1. Structural Biology and Molecular Biophysics
  2. Microbiology and Infectious Disease
Download icon

Bacterial flagella grow through an injection-diffusion mechanism

  1. Thibaud T Renault
  2. Anthony O Abraham
  3. Tobias Bergmiller
  4. Guillaume Paradis
  5. Simon Rainville
  6. Emmanuelle Charpentier
  7. Călin C Guet
  8. Yuhai Tu  Is a corresponding author
  9. Keiichi Namba  Is a corresponding author
  10. James P Keener  Is a corresponding author
  11. Tohru Minamino  Is a corresponding author
  12. Marc Erhardt  Is a corresponding author
  1. Helmholtz Centre for Infection Research, Germany
  2. Max Planck Institute for Infection Biology, Germany
  3. Osaka University, Japan
  4. Institute of Science and Technology Austria, Austria
  5. Laval University, Quebec City, Canada
  6. IBM Thomas J Watson Research Center, United States
  7. RIKEN Quantitative Biology Center, Japan
  8. University of Utah, United States
Research Article
  • Cited 13
  • Views 2,477
  • Annotations
Cite as: eLife 2017;6:e23136 doi: 10.7554/eLife.23136

Abstract

The bacterial flagellum is a self-assembling nanomachine. The external flagellar filament, several times longer than a bacterial cell body, is made of a few tens of thousands subunits of a single protein: flagellin. A fundamental problem concerns the molecular mechanism of how the flagellum grows outside the cell, where no discernible energy source is available. Here, we monitored the dynamic assembly of individual flagella using in situ labelling and real-time immunostaining of elongating flagellar filaments. We report that the rate of flagellum growth, initially ∼1,700 amino acids per second, decreases with length and that the previously proposed chain mechanism does not contribute to the filament elongation dynamics. Inhibition of the proton motive force-dependent export apparatus revealed a major contribution of substrate injection in driving filament elongation. The combination of experimental and mathematical evidence demonstrates that a simple, injection-diffusion mechanism controls bacterial flagella growth outside the cell.

https://doi.org/10.7554/eLife.23136.001

eLife digest

Most bacteria are able to move in a directed manner towards nutrients or other locations of interest. Many move by rotating long tail-like filaments called flagella that stick out from the cell. The flagellum is a remarkably complex nanomachine. It is several times longer than the main body of the bacterial cell body and its external filament is made of thousands of building blocks of a single protein called flagellin. This protein is made inside the cell and a structure at the base of the flagellum known as a type III secretion system uses chemical energy to pump it out of the cell so that it can be incorporated into the growing flagellum. The exported building blocks travel through a narrow channel within the flagellum and self-assemble at the tip.

It has been a mystery for several decades how bacteria manage to assemble the building blocks of flagella outside of the cell, where no discernible energy source is available. Renault et al. used mathematical modeling, biochemical and microscopy techniques to observe how the flagella of a bacterium called Salmonella enterica assemble in real time. The experiments demonstrate that simple biophysical principles regulate the assembly of the flagellum. The building blocks are pumped into the channel of the flagellum by the type III secretion system and then diffuse to the tip of the filament. Accordingly, the longer the flagellum gets, the slower it grows. This molecular mechanism also explains why the growth of bacterial flagella will eventually stop even without any other control mechanisms in place.

Further work will be needed to understand how the type III secretion system harnesses chemical energy to drive the movement of flagellin out of the cell into the growing flagellum. A molecular understanding of these processes will aid the design of new antibiotics targeted against type III secretion systems.

https://doi.org/10.7554/eLife.23136.002

Introduction

Many bacteria move by rotation of a helical organelle, the flagellum. The external flagellar filament is several times longer than a bacterial cell body and is made out of up to 20,000 flagellin subunits (Berg and Anderson, 1973; Chevance and Hughes, 2008; Macnab, 2003; Silverman and Simon, 1974) (Figure 1a). A type III export apparatus located at the base of the flagellum utilizes the proton motive force (pmf) as the primary energy source to translocate axial components of the flagellum across the inner membrane (Minamino and Namba, 2008; Paul et al., 2008; Minamino et al., 2011; Erhardt et al., 2014). Exported substrates travel through a narrow 2 nm channel within the structure and self-assemble at the tip of the growing flagellum. It has been a mystery how bacteria manage to self-assemble several tens of thousands protein subunits outside the cell, where no discernible energy source is available. Previous reports in the literature concerning the mechanism of flagellum growth have been conflicting (Iino, 1974; Aizawa and Kubori, 1998; Turner et al., 2012; Evans et al., 2013). An exponential decay of filament elongation with length was observed using electron microscopic measurements, which was proposed to be a result of decreased translocation efficiency (Iino, 1974; Tanner et al., 2011). A recent study used dual-colour fluorescent labelling of flagellar filaments to distinguish basal from apical filament growth and found that the rate of polymerization was independent of filament length (Turner et al., 2012; Stern and Berg, 2013). A model based on the pulling force of a filament-spanning chain of flagellin subunits was proposed to explain the apparent length-independent growth (Evans et al., 2013).

Figure 1 with 2 supplements see all
Flagellin protein export and flagella growth rate decrease with filament length.

(a) Schematic depiction of the bacterial flagellum and proposed models to explain the filament elongation dynamics (Iino, 1974; Turner et al., 2012; Evans et al., 2013). OM=outer membrane, IM=inner membrane. (b) Top: Electron micrograph images of mutants deficient in the hook-filament junction protein FlgK or the flagellin-specific chaperone FliS. Bottom: Immunoblotting of cellular and Coomassie-staining of secreted flagellin (FliC) in ∆flgK and ∆fliS mutant strains (relative secreted flagellin levels report mean ± s.d., n = 3). (c) Representative images of a population-based flagellin immunostaining time-course. Time in minutes after induction of flagellin synthesis is indicated. (d) Continuous in situ flagellin immunostaining reveals elongation kinetics of individual filaments in real time. Exemplary movie frames are shown and elapsed time in minutes after start of imaging is indicated. (e) Quantification of the population immunostaining. Measured filaments per group: t15’ (n = 187), t30’ (n = 206), t45’ (n = 480), t60’ (n = 648), t90’ (n = 700), t120’ (n = 827), t180’ (n = 302), t240’ (n = 172). The box plot reports the median (in red), the 25th and 75th quartiles and the 1.5 interquartile range. (f) Quantification of the continuous in situ flagellin immunostaining. The dark line represents the global, averaged fit of 8 individual filaments. Raw data shown as coloured dots excluding measurement incidents as explained in Figure 1—figure supplement 2. The initial velocity (Vi) was measured on the initial, linear part of the growth curve. Scale bars 2 µm.

https://doi.org/10.7554/eLife.23136.003

Results and discussion

Enhanced flagellin export in the absence of assembled filament

In order to test whether filament length itself affects the export rate of flagellin subunits during filament formation, we constructed a flagella-assembly mutant deleted for the first hook-filament junction protein (ΔflgK). This resulted in direct secretion of flagellin monomers into the culture media without transport through the elongated filament. The total amount of extracellular flagellin was analysed in the wild-type and the ΔflgK mutant by de-polymerizing flagellar filaments into flagellin monomers using heat treatment at 65°C. The amount of extracellular flagellin was approximately 1.6-fold higher in the ΔflgK mutant compared to wild-type cells. Consistently, cytoplasmic flagellin was substantially more abundant in the wild-type than in the ΔflgK mutant (Figure 1b). Measurements of flagellin leakage during filament formation revealed that only a small fraction of the total flagellin is leaked in monomeric form by wild-type cells during filament formation (Figure 1—figure supplement 1), demonstrating that the majority of exported flagellin subunits are incorporated into the growing filament under our experimental conditions. These results indicate that the presence of an assembled filament decreases the rate of flagellin transport, which is consistent with the decreased rates of FlgE and FliK export in a long hook mutant (Koroyasu et al., 1998; Erhardt et al., 2011). A similar filament length-dependent effect on flagellin transport was also observed in a mutant of the flagellin-specific cytoplasmic chaperone FliS (Figure 1b). FliS promotes docking and subsequent unfolding of flagellin at the export apparatus (Kinoshita et al., 2013; Furukawa et al., 2016), suggesting that the flagellin injection rate at the export apparatus substantially contributes to the flagellum growth dynamics.

The elongation rate of bacterial flagella inversely correlates with filament length

We next measured the growth kinetics of flagellar filaments to determine the relation between growth rate and filament length. We engineered a Salmonella strain where the production of flagellar basal bodies (using the flhDC flagellar master regulatory operon under control of a anhydrotetracycline inducible promoter) is uncoupled from the expression of chromosomally-encoded flagellin (using the flagellin gene fliC under control of an arabinose inducible promoter). This well-established setup allowed for synchronization of flagella production (Erhardt et al., 2011; Karlinsey et al., 2000) by first assembling basal bodies before initiating filament synthesis. The flagella of the synchronized culture were immunostained after increasing growth times (Figure 1c). The initial filament growth rate was ~83 nm∙min−1, which decreased over time (Figure 1e). In a complementary approach, we monitored, in real-time, the dynamic assembly of individual filaments by employing a continuous in situ immunostaining approach (Berk et al., 2012) to visualize growing flagella (Figure 1d, Video 1). A Salmonella strain harbouring a functional, hemagglutinin-epitope tagged flagellin variant under its physiological promoter was grown in a microfluidic device in the presence of labelled, primary antibodies. We observed an initial filament growth rate of ~100 nm∙min−1, which decreased over time similar as for the population-wide approach described above (Figure 1f, Figure 1—figure supplement 2).

Video 1
Real-time flagellum growth observed using in situ continuous flow immunostaining.

The animation represents the raw data of the filament length measurements of five representative flagella as a function of time. The inset depicts a 400× time-lapse movie of the corresponding microcolony grown in a CellASIC microfluidic device in the presence of 10 nM anti-HA fluorochrome-coupled primary antibodies. Elapsed time is depicted in min’sec’’. Coloured circles highlight the onset of filament assembly of the respective length measurement data. Arrows denote growth or measurement incidents (e.g. filament flipped out of focus or broke off). Scale bar 1 µm.

https://doi.org/10.7554/eLife.23136.006

In a previous study, Turner et al. (2012) measured the growth kinetics of individual filaments in Escherichia coli by site-specific labelling of flagellin subunits containing an exposed cysteine residue using sulfhydryl-specific (maleimide) fluorochromes and reported a length independent growth rate of ~13 nm∙min−1. We optimized this method to exchange dyes multiple (three to six) times in situ during normal culture growth with minimal perturbation of bacterial growth (Figure 2, Figure 2—figure supplement 1, Figure 2—figure supplement 2, Figure 3, Figure 3—figure supplement 1). The labelling of successive fragments of the flagellum with maleimide fluorochromes in situ allows observation of the filament growth dynamics at the end of the experiment. Triple labelling (exchange of dyes three times) demonstrated that the extension length of the filament (apical fragment) is inversely proportional to its initial length (basal fragment), until the growth rate for long filaments decreases to a point where it becomes minimal (Figure 2). Using this setup, the dynamic range of basal fragment lengths was increased by performing the experiment with varying growth durations (15 to 180 min).

Figure 2 with 2 supplements see all
In situ filament labelling reveals a negative correlation between filament length and elongation rate.

(a) Experimental design of the in situ triple-colour labelling time-course. Basal (F1) and apical (F2) fragments were grown for 15–180 min and 30 min, respectively. The growth duration of basal fragments is indicated in the legend. Coloured arrows indicate the coordinates of the representative example images. The fit represents the injection-diffusion model with parameters kon ≈ 33.35 s−1and D ≈ 5.90 × 10−13 m2 ⋅ s−1. Scale bar 2 µm. (b) Average size of the individual fragments for different durations of elongation of the first fragment. Error bars represent the 95% confidence interval of mean estimation. (c) Relation between the size of the second and third fragment. 93.4% of the filaments have F3 fragments shorter than the F2 fragment with the difference increasing with the length of F2. (d) Flagella labelled in panel a were measured and sorted according to the length of F1, which reveals the inverted relationship between the initial length and extension length of the filament. Each vertical line represents an individual filament (n = 1254).

https://doi.org/10.7554/eLife.23136.007
Figure 3 with 2 supplements see all
Growth kinetics of individual flagella revealed by in situ, multicolour labelling.

(a) Left: Experimental design of the in situ, multicolour labelling. Right: Representative fluorescent microscopy image for multiple labelling of flagellar filaments with a series of maleimide dyes. TB: tryptone broth without dye, AnTc: anhydrotetracyline induction of flagella genes. Scale bar 2 µm. (b) Basal/apical length coordinates were obtained by varying the duration of basal growth and successive fragments were combined to generate a total of 1276 basal/apical coordinates from 291 filaments. The growth duration of the apical fragment was 30 min. Average speeds are calculated from the average elongation per 30 min (<1 µm or >8 µm). The fit represents the injection-diffusion model with parameters kon ≈ 27.09 s−1and D ≈ 5.41 × 10−13 m2 ⋅ s−1. (c) Basal/apical length coordinates were obtained for various durations of apical growth (30–150 min) from the multiple labelling data shown in panel b. (n = 1276 for 30 min, n = 986 for 60 min, n = 697 for 90 min, n = 422 for 120 min, n = 169 for 150 min). The fit for various durations of apical growth represents the injection-diffusion model with parameters kon and D (60 min: kon ≈ 27.72 s−1, D ≈ 5.56 × 10−13 m2 ⋅ s−1; 90 min: kon ≈ 28.06 s−1, D ≈ 5.63 × 10−13 m2 ⋅ s−1; 120 min: kon ≈ 27.03 s−1, D ≈ 5.42 × 10−13 m2 ⋅ s−1; 150 min: kon ≈ 26.36 s−1, D ≈ 5.29 × 10−13 m2 ⋅ s−1). Average growth rates were estimated from the Y-intercept of the fit curve. The inset presents the average growth plotted against time. (d) Filament length as a function of time of individual flagella from the multiple labelling data. Each grey line represents the growth curve of an individual filament. The average growth rates estimated in panel c are plotted for comparison. (e) Quality of multiple labelling data. Only a minor fraction of the filaments were broken or stalled (highlighted as red dots, Figure 3—figure supplement 1a), which has limited effect on the parameter fit.

https://doi.org/10.7554/eLife.23136.010

Next, multiple labelling (exchange of dyes six times) of flagellar filaments allowed us to compute various basal/apical couples and increased the dynamic range of the growth rate data for individual flagella. The multiple labelling of flagellar filaments confirmed the length-dependent elongation mechanism with an elongation speed decreasing gradually from ~100 nm∙min−1 to ~20 nm∙min−1 (Figure 3, Figure 3—figure supplement 1). Alternative combination of the fragments allowed us to determine the filament elongation kinetics for various growth durations and in fine to derive a growth curve (Figure 3c–d). Our method further allowed us to exclude stalled or broken filaments and study the filament elongation dynamics under normal cultivation conditions for a wide range of fragment lengths. We note that we only observed a minor fraction of flagella that broke or stopped growing during the experiment (Figure 3e).

An injection-diffusion mechanism explains the growth dynamics of flagellar filaments

The solid curves in Figure 2 and Figure 3 represent the best fit of the data to a growth curve for which the growth rate is a function of the length L of the form ab+L, where the parameter a has units of a diffusion coefficient, and b has units of length. Derivation of this formula is based on an injection-diffusion model where flagellin monomers, which are at least partially α-helical inside the channel (Shibata et al., 2007), are pushed by a pmf-driven export apparatus into the channel and move diffusively in one dimension through the length of the flagellum (Stern and Berg, 2013; Keener, 2006). An analytical expression for the flagellum length dependent growth rate is based on a continuum injection-diffusion model for the growth of flagellar filaments. Monomers (each of length l) in the growing filament are assumed to move diffusively. Because the filaments are long narrow tubes, monomers are partially unfolded and diffusion is constrained to be strictly one-dimensional, i.e. no passing allowed. In the corresponding continuum model, we define u(x,t)l as the density of monomers per unit length at position x and time t. Then u satisfies the diffusion equation

(1) ut=Duxx.

Here, D is the diffusion coefficient of the monomers. We assume that all end-to-end collisions between monomers are ballistic, with no end-to-end binding. For this, Fickian diffusion is the appropriate description of diffusion, even at high densities. We assume that at the growing end X=L, monomers are quickly removed by folding/polymerization so that effectively u(L,t)=0.

The details of the mechanism by which monomers are secreted at the basal end X=0 is not known, but it is known to be related to the pmf (Paul et al., 2008). We assume that the rate of secretion (number of monomers per unit time) into an empty filament is Kon, but if it is not empty, then the rate of secretion is decreased because of the no-passing restriction. Consequently, the flux J0 (number of monomers per unit time at the basal end) is taken to be

(2) J0=Dlux(0,t)=Kon(1u(0,t)).

Finally, the rate of growth of the filament is given by

(3) dLdt=βJL=Dβlux(L,t),

where β is the length increment of the filament due to polymerization of a single monomer.

Since the filament growth rate is small compared to the average velocity of monomers, it is reasonable to take the monomer diffusion to be in quasisteady state, i.e. uxx=0. Thus, the monomer density in the filament is a linearly decreasing function and ux is the constant u(0)L. It follows that the filament growth rate is

(4) dLdt=βDl1Dkonl+L=ab+L,

where a=βDl, with units of diffusion, and b=Dkonl, with units of length. This is readily solved to find the filament length as a function of time

(5) L(t)=b+b2+2at.

We can estimate the diffusion coefficient using a=βDl, so that

(6) D=alβ.

From all the datasets presented above, we determined a ≈ 0.2 µm2 ⋅ min−1. Using β = 0.47 nm (a flagellar filament of 1 µm length is composed of approximately 2130 flagellin subunits [Yonekura et al., 2003]), l = 74 nm (assuming an extended, α-helical flagellin molecule) this leads to an estimate of D ≈ 5.25 × 10−13 m2 ⋅ s−1. Stern and Berg (Stern and Berg, 2013) estimated D ≈ 5.78 × 10−11 m2 ⋅ s−1 for freely moving α-helical flagellin in water. The actual diffusion coefficient for movement in the narrow 2 nm channel would be substantially smaller, however. Stern and Berg (Stern and Berg, 2013) (their Figure 2) used a 480 times smaller diffusion coefficient (D ≈ 1.25 × 10−13 m2 ⋅ s−1) for numerical simulations that resulted in a declining growth curve, which closely resembled the filament growth kinetics presented above.

Our triple and multiple labelling experiments demonstrated that the growth of a new part of the filament (apical fragment) shows a strong inverse dependence on its initial length (basal fragment) for short filaments, while the growth rate for long filaments decreases to a point where this dependence becomes minimal (Figure 2, Figure 3, Figure 3—figure supplement 1). We note that several differences in the experimental setup of Turner et al. (2012) from ours might have affected the injection rate and frequency of filament breakage. As described in detail in Appendix 1, the possibility of broken/stalled filaments and possible perturbations of the injection rate reconcile our data with the reported filament growth data of Turner et al. (2012) and explains why we observed a length-dependent decrease in growth rate. In support, we simulated in Figure 3—figure supplement 2 the effects of filament breaking/stalling events and heterogeneous injection rates. The simulated broken/stalled filaments accumulate on the x-axis, which results in a quasi-linear fit of the complete filament growth rate data, similar to the linear filament growth observed by Turner et al. (2012).

We further note that a length-dependent decrease in filament growth rate would explain why flagellar filaments do not growth indefinitely. However, flagellar filaments broken by mechanical shearing forces can re-grow (Turner et al., 2012; Rosu and Hughes, 2006; Vogler et al., 1991). The injection-diffusion model predicts that the elongation rate of re-growing filaments would increase compared to unbroken filaments. We performed multiple labelling in situ to determine the growth rate of individual filaments that had been broken using mechanical shearing forces. Consistent with the injection-diffusion mechanism, the elongation rate of re-growing, previously broken filaments was substantially faster than the elongation rate of unbroken filaments and was dependent on the length of the basal filament segment, which remained attached to the bacterial cell surface (Figure 4).

Figure 4 with 1 supplement see all
Elongation rate of re-growing filaments increases after mechanical shearing.

(a) Experimental design to determine filament elongation rate after mechanical shearing using multicolour labelling. (b) A successful shearing event removed fragment F3 and partially or completely fragment F2. (c) Representative example images of control filaments and filaments broken using mechanical shearing forces. Flagellar filaments were sheared by passing the bacterial culture five times (mild shearing) or up to 30 times (strong shearing) in and out of a 22-gauge needle. Scale bar 2 µm. (d) Left panel: length of the basal, cell-attached filament after mechanical shearing demonstrating successful filament breakage. Right panel: length of apical, re-growing filament fragments demonstrating a length-dependent increase in filament elongation rate. The box plots reports the median, the 25th and 75th quartiles and the 1.5 interquartile range. Data points represent individual filament fragments. Statistical significance according to a two-tailed Student’s t-test is indicated. F4 strong vs. control: p-value=0.000026 (***); F5 strong vs. control: p-value=0.002452 (**); F6 strong vs. control: p-value=0.034514 (*); F7 strong vs. control: not significant (n.s.).

https://doi.org/10.7554/eLife.23136.013

Inter-subunit chain formation does not contribute to flagella growth dynamics

Based on the observations of Turner et al. (2012), Evans et al. (2013) developed a model where folding of newly arriving subunits at the tip of the flagellum would provide energy to pull successive subunits through the channel at a constant rate. Evans et al. demonstrated that N-terminal regions of flagellar substrates (FlgD, FlgE, FlgG and FliK) can bind to the C-terminal cytoplasmic domain of FlhB, which is a component of the pmf-driven transmembrane export gate complex. Further, site-specific cysteine-cysteine crosslinking showed that the N- and C-terminal regions of hook (FlgE) and flagellin (FliC) can interact to form head-to-tail dimers. They hypothesized that formation of inter-subunit chains resulting from those interactions could enable their transport at a length-independent speed, as the folding of the exported molecules at the filament tip would provide a continuous pulling force. While the N- and C-terminal interactions of flagellar substrates might play an important role during substrate docking and in the final fold of assembled hook and filament subunits, the proposed inter-subunit chain mechanism for flagellin transport and filament assembly raises several issues that are incompatible with the known biophysical properties of flagellum assembly (Yonekura et al., 2003; Samatey et al., 2001). A flagellum-spanning chain requires interactions of the N- and C-terminal α-helical domains of flagellin, but the 2 nm wide filament channel (Yonekura et al., 2003) is too narrow to accommodate the secretion of much more than one folded α-helix (Figure 5a). The chain mechanism hypothesizes that folding of a flagellin subunit at the tip of the flagellum can pull a chain of succeeding subunits, but the N- and C-termini of successive flagellin molecules are anti-parallel and far apart in the polymerized filament structure (∼17 Å on average) (Yonekura et al., 2003; Samatey et al., 2001) (Figure 5b). Further, the chain mechanism is not compatible with simultaneous secretion of non-chaining substrates (Figure 5d). Flagellar substrates such as FlgM or excess hook-associated proteins (FlgK, FlgL, FliD) are constantly exported during flagellum growth (Komoriya et al., 1999) and do not interact with flagellin (Furukawa et al., 2002). Also, premature termination of translation is occurring frequently (~1∙10−4 to ~5∙10−4 events per codon) (Sin et al., 2016). Thus, a high proportion of 5–20% newly synthesized flagellin might be truncated for the C-terminal domain needed for head-to-tail chain formation. We estimate that secretion of as little as one non-chaining substrate every 10,000 full-length flagellin molecules would prevent filament elongation if a chain mechanism drives flagellum growth (Figure 5d–g).

Figure 5 with 3 supplements see all
The contribution of inter-subunit chains for filament elongation rate.

(a) The 2 nm wide filament channel only accommodates one folded α-helix. (b) The N- and C-termini of successive flagellin molecules are anti-parallel and far apart in the polymerized filament structure. (c) Top: Structure, domains, and secondary structures of flagellin FliC (PDB: 1UCU). Mutant flagellins lacking combinations of the N- and C-terminal domains required for head-to-tail coiled-coil chaining (ΔN, ΔCS, ΔCL) were co-expressed together with endogenous flagellin (FliC) to disrupt chain formation. Bottom: Flagellin immunoblotting on cellular and secreted fractions (relative full-length flagellin levels report mean ± s.d., n = 3). (d) Simultaneous secretion of non-chaining substrates breaks a filament-spanning chain of flagellin molecules. A strict chain model requires the chain to span the entire filament and does not allow for disruptions of the chain. A chain model with the possibility of recovery by diffusion of broken chains is discussed in Figure 5—figure supplement 1. (e) In situ, multicolour labelling of flagellar filaments during competitive co-expression of chain-disrupting mutant flagellins. The average growth of fits computed from basal/apical coordinates presented in Figure 5—figure supplement 3c and as described in Figure 3c is shown as a function of time. Basal/apical coordinates were derived from multiple labelling data of individual filaments: n = 399 from 89 filaments (−), n = 271 from 58 filaments (WT), n = 278 from 62 filaments (∆CL), n = 412 from 93 filaments (∆N ∆CL), n = 209 from 46 filaments (∆CS), n = 312 from 73 filaments (∆N ∆CS). The fits represent the injection-diffusion model and parameters kon and D are given in Figure 5—source data 1. (f) Probability of existence of n-long chains defined by the binomial law. Long chains are highly improbable for a 15% proportion of competing substrates (i.e. formation of a more than 2.4 µm long chain (n > 33) has a probability of 1%). The bars show the individual probability of existence, the dotted blue line the cumulated probability of existence of chains longer than the number on the x-axis. The grey curve indicates the chain length in µm, which reflects that filaments cannot grow longer than a few hundred nanometres with a chain-based mechanism. (g) Simulation of filament growth dependent on inter-subunit chains or the injection-diffusion model in presence of random proportion of competing substrate. The injection-diffusion model fit represents the mean of the multi-labelling data set of Figure 3 with parameters kon ≈ 27.25 s−1and D ≈ 5.46 × 10−13 m2 ⋅ s−1. Dashed white line: median length of the filament for chain-model dependent growth. Grey box: expression range of chain-disrupting mutant flagellins used in panel e and Figure 5—figure supplement 1a.

https://doi.org/10.7554/eLife.23136.015

To test the requirement of subunit chain formation for flagellum growth in more detail, we generated flagellin mutants truncated for the N- and C-termini that render head-to-tail linkage impossible (Figure 5c). All flagellin truncation mutants were secreted, but were deficient in flagellum assembly due to deletions in the D0 and D1 domains needed for filament polymerization and FliS chaperone binding (Yonekura et al., 2003) (Figure 5—figure supplement 1a, Figure 5—figure supplement 3). We expressed those non-chaining, but secreted flagellin mutants in trans to disrupt formation of a chain of wild-type flagellin molecules (Figure 5d). Competitive secretion of the flagellin truncation mutants did not affect endogenous flagellin transport during filament formation (Figure 5c). Filament extension kinetics were determined using multiple labelling of individual flagellar filaments and, similarly, no significant difference was observed when chain-disrupting flagellin mutants were co-expressed (Figure 5e, Figure 5—figure supplement 3c).

Mathematical modelling of the chain model-dependent filament elongation dynamics predicted a linear growth up to a very long flagellum (>0.1 mm), which is in clear contradiction with the experimental observations (Appendix 2).

Inhibition of the pmf-dependent protein export prevents filament elongation

Our high-resolution filament growth rate data and the previous observations by Stern and Berg (2013) suggested that two major components drive flagellin export: pmf-dependent injection of subunits by the type III export apparatus at the base of the flagellum and diffusion of subunits along the length of the flagellum. We used carbonyl cyanide m-chlorophenyl hydrazone (CCCP) to disrupt the pmf, which is required for substrate translocation via the export apparatus into the central channel of the growing flagellar structure (Minamino and Namba, 2008; Paul et al., 2008). The injection-diffusion model predicts that a decrease in the injection rate Kon results in slow, quasi-linear growth for sufficiently small Kon. As expected, CCCP treatment resulted in impaired filament extension in a dose-dependent manner, which recovered upon removal of the uncoupler (Figure 6a, Figure 6—figure supplement 1). We hypothesized that in presence of high concentration of CCCP, the injection of substrate would be strongly reduced and result in low-speed growth. As shown in Figure 6c, the filament elongation rate for the highest CCCP concentration (~18 nm∙min−1) was virtually independent of the length of the filament as predicted by the model. Interestingly, some filaments were unaffected by the CCCP treatment, likely due to the action of multidrug transporters (Lomovskaya and Lewis, 1992), and displayed kinetics similar to the untreated population (Figure 6—figure supplement 1d), highlighting the major contribution of the pmf in energizing export.

Figure 6 with 1 supplement see all
The effect of pmf on flagellin injection and filament growth rate.

(a) Top: Experimental design. Carbonyl cyanide m-chlorophenyl hydrazone (CCCP) reduces the proton motive force (pmf) and was present during growth of the second fragment (60 min) and removed during growth of the third fragment, which allowed the pmf to regenerate. TB: tryptone broth without dye, AnTc: anhydrotetracyline induction of flagella genes. Bottom: Fragment lengths represented as basal/apical (F1/F2) coordinates (n = 255 for 0 µM CCCP, n = 395 for 10 µM CCCP, n = 371 for 20 µM CCCP, n = 353 for 30 µM CCCP). The fits represent the injection-diffusion model with parameters D ≈ 5.25 × 10−13 m2 ⋅ s−1, and kon ≈ 26.10, 3.19, 1.19, 0.70 s−1 for 0 µM, 10, 20, 30 µM CCCP respectively. Representative fluorescent microscopy images of labelled flagella and matching coordinates are highlighted by coloured frames and arrows. Scale bar 2 µm. (b) Filament length as a function of time for decreasing values of kon. For small values of kon, the injection rate but not flagellin transport is rate-limiting, which results in a quasi-linear growth. (c) Growth curves for the CCCP raw data of panel a determined by fitting the data to the injection-diffusion model with a fixed parameter a. The values for kon decrease by a factor of 8 (10 µM CCCP), 22 (20 µM CCCP), and 38 (30 µM CCCP), compared to the untreated control. (d) Equation and biophysical parameters of the injection-diffusion model.

https://doi.org/10.7554/eLife.23136.020

Conclusion

The bacterial flagellum is a remarkably complex nanomachine. Here, we present the first real-time visualization and experimentally supported biophysical model of the dynamic self-assembly process of this large, widely conserved nanomachine. We propose that bacterial flagella grow through an injection-diffusion mechanism (Figure 6d), which provides a simple explanation why the flagellar filament does not grow infinitely in the absence of any other length-control mechanism. It appears likely that similar biophysical principles are conserved for effector protein secretion in the evolutionary related, virulence-associated injectisome with important implications for the rational design of novel anti-infectives targeted against type III secretion systems.

Materials and methods

Bacteria, plasmids and media

Salmonella enterica serovar Typhimurium strains and plasmids used in this study are listed in Table 1. Lysogeny broth (LB) contained 10 g of Bacto-Tryptone (Difco), 5 g of yeast extract, 5 g of NaCl and 0.2 ml of 5N NaOH per litre. Soft agar plates used for motility assays contained 10 g of Bacto-Tryptone, 5 g of NaCl, 3.5 g of Bacto-Agar (Difco) and 0.2 ml of 5N NaOH per liter. Tryptone broth (TB) contained 10 g of Bacto-Tryptone and 5 g of NaCl. Ampicillin was added to the medium at a final concentration of 100 µg/ml, L-arabinose at a final concentration of 0.2% and anhydrotetracyline at a final concentration of 100 ng/ml if required.

Table 1

Strains and plasmids used in this study.

https://doi.org/10.7554/eLife.23136.022
StrainRelevant characteristicsSource or reference
SJW1103Salmonella enterica serovar Typhimurium wild-type strain SJW1103 for motility and chemotaxis(Yamaguchi et al., 1984)
TM113SJW1103 ∆fliCT. Miyata, unpublished
NH001SJW1103 ∆flhA(Hara et al., 2011)
MM1103iSSJW1103 ∆fliS::km(Furukawa et al., 2016)
MM1103gKSJW1103 flgK::Tn10This study
MM1103gKiSSJW1103 ∆fliS::km flgK::Tn10This study
MM1103CPOPSJW1103 ∆PfliC::tetRA-62This study
TH437Salmonella enterica serovar Typhimurium wild-type strain LT2lab collection
TH15801LT2 PflhDC5451::Tn10dTc[del-25] ∆hin-5717::FCFlab collection
EM1237LT2 ∆araBAD1026::fliCfliC7861::FRT ∆hin-5717::FCF PflhDC5451::Tn10dTc[del-25]This study
EM2046LT2 ∆hin-5717::FRT fliC6500 (T237C) PflhDC5451::Tn10dTc[del-25]This study
EM2400LT2 ∆hin-5717::FRT fliC6500(T237C) ∆araBAD1005::FRT PflhDC5451::Tn10dTc[del-25]This study
EM4076LT2 ∆hin-5717::FRT fliC7746::3xHA (∆aa201-213::3xHA) motA5461::MudJ PflhDC5451::Tn10dTc[del-25] ∆sseA-ssaU::FCF (deletes Spi-2)This study
PlasmidsRelevant characteristicsSource or reference
pBAD24Expression vectorInvitrogen
pAOA001pBAD24/FliCThis study
pAOA002pBAD24/FliC(∆29–32)This study
pAOA003pBAD24/FliC(∆11–18)This study
pAOA004pBAD24/FliC(∆11–18/∆29–32)This study
pAOA005pBAD24/FliC(∆310–495)This study
pAOA006pBAD24/FliC(∆29–32/∆310–495)This study
pAOA007pBAD24/FliC(∆450–495)This study
pAOA008pBAD24/FliC(∆29–32/∆450–495)This study

DNA manipulations

DNA manipulations were carried out as described before (Hara et al., 2011). Site-directed mutagenesis was carried out using QuickChange site-directed mutagenesis method as described by Agilent Technologies, Santa Clara, CA, USA. DNA sequencing reactions were carried out using BigDye v3.1 as described in the manufacturer’s instructions (Applied Biosystems, Foster City, CA, USA), and then the reaction mixtures were analysed by a 3130 Genetic Analyzer (Applied Biosystems).

Motility assays in soft agar

To check motility of the Salmonella SJW1103 (wild-type) and TM113 (∆fliC) cells carrying a pBAD24-based plasmid encoding wild-type or FliC deletion variants, motility assays were performed in soft agar plates. Single colonies of the cells were inoculated into soft agar plates containing ampicillin and 0.2% arabinose. Plates were then incubated at 30°C for the required period of time. Their motility was observed as a ring of migrating cells emanating from the point of inoculation.

Flagellin transport assay

Salmonella cells were grown with shaking in 5 ml of LB at 30°C until the cell density had reached an OD600nm of approximately 1.0–1.2. To see the effect of the flagellar filament on flagellin transport during filament assembly, the cultures were heated at 65°C for 5 min to depolymerize the filaments into flagellin monomers and were centrifuged to obtain cell pellets and culture supernatants, which contains the cytoplasmic flagellin subunits and flagellins transported by the flagellar type III export apparatus, respectively. To test the effect of flagellin subunit linkage on the flagellar growth rate (compare Figure 5c), strain MM1103CPOP carrying a pBAD24-based plasmid encoding FliC(∆310–495), FliC(∆29–32/∆310–495), FliC(∆450–495) or FliC(∆29–32/∆450–495) was grown with shaking in 5 ml of LB containing ampicillin at 30°C until the cell density had reached an OD600 of approximately 0.6–0.8. To induce the expression of chromosomally encoded wild-type FliC (from a tetracycline-inducible promoter in the native fliC locus) and its deletion variant (from an arabinose-inducible promoter encoded on pBAD24), we added tetracycline and L-arabinose at the final concentrations of 15 µg/ml and 0.2%, respectively, and the incubation was continued for another hour. The cultures were directly heated at 65°C for 5 min, followed by centrifugation to obtain cell pellets and culture supernatants. Cell pellets were resuspended in the SDS-loading buffer, normalized to a cell density to give a constant amount of cells. Proteins in the culture supernatants were precipitated by 10% trichloroacetic acid, suspended in the Tris/SDS loading buffer and heated at 95°C for 3 min. After SDS-PAGE, both CBB-staining and immunoblotting with polyclonal anti-FliC antibodies were carried out as described before (Minamino and Macnab, 1999). Detection was performed with an ECL plus immunoblotting detection kit (GE Healthcare, Tampa, FL, USA). At least six independent experiments were performed.

Flagellin leakage measurements during filament assembly

Salmonella cells were grown with gentle shaking in 5 ml of LB at 30°C until the cell density had reached an OD600 of approximately 1.0. After centrifugation, the cell pellets and the culture supernatants were collected separately. The culture supernatants were ultracentrifuged at 85,000 × g for 1 hr at 4°C and the pellets and the supernatants, which contain flagellar filaments detached from the cell bodies during shaking culture and flagellin monomers leaked out the culture media during filament formation, respectively, were collected separately. The cell pellets were suspended in 5 ml PBS and then were heated at 65°C for 5 min, followed by centrifugation to obtain the cell pellets and supernatants, which contained the cytoplasmic flagellin molecules and depolymerized flagellin monomers, respectively. The cell pellets and the pellet fractions after ultracentrifugation were resuspended in the SDS-loading buffer, normalized to the cell density to give a constant amount of cells. Proteins in the supernatants were precipitated by 10% trichloroacetic acid, suspended in Tris/SDS loading buffer and heated at 95°C for 3 min. After SDS-PAGE, both CBB-stating and immunoblotting with polyclonal anti-FliC antibodies were carried out. At least six independent experiments were performed.

Electron microscopy observation of negatively stained Salmonella cells

Salmonella cells were exponentially grown with gentle shaking in 5 ml LB at 30°C. 5 µl of the cell culture were applied to carbon-coated copper grids and negatively stained with 0.5% (W/V) phosphotungstic acid. Micrographs were recorded at a magnification of 1200× with a JEM-1010 transmission electron microscope (JEOL, Tokyo, Japan) operating at 100 kV.

Microscopy of flagellar filaments

For immunolabelling of flagellar filaments, polyclonal anti-FliC and anti-rabbit IgG antibodies conjugated with Alexa Fluor 488 and 594 (Invitrogen, Carlsbad, CA, USA) were used as described (Erhardt et al., 2011; Minamino et al., 2014).

For in situ labelling of flagellar filaments of the FliCT237C cysteine replacement mutant, an overnight culture was diluted 1:100 into 10 ml fresh TB in a 125 ml flask and grown at 30°C for 2 hr until OD600nm of 0.6. Production of the flagellar master regulatory operon flhDC was induced by addition of 100 ng/ml anhydrotetracycline (AnTc) for 30 min. Afterwards, the culture was centrifuged for 3 min at 2500 × g, resuspended in 10 ml fresh TB and grown at 30°C for 30 min. An aliquot was transferred to a 2 ml Eppendorf tube and grown with shaking at 30°C for 30 min in the presence of 10–25 µM Alexa or DyLight-coupled maleimide dye (ThermoFisher, Tampa, FL, USA). After the incubation, the dye was removed by centrifugation for 2 min at 2500 × g. The culture was resuspended in 1 mL fresh TB and incubated for additional 30 min in the presence of 10–25 µM Alexa or DyLight-coupled maleimide dye at 30°C. Dye removal and incubation with DyLight-coupled maleimide dye was repeated to label up to six flagellar filament fragments. After the final labelling period, the bacteria were resuspended in PBS and an aliquot was applied to a custom-made flow cell (Wozniak et al., 2010) with the modification of using Polysine microscope slides (ThermoFisher). Non-adhering cells were flushed by addition of PBS and bacteria were fixed by addition of 2% formaldehyde, 0.2% glutaraldehyde in PBS for 5 min, followed by a washing step with PBS. Fluoroshield mounting medium (Sigma-Aldrich, St. Louis, MO, USA) was added and the cells were observed by fluorescent microscopy using a Zeiss (Oberkochen, Germany) Axio Observer microscope at 100× magnification. Fluorescence images were analysed using ImageJ software version 1.48 (National Institutes of Health).

Continuous flow in situ immunostaining of 3× hemagglutinin epitope tagged FliC filaments was performed as described by Berk et al. (2012) with the following adaptions. Strain EM4076 expressing mCherry from pZS*12-mCherry (mCherry under control of Plac [Lutz and Bujard, 1997]) was grown to mid-log phase in M9-glucose minimal medium supplemented with 0.2% casamino acids and 0.1% bovine serum albumin (BSA) and induced for 30 min with 100 ng/ml AnTc. Bacteria were diluted 10-fold, and applied to a continuous flow CellASIC microfluidic plate (B04A; Merk Millipore, Billerica, MA, USA). Approximately 10 nM anti-HA Alexa Fluor488 fluorochrome-coupled primary antibodies (Thermo Fisher A-21287, final concentration 1 µg/ml) were added to the flow medium, which was identical to the above mentioned growth medium without addition of AnTc. Cells were imaged at 30°C with a temperature-controlled Olympus total internal reflection fluorescence microscope equipped with a water-cooled Hamamatsu (Hamamatsu City, Japan) ImageEM C9100-13 with a pixel size of 160 µm using a NA1.4 100× objective and an additional 1.6× tubular lens at a highly-inclined above-critical angle. To image anti-HA Alexa Fluor488 decorated flagellin and mCherry, a 488 nm diode laser set to 0.25 mW and a 561 nm solid-state laser set to 0.85 mW were used. Images were taken every 10 s with exposure times of 15 msec for 488 nm and 8 msec for 561 nm at low camera gain settings.

Data reporting

No statistical methods were used to predetermine sample size. The experiments were not randomized and the investigators were not blinded to allocation during experiments and outcome assessment.

Statistical analysis

Biochemistry experiments were performed at least three times and representative experiments are reported in the figures. Where indicated, mean values and standard deviations were obtained from at least three independent biological replicates. All microscopy experiments were performed at least twice and the figures present individual data points of a representative experiment. Box plots report the median (in red), the 25th and 75th quartiles and the 1.5 interquartile range. Error bars of bar graphs represent the 95% confidence interval of mean estimation.

Fitting experimental data by the growth model

To compare the model with data, we need to find a best fit for the parameters a and b using the growth function (Equation 4). Accordingly, note that if F1 is the amount of filament growth in time ∆T following an initial growth of length F0, then

(7) F0F0+F1(b+L)dL=aΔT,

which reduces to the equation

(8) L(L+2b)|F0+F1F0=2aΔT,

or

(9) bF1+12(2F0F1+F12)=aΔT.

This could be solved for F0 as a function of F1 and then fitted by standard regression to find parameters a and b. However, to do so would ignore the important fact that there is measurement error in both of the measurements F0 and F1. Consequently, a different method of fitting this curve is needed.

The method used here is to seek numbers W0 and W1, which are approximations to F0 and F1 and satisfy the relationship

(10) bW1+12(2W0W1+W12)=aΔT

This can be done by minimizing the function

(11) E=N((F0W0)2+(F1W1)2+λ(bW1+12(2W0W1+W12)aΔT)2),

where λ is a fixed constant. In this way, both F0 and F1 are treated as noisy data values which need to be fitted.

However, for this analysis, we found it better to introduce the change of variables L=bU1U=g(U), U=LL+b and then to find numbers U0 and U1, α=aΔTb2 and b so that

(12) E=N((F0bg(U0))2+(F0+F1bg(U1))2+λ(f(U1))f(U0)α)2)

is minimized, where f(U)=1b2(bL+12L2)12U(2U)2(1U)2. The minimization of E is equivalent to finding the solution of the system of 2N + 2 nonlinear algebraic equations

(13)α:N(f(U1)f(U0)α)=0,(14)b:N(F0bg(U0))g(U0)+N(F0+F1bg(U1))g(U1)=0,(15)U0:b(F0bg(U0))g(U0)+λ(fU1)f(U0)α(f(U0)=0,(16)U1:b(F0+F1bg(U1))g(U1)+λ(f(U1)f(U0)α)f(U1)=0.

This system of equations is readily solved with an iterative solution method such as Newton’s Method, details of which are not described here.

Once U0 and U1 are known, so also are W0=bU01U0 and W1=bU11U1W0. From this we can estimate the time at which the F0 phase of growth ended to be

(17) t0=1a(bW0+W022),

and the time at which the F1 growth phase ended is t1=t0+ΔT. This information enables us to plot the growth curve and plot the F0 and F1 measurements at the appropriate times.

Simulation of filament growth in presence of competing substrates

Substrates arriving at the export gate were randomly chosen with a probability p = r / (1+r) to be a competing substrate (i.e., non-chaining or not incorporated in the filament), where r is the ratio of competing molecules relative to flagellin. The following rules were used:

  1. 1)Unaltered growth (i.e. without competing substrate) followed the kinetics determined experimentally: L(t)=b+b2+2at with a = 0.208 and b = 0.271. Note that this observed L(t) dependence does not preclude the chain formation model, which may also lead to the same form of growth kinetics, but only for growth without any chain breakage. However, the general conclusion is independent of the specific growth form, e.g., a linear growth kinetics lead to the same conclusion.

  2. 2)Competition for injection was considered to induce, per competing substrate, a delay, with a time scale that is taken to be the same as the injection time ton=kon138ms.

  3. 3)For the chain model, chain breakage due to competing substrates induced either an arrest of elongation in the strict chain model (see Figure 5) or a delay in growth in the chain recovery model (see Figure 5—figure supplement 1 ) with a delay time given by (tb − ta), where:

    1. (i)tb is the time required for the basal chain to diffuse to the tip defined as tb=ηLa2D0 with D0 the diffusion coefficient of a flagellin monomer, La the length to diffuse to reach the tip, and n the number of subunits in the chain.

    2. ta is the time required for the apical chain to fold according to the kinetic of unaltered growth.

In Figure 5 panel g and Figure 5—figure supplement 1 panel d, we simulated filament growth over 250 min for 20,000 filaments and assumed a mechanism based on the chain model (strict in blue, with recovery in yellow) or the injection-diffusion model (in red), in the presence of a random proportion of competing substrates (r) between 10−9 and 1,000. The simulation of chain model-dependent filament growth is illustrated in Figure 5—figure supplement 2.

The range of competing substrates compatible with a chain-driven elongation is very low (<10−4–10−5), while the injection-diffusion model allows for robust filament growth over a much broader range of competing substrate (up to about a 10-fold excess of competing substrates).

Complementary to the simulation, the median length of the filament under chain model-dependent growth and in presence of competing substrates can be calculated as follows:

The probability of sequentially forming a chain of exact length n is Pn=pn(1p).

The expected number of molecules in the chain is:

(18) E(p)=(1p)nnpn=p1p=1x

Thus, the median length of a filament grown from a continuous chain is , where β = 0.47 nm and k can be determined by:

12=nkPn=nk(1p)pn=1pk+1,

which leads to:

(20) k=ln2ln(1+x)1.

Appendix 1

Differences in the experimental design explain the apparent differences in filament growth rate observed by Turner et al. (2012)

In the following, we describe differences in the experimental setup of Turner et al. (2012) from ours, which readily explain the apparent differences in growth for short filaments and thus reconcile our results with the previous work.

First, the filament labelling protocol used by Turner et al. (2012) included multiple, long-term centrifugation steps to remove excess dye and wash the samples. We found the maleimide labelling of the exposed cysteine residue to be very specific and a single centrifugation step was sufficient to remove residual maleimide dye prior to the next labelling step. Thus, our samples were exposed to only 3–6 short-term, low speed centrifugation steps for a total duration of 6–12 min (for the triple and multi-colour labelling, respectively). In comparison, the samples of Turner et al. (2012) were exposed to three long-term, repeated centrifugation and resuspension washes for a total duration of 187 min. Flagellar filaments can easily break due to the shearing forces of centrifugation or repeated pipetting. It thus appears possible that the frequent centrifugation steps increased the frequency of broken filaments during the experiment of Turner et al. (2012), which possibly contributed to the fraction of first-fragment-only (= broken or stalled) filaments observed in Figure 3 of Turner et al. (2012). While we do not know how to exactly convert the experimental conditions of Turner et al. (2012) quantitatively into our model, we performed a simulation of increasing fractions of broken filaments using our multi-color data set. As shown in Figure 3—figure supplement 2, the broken/stalled filaments accumulate on the x-axis and below the fit curve and thus result in a quasi-linear fit of the complete filament growth data set.

Further, the filament labelling protocol of Turner et al. (2012) included a long-term incubation step overnight at 7°C in contrast to the in situ labelling in our experimental setup, where we added the maleimide dyes during normal culture growth to minimize perturbations. It appears possible that long-term incubation of samples at low temperatures might have negatively affected the injection rate of flagellin subunits into the growing filament e.g. by alterations in protein translation efficiency or changes in the available proton motive force. Supporting this possibility, we also observed quasi-linear growth of the filament if the injection rate and not flagellin transport was rate-limiting (Figure 3—figure supplement 2, Figure 6).

Finally, the growth rate data of Turner et al. (2012) contain only few measurements of short filaments for which we observed faster growth (the majority of measured filaments were 4–6 µm long), while our filament growth data report filaments ranging from 0.2–10 µm. In summary, the extended range of filament lengths, the possibility of broken/stalled filaments and possible perturbations of the injection rate reconcile our data with the reported filament growth data of Turner et al. (2012) and explains why we observed a clear length-dependent decrease in growth rate.

Appendix 2

Dynamics of the chain model and comparison to the injection-diffusion model

In the following, we describe the differences between the chain model proposed by Evans et al. (2013) and our injection-diffusion model for flagellum growth. For a chain of length L, there are a total of N = L/l monomers, where l = 74 nm is the length of the unfolded monomers. For a freshly arrived lead-monomer (of the chain) at the distal end to grow into the flagellum, two things have to happen:

  1. i)The lead-monomer will take some time to initiate the folding and then 'crystallize', which takes a total time tf.

  2. The whole chain has to move a distance l driven by the folding.

After these two steps, a new lead-monomer will arrive and the chain is ready to go through the same process to continue growth. If the folding of the monomer provides a force f0, and the friction constant of the chain is Nη0, where η0 is the monomer friction constant, then the moving speed is f0 / (Nη0), and the moving time is:

(A1) tm=l/(fo/Nη0))=Nlη0f0=η0Lf0.

Now, if we assume tf is mostly dominated by the initiation time, the total time it takes for one monomer to be fully incorporated into the flagellum and to be ready again for further growth is:

(A2) tg=tf+tm,

which leads to an equation of growth with the same form to our injection-diffusion growth model:

(A3) dLdt=β/tg=βtf+η0f0L

Despite its similar form, the meaning of this equation is completely different from our model. For comparison, our injection-diffusion model is given here again:

(A4) dLdt=βkon1+lD0L,

where D0 is the diffusion constant of a monomer.

The two growth models differ in the two terms in the denominators in the right hand side of the growth equations. A careful look at these two terms can help us distinguish these two models as discussed in the following:

The first term in the denominators controls the initial linear growth. In our injection-diffusion model, it is given by the injection time , tonkon1,which is the time for a monomer to be unfolded and injected at the basal end of the flagellum; whereas in the chain-forming model, it is given by the crystallization/folding time tf at the distal end. The values of kon or tg can be obtained from the initial growth rate measured in the experiments.

The second term in the denominator is more revealing. Due to the extremely large folding force f0, the second term (the L-dependent term) is much smaller in the chain model than in our model.

Since this second term is responsible for the slower t, the chain-forming model would predict a linear growth dynamics up to a very large flagellum length, beyond the longest flagellum length observed, which is obviously in contradiction with the observations.

Quantitatively, we can compute the ratio of the two terms from the two models by using the Einstein relationship D0η0=kBT:

(A5) (η0f0L)(lDL)=kBTf0l=kBTΔEf,

where ΔEf=f0l should be comparable to the folding free energy, which is ≫kBT with kBT the thermal energy at room temperature (kBT ≈ 4 pN ∙ nm).

The second term of the chain-forming model is negligible with values of f0 = 10–30 pN (Evans et al., 2013) and l = 74 nm. Accordingly, as noted by Evans et al. (2013), friction is not the rate-limiting factor for movement of an inter-subunit chain in the channel and would follow the rate of crystallization at the filament tip.

In the chain-forming model, the crossover length, Lc = tf f0 / η0, is much larger (could be > 100 µm) than in our model (~0.25–2 µm), and one would not observe the cross over to the slower t growth, which is in clear contradiction with the experimental observations.

All the above assumes an end-to-end chain does form, however. Our experimental evidence suggests that such long chains do not form (Figure 5); and perhaps even more importantly, the growth works fine with the injection-diffusion model where there is no chain.

References

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17
  18. 18
  19. 19
  20. 20
    Components of the Salmonella flagellar export apparatus and classification of export substrates
    1. T Minamino
    2. RM Macnab
    (1999)
    Journal of Bacteriology 181:1388–1394.
  21. 21
  22. 22
  23. 23
  24. 24
  25. 25
  26. 26
  27. 27
  28. 28
  29. 29
  30. 30
  31. 31
  32. 32
  33. 33
  34. 34
  35. 35
  36. 36

Decision letter

  1. Frank Jülicher
    Reviewing Editor; Max Planck Institute for the Physics of Complex Systems, Germany

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article "Bacterial flagella grow through an injection-diffusion mechanism" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by Frank Jülicher as the Reviewing Editor and Richard Aldrich as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Richard M Berry (Reviewer #1); Victor Sourjik (Reviewer #2).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

The manuscript of Renault et al. addresses a highly interesting and controversial topic of how bacterial flagellar filaments, by far the most prominent extracellular structure known in bacteria, are assembled. It is well established that flagellar assembly occurs at the tip, meaning that the subunits need to travel across the pore within a filament is a semi-unfolded state and polymerize at the exit site. However, it remains unclear how this mode of assembly is regulated, and particularly how it leads to the formation of filaments of defined length. In their study, Renault et al. combine elegant microscopy experiments with theory to provide very strong evidence in favour of the injection-diffusion model of assembly. The authors further provide convincing experimental demonstration that mutants lacking chain-forming domains that are implicated in a competing model of flagellar export are secreted without disrupting normal filament growth. This provides strong evidence against the chain model. Altogether, the results of this manuscript are compelling and the analysis is solid. There is only one important point that needs to be addressed prior to publication.

Essential revisions:

The results of this manuscript apparently contradict a previous study (Turner et al., 2012) that concluded that growth rate of flagellar filaments is length-independent. The authors clearly cite that previous study and point to the discrepancy in the Results, and they also briefly mention differences in the experimental design. However, it would be important to discuss this discrepancy more extensively, because it relates to the central conclusion of this manuscript. The authors' analysis presented here is convincing, but it is still unclear why different conditions used by Turner et al. led to the opposite conclusion. Possible reasons for previous reports of slower growth should be pointed out explicitly. Differences with previous work that could be relevant should be explained in the Discussion. Since the authors have a mathematical model at hand, they might even be able to simulate filament growth under conditions used by Turner et al., to reconcile their results with that previous work.

https://doi.org/10.7554/eLife.23136.025

Author response

Essential revisions:

The results of this manuscript apparently contradict a previous study (Turner et al., 2012) that concluded that growth rate of flagellar filaments is length-independent. The authors clearly cite that previous study and point to the discrepancy in the Results, and they also briefly mention differences in the experimental design. However, it would be important to discuss this discrepancy more extensively, because it relates to the central conclusion of this manuscript. The authors' analysis presented here is convincing, but it is still unclear why different conditions used by Turner et al. led to the opposite conclusion. Possible reasons for previous reports of slower growth should be pointed out explicitly. Differences with previous work that could be relevant should be explained in the Discussion. Since the authors have a mathematical model at hand, they might even be able to simulate filament growth under conditions used by Turner et al., to reconcile their results with that previous work.

This is an important point and we thank the referees for raising it. We are convinced that differences in the experimental setup and data analysis of Turner et al. 2012 readily explain the apparent differences in growth for short filaments and thus reconcile our results with the work of Turner et al. 2012.

In particular, we believe that multiple, long-term centrifugation steps and long-term incubation at low temperatures of the experimental setup of Turner et al. 2012 might have negatively affected the injection rate and frequency of filament breakage. We thus took great care to optimize our experimental setup in order to minimize such perturbations of flagellum growth.

Accordingly, we improved our filament labelling approach to exchange dyes multiple times with minimal perturbation of bacterial growth. Importantly, we label the filaments in situ during normal culture growth, which does not affect the flagellum growth rate (Figure 2—figure supplement 1).

We include now a detailed comparison of our experimental approaches with the approach of Turner et al. 2012 in the revised manuscript (Appendix 1) and the main differences are summarized below:

1) The filament labelling protocol used by Turner et al. 2012 included multiple, long-term centrifugation steps to remove excess dye and wash the samples. Each of those centrifugation (centrifugation 3-4 times at 1.400 × g for 12 minutes) and resuspension manipulations spanned a duration of 51–68 min per labelling in contrast to a single, short 2 minutes centrifugation step at 2.500 × g per labelling in our experimental setup.

We found the maleimide labelling of the exposed cysteine residue to be very specific and a single centrifugation step was sufficient to remove residual maleimide dye prior to the next labelling step. Thus, our samples were exposed to only 3–6 short-term, low speed centrifugation steps for a total duration of 6–12 minutes (for the triple and multi-colour labelling, respectively). In comparison, the samples of Turner et al. 2012 were exposed to three long-term, repeated centrifugation and resuspension washes for a total duration of 187 minutes.

It is important to note that flagellar filaments can easily break due to the shearing forces of centrifugation or repeated pipetting. It thus appears possible that the frequent centrifugation steps increased the frequency of broken filaments during the experiment of Turner et al. 2012, which likely contributed to the large fraction of 1st fragment-only (= broken or stalled) filaments that are visible in Figure 3 of Turner et al. 2012.

In this respect, we would like to emphasize that in our experimental setup, only a minimal fraction of the data points (<2%) resulted from broken or stalled filaments (see also Author response image 1 and Figure 3—figure supplement 1A of our manuscript) and had no impact on the model fit.

2) In respect to the data analysis, Turner et al. 2012 did not exclude filaments that broke or stopped growing during their experiment because of the limitations of the 2-color approach. A large fraction of the analysed filaments of Turner et al. 2012 indeed appear to have stopped growing or were broken (compare Figure 3 of Turner et al. 2012 and Author response image 1A, where many filaments with only the basal fragment (= zero 2nd fragment growth) are apparent).

The authors did not exclude those filaments, in contrast to our approach, where we could readily identify and exclude them from our data analysis using a 3- or 6-color approach (Author response image 1B). We note that we observed only very few broken/stalled filaments in our data, likely due to the more physiological culture growth conditions.

3) While we do not know how to exactly convert the experimental conditions of Turner et al. 2012 quantitatively into our model, we performed a simulation of increasing fractions of broken filaments using our multi-colour data set. As shown in Author response image 1B and the new Figure 3—figure supplement 2, the broken/stalled filaments accumulate on the x-axis and below the fit curve.

Accordingly, we conclude that a high fraction of broken/stalled filaments would mask the otherwise obvious length-dependency of filament growth and prevents an accurate fit. We believe that if broken/stalled filaments were excluded from Figure 3 of Turner et al. 2012, their data would very likely also reveal that growth rate decreases with increasing filament length.

Author response image 1
Comparison of the 2-color filament growth rate measurement of Turner et al. 2012 with our multi-colour filament growth rate data.

a. 2-color growth rate data reported in Figure 3 of Turner et al. 2012; (A) represents unsheared filaments and (B) represents data from sheared filaments. The high number of points on the x-axis suggests that many filaments are broken or stalled. b. Raw data of our multi-colour filament growth rate measurements. Upper left panel represents the raw multi-colour data reported in the present manuscript and highlights apparently stalled or broken filaments. Lower panel represents the basal-apical growth coordinates from the multi-colour data and highlights as red dots the data derived from apparently stalled or broken filaments. Importantly, those data points accumulate below the fit curve, which prevents an accurate fit when the proportion of broken/stalled filaments is too high. c. Simulation of random filament breakage (of probability pbreak) on our dataset demonstrate that data points accumulate on the x-axis and below the fit curve (in red). It is crucial to note that a high fraction of broken filaments masks the obvious length-dependency of filament growth and prevents an accurate fit on the complete set of points (linear fit in blue; compare with Figure 3 of Turner et al. 2012).

https://doi.org/10.7554/eLife.23136.023

4) We note that our filament growth data report filaments ranging from 0.2–10 µm, which is a substantially wider range compared to the distribution of filaments from Turner et al. 2012 (primarily filaments of 4–6 µm length were measured). In this respect, Figure 5 of Turner et al. 2012 does not report the true spread of the data and thus the apparent linear fit is difficult to interpret.

5) The filament labelling protocol of Turner et al. 2012 further included a long-term incubation step overnight at 7 °C in contrast to the in situ labelling in our experimental setup (We added the maleimide dyes during normal culture growth to minimize perturbations. This procedure did not affect bacterial growth or the growth rate of flagellar filaments. See also Figure 2—figure supplement 1A of our manuscript). Further, Turner et al. 2012 used substantially higher maleimide dye concentrations, which might have had additional effects on culture growth (40×–100× more dye than we used during our experiments = 1 mM dye compared to 10-25 µM used by us).

It appears possible that long-term incubation of their samples at 7 °C overnight might have negatively affected the rate of filament elongation. The injection rate of flagellin subunits into the growing filament would be readily affected by altered protein translation efficiency and changes in the available proton motive force (compare also Figure 6 of our manuscript). Supporting this possibility, we also observed quasi-linear growth of the filament if the injection rate and not flagellin transport was rate-limiting.

We thus speculate that the long manipulations and storage of the cells at 7 °C might have affected the filament growth rate of a subpopulation of the samples of Turner et al. 2012 due to perturbations of the injection rate. Changes in the cell's available proton motive force could negatively affect the injection rate and increase the dispersion of the data. This is emphasised by a comparison of Figure 3 of Turner et al. 2012 with our growth rate experiment under conditions of reduced proton motive force (Author response image 2 and new Figure 3—figure supplement 2).

Author response image 2
Filament growth rate under conditions of reduced proton motive force.

a. Basal-apical length coordinates based on the 2-color filament length data reported in Figure 3 of Turner et al. 2012. b. Basal-apical length coordinates of our growth rate experiment under conditions of reduced proton motive force. The curve in red represents the observed filament growth under physiological proton motive force. We presume that the length data reported in Figure 3 of Turner et al. 2012 comprises sub-populations of bacteria with decreased proton motive force due to extensive experimental manipulations. Please note that the duration of apical fragment growth was 60 minutes in our experiment, in contrast to 90 minutes in Turner et al. 2012.

https://doi.org/10.7554/eLife.23136.024

6) Finally, it is important to highlight that we obtained very similar length-dependent filament growth dynamics and growth rates using three independent experimental approaches – and only one is similar (but improved) to the approach used by Turner et al. 2012:

First, we used population-immunostaining of filaments, where we determined the length of filaments at the end of the experiment. Here, the bacteria grew normally in batch culture without any manipulations prior to fixation (Figure 1C and E, Figure 2—figure supplement 1B).

Second, we performed continuous flow immunostaining of individual filaments during normal culture growth (Figure 1D and F, Figure 1—figure supplement 2). Again, the bacteria were not manipulated during filament assembly and filament growth was observed in real-time.

Third, we significantly improved the quantity and resolution of our filament growth data using a 3- and 6-color sequential labelling approach. As described above in detail, we performed the filament labelling in situ during normal culture growth in order to minimize potential perturbations (Figure 2, Figure 3).

https://doi.org/10.7554/eLife.23136.026

Article and author information

Author details

  1. Thibaud T Renault

    1. Junior Research Group, Infection Biology of Salmonella, Helmholtz Centre for Infection Research, Braunschweig, Germany
    2. Max Planck Institute for Infection Biology, Berlin, Germany
    Contribution
    TTR, Conceptualization, Formal analysis, Investigation, Visualization, Writing—original draft, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0002-1530-2613
  2. Anthony O Abraham

    Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan
    Contribution
    AOA, Formal analysis, Investigation, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0002-8710-1351
  3. Tobias Bergmiller

    Institute of Science and Technology Austria, Klosterneuburg, Austria
    Contribution
    TB, Investigation, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
  4. Guillaume Paradis

    Department of Physics, Engineering Physics and Optics, Laval University, Quebec City, Quebec, Canada
    Contribution
    GP, Conceptualization, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
  5. Simon Rainville

    Department of Physics, Engineering Physics and Optics, Laval University, Quebec City, Quebec, Canada
    Contribution
    SR, Conceptualization, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
  6. Emmanuelle Charpentier

    Max Planck Institute for Infection Biology, Berlin, Germany
    Contribution
    EC, Funding acquisition, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
  7. Călin C Guet

    Institute of Science and Technology Austria, Klosterneuburg, Austria
    Contribution
    CCG, Funding acquisition, Writing—review and editing
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0001-6220-2052
  8. Yuhai Tu

    IBM Thomas J Watson Research Center, New York, United States
    Contribution
    YT, Conceptualization, Formal analysis, Writing—original draft, Writing—review and editing
    For correspondence
    yuhai@us.ibm.com
    Competing interests
    The authors declare that no competing interests exist.
  9. Keiichi Namba

    1. Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan
    2. RIKEN Quantitative Biology Center, Suita, Japan
    Contribution
    KN, Conceptualization, Supervision, Funding acquisition, Writing—review and editing
    For correspondence
    keiichi@fbs.osaka-u.ac.jp
    Competing interests
    The authors declare that no competing interests exist.
  10. James P Keener

    Department of Mathematics, University of Utah, Salt Lake City, United States
    Contribution
    JPK, Conceptualization, Formal analysis, Writing—original draft, Writing—review and editing
    For correspondence
    keener@math.utah.edu
    Competing interests
    The authors declare that no competing interests exist.
  11. Tohru Minamino

    Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan
    Contribution
    TM, Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Writing—original draft, Writing—review and editing
    For correspondence
    tohru@fbs.osaka-u.ac.jp
    Competing interests
    The authors declare that no competing interests exist.
  12. Marc Erhardt

    Junior Research Group, Infection Biology of Salmonella, Helmholtz Centre for Infection Research, Braunschweig, Germany
    Contribution
    ME, Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Writing—original draft, Writing—review and editing
    For correspondence
    marc.erhardt@helmholtz-hzi.de
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0001-6292-619X

Funding

Helmholtz-Gemeinschaft (VH-NG-932)

  • Marc Erhardt

Max-Planck-Gesellschaft

  • Emmanuelle Charpentier

National Institutes of Health (R01GM081747)

  • Yuhai Tu

European Commission (334030)

  • Marc Erhardt

Japan Society for the Promotion of Science (25000013)

  • Keiichi Namba

Natural Sciences and Engineering Research Council of Canada

  • Simon Rainville

Alexander von Humboldt-Stiftung

  • Thibaud T Renault

Japan Society for the Promotion of Science (26293097)

  • Tohru Minamino

Ministry of Education, Culture, Sports, Science and Technology (24117004)

  • Tohru Minamino

Ministry of Education, Culture, Sports, Science and Technology (15H01640)

  • Tohru Minamino

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank to Howard Berg, David F Blair and Kelly T Hughes for useful discussions and generous donation of strains, Takuma Fukumura and Nadine Körner for expert technical assistance and Tomoko Miyata for her kind gift of TM113. This work was supported in part by JSPS KAKENHI grant 25000013 (to KN) and 26293097 (to TM) and MEXT KAKENHI grant 24117004 and 15H01640 (to TM), the CFI, NSERC and CREATE (to SR), the Max Planck Society (to EC), NIH grant R01GM081747 (to. YT) and the Helmholtz Association Young Investigator grant VH-NG-932 and the People Programme (Marie Curie Actions) of the Europeans Unions’ Seventh Framework Programme grant 334030 (to ME). TTR gratefully acknowledges fellowship support by the Alexander von Humboldt Foundation.

Primary correspondence and requests for materials should be addressed to M.E. (marc.erhardt@helmholtz-hzi.de). Correspondence concerning the mathematical injection-diffusion model should be addressed to J.P.K. (keener@math.utah.edu) and Y .T . (yuhai@us.ibm.com). Correspondence concerning flagellin competition experiments should be addressed to T.M. (tohru@fbs.osaka-u.ac.jp) and K.N. (keiichi@fbs.osaka-u.ac.jp).

Reviewing Editor

  1. Frank Jülicher, Reviewing Editor, Max Planck Institute for the Physics of Complex Systems, Germany

Publication history

  1. Received: November 11, 2016
  2. Accepted: March 4, 2017
  3. Accepted Manuscript published: March 6, 2017 (version 1)
  4. Version of Record published: April 10, 2017 (version 2)

Copyright

© 2017, Renault et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 2,477
    Page views
  • 747
    Downloads
  • 13
    Citations

Article citation count generated by polling the highest count across the following sources: Scopus, Crossref, PubMed Central.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)

Further reading

    1. Biochemistry and Chemical Biology
    2. Structural Biology and Molecular Biophysics
    Michael Luke Carlson et al.
    Tools and Resources
    1. Neuroscience
    2. Structural Biology and Molecular Biophysics
    Doreen Matthies et al.
    Research Article