Substrate stiffness impacts early biofilm formation by modulating Pseudomonas aeruginosa twitching motility

The transition of bacteria from a planktonic to a surface-attached state is of paramount importance in biofilm formation. In consequence, the way bacteria sense and respond to the close proximity of a surface has been the subject of intense scrutiny (Dufrêne and Persat, 2020; Laventie and Jenal, 2020). This interaction involves different aspects of bacterial motility: swimming toward the surface, but also swarming, gliding or twitching that are used by attached bacteria to explore the surface collectively or individually (Wadhwa and Berg, 2022; Conrad et al., 2011). Eventually, permanent bacterial adhesion and microcolony structuration may arise, through mechanisms which essential ingredients are known (production of matrix, loss of motility), but in response to cues that remain unclear.

Bacteria are ubiquitous and can successfully colonize a wide range of biological tissues and abiotic surfaces (Stoodley et al., 2002; Mann and Wozniak, 2012). Different environments often result in different phenotypes for a given microorganism (Dötsch et al., 2012; Cornforth et al., 2018). However, although chemical signaling has long been known to impact bacterial gene regulation, it remains unclear how the mechanical properties of the encountered surface might impact bacterial behavior (Persat et al., 2015b). In this paper, we investigate how the rigidity of a substrate modifies bacterial motility, and by doing so impacts microcolony morphogenesis and early biofilm development.

Pseudomonas aeruginosa (PA) is an opportunistic rod-shaped pathogen that contaminates a wide range of substrates, from very soft tissues to rigid implants (Moradali et al., 2017; Chang, 2017). A particularly gifted and versatile biofilm-former, it is extremely prone to developing antibiotic resistance (Pang et al., 2019; Boucher et al., 2009). PA has developed an arsenal of techniques to move on surfaces: among them is twitching motility, that allows single bacteria to translocate across surfaces using type IV pili (T4P) (Maier and Wong, 2015). T4P are thin protein filaments on the bacterial surface that can extend and contract by assembly and disassembly of the protein subunit PilA. The tip of T4P acts as a promiscuous hook that can grasp most surfaces. Attachment, contraction, detachment and extension cycles propel bacteria (Merz et al., 2000; Maier and Wong, 2015; Skerker and Berg, 2001; Talà et al., 2019). This surface motility is important for bacteria to efficiently settle on surfaces, but the exact mechanisms at play are unknown (O’Toole and Kolter, 1998; Leighton et al., 2015; Craig et al., 2019). The function of T4P and the fact that it exerts forces on its environment make it an obvious candidate for surface-sensing mechanisms (Merz et al., 2000; Dufrêne, 2015; Sahoo et al., 2016). Recent results have shown that the polar localization of pili in PA could happen in response to surface-sensing (Cowles and Gitai, 2010). Polarly localized pili lead to persistent rather than random displacements, as well as specific effects such as the upstream migration of bacteria submitted to strong flows (Shen et al., 2012). Reversal of twitching bacteria is rapidly induced upon meeting obstacles, suggesting a mechanical feedback from T4P (Kühn et al., 2021). In addition, PA can exert different types of virulence, from acute attacks to chronic infections (Furukawa et al., 2006; Valentini and Filloux, 2016), and specific host-pathogen interactions have traditionally been considered as the key players in the regulation of these virulence pathways (Gellatly and Hancock, 2013). However, surface-sensing in itself has recently appeared as a potential signal that could trigger the upregulation of virulence-associated genes (Islam and Krachler, 2016; Persat et al., 2015a; Siryaporn et al., 2014). Although the global effect of surface rigidity on bacterial adhesion and biofilm formation has sometimes been addressed (Saha et al., 2013; Song and Ren, 2014; Song et al., 2018), so far how the micromechanical environment experienced by individual bacteria impacts their behavior is still unclear, possibly because of the difficulty to design and control microenvironments that allow for a fine tuning of mechanical properties at the bacterial scale, along with negligible changes of the chemical environment.

In this study, we use a home-designed microfluidic setup to investigate at the single-cell level the influence of substrate rigidity on PA bacteria adhering to an open surface, under controlled flow conditions. We first demonstrate that substrate elasticity strongly impacts early microcolony development. Focusing on single-cell behavior, we then study quantitatively how rigidity modulates bacterial motility and propose a purely mechanistic model to account for our observations. Finally, we demonstrate that this mechanical tuning of the motility explains rigidity-induced changes in early surface colonization: we explore its consequences in terms of microcolony morphology, matrix deposition, strain mixing, and long-term gene expression.

In order to explore in situ the effect of substrate rigidity on the behavior of adhering bacteria, we have developed an experimental approach to include mechanically well-defined hydrogel pads in a microfluidic channel providing controlled flow conditions and allowing confocal imaging (Figure 1A). We use the biocompatible hydrogel polyacrylamide (PAA), which has been extensively used to investigate cell-substrate interaction and mechanotransduction in mammalian cells. By varying the amount of bisacrylamide cross-linker during its preparation, PAA can span a biologically-relevant range of rigidities (from ∼1–100 kPa) while keeping a low viscous dissipation. Several pads, with different’s modulus values ranging from ∼3 to 100 kPa (see Figure 1—figure supplement 1, and Materials and methods), are used in each single experiment, and bacteria adhering on PAA and glass surfaces are imaged with high-resolution phase-contrast and fluorescence time-lapse imaging, from very low surface coverage up to the formation of microcolonies (1 frame/min over ∼10 hr).

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Substrate elasticity modifies bacterial colonization of PAA in a T4P-dependent manner

We first focus on the effect of substrate rigidity on early microcolony formation. Straightforward observations with phase-contrast imaging show a striking impact on the shape of microcolonies after a few hours (Figure 1B and Video 1): on the softest hydrogels (<10 kPa), bacteria form well-defined, dense hemispherical colonies; in contrast, on stiff hydrogels, bacteria are distributed in a thin layer covering most of the surface, a morphology closer to what we observe on glass. To rule out any effect due to changes in the bacterial growth rate, we quantified the division time of bacteria (Figure 1C), and the volume occupied by bacterial colonies after a few hours (Figure 1D and E) on different substrates: both were found to be unaffected, suggesting that bacteria develop and colonize substrates at the same rate irrespective of rigidity, but that the processes that drive their self-organization into colonies are modified. In contrast, a change in the morphology of the colonies could be confirmed by quantifying the characteristic roughness of the bacterial layer, which decreases as rigidity increases (Figure 1E), and the distribution of bacteria with the distance from the surface, which spreads further for soft hydrogels (Figure 1F). To control that this is a robust phenomenon driven by substrate elasticity rather than specific chemical interactions, we reproduced this assay using polyethylene glycol (PEG) hydrogels, which are chemically different from PAA but can span a similar range of rigidities. We obtained very similar results regarding the phenotype of colonies, which further confirms a role for the mechanical properties of the substrate in bacterial self-organization (Figure 1—figure supplement 2). Finally, because shear flow can orient polarly-attached bacteria, direct motility, disperse quorum-sensing molecules, and generally impact spatial organization into colonies, we carried out experiments on hydrogels immobilized at the bottom of wells, without any agitation of the above medium. Although long-term observations are rendered difficult in that case by swimming bacteria, we clearly observed the formation of denser colonies on softer PAA (Figure 1—figure supplement 3), which further demonstrates that substrate stiffness modifies bacterial behavior after attachment in a wide variety of environments.

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Since surface motility is known to be important for initial self-organization of PA, we hypothesize that it could play a role in the different microcolony shapes that we observe. This link was explored by carrying out experiments using a mutant deprived of type IV pili (T4P), and thus unable to twitch on surfaces (mutant PAO1 $pilA$::Tn5, Figure 1—figure supplement 4). In these assays, the dependence of microcolony morphology on substrate rigidity is abolished and bacteria form dense hemispherical colonies on all PAA substrates. We therefore conclude that T4P-mediated surface motility (‘twitching’) plays a key role in the rigidity modulation of microcolony formation by WT PAO1 on soft elastic substrates.

Substrate elasticity modulates twitching motility

Experimental results - global motility

To quantify the coupling between the elasticity of the substrate and the twitching motility of bacteria, we analyzed time-lapse phase contrast images of adhering bacteria in flow cells. These images allow segmentation of individual bacteria (SI subsection I.A) from the start of the acquisition (with a few isolated bacteria per field of view) until the transition to out-of-plane growth, after which individual bacteria cannot be easily separated anymore. From segmented binary images at early imaging stages (<100 min), we obtain the surface coverage $A(t)$ as the fraction of occupied pixels, and the cumulative explored area $S(t)$ as the fraction of pixels that has been explored at time $t$ (Figure 2A). The evolution of $A(t)$ reflects the exponential growth of initially attached bacteria on the surface, as well as potential attachment and detachment events during the acquisition. However, in our experiments initial surface coverage is extremely low, and at early times the number of bacteria in the clean flowing medium is negligible so that attachment events are rarely observed. We can thus consider that

(1) ${\displaystyle \frac{dA}{dt}=(k_{di}-k_{de})A(t).}$

The bacterial division rate $k_{di}$ does not depend on the substrate (Figure 1C), and was measured for each experiment ($k_{di}^{-1}$=27.8 ± 1.4 min). Figure 2B shows the experimental time evolution of $A(t)$ depending on the gel rigidity, which can indeed be well described by a simple exponential (straight line in the semi-log presentation with slope $k_{di}-k_{de}$). The slope of $A(t)$ slightly increases with gel rigidity, suggesting a higher detachment rate $k_{de}$ on softer hydrogels at early acquisition times.

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Surface coverage and explored area vs time.

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Compared to $A(t)$, there is a quantitatively much larger dependence of the cumulative surface coverage $S(t)$ on the substrate rigidity (Figure 2B). We propose that this result directly reflects a change of the global motility $V_g$ of bacteria on the surface. Indeed, neglecting bacterial surface attachment, the evolution of $S$ can be written as

(2) ${\displaystyle \frac{dS}{dt}=k_{di}A+V_g{w}_{b}N=(k_{di}+\frac{V_g}{l_b})A.}$

where $N$ denotes the number of bacteria on the surface, and the typical size of a rod-shaped bacterium is $w_b{l}_b$ (width × length), so that the occupied area is $A=N{w}_b{l}_b$. Here we have assumed that bacteria tend to move along their major axis, neglecting reorientations, based on previous findings about the polar localization of T4P (Cowles and Gitai, 2010; Jin et al., 2011; Kühn et al., 2021) and our own observations. (Considering that bacteria can move in any direction would lower velocity values by a factor $\sqrt{\frac{l_b}{w_b}}\approx \sqrt{3}$, and not change significantly the coming discussion.) The average bacterial size was measured in each experiment (l_b =2.8 ± 0.13 $\mathrm{\mu }m$, w_b =0.8 ± 0.13 $\mathrm{\mu }m$). For each monitored position, we determined $dS/dt$ and $A(t)$ experimentally. The global bacterial velocity $V_g$ was then estimated using Equation 2, by averaging over the first 100 experimental time points.

During the first 100 min under flow, $V_g$ exhibits a clear dependence on substrate elasticity (Figure 2C). Motility values are close to zero on very soft substrates (3–6 kPa), and progressively increase to reach ${\displaystyle \sim 0.5\pm 0.25}$ μm/min on the stiffest hydrogels tested in this study (84 kPa). We wondered whether this dependence of surface motility on substrate elasticity could result from intracellular modifications in response to bacterial surface-sensing. In P. aeruginosa, two main surface-sensing systems have been unveiled so far: the Pil-Chp system that involves T4P retraction-mediated force sensing Webster et al., 2021, and the Wsp system believed to be activated by cell envelop stress O’Neal et al., 2022; both systems have been shown to activate biofilm formation pathways following bacterial adhesion Chang, 2017. Sessility and matrix production are promoted by increasing intracellular c-di-GMP levels, which production is catalyzed by diguanylate cyclases (DGCs). We carried out experiments with wspR and sadC mutants, two DGCs known to be involved in the surface-sensing response. Although impaired in c-di-GMP regulation, both mutants still exhibited a stiffness-dependent twitching motility (Figure 2—figure supplement 1). Even though other DGCs might be involved, these initial results suggests that our observations at early timescales could be mainly governed by the mechanical interaction of bacteria with their substrate, with gene regulation playing a secondary role. This rational motivates the simple kinetic modeling presented next.

Minimal kinetic modeling

Because a difference in twitching velocity is observed almost immediately upon attachment of bacteria onto the surface, a simple hypothesis could be that a modulation of the twitching efficiency arises through mechanical factors – the interplay between the T4P extension/retraction mechanism and the linear elasticity of the substrate – without the need for mechanotransduction mechanisms. To test this minimal hypothesis, we have developed a kinetic model, schematically described on Figure 2D.

Briefly (more details can be found in appendix 1), we consider a bacterium adhering onto an elastic substrate with a single effective pilus. The pilus is modelled as a rigid inextensible filament (Beaussart et al., 2014) and attaches to the substrate via its extremity with a typical adhesion size $\lambda$. This simple choice is motivated by microscopic observations of pilus straightening over its whole length during retraction Talà et al., 2019 and an estimation of the pilus attachment spot size of $\approx 1$ nm from traction force microscopy measurements Koch et al., 2022. Note, that multiple attachments of pili over extended regions to the substrate have also been suggested Lu et al., 2015. However, in our simple approach, we do not consider this possibility. The cell actively retracts its pilus until it detaches from the substrate with the force dependent velocity $v_{\mathrm{R}}(F)=v^0(1-\frac{F}{F_{\mathrm{R}}})$(Marathe et al., 2014), where $F$ denotes the tensile load on the pilus, $F_{\mathrm{R}}$ the retraction stall force and $v^0$ the retraction speed at zero load. Assuming linear elasticity, the tensile load $F$ is related to the substrate displacement $u$ at the pilus adhesion patch by $F=Yu$, where $Y\sim E\lambda$ and $E$ is the Young’s modulus of the substrate. Since the typical size of the bacterial body l_b is much larger than $\lambda$, we neglect the deformation of the substrate induced by the bacterial body. Instead we assume that the pilus tension leads to a forward sliding of the bacterial body with a linear force-velocity relationship $v_{\mathrm{B}}(F)=v^0\frac{F}{F_{\mathrm{B}}}$ (see SI subsection II.B and Sens, 2013), reducing the substrate deformation and the load in the pilus. Here, the ratio $\eta =\frac{F_{\mathrm{B}}}{v_0}$ denotes the mobility constant of the cell on the substrate. With this model, the evolution of the pilus tension $F$ is thus given by

(3) ${\displaystyle \frac{\mathrm{d}F}{\mathrm{d}t}=Y\frac{\mathrm{d}u}{\mathrm{d}t}=v_{\mathrm{R}}(F)-v_{\mathrm{B}}(F)}$

which is solved by

(4) ${\displaystyle F(t)=F_0\left(1-e^{-\frac{Y{v}^0}{F_0}t}\right)}$

with the naturally arising force scale

(5) ${\displaystyle F_0=\frac{F_{\mathrm{B}}{F}_{\mathrm{R}}}{F_{\mathrm{R}}+F_{\mathrm{B}}}.}$

From $\frac{\mathrm{d}{x}_{\mathrm{B}}}{\mathrm{d}t}=v_B(F)$ we obtain the bacterial sliding distance during the pilus retraction

(6) ${\displaystyle x_{\mathrm{B}}(t)=\frac{F_0}{F_{\mathrm{B}}}\left[v^{0}t+\frac{F_0}{Y}\left(e^{-\frac{Y{v}^0}{F_0}t}-1\right)\right].}$

While retracting the pilus will detach with a rate constant k_off from the substrate. Assuming a force-independent off-rate constant $k_{\mathrm{off}}=k_{\mathrm{off}}^0$ (and hence a mean pilus adhesion time ${\left(k_{\mathrm{off}}^0\right)}^{-1}$) and a pilus retraction frequency $k_{\mathrm{p}}$, we obtain an effective bacteria velocity:

(7) ${\displaystyle v_{\mathrm{e}\mathrm{f}\mathrm{f}}=k_{\mathrm{p}}⟨x_{\mathrm{B}}⟩=k_{\mathrm{p}}{k}_{\mathrm{o}\mathrm{f}\mathrm{f}}^0{\int }_0^{\mathrm{\infty }}{x}_{\mathrm{B}}(t)e^{-k_{\mathrm{o}\mathrm{f}\mathrm{f}}^{0}t}\mathrm{d}t=V_{\mathrm{m}\mathrm{a}\mathrm{x}}\frac{E}{E+E_0}.}$

Here, $⟨x_{\mathrm{B}}⟩$ denotes the mean bacterial sliding distance per pilus retraction event and $V_{\max }$ denotes the maximum effective speed a bacterium can reach on a given substrate at infinite rigidity. It is given by

(8) ${\displaystyle V_{\mathrm{m}\mathrm{a}\mathrm{x}}=v^0\frac{k_{\mathrm{p}}}{k_{\mathrm{o}\mathrm{f}\mathrm{f}}^0}\frac{F_{\mathrm{R}}}{F_{\mathrm{B}}+F_{\mathrm{R}}}.}$

E₀ denotes the rigidity at half-maximal speed and is given by

(9) ${\displaystyle E_0=\frac{F_{\mathrm{B}}{F}_{\mathrm{R}}{k}_{\mathrm{o}\mathrm{f}\mathrm{f}}^0}{(F_{\mathrm{B}}+F_{\mathrm{R}})v^0\lambda }.}$

Fitting (A11) against experimentally measured effective bacterial velocities $V_g$ provides a quantitative description of the data for ${\displaystyle V_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.77\pm 0.35}$ μm.min^-1 and $E_0=84\pm 68$ kPa. The error estimates for $V_{\max }$ and E₀ were calculated directly from the co-variance matrix of the fit function and the variance of residuals (chi-squared sum divided by the number of degrees of freedom) and are reflective of the wide scattering of measured velocities between different experiments. Conversely, we can estimate $V_{\max }$ and E₀ from values of the parameters used in the model: assuming a typical pilus retraction speed ${\displaystyle v^0=1}$ m.s^-1 (Marathe et al., 2014), a stall force of the order $F_{\mathrm{R}}=100$ pN (Marathe et al., 2014; Koch et al., 2022), a pilus off-rate constant $k_{\mathrm{off}}^0=1$ s^-1 (Talà et al., 2019), a contact size of $\lambda =1$ nm (Koch et al., 2021), a high friction surface with $F_{\mathrm{B}}=1$ nN and a typical pilus retraction frequency (Here we assume that one single effective pilus is active during a retraction event. Using a typical pilus length of 5 μm with retraction speed of ${\displaystyle v_0=1}$ μm.s^-1 we obtain a duration of 5  s per retraction and a retraction frequency of 0.2 s^-1) of $k_{\mathrm{p}}=0.2$ s^-1 we obtain $V_{\max }\sim 1$ μm.min^-1 and a substrate rigidity at half maximum speed of $E_0=100$ kPa, which are within 30% of the fitted values.

In addition, our model [Equation 8] shows that two separate effects translate a (fast) load-free microscopic pilus retraction speed $v^0$ into a (slow) macroscopic bacterial speed $V_{\max }$. First, the bacterium only translocate during a fraction of the pilus cycle of extension and retraction $\frac{k_{\mathrm{p}}}{k_{\mathrm{off}}}$ over the substrate. Second, the pilus retraction speed slows down in a load dependent manner $F_{\mathrm{R}}/(F_{\mathrm{B}}+F_{\mathrm{R}})$. Both effects together reduce the local speed by an order of magnitude from $\mathrm{\mu }m.s^{-1}$ to $\mathrm{\mu }m.mi{n}^{-1}$.

Together this demonstrates that our experimental results on bacterial effective motility on elastic substrates can be interpreted as the result of a simple interplay between the pilus retraction mechanism, the deformation of the elastic substrate, and the friction of the bacterial body on this substrate.

Analysis of individual trajectories

The simple approach presented Figure 2 yields a population-averaged value of the bacterial velocity $V_g$. Yet, bacterial populations can be heterogeneous, and moreover the model we have used Equation 2 to determine $V_g$ relies on a number of strong assumptions, such as neglecting detachment and re-attachment events. To go further in dissecting bacterial motility on PAA substrates, we developed a segmentation and tracking protocol in order to obtain the individual tracks of all the bacterial cells visible over the course of the acquisiton (Figure 3A, Video 2 and Materials and methods for details). This thorough approach allows us to measure the velocity associated with each 1 min displacement step.

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Instant velocity values from bacterial tracking.

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Can a characteristic twitching velocity be defined for all bacteria? or do phenotypically distinct populations of slow and fast bacteria cohabit on the surface? To answer these questions, we labeled each track, defined as the displacement of a bacterium between two successive division events (Figure 3A). We expected track duration to be similar to the characteristic division time shown on Figure 1C. However, we obtained a bimodal distribution, with two peaks centered at times unaffected by the substrate rigidity: one peak indeed centered on the division time (∼27 min), and a second one that corresponds to bacteria spending 5–10 min on the surface before detaching (Figure 3—figure supplement 1A). The velocity distribution corresponding to each population is similar (Figure 3—figure supplement 1B). This observation is consistent with a phenotypical difference between daughter cells, in agreement with the results of Laventie et al., 2019 Indeed, the duration of the track before detachment tends to be shorter on soft substrates, but the fraction of bacteria that detach from the substrate ($35\pm 2$ %) is independent of the substrate rigidity. We thus assume that at early experimental timepoints, after moving in sync with the first daughter cell, the second one sometimes detaches from the substrate (about 70% of the time). This feature might change at later timepoints - bacterial tracking was interrupted at the onset of 3D spatial organization (∼100 min on the softest hydrogels, see next section for a full description).

Considering only adhering offsprings, for which full tracks were recorded, we normalized tracks with respect to their initial position, yielding Figure 3A. These homogeneous radial distributions confirm that shear does not influence bacterial orientation in our experiments. As expected, track extension becomes larger as substrate rigidity increases. The distribution of the mean velocity of tracks does not allow us to distinguish different bacterial sub-populations: it reaches higher values on stiffer hydrogels, but it is broad, continuous with an exponential decay (reflecting the diversity of behaviors expected in a population of cells; Figure 3B). In addition, for each track the standard deviation of this mean velocity is comparable and proportional to its mean (Figure 3—figure supplement 2), suggesting a stochastic distribution of twitching steps within a given trajectory.

Focusing next on 1 min displacement steps, and pooling all monitored events during the first 100 min of experiments (which provides more data than only analysing full tracks within the same time window), we obtained the typical velocity distributions shown on Figure 3C. These distributions further confirm that bacterial displacements are very heterogeneous, and present an exponentially decreasing tail which fitting yields a characteristic velocity $V_C$ for the bacterial population on a given substrate, that is:

(10) ${\displaystyle N(V>V_0)=N_0\exp (-\frac{V-V_0}{V_C}),}$

(V₀=0.08 μm/min denotes a visual cutoff for low velocities).

To rationalize the meaning of $V_C$, we reasoned that displacement steps are the sum of a passive velocity due to bacterial elongation, local reorganizations and experimental noise, and an active velocity powered by T4P. The velocity distribution obtained using a $pilA$ mutant is purely exponential, and was used to determine the characteristic passive motility, which does not significantly depend on substrate rigidity (${\displaystyle V_C(pilA)=V_{C,p}=0.044}$ μm/min, see Figure 3D). In the case of motile strains, assuming that active and passive displacements are incoherent, our numerical calculations (Figure 3—figure supplement 3) show that in the limit $V_C$>$V_{C,p}$, the fitted characteristic velocity $V_C$ obtained as described above reflects the active twitching motility of the population, and is not significantly affected by passive movements. A detailed justification for our analysis of the probability distributions of displacement steps is given in the Methods section.

This analysis, which does not rely on any strong assumption, yields active velocity values for the WT strain (Figure 3D) in very good qualitative agreement with the global velocity analysis described earlier ($V_g$, Figure 2C, and Figure 3—figure supplement 4). Again, our kinetic model describes the data quantitatively with values very close to the ones fitted and calculated in the previous subsection (${\displaystyle V_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.48\pm 0.12}$ μm.min^-1 and $E_0=32\pm 30$ kPa). The large error bars on fitting parameters reflect the dispersion of experimental measurements, despite our efforts to reproduce identical experiments. However, velocity values measured in a given experiment always exhibit a similar dependence on substrate rigidity, that is a clear increase of motility as rigidity increases. In addition, we characterized the velocity of the 5% fastest bacterial displacement steps (Figure 3E) on each type of substrate. This analysis confirms the dependence of twitching velocity on substrate rigidity, but also yields higher velocity values, in good quantitative agreement with those reported in the literature using other experimental approaches (Talà et al., 2019), which might be biased toward more active bacteria. Finally, this approach was used to quantify bacterial motility in experiments on PEG hydrogels (shown Figure 1—figure supplement 1–pp.), which confirms the very similar bacterial behavior on the two kinds of substrates we have used (Figure 3—figure supplement 5).

Rigidity-modulated bacterial motility governs the spatial characteristics of early surface colonization

In-plane to 3D transition of emerging colonies

To understand the way rigidity-modulated bacterial motility impacts the process of microcolony formation, we studied in details the way colonies transition to out-of-plane growth. Several experimental and theoretical approaches have been developed in the past to decipher this process: for confined colonies, the switch from planar to 3D growth takes place when it becomes energetically too costly to push neighboring cells outwards. In that case, the adhesion forces between the bacteria and their underlying substrate play a key role: strongly adhering bacteria transition to 3D colonies earlier in their development (Duvernoy et al., 2018; Grant et al., 2014). In our experiments, there is no strong vertical or lateral confinement: bacteria can move on the substrate or away from it, so that cells stemming from a given progenitor do not necessarily stay in contact with each other. However, the twitching velocity determines how much cells, on average, move away from one another between two successive division events, thereby creating space to accommodate new offsprings on the surface.

To investigate the possible link between twitching motility and 2D to 3D transition of growing microcolonies, we sought to determine $N_c$, the number of adhered cells in a progeny (i.e. stemming from successive divisions of a given bacterium) when the 2D to 3D transition takes place, as a function of the twitching velocity. For softer substrates, all bacteria can be imaged, and $N_c$ is directly measured; we also determined the average number of colonies per unit area. On stiffer substrates, it is impossible to track all bacteria stemming from a mother cell, since they are very motile and sometimes move out of the field of view. We assume that bacteria from other progenies are equally likely to move inside the field of view, so that measuring the number of bacteria on the image at t_c (the time at which transition to 3D is first observed), divided by the average microcolony density determined on softer substrates earlier gives a good approximation of $N_c$. Figure 4A shows $N_c$ as a function of the center-of-mass characteristic velocity $V_C$ determined above (Figure 3D), on different substrates and for nine different experiments. $N_c$ consistently increases with the twitching velocity, indicating a strong correlation between the twitching efficiency and the shape of early colonies and shedding light on our initial observations of variations in microcolony morphology as a function of the substrate rigidity (Figure 1B and D–F).

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To decipher the link between $N_c$ and $V_C$, we have built a simple kinetic model with a single unknown parameter (see appendix 2 for details). Briefly, we assume that the 2D to 3D transition takes place when the area occupied by bacteria reaches a fraction of the equivalent ‘microcolony size’, defined as the characteristic area explored by bacteria in a progeny. Assuming that bacteria explore the surface through a random walk with persistence (Marathe et al., 2014), the characteristic area accessible to bacteria in a microcolony over time can be written as $a(t)=a_0(1+\alpha V_{C}t)$ where ${\displaystyle a_0}$ is the area of one bacterium and $\alpha$ is a parameter related to the properties of the random walk. Our experimental data show that not only the velocity, but also the contour length of the trajectories of bacteria increases with the rigidity since the duration of these trajectories is mostly constant (Figure 4B and Figure 3—figure supplement 1). Area $a(t)$ is related, but not equal, to the area over which the microcolony spreads. Indeed, bacteria are not evenly distributed within the microcolony area, and we observe strong local density fluctuations. If we now consider an exponential growth of the number of bacteria on the surface due to the balance of cell division and detachment, it follows that the increase in the number of cells, and hence the area required to accommodate these cells on the surface, grows faster than the accessible area, driving a transition to 3D growth. Expressing the number of cells $N_c$ in the microcolony at the time when this transition stochastically occurs leads to the following dependence as a function of $V_C$:

(11) $N_c=1+\gamma V_C\log (N_c)$

$\gamma$ is an unknown parameter related to the properties of the random walk and the growth rate of bacteria on the surface that can be measured for each experiment. On Figure 4A, we have plotted the corresponding curve using the average of experimental values for $\gamma$ (solid line) ± their standard deviation (dotted lines). We observe an excellent agreement between this simple kinetic model and our experimental data over a wide range of velocities, including the T4P deficient mutant and the WT strain adhering on glass. This hints that elasticity is a key factor shaping the organization of early colonies on elastic substrates, and that it is the main determinant of the colony shapes observed in our experiments on chemically identical substrates with varying rigidities (rather than energy minimization whereby bacteria would either favor adhesion to other cells or to the substrate depending on its rigidity).

Surface decoration by extracellular matrix

One consequence of the modulation of twitching efficiency by the substrate elasticity could be a variation in matrix distribution on the surface. Indeed, P. aeruginosa can secrete an extracellular matrix mostly composed of exopolysaccharides (EPS), which was shown to result in the deposition of ‘trails’ by twitching bacteria on glass substrates. By mediating the attachment of the cell body to the underlying substrate such deposits are inferred to facilitate further colonization by bacteria and to impact microcolony formation (Liu et al., 2007; Zhao et al., 2013). To investigate matrix deposition on hydrogel substrates, we introduced a fluorescent dye (lectin concanavalin A, see Materials and methods) in the nutrient medium infused in our device. The main component of PAO1 matrix, psl (Jackson et al., 2004), is rich in mannose, that conA specifically binds (Ma et al., 2007).

For high stiffness substrates where bacteria explore the surface efficiently, this staining confirms that trails of matrix decorate a significant fraction of the surface; on the contrary, nearly immobile bacteria on soft substrates accumulate matrix locally, leaving most of the surface unmodified (Figure 4C and D). This difference in matrix distribution is maintained at a later stage of surface colonization (Figure 4—figure supplement 1). While on rigid hydrogels, most of the surface is covered by bacteria-secreted matrix, lectin staining on soft hydrogels is only present on compact colonies separated by regions completely devoid of EPS. While proper quantification of the total amount of matrix produced in each case is difficult (staining efficiency might be impacted by lectin diffusion inside dense colonies), our results confirm that substrate rigidity impacts bacterial propensity to modify hydrogel substrates via matrix deposits.

Substrate rigidity affects bacterial mixing

Real-life biofilms generally comprise several species: pathogens can compete or help each other (DeLeon et al., 2014; Orazi and O’Toole, 2017), and commensal strains protect organisms from detrimental ones (Aoudia et al., 2016). To further investigate how modulation of surface colonization with rigidity impacts the structure of forming biofilms, we studied the model co-colonization of hydrogels by two PAO1 strains constitutively expressing two different fluorescent proteins. Beside their fluorescence, the two strains exhibit identical properties (motility, division rate, etc.), similar to that of WT PAO1. Through fluorescent confocal imaging, the strains were spectrally separated to study their spatial distribution at different stages of surface colonization. As expected, rigidity-modulated motility impacts the co-colonization of the hydrogels from early stages (Figure 5—figure supplement 1): on rigid substrates, high motility promotes mixing of the offsprings of different cells, resulting in a spatial distribution of the two strains close to random (a residual correlation between the colour of neighboring cells is always found due to the presence of cells that have just divided). Conversely, nearly immobile cells on soft substrates exhibit strong correlations between neighboring cells, which mostly arise from a single progenitor cell. This striking difference in strain mixing during surface co-colonization is maintained at later stages of biofilm formation: on soft substrates, quasi-monoclonal colonies with complete spatial segregation are observed, while biofilms forming on rigid surfaces exhibit a close-to-random distribution of the two strains at the 10-μm scale (Figure 5A). To quantify this effect, we have used Moran’s I index, a statistical tool designed to quantify the spatial clustering of species. It provides a measure of the local spatial correlations and takes values ranging from 1 (perfectly correlated values) to –1 (perfectly anti-correlated values), with 0 corresponding to a spatially random distribution of the variable (see Materials and methods for details). The resulting quantitative analysis (Figure 5B) confirms the decisive impact of rigidity on the structure of mixed biofilms, with potentially far-reaching consequences on the interactions of different strains in multi-species biofilms.

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Surface rigidity impacts gene expression

Cell-cell communication, either via exported molecules or by direct contact is crucial during biofilm development (Shrout et al., 2011). Modifications of bacterial distribution as described above could thus likely impact gene regulation in surface-attached bacteria. To start addressing this complex question, we focused on the expression level of cyclic-di-GMP (c-di-GMP), a second messenger that controls the motile-to-sessile transition in P. aeruginosa (Rodesney et al., 2017). We used a post-transcriptional fluorescent reporter build on the promoter of the gene cdrA, which encodes an exported protein involved in matrix cohesion, upregulated during biofilm formation by PAO1 (Reichhardt et al., 2018). The PcdrA-gfp intracellular reporter provides a measure of the integrated production of CdrA with a ∼40-min delay between expression of the gene and fluorescence detection (Rybtke et al., 2012). Figure 6 shows how crdA expression is modulated by rigidity on 4 substrates included in the same microfluidic device. For this reporter, the degradation rate of gfp occurs over several hours, and its dilution due to growth and division of bacteria occurs at the same rate on all surfaces (see Figure 1C). The increase rate of the fluorescence signal is thus a direct proxy to the expression rate of gene cdrA, and thus to the changes in c-di-GMP level.

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During a first phase of surface colonization, fluorescence remains low on all surfaces. The signal subsequently starts increasing linearly, roughly at the same time for all surfaces (within the uncertainty of fluorescence quantification, that is ≈10 min). This second phase ends with the onset of a plateau, again around the same time for all surfaces, at the end of the exponential growth of bacteria adhered on the surface, possibly as a result of oxygen depletion in the flowing medium that would be sensed simultaneously on all surfaces (Figure 6—figure supplement 1). This linear increase in fluorescence directly translates into a constant production rate of CdrA that can be compared for the 4 surfaces (Figure 6C): our analysis shows a marked increase in CdrA expression with the substrate rigidity.

In this study, we have designed an experimental approach to investigate early microcolony formation by P. aeruginosa on hydrogels with different elastic moduli, under constant flow rate. By continuously imaging surface-attached bacteria in situ, we show that substrate rigidity influences the twitching motility of individual bacteria, therefore strongly impacting the process of microcolony formation. Through two different analyses of the surface motility of the bacterial population, either via the global evolution of the explored area or via the tracking of individual cells, we find that the characteristic twitching velocity increases with substrate stiffness (from 0.02 to 0.4 μm/min when rigidity goes from ∼3 to 80 kPa).

The encounter between bacteria and a substrate generates mechanical stress. Deciphering surface-sensing, that is understanding how the mechanical feedback resulting from this interaction translates into chemical signals that will in turn tune bacterial behavior has been the focus of a lot of recent research. It is now clear, for instance, that T4P contraction acts as a force sensor that transmits signals to the bacterium at the single-cell level (Webster et al., 2021), and triggers a response that involves an increase in c-di-GMP level (Armbruster et al., 2019). Furthermore, recent results suggest that pili can differentiate substrate rigidity, yielding a maximum response for stiffness values ∼300 kPa Koch et al., 2022.

However, in our experiments a difference in bacterial motility can be observed almost immediately upon surface adhesion to soft or rigid PAA, and this behavior is not modified in mutants impaired in c-di-GMP regulation ($wspR$ or $sadC$). We thus propose a physical model to account for the modulation of the twitching motility. This 1D model is based on a force balance between (i) a pilus that extends, attaches and retracts with a defined frequency; (ii) the deformation of the underlying substrate at the pilus tip upon retraction; and (iii) the friction force due to adhesion of the bacterial body when it is dragged across the surface at the other end of the pilus. In this balance, the detachment rate of the pilus tip from the substrate is a key parameter in the resulting bacterial velocity. We have assumed a force-independent off-rate constant for the pilus. In a more complex scenario, the contact between the pilus and substrate may act as a slip bond or a catch bond. For completeness we show some numerical results for slip and catch bond behavior in the SI (section I.D), which do not increase however the quality of fit between experimental and theoretical velocity data. In addition, although we have explored the possibility that substrate rigidity, which is directly correlated to the mesh size of the hydrogel network, could impact the frequency of attachment of T4P, this was not necessary to efficiently account for the variation in motility we observe, which we instead solely attribute to the elastic deformation of the substrate.

Strikingly, our minimal mechanistic model thus suggests that a variety of observed phenomena (3D structure of colonies; EPS deposition on the surface; strain mixing during co-colonization) can all derive from a modulation of the efficiency of pili activity by the deformability of soft substrates. This purely mechanical model may be of particular importance for surface colonization, since the adaptation of bacterial behavior to the environment can thus be instantaneous - possibly a key to PA ability to efficiently colonize extremely different microenvironments.

While this model is sufficient to account for our observations (twitching velocity, microcolony formation), it certainly does not rule out a regulatory response of the bacteria, which probably takes place in parallel. Such a response can happen on two levels: at the single-cell level, mechanotransduction processes mediated for instance by adhesion and retraction of T4P can influence gene expression at short timescales (∼1 hour) Armbruster et al., 2019; Song et al., 2018. At longer timescales, in developing microcolonies, cell-cell interactions could in turn modulate the bacterial transcriptome, which depends on microcolony characteristics (e.g. shape, cell density, matrix content) Livingston et al., 2022. Our attempt at quantifying c-di-GMP expression using a fluorescent intracellular reporter does evidence a difference in bacterial regulatory response depending on substrate stiffness. While the level of expression of the gene is clearly impacted by the substrate rigidity, differences in expression level are detected only 6–7 hr after the onset of surface colonization, with a first phase characterized by low c-di-GMP level on all surfaces. This timeframe suggests that the difference in gene expression that we observe is probably not due to a direct sensing of the substrate rigidity by individual bacteria, but rather a consequence of their organization into more or less dense colonies. Of note, when the increase in c-di-GMP takes place bacteria have stopped twitching and immobilized into colonies. We do not observe the early increase in c-di-GMP described in the litterature, possibly because we initially only track a very small number of bacteria on the surface, and the expression signal is stochastic. Further investigating c-di-GMP expression in WT and mutant strains upon adhesion to mechanically different substrates could help reveal which pathways are differently activated on soft substrates.

Interestingly, our results show that microcolony phenotype may not be indicative of a specific c-di-GMP regulation. The dense colonies observed on soft hydrogels correspond to lower c-di-GMP levels than the flat bacteria carpets that grow on rigid substrates, a somehow counter-intuitive result given the paradigm that c-di-GMP production upregulates biofilm-inducing genes, in particular matrix production, while downregulating motility. Here, we describe a case when motility is rendered impossible by the micromechanical properties of the environment rather than by the absence of functional pili, thus resulting in the rapid formation of compact colonies on soft substrates. Further exploring the density and the exact composition of the extracellular matrix in these colonies would be interesting since this parameter could influence the subsequent fate of bacteria on the surface. EPS distribution, composition and concentration may also be significant for the recruitment of new cells on the surface: indeed, previously deposited matrix is thought to strengthen adhesion of $P.aeruginosa$ bacteria (Zhao et al., 2013), and could also possibly mediate adhesion of other microorganisms.

In a wider context, the process we observe could also be envisioned as a strategy to optimize bacterial colonization of mechanically heterogenous environments by ensuring accumulation of bacteria into dense colonies located in the softer regions of their environment, for example over cellular tissues. Recently, Cont et al., 2020 have shown that dense colonies were able to deform soft substrates and exert forces that could disrupt an epithelium layer: rigidity-modulated twitching could thus provide Pseudomonas aeruginosa with a convenient means of targeting soft tissues for cooperative disruption and subsequent invasion.

The phenotypic differences that we report for colonies are likely to impact subsequent interactions of bacteria with their environment: response to changes in nutrient or oxygen availability, and chemical signals in general which will not efficiently penetrate inside dense colonies. This could in particular influence susceptibility to antibiotics, as confirmed by very recent work Cont et al., 2023. This is all the more relevant that PA can invade many different environments, and might have to be treated differently when it settles in the lungs of cystic fibrosis patients, or on the surface of rigid implants.

Finally, our data show that rigidity-modulated twitching has a striking impact on the mixing of different strains upon surface colonization. Understanding the mechanisms governing the formation of mixed-species communities is one of the key challenges of current biofilm research. Since the motility modulation mechanism described here is quite general and should be marginally affected by the particulars of different strains/species moving through elongation/retraction of an appendage, we expect it to provide a relevant framework to study co-colonization in different mechanical micro-environments.

Figure 2—source data and Figure 3—source data contain the numerical data used to generate the figures.

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