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Biophys J. 2013 May 7; 104(9): 2051–2057.
PMCID: PMC3647160
PMID: 23663848

Isopeptide Bonds Mechanically Stabilize Spy0128 in Bacterial Pili

Bo Wang,† Shijun Xiao,† Scott A. Edwards,†‡ and Frauke Gräter†§*
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Associated Data

Supplementary Materials

Abstract

Pili on the surface of Streptococcus pyogenes play a crucial role in adhesion to and colonization in human cells. The major pilin subunit, Spy0128, features intramolecular covalent isopeptide bonds that autocatalytically form between the side chains of lysine and asparagine residues and are regarded as important factors in conveying structural stability. In support of this notion, single-molecule force spectroscopy experiments with Spy0128 recently demonstrated the inextensibility of these bonds under mechanical load. However, the molecular determinants of their apparent absolute durability remain unknown. Here, we studied the impact of the isopeptide bond in the Spy0128 C-terminal domain on the mechanical properties of this subunit using force-probe molecular dynamics simulations and force distribution analysis. Even in the presence of the covalent cross-link, the pili β-sandwich domain undergoes partial unfolding, albeit at ∼50% higher rupture forces and with the ability to rapidly refold on the nanosecond timescale. We find that the isopeptide bond is located right at the point of stress concentration in the protein, leading to relative, yet not absolute, mechanical stabilization by the additional cross-link. Our findings indicate how the isopeptide bond enhances the mechanical stability and refolding capability at the molecular level, ensuring that the domain remains predominantly in a potentially adhesive conformation.

Introduction

Streptococcus pyogenes, a gram-positive bacterial pathogen, can infect human cells and cause a variety of diseases, ranging from relatively mild superficial infections such as tonsillitis, impetigo, pyoderma, and scarlet fever to severe infections, e.g., streptococcal toxic-shock-like syndrome and necrotizing fasciitis (1–4). These bacteria have long (>1 μm) and thin (∼2 nm in diameter) polymeric appendages known as pili extending from their surface (5–9). Pili are essential for adhesion and colonization (6–10). Establishing the mechanical linkage between the motile bacterium and its hydrodynamic and adhesive surrounding, pili function in a fluctuating extracellular environment, which constantly exposes them to mechanical forces (6,7,11,12).

Recent studies on pilus structure have shown that the central part of the pilus protein, the backbone pilin, is composed of repeats of the Spy0128 subunit (PDB ID 3B2M) (10). There are two elongated domains in the Spy0128 monomer, reaching a total length of 10 nm and a width of 2–3 nm. Both domains have immunoglobulin (IG)-like all-β structures, each featuring an unusual intramolecular covalent bond called an isopeptide bond that links two terminal peptide strands in a subunit (Fig. 1, A and D). The isopeptide bond is usually formed between a lysine ε-amino group and the δ-carboxyamide group of asparagine (Fig. 1, B and C) and is catalyzed by a proximal glutamic acid (10,13).

An external file that holds a picture, illustration, etc. Object name is gr1.jpg

The structure of the Spy0128 C-terminal domain and the initial atomic model for MD simulations. (A) The structure of Spy0128 C-terminal domain is shown in ribbon representation and the isopeptide-bond-related atoms are shown as spheres. Terminal β-strands accommodating the isopeptide-bonded residues are shown in cyan. (B and C) Atomic models for Spy− (isopeptide bond absent (B)) and Spy+ (isopeptide bond present (C)); the residues Lys179 and Asn303 that participate in the isopeptide bond are highlighted in ball-stick representation. (D) Scheme: β-sheet topology of the Spy0128 C-terminal domain, with the isopeptide bond shown as a gray bar.

Pilin subunits are constantly exposed to a complex hydrodynamic environment and, in particular upon adhesion, to supposedly large mechanical forces, the magnitude of which, however, is currently unknown. A stalling force of 110 pN in the type IV pili retraction has been observed (14). Recent single-molecule force spectroscopy experiments have shown that Spy0128 is inextensible at forces up to 800 pN (15). However, removing the isopeptide bonds results in domain unfolding of the two distinct IG-like domains at pulling forces of only 172 pN (N-terminal domain) or 250 pN (C-terminal domain). It has been argued that the high resilience of the isopeptide-bonded domain provides structural integrity and thus the ability for protein-protein interactions as needed for adhesion of the pilin protein even at the large forces (15).

However, the molecular determinants of the isopeptide-mediated stability and the structural response of pilin to external forces when clamped by isopeptide bonds are not just a straightforward matter of the bonds locking the structure in its folded state. More specifically, the question remains whether the experimentally observed inextensibility due to the presence of the isopeptide bond can also be interpreted as corresponding to an absence of any structural change within the Spy0128 subunit. Here, using force-probe molecular dynamics (MD) simulations, we study the impact of the isopeptide bond in the Spy0128 C-terminal domain on the mechanical properties of this subunit (16). We find that Spy0128 undergoes partial unfolding even when the isopeptide bond is present, albeit at forces significantly larger than would be required for the noncross-linked domain. Crucially for the interpretation of single-molecule experiments, this occurs without any observable extension of the protein. We use force distribution analysis (FDA) to calculate internal stresses within Spy0128 under external load (17,18), revealing that the isopeptide bond is placed right where stresses concentrate, thereby reducing the overall stress within the domain structure. These computational findings reveal, at the molecular level, how the covalent link provides an increased yet not absolute stability when bacterial pili are stretched.

Methods

Simulation setup

To inspect the mechanical function of the isopeptide bond in Spy0128, we used two models based on the crystal structure of the Spy0128 C-terminal domain (residues 173–307 according to Kang et al. (10)). One is the original crystal structure of Spy0128 with the isopeptide bond present (hereafter referred to as Spy+ (Fig. 1 C)) and the other is a modified Spy0128 in which the isopeptide bond is cleaved by restoring the two involved residues, Lys179 and Asn303 (Spy− (Fig. 1 B)). All MD simulations were performed with these two models. Protein structures were visualized with VMD (19).

The simulation system was set up as follows. For the simulations of Spy+ (Fig. 1 C), the protein was solved in a 7.4 × 5.9 × 5.4 nm3 box of water molecules with a physiological ion strength of 0.1 M. The resulting system size was 30,602 atoms. For the simulations of Spy−, the isopeptide bond was divided into a lysine residue and an asparagine residue (Fig. 1 C), solved in a 7.4 × 5.9 ×5.4 nm3 box of water molecules with 0.1 M sodium and chloride ions. Glu258 and Lys179 were defined to be neutral, as suggested by their hydrophobic environment (10) and as also supported by quantum mechanical calculations (13). The resulting system size was 30,622 atoms.

MD simulations and force-probe MD simulations

All MD simulations were carried out with GROMACS 4.0.5 (20). The OPLS all-atom force field (21) and the TIP4P (22,23) water model were employed. Simulations were run in the NpT ensemble with periodic boundary conditions. The temperature was kept constant at T = 300 K by coupling to a Nosé-Hoover thermostat (24,25) with a coupling time of τT = 0.1 ps. The pressure was kept constant at p = 1 bar using an isotropic coupling to a Parrinello-Rahman barostat (26) with τp = 4.0 ps and a compressibility of 4.5 × 10−5 bar−1. Lennard-Jones (27) and electrostatic interactions were calculated explicitly within a cutoff of 10 Å, and long-range electrostatic interactions were calculated by particle mesh Ewald summation (28). The time step was 0.002 ps, and all bonds were constrained using the LINCS (29) algorithm.

An energy minimization of 1000 steps using the steepest descent algorithm was followed by a 1000-ps position-restrained simulation with harmonic constraints on all protein atoms (force constant k = 1000 kJ mol−1 nm−2) to equilibrate the water and ions. A subsequent MD simulation of 1500 ps length was performed to equilibrate the whole system. The resulting equilibrated simulation systems showed a low root-mean-square deviation of the protein of ∼0.1 nm (Fig. S1 in the Supporting Material) and served as starting points for force-probe (FPMD) and force-clamp MD (FCMD) (16) simulations.

For the FPMD simulations, the pulling velocity was 0.2 nm ns−1 and the spring constant was 300 pN nm−1, resulting in a loading rate of 60 pN ns−1, as compared to the experimental rate of ∼10−5 pN ns−1 (15). The simulated time to monitor full rupture was 20 ns. These nonequilibrium MD simulations were performed using the same simulation parameters as in the above equilibrium simulations. Mechanical stability was characterized by the rupture force, which is the maximal force observed for unfolding the protein structure.

Force-clamp MD simulations and force distribution analysis

FDA (17,18) was employed to determine the internal force propagation in the Spy0128 C-terminal domain before rupture. FDA is based on forces Fij between each atom pair i, j. Pairwise forces include individual bonded (bond, angle, dihedral) and nonbonded (electrostatic, van der Waals) terms below the cutoff distance of 1 nm. The force between an atom pair is represented as the norm of the force vector. Attractive forces are negative and repulsive forces are positive. The force between each atom pair is considered, since the time average of these pairwise forces can differ from zero, even though the atomic forces, defined as the sum over all force vectors acting on each individual atom, must average out to zero at equilibrium.

Forces were monitored as the protein structure was subjected to external constant forces which were applied to the terminal amino acids along the β-strand direction in FCMD simulations. Each molecular structure was simulated for 20 ns in a relaxed state with a lower force of 10 pN and in a stretched state with a higher force of 300 pN. A difference in pairwise force between these two states reflects internal force propagation, and is considered as a measure for load-bearing interactions. Accordingly, the distribution of the externally applied force into interatomic interactions is obtained from the differences in force, Fij, between the stretched and relaxed state, defined as

ΔFij=Fij300pN−Fij10pN,
(1)

where Fij300pN and Fij10pN represent the force between atoms i and j in the stretched and relaxed states, respectively. The mechanical coupling of a single atom with respect to all other atoms is then defined as the absolute sum of changes in force ΔFj:

ΔFj=|∑iΔFij|.
(2)

The summation is performed over j interactions of atom i with all atoms j within the nonbonded cut-off distance, i.e., forces from particle mesh Ewald are ignored. We note that ΔFj would be zero if we summed up over force difference vectors ΔFij. Individual hydrogen bond forces were obtained from summing up over pairwise Lennard-Jones and Coulombic forces between all atom pairs of the C=O and N-H groups.

Hydrogen-bond prestress

To study the preexisting tensile and compressive forces in the β-sheet hydrogen bonds, we adapted the method described in Edwards et al. (30). Simulations totaling 100 ns were carried out with no external forces applied to the protein. For each run, all pairwise atomic forces within the protein were output with a frequency of 1 ps. For every hydrogen bond, the pairwise atomic forces for the pair of C=O and N-H groups comprising the hydrogen bond were summed in a vector-wise fashion, for each frame of the trajectory; this total force vector was then projected on the vector connecting the Cα atoms of the two residues at the instant of the simulation. The resulting values for the projected hydrogen-bond forces were then averaged for each residue pair over the full duration of the simulation to give the time-averaged force for each hydrogen bond in the protein. This procedure was carried out for both structures—with (Spy+) and without (Spy−) the isopeptide bond—to allow for comparison between the two.

Results and Discussion

Isopeptide-bond-dependent rupture

The isopeptide bond between the two terminal β-strands of the Spy0128 C-domain has been reported to lock the IG-like domain in its folded state (15). We here examine the molecular details of Spy0128 under a stretching force and compare the Spy+ protein to the Spy− protein. We carried out FPMD simulations at a constant pulling speed of 0.2 nm ns−1, with 20 independent simulations for each Spy+ and Spy−. Each gray curve in Fig. 2 shows the resulting force profile of one FPMD simulation; one representative force-extension curve is highlighted in black. In the absence of the isopeptide bond (Fig. 2, upper), the protein structure unfolded virtually within a single step, as reflected by the single peak in the force profile and the concurrent rupture of all hydrogen bonds between the two terminal β-strands (Fig. 3 A). Unfolding occurred at spring positions between 1.7 and 2.8 nm and at a mean rupture force of 531 ± 28 pN. As expected, rupture forces are more than two orders of magnitude higher than those measured experimentally (250 ± 96 pN), as we employed pulling velocities ∼5 orders of magnitude larger than the velocities used in AFM experiments (15,31).

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Force profile for FPMD of Spy− (upper) and Spy+ (lower) domains. A representative force-extension curve with a rupture force close to the average over all simulations is shown as a black curve; others are shown in gray. Red lines mark where the abrupt rupture occurs for each trajectory, with the solid line indicating the representative trajectory.

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Hydrogen bond rupture and reformation for Spy− and Spy+. Hydrogen-bond interaction energy monitored during FPMD simulation, as well as after the external force is removed, for Spy− (A) and Spy+ (B). The red dashed line indicates the rupture, as in Fig. 2, and the blue dashed line shows the time when the external force was released. SP, spring position.

In contrast, we did not observe any obvious unfolding peak in the force profiles sampled for Spy+, confirming that the isopeptide bond renders Spy0128 inextensible. However, it does not follow that the structure of the protein is unaffected. In the presence of the isopeptide bond, in all 20 trajectories, the RMSD of the two terminal β-strands shows an abrupt increase (Fig. S2), reflecting the terminal β-sheet rupture. The increase in RMSD coincides with the rupture of all interstrand hydrogen bonds (Fig. 3 B), which are partially substituted by a set of one to three new hydrogen bonds formed between the same two terminal β-strands. This mechanism, which we observe in 17 of 20 trajectories, corresponds to a sliding-snapping mechanism observed in previous studies (32,33). By mapping the observed structural change onto the featureless force profile (Fig. 2, lower), we obtained an average rupture force of 808 ± 26 pN. This rupture force of Spy+ thus is significantly higher than the rupture force of Spy− (p = 9.6 × 10−15).

However, the isopeptide bond in Spy+ prevented the IG domain from completely unfolding and instead locked the structure in an intermediate with all secondary and tertiary structure intact except the terminal β-strands. Interestingly, this intermediate vastly differs from the unfolding intermediate observed for titin I27 after rupture of the first part of the interstrand hydrogen bonds, the so-called force buffer (34). The force buffer protects the IG domain from complete unraveling. Thus, the isopeptide bond can be considered as a mechanism by which the force buffer is replaced by an ultrastrong link, thereby allowing partial unfolding only from the opposite side of the β-sheet. The isopeptide-bond-mediated locking also halts the shearing of the two β-strands relative to each other, thereby allowing the formation of nonnative hydrogen bonds (Fig. 3 B). Thus, our results suggest that the covalent bond has two effects, a significant increase in rupture force by ∼50% and locking of the structure in an only partially distorted unfolding intermediate. Overall, this results in an inextensibility of Spy+ (note the featureless force-extension curve in Fig. 2, lower), in agreement with observations for single-molecule force spectroscopy experiments, although it hides the underlying molecular rupture.

Force distribution in Spy0128

The observed rupture forces suggest that Spy+ largely outperforms Spy− in terms of mechanical stability. What are the determinants of the increase in mechanical robustness achieved by covalent connection of the terminal β-strands by an isopeptide bond? Is most of the external mechanical load propagating through this additional interstrand chemical bond, thereby reducing the load on the interstrand hydrogen bonds? To reveal the force distribution pattern within the physiologically relevant force-bearing structure and thereby rationalize the higher stability of Spy+, we performed a force distribution analysis. In this analysis, residue pairwise forces were obtained from the stretched structures, held at a constant force of 10 pN and 300 pN, respectively, in independent FCMD simulations. A constant force of 300 pN was applied, as this is below the lowest unfolding force observed in the FPMD simulations (Fig. 2) and is found to keep the Spy0128 C-terminal domain intact within the nanosecond timescale of the simulations (Fig. S3). We calculated the internal force distributions in Spy+ and Spy− from the differences in the residue pairwise forces between the resulting stretched and relaxed states. The residue forces were averaged over five 20-ns simulations for each state. The stress on each residue was then obtained by summing up the absolute scalar forces acting on this residue as a measure for how much this residue contributes to bearing the external pulling force. (See Methods for details. We here refer to this sum of scalar forces as stress, even though no normalization by area has been carried out.)

For Spy+ (Fig. 4, lower), the stresses due to external loading are maximal at the points of force application and decay horizontally along the β-strands and vertically toward the outside of the β-sheet. The residues distant from the points of force application, most obviously the other β-sheet of the IG-like β-sandwich structure (visible in Fig. 4 at the back of the protein), do not take part in carrying any remarkable load. Thus, the stress is particularly large in β1 and β11, of intermediate magnitude in β6 and β8, and small elsewhere (see Fig. 1 D for strand nomenclature).

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Force distribution in Spy− (upper) and Spy+ (lower) under external mechanical load along the amino acid sequence (left) is mapped onto the 3D domain structure (right). The color scheme, from red (big force) to blue (small force) represents the force magnitude. The red dashed lines at left show the location of the two residues, Lys179 and Asn303, that form the isopeptide bond.

This overall stress distribution pattern is altered when removing the isopeptide bond (Fig. 4, upper). Although Spy+ showed stresses always <1000 pN in all of the residues, stresses increased up to 1600 pN in Spy−. Spy− features particularly high stresses in the region where the peptide bond has been removed, with the otherwise isopeptide-bonded residue Asn303 exhibiting the maximal stress. Interestingly, the removal of the isopeptide bond gives rise to stress changes as distant as in the region around Leu230 in β6, a hydrophobic packing interaction adjacent to the hot spot in β1–β11, suggesting a weakening not only in the load-bearing force clamp but also in the protein’s hydrophobic core. Thus, the isopeptide-bonded residue pair in Spy+ carries much smaller forces than the same pair in Spy−. The additional covalent bond thus does not play the role of a force-bearing element in the force network of Spy0128, but instead has the indirect effect of reducing the forces in its neighborhood. Also, the total stress, i.e., the sum over all residue-wise stresses, is significantly higher in Spy− (33,340 ± 943 pN) than in Spy+ (28,465 ± 937 pN). We conclude that the isopeptide bond causes a more homogeneous distribution of forces, by means of which it can largely reduce the stress concentration at the terminal strands.

Isopeptide-bond-dependent interstrand hydrogen bonding

As described above, Spy0128 unfolding proceeds via the rupture of hydrogen bonds between the two terminal β-strands, β1 and β11, as shown within the Spy0128 structure in Fig. 5 A (Fig. 1 D, cyan). Our force distribution analysis suggested that the effect of the isopeptide bond is primarily on the forces within these two strands. To analyze this in further detail, we next determined the forces in the β1-β11 hydrogen bonds in the absence and presence of the isopeptide bond (Fig. 5 B). We note that in contrast to Fig. 4, Fig. 5 B shows the force between hydrogen bonds, i.e., only including nonbonded interactions that take place between the involved C=O and N-H groups observed for Spy0128 in equilibrium.

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Hydrogen bonds between the two terminal β-strands, β1 and β11. (A) Three-dimensional view of the hydrogen bonds (blue dashed line) and the isopeptide bond (gray) between the two β-strands. (B) The interaction forces in Spy− (black) and Spy+ (red) domains. Positive and negative values represent repulsive and attractive forces, respectively. The error bars represent the standard deviation of hydrogen-bond forces measured over 100 ns of equilibrium simulations. (C) The hydrogen-bond lengths and the center-of-mass distance of the two terminal β-strands (inset) in Spy− (black) and Spy+ (red).

The six major interstrand hydrogen bonds of the parallel β-sheet are nonzero, even in the absence of an external stretching force. Instead, they show a zig-zag pattern in their forces, with alternating magnitudes of prestress up to 100 pN (Fig. 5 B). Most of these hydrogen bonds are obviously compressed (>0 pN), with the Lys178-Phe301 and the Lys180-Asn303 hydrogen bonds featuring attractive or negligibly small forces. Prestress in hydrogen bonds has been observed earlier in globular proteins, with predominantly repulsive forces in antiparallel β-sheets (30). Here, the alternating force pattern apparently reflects the zig-zag geometry of hydrogen bonds typically found in parallel β-sheets (Fig. 5 A).

Remarkably, formation of the isopeptide bond cross-linking the two β-strands under consideration maintains the average hydrogen bond prestress at ∼55 pN (Fig. 5 B). However, the deviation of individual hydrogen-bond forces from this average, as found for Spy−, is remarkably reduced by the isopeptide bond. In fact, the additional cross-link results in a shift of the two strands with respect to each other such that every other hydrogen bond is compressed (stretched) in Spy+ relative to Spy−. This is similarly reflected in the minor yet obvious alternating increases and decreases in hydrogen-bond distances of up to 0.17 Å along the β-strands (Fig. 5 C). The relative shift of strands against each other upon isopeptide-bond formation also involves an overall compression of the two strands against each other, as we observe a decrease in the distance between the centers of mass of the β1 and β11 strands (Fig. 5 C, inset, p < 2.2 × 10−16). From the decrease in the maximal tensile prestress in the interstrand hydrogen bonds from ∼100 to ∼70 pN, we estimate a decrease in rupture rate by ∼1 order of magnitude (30), i.e., a pronounced stabilization, as also observed in FPMD simulations. Thus, even though the changes in hydrogen-bond lengths are in the sub-Ångstrom regime, they can have biophysical consequences.

In conclusion, the isopeptide bond formed between residues Asn303 and Lys179 compresses otherwise comparably stretched hydrogen bonds in its vicinity, resulting in a homogeneous compressive prestress between the two crucial terminal strands of Spy+. This effect might contribute to the increased rupture force we observed for Spy+ as compared to Spy− by stabilizing the protein, since due to the isopeptide linkage each of the six parallel hydrogen bonds needs to be pulled out of the compressed state.

Isopeptide-bond-assisted refolding

As observed in our FPMD simulations, the presence of the isopeptide bond locks Spy+ in an intermediate structure in which the strands continue to interact via a set of newly formed hydrogen bonds (Fig. 3). We asked if this intermediate is able to reestablish the native hydrogen bonds and thereby the native fold of Spy0128 upon release of force within the nanosecond timescale of our simulations. This would suggest that the isopeptide bond assists in refolding considerably, as IG domains without isopeptide bonds have been found to exhibit refolding times on the order of seconds (35).

To answer this question, we equilibrated the protein in the absence of an external force after the hydrogen bonds between the two terminal β-strands had completely ruptured in FPMD simulations. For the sample trajectory shown in Fig. 3 B, force was released when a spring position of 4 nm was reached. Indeed, all of the six primary β1-β11 hydrogen bonds were reestablished within ∼70 ns. We monitored this refolding in 8 of 10 trajectories (with partial reformation of native hydrogen bonding occurring in 9 of 10). In accordance, refolding also involved a significant decrease in root-mean-square deviation from that observed for the fully folded state during the equilibrations of the ruptured conformations in the same eight cases (Fig. S4). In sharp contrast, Spy− was totally unfolded and thus is not able to refold even partially on the same timescale. (Fig. 3 A) This indicates that the isopeptide bond promotes the structural—and probably also the functional—recovery of the protein.

Conclusions

Here, we studied the mechanical function of the isopeptide bond in Spy0128 with MD simulations and FDA. Even though Spy0128 was found in experiments to be inextensible, we here find that it shows a partial mechanical unfolding, though at stretching forces 50% higher than those required in the absence of the isopeptide bond. We attribute the increased mechanical stability of the isopeptide-bonded IG-like domain to the overall reduction in internal stresses upon introducing the covalent cross-link. In fact, we find the isopeptide bond to be located in Spy0128 right at the point of force concentration in the mechanically loaded structure, which we detect at the C-terminal half of the β1 and β11 strands. We therefore speculate that the isopeptide bond has been introduced during evolution into the IG-like fold right at the weakest link and rupture point of the structure. The reduction in stress concentration by the isopeptide bond is achieved by a compression of proximal hydrogen bonds, which enhances their resistance to force. We previously observed a similar case of mechanical stabilization by compressive prestress in hydrogen bonds for ubiquitin (30), suggesting that this mechanism is a general phenomenon for mechanically strong β-sheet protein domains.

We find that the isopeptide bond locks Spy0128 not in the fully folded protein structure, as suggested by previous AFM experiments (15), but instead in an unfolding intermediate, in which most of the protein core has remained intact. As this intermediate features virtually the same end-to-end distance as the native fold, the rupture event is undetectable in the experiments. Our observation of the unfolding intermediate raises the question of whether Spy0128 and other isopeptide-bonded domains in pili are able to maintain protein-protein interactions involved in adhesion, even under high mechanical load, as is present in pili. We speculate that the fast refolding of Spy0128 on nanosecond timescales aided by the isopeptide bond helps to restore native Spy0128, thereby ensuring the virtually instantaneous recovery of adhesive function. Experimentally probing the partial unfolding and refolding equilibrium in pili Spy0128 domains under mechanical load could help to further elucidate whether mechanical regulation of adhesion to isopeptide-bonded pili proteins as suggested by our study is indeed a plausible mechanism.

The question remains whether the difference in mechanical response of Spy0128 observed in this study only at >300 pN is of physiological significance. Given the experimental and simulated unfolding forces of ∼250 pN (15) and ∼530 pN, respectively, in the absence of an isopeptide bond, we estimate that a partial unfolding of isopeptide-linked Spy0128 monitored at ∼800 pN in our simulations occurs at 300–400 pN at smaller experimental loading rates. We note that more accurate estimates would require measuring experimental or simulated rupture forces at varying loading speeds. Such high forces have not been observed in vivo, but also cannot be excluded, given the potential turbulent flows a bacterium adhering via single strings of pili can be subjected to. Further experiments assessing retraction rates or tensile forces in various pili might help to shed light on putative unfolding and refolding mechanisms of pili in vivo.

Acknowledgments

We thank Senbo Xiao for helpful discussions.

We acknowledge financial support by the Klaus Tschira Foundation. S.A.E. acknowledges support from the Max Planck Society, a Chinese Academy of Sciences Young International Scientist Fellowship (O91GC11401), and an National Natural Science Foundation of China Research Fellowship for International Young Scientists (O93DC11401).

Supporting Material

Document S1. Figs. S1–S4:

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