, W., Mark, A., 1999.Peptide folding: when simulation meets experiment. Angew. Chem., Int. Ed. 38,236–240.

Dominguez, C., Boelens, R., Bonvin, A.M.J.J., 2003. HADDOCK: a protein–proteindocking approach based on biochemical or biophysical information. J. Am.Chem. Soc. 125, 1731–1737.

Güntert, P., 2009. Automated structure determination from NMR spectra. Eur.Biophys. J. 38, 129–143.

Hansen, J.K., Forest, K.T., 2006. Type IV pilin structures: insights on sharedarchitecture, fiber assembly, receptor binding and type II secretion. J. Mol.Microbiol. Biotechnol. 11, 192–207.

Hazes, B., Dijkstra, B.W., 1988. Model building of disulfide bonds in proteins withknown threedimensional structure. Protein Eng. 2, 119–225.

Hazes, B., Sastry, P.A., Hayakawa, K., Read, R.J., Irvin, R.T., 2000. Crystal structure ofPseudomonas aeruginosa PAK pilin suggests a main-chain-dominated mode ofreceptor binding. J. Mol. Biol. 299, 1005–1017.

Herrmann, T., Güntert, P., Wüthrich, K., 2002. Protein NMR structure determinationwith automated NOE assignment using the new software CANDID and thetorsion angle dynamics algorithm DYANA. J. Mol. Biol. 319, 209–227.

Karaca, E., Melquiond, A.S.J., deVries, S.J., Kastritis, P.L., Bonvin, A.M.J.J., 2010.Building macromolecular assemblies by information-driven docking. Mol. CellProteomics 9, 1784–1794.

Keizer, D.W., Slupsky, C.M., Kalisiak, M., Campbell, A.P., Crump, M.P., Sastry, P.A.,Hazes, B., Irvin, R.T., Sykes, B.D., 2001. Structure of a pilin monomer fromPseudomonas aeruginosa: implications for the assembly of pili. J. Biol. Chem.276, 24186–24193.

Köhler, R., Schäfer, K., Müller, S., Vignon, G., Diederichs, K., Philippsen, A., Ringler, P.,Pugsley, A.P., Engel, A., Welte, W., 2004. Structure and assembly of thepseudopilin PulG. Mol. Microbiol. 54, 647–664.

Korotkov, K.V., Gray, M.D., Kreger, A., Turley, S., Sandkvist, M., Hol, W.G.J., 2009.Calcium is essential for the major pseudopilin in the type 2 secretion system. J.Biol. Chem. 284, 25466–25470.

Lasker, K., Phillips, J.L., Russel, D., Velazquez-Muriel, J., Schneidman-Duhovny, D.,Tjioe, E., Webb, B., Schlessinger, A., Sali, A., 2010. Integrative structure modelingof macromolecular assemblies from proteomics data. Mol. Cell Proteomics 9,1689–1702.

Laskowski, R.A., MacArthur, M.W., Moss, D.S., Thornton, J.M., 1993. PROCHECK: aprogram to check the stereochemical quality of protein structures. J. Appl.Crystallogr. 26, 283–291.

Li, J., Lim, M.S., Li, S., Brock, M., Pique, M.E., Woods, V.L., Craig, L., 2008. Vibriocholerae toxin-coregulated pilus structure analyzed by hydrogen/deuteriumexchange mass spectrometry. Structure 16, 137–148.

Linge, J., O’Donoghue, S.I., Nilges, M., 2001. Automated assignment of ambiguousnuclear Overhauser effects with ARIA. Meth. Enzymol. 339, 71–90.

Linge, J., Williams, M.A., Spronk, C.A.E.M., Bonvin, A.M.J.J., Nilges, M., 2003.Refinement of protein structures in explicit solvent. Proteins 50, 496–506.

Moulinier, L., Case, D.A., Simonson, T., 2003. Reintroducing electrostatics intoprotein X-ray structure refinement: bulk solvent treated as a dielectriccontinuum. Acta Crystallogr. D: Biol. Crystallogr. 59, 2094–2103.

Ng, S.Y.M., Chaban, B., Jarrell, K.F., flagella, Archaeal, 2006. bacterial flagella and typeIV pili: a comparison of genes and posttranslational modifications. J. Mol.Microbiol. Biotechnol. 11, 167–191.

Nilges, M., 1993. A calculation strategy for the structure determination ofsymmetric dimers by 1H NMR. Proteins 17, 297–309.

Nilges, M., 1995. Calculation of protein structures with ambiguous distancerestraints: automated assignment of ambiguous NOE crosspeaks anddisulphide connectivities. J. Mol. Biol. 245, 645–660.

Nilges, M., O’Donoghue, S.I., 1998. Ambiguous NOEs and automated NOEassignment. Progr. Nucl. Magn. Reson. Spectrosc. 32, 107–139.

Nilges, M., Bernard, A., Bardiaux, B., Malliavin, T., Habeck, M., Rieping, W., 2008.Accurate NMR structures through minimization of an extended hybrid energy.Structure 16, 1305–1312.

Nilges, M., Malliavin, T., Bardiaux, B., 2010. Protein structure calculation usingambiguous restraints. In: Encyclopedia of Magnetic Resonance. John Wiley &Sons, Ltd. doi:10.1002/9780470034590.emrstm1156.

Parge, H.E., Forest, K.T., Hickey, M.J., Christensen, D.A., Getzoff, E.D., Tainer, J.A.,1995. Structure of the fibre-forming protein pilin at 2.6 Å resolution. Nature378, 32–38.

Pelicic, V., 2008. Type IV pili: e pluribus unum? Mol. Microbiol. 68, 827–837.Ramboarina, S., Fernandes, P.J., Daniell, S., Islam, S., Simpson, P., Frankel, G., Booy, F.,

Donnenberg, M.S., Matthews, S., 2005. Structure of the bundle-forming pilusfrom enteropathogenic Escherichia coli. J. Biol. Chem. 280, 40252–40260.

Rieping, W., Habeck, M., Nilges, M., 2005. Modeling errors in noe data with alognormal distribution improves the quality of NMR structures. J. Am. Chem.Soc. 127, 16026–16027.

Rossmann, M.G., Morais, M.C., Leiman, P.G., Zhang, W., 2005. Combining X-raycrystallography and electron microscopy. Structure 13, 355–362.

Sauvonnet, N., Vignon, G., Pugsley, A.P., Gounon, P., 2000. Pilus formation andprotein secretion by the same machinery in Escherichia coli. EMBO J. 19, 2221–2228.

Schröder, G.F., Brunger, A.T., Levitt, M., 2007. Combining efficient conformationalsampling with a deformable elastic network model facilitates structurerefinement at low resolution. Structure 15, 1630–1641.

Schröder, G.F., Levitt, M., Brunger, A.T., 2010. Super-resolution biomolecularcrystallography with low-resolution data. Nature 464, 1218–1222.

Steinbach, P., Brooks, B., 1994. New spherical cutoff methods for long-range forcesin macromolecular simulation. J. Comput. Chem. 15, 667–683.

Strom, M.S., Lory, S., 1991. Amino acid substitutions in pilin of Pseudomonasaeruginosa: effect on leader peptide cleavage, amino-terminal methylation, andpilus assembly. J. Biol. Chem. 266, 1656–1664.

Volkmann, N., Hanein, D., 2003. Docking of atomic models into reconstructionsfrom electron microscopy. Meth. Enzymol. 374, 204–225.

Xu, X.-F., Tan, Y.-W., Lam, L., Hackett, J., Zhang, M., Mok, Y.-K., 2004. NMR structureof a type IVb pilin from Salmonella typhi and its assembly into pilus. J. Biol.Chem. 279, 31599–31605.