Bacterial filamentation accelerates colonization of adhesive spots embedded in biopassive surfaces

Sessile bacteria adhere to engineered surfaces and host tissues and pose a substantial clinical and economical risk when growing into biofilms. Most engineered and biological interfaces are of chemically heterogeneous nature and provide adhesive islands for bacterial attachment and growth. To mimic either defects in a surface coating of biomedical implants or heterogeneities within mucosal layers (Peyer's patches), we embedded micrometre-sized adhesive islands in a poly(ethylene glycol) biopassive background. We show experimentally and computationally that filamentation of Escherichia coli can significantly accelerate the bacterial surface colonization under physiological flow conditions. Filamentation can thus provide an advantage to a bacterial population to bridge non-adhesive distances exceeding 5 μm. Bacterial filamentation, caused by blocking of bacterial division, is common among bacterial species and can be triggered by environmental conditions or antibiotic treatment. While great awareness exists that the build-up of antibiotic resistance serves as intrinsic survival strategy, we show here that antibiotic treatment can actually promote surface colonization by triggering filamentation, which in turn prevents daughter cells from being washed away. Our combined microfabrication and computational approaches provide quantitative insights into mechanisms that enable biofouling of biopassive surfaces with embedded adhesive spots, even for spot distances that are multiples of the bacterial length.


Introduction
Bacterial attachment is the first step in the colonization of surfaces and biofilm growth. As the preferred mode of microbial life, biofilms consist of surface attached and densely packed populations of bacteria, held together by a self-produced matrix [1]. Biofilms growing on medical devices and biomedical implants are generally accepted to be the major cause of bacterial infections in clinical environments [2], causing tremendous clinical and economical complications [3]. Commonly, bacterial infections are treated by antibiotic therapies, but due to an increasing number of antibiotic-resistant bacterial strains, pharmaceutical agents become ineffective and new ways to prevent bacteria borne infections need to be explored [4][5][6]. One alternative strategy to deal with bacteria-related infections is to interfere with the initial adhesion of planktonic (free floating) bacteria to biomedical and technical surfaces by rendering the surfaces biopassive [7][8][9][10][11]. Upon exposure to the environment however, biopassive coatings can be subjected to degradation and corrosion [12]. Defects within the antimicrobial coating in turn can provide adhesion sites for bacteria, serving as nucleation points for the formation of confluent surface biofilms. Bacteria not only adhere to but colonize engineered materials. To invade the host, pathogens adhere to host tissues by specific surface receptor-ligand interactions. The mammalian intestine is a preferred area of infection as it provides a large epithelial surface that can be colonized by potentially pathogenic microorganisms [13]. Within the intestine epithelium, Peyer's patches, i.e. groups of lymphoid follicles, provide a transport system for antigens as an essential part in the immune defence. Several pathogenic bacteria bind preferentially to cell types found in Peyer's patches [14] as the non-adhesive mucous layer is thin compared to the surrounding tissue, making Peyer's patches a preferred site for invasion of pathogens into the host tissue [15]. Peyer's patches within the intestine epithelium therefore have similar properties to the adhesive defects in antimicrobial coatings described above: they present preferred sites for bacterial attachment within a non-adhesive surface.
To form a confluent bacterial layer as a requisite for biofilm development, the adherent bacteria have to bridge the non-adhesive areas on those heterogeneously adhesive interfaces. Escherichia coli (E. coli), one of the best-studied intestinal microorganisms, are rod-shaped bacteria with a length of 2-4 µm [16]. However, the morphology and in particular the aspect ratio of E. coli can largely change upon exposure to antibiotics and non-optimal growth conditions [17]. Filamentation occurs when cell division is blocked while growth continues, resulting in filaments with high aspect ratios of several tens of micrometres. As a survival strategy, filamentation can slow down the phagocytic uptake of bacteria by immune cells [18], promoting their survival within host tissues [19,20]. Since bacterial filaments are commonly observed in patients being treated with antibiotics [21], it has been proposed that filamentation might be a defence mechanism to temporarily withstand treatment with β-lactam antibiotics, e.g. cephalexin [22,23]. Cephalexin belongs to the family of β-lactams and targets FtsI, a penicillin binding protein of the divisome complex that is required for bacterial division. It is among the largest selling antibiotics worldwide and is applied against otitis media and urinary tract infections.
Since the exposure to antibiotics or the local growth conditions that promote filamentation can change quickly in natural environments, we ask here whether filamentation offers a selective advantage to colonize heterogeneously adhesive surfaces. Using E. coli as the model organism, we hypothesize that filamentous bacteria bridge non-adhesive regions between adhesive spots faster than non-filamentous bacteria. To test our hypothesis, we performed live cell microscopy and analysed the kinetics of E. coli adhesion and growth on heterogeneous surfaces. To allow for firm adhesion of E. coli under physiological flow conditions [24,25], we used a photoresist lift-off process to micropattern the glycoprotein ribonuclease B (RNaseB) to which E. coli bind by their type 1 fimbriae. Adhesive RNaseB islands of 10 µm in diameter were spaced at distances reaching many multiples of the bacterial length. Unspecific adhesion was blocked by passivation with PLL-g-PEG [9,26]. E. coli filamentation was induced by cephalexin. Based on the experimentally derived parameters of bacterial adhesion and growth, we implemented a Monte Carlo simulation of bacterial surface colonization to confirm the experimental data and obtained additional predictions for the impact of filamentation, flow and adhesive spot distances on the bacterial surface colonization kinetics. This study provides novel mechanistic insights into the initial stages of surface biofouling and it highlights the selective advantage of bacterial shape adaptation to colonize heterogeneously adhesive substrates.

Preparation of adhesive glycoprotein patterns and unpatterned adhesive surfaces
RNaseB glycoprotein patterns [29] with a diameter of 10 µm, spaced by 5, 10 and 20 µm were prepared using a combined photolithography and lift-off process (figure 1). The MAPL protocol [30] was adapted to pattern proteins onto glass substrates. Photoresist patterns on glass cover slides were created using positive S1818 photoresist. Briefly, undiluted S1818 photoresist (Microposit) was spin coated on the cover glasses in a two-step spin process with 2000 rpm for 5 s (ramp step of 500 rpm s −1 ) and 4000 rpm for 90 s (ramp step of 800 rpm s −1 ), respectively, followed by soft baking for 60 s at 100 • C and UV light exposure (Karl Süss MA6 mask aligner) with an energy dose of 150 mW cm −2 at 405 nm. Exposed resist was developed in undiluted MF319 developer (Microposit) for 60 s. The resist micropatterns were rendered biopassive by 1 h incubation at room temperature with 100 µg ml −1 PLL-g[3.5]-PEG(2) (SuSoS AG) in PBS. For enhanced stability of the polymer layer, the glass surface was coated with 21 nm niobium oxide prior to photolithography. The photoresist was removed by chemical lift-off with N-methyl-2-pyrrolidone (NMP, Sigma 494496), leaving PLL-g-PEG coated regions on the surface. The non-PEGylated areas were backfilled by 30 min incubation at room temperature with 100 µg ml −1 Alexa Fluor 488 labelled RNaseB. The terminal mannoses of the N-linked glycans present on RNaseB served as receptors for the bacterial type 1 fimbriae tip adhesin FimH. The biopassive properties of PLL-g-PEG blocked the adsorption of RNaseB to previously passivated areas [26]. The unpatterned adhesive surfaces were prepared by incubating glass slides 30 min at room temperature with 100 µg ml −1 unlabelled RNaseB.

Parallel plate flow chamber experiments
The flow chamber comprised of a vacuum mediated assembly of an acrylic top, a silicone separating gasket and a glass cover slide. A channel of 2.5 mm width was cut into the silicone gasket. The channel height was defined by the gasket thickness of 0.254 mm. The channel dimensions and the volumetric flow rate of 1 ml min −1 defined a shear stress of 0.6 pN µm −2 applied to the surface-bound E. coli. The flow cell set-up was placed within a microscope incubation box heated to 37 • C. A custom-made bubble trap that was incorporated upstream of the flow chamber inlet reduced the probability of air bubbles running into the flow chamber. LB medium supplemented with 10 µg ml −1 chloramphenicol was circulated through the flow chamber set-up for at least 1 h prior to each experiment to equilibrate the system. To seed the glass surface with bacteria, the flow was stopped, the tubing clamped and disconnected at the flow chamber inlet port. A syringe with the inoculation culture was used to inject the bacteria  directly into the inlet port of the flow chamber. The bacteria were allowed to adhere to the surface for 1 min. The tubing was reconnected and the flow resumed. Unbound bacteria were washed off by the medium flow. Bacterial filamentation was induced by supplementing the LB medium with 20 µg ml −1 cephalexin. To restore bacterial division, the medium was exchanged with cephalexin-free LB medium. The medium change led to gradual dilution of the cephalexin in the set-up over time.

Microscopy
Flow chamber assays were performed on an inverted live cell microscope (Nikon TE2000-E) equipped with an electron multiplying charge-coupled device (EM-CCD) camera (Hamamatsu 9100-02). Time-lapse movies of multiple stage positions were acquired every 3 min for up to 4 h with a 40× phase contrast objective. Fluorescence images were acquired with a fluorescein isothiocyanate (FITC) bandpass filter set (Chroma 49002).

Data analysis
2.5.1. Surface colonization kinetics. To determine the colonized area fraction, phase contrast images were thresholded within a rectangular region of interest including multiple adhesive spots in the direction of flow. To include bacterial growth perpendicular to the flow, the region of interest was two times wider than the spot width and centred over the spots (figure 2(b)). The area fraction is calculated as the ratio of thresholded pixels by the total number of pixels in the region of interest. To assess differences in the initial surface coverage, individual plots were fitted and the parameters obtained for generation times were corrected.

Bacterial bridging of passivated areas between adhesive spots.
The position of the adhesive spots was determined from fluorescent images of Alexa Fluor 488 labelled RNaseB. A position mask of the adhesive islands was created and overlaid with the phase contrast images to visualize the adhesive spots in the images and time-lapse movies. Bridge advancement was measured from phase contrast images in between two neighbouring spots in flow direction. Bacteria growing beyond the border of an upstream spot towards an adjacent downstream spot contributed to the bridge advancement. Pairs of adhesive spots (n = 10) were randomly chosen and the bridge advancement was determined by measuring the distance that the bacteria advanced from the border of the upstream spot towards the downstream spot. The maximum distance of bridge advancement was the edge-to-edge distance between two spots (5, 10 or 20 µm, respectively). Bridging time was defined as the time point when bacteria from an upstream adhesive spot connected to the next downstream spot. Analysis of E. coli filaments was restricted to the time interval where filamentation occurs and before bacteria lysed.

Bacterial length doubling time measurements.
For filamentous E. coli, the time a filament needed to double in length was considered to be an adequate measure of growth and was determined from the pole-to-pole length of a filament. The filament length (n = 10) was measured every 3 min for 2 h. The data was plotted and fitted with theoretical growth curves to obtain the length doubling time. To compare the length doubling time of filaments with non-filamentous E. coli, the pole-to-pole length of all progeny of non-filamentous E. coli (n = 10) was summed up at each time point and a length doubling time was derived likewise. Data analysis was performed using ImageJ software.

Computational modelling of surface colonization kinetics
Two-dimensional (2D) Monte Carlo simulations of a model describing the bacterial growth on adhesive spots were performed using MATLAB (MathWorks, version R2010b). The surface was modelled as a lattice in which bacteria occupy one lattice site, corresponding to an area of 1 µm 2 . The parameters of the model were the doubling time T d of filamentous and non-filamentous E. coli as derived from experimental data, a probability P filament for growth without septation, resulting in filaments, a probability P divide to account for septation (as observed in undisturbed bacterial growth as well as for filaments when removing cephalexin antibiotics) and a probability P wash−off for bacteria being washed off from the edge of the colony over biopassivated surface areas. The wash-off probability depends on the magnitude of flow, modelled by a flow factor F, and the position of the bacteria relative to the flow direction, described by an anisotropy factor A. A more detailed description of the model and implementation is found in the supplementary information (available from stacks.iop.org/NJP/15/125016/mmedia).

Increasing distances of adhesive spots slow the formation of a confluent layer of non-filamentous Escherichia coli
To quantify the surface colonization kinetics of non-filamentous E. coli on heterogeneously adhesive surfaces, we prepared mannosylated RNaseB glycoprotein patterns within a stable biopassive PLL-g-PEG layer [9,31] by adaptation of a combined photolithography and molecular assembly process (figure 1) [30]. The lift-off process rendered the glass surfaces with a distinct pattern of circular RNaseB spots as it was visualized by fluorescence microscopy. No fluorescent signal was detected within the biopassive PLL-g-PEG coated areas (figure 1(iv)). The RNaseB pattern promoted firm adhesion of type 1 fimbriated E. coli under physiological flow conditions [24] and no bacterial adhesion to the passivated areas was observed (figure 1(v)).
To analyse the effect of surface patterning on the kinetics of bacterial surface colonization, E. coli were incubated on adhesive RNaseB spots of 10 µm in diameter separated by distances of 5, 10 and 20 µm. Surface-attached E. coli were grown under physiological relevant shear stress (1 ml min −1 flow rate; 0.6 pN µm −2 wall shear stress) [32][33][34]. The surface colonization kinetics on the different patterns was quantified from time-lapse movies for a region of interest that included multiple adhesive spots within the direction of medium flow (figure 2(b), supplementary movies S1 and S2, available at stacks.iop.org/NJP/15/125016/mmedia). Starting from single adherent E. coli, bacterial microcolonies grew in size by cell division until the edge of an adhesive spot was reached. An almost confluent bacterial layer was observed after 4 h for a spot distance of 5 µm (figure 2(a), top). With increased spot distances of 10 and 20 µm, the bacterial surface coverage decreased and characteristic colonization patterns were observed (figure 2(a), middle and bottom). E. coli microcolonies on unpatterned adhesive surfaces merged into a confluent bacterial layer after 4 h ( figure 2(b)). Non-filamentous E. coli colonized surfaces with 5 and 10 µm spot distances with very similar kinetics to unpatterned adhesive RNaseB surfaces. No confluent layer had formed on surfaces with 20 µm spot distances (figure 2(c)). Since the initial number of adherent E. coli per field of view was higher for surfaces with higher adhesive spot densities, we corrected the colonization kinetics analysis accordingly. By image thresholding of the phase contrast time-lapse movies, the fractions of pixels covered by bacteria were determined. This analysis was very robust for low to moderate bacterial surface coverage. At higher surface coverage though, light halos around the bacteria occurred such that the phase contrast imaging and thresholding was not an accurate measurement of surface coverage any longer. We estimated that a pixel threshold of 58% corresponds to a confluent E. coli monolayer (figure 2(c)).  To study the impact of bacterial filamentation on the bridging of non-adhesive regions, we compared the bridging of non-adhesive spot-to-spot distances of 5, 10 or 20 µm for filamentous and non-filamentous E. coli. Non-filamentous E. coli divided and grew on the adhesive patterns until the edge of the spots was reached ( figure 3(a)). Once the spot edge was reached, we observed that daughter cells that grew into the passivated area were frequently washed away by the fluid flow after the division was completed ( figure 3(a), bottom panel and supplementary movie S4). This behaviour led to a characteristic 'shark-tooth' pattern in the bridge advancement (figures 3(a) and (b), blue lines and arrow 1 and 2). When an adhesive spot became crowded after 2-2.5 h, daughter cells were no longer washed away and the bridge advancement accelerated until the full distance of 20 µm to the downstream patch was bridged ( figure 3(a)). Analysing the bridge advancement for different pairs of adhesive spots revealed substantial heterogeneity in the colonization kinetics of non-filamentous E. coli ( figure 3(b), blue lines showing three representative measurements). In contrast, filaments were able to grow and extend across the non-adhesive areas beyond the pattern edges ( figure 3(b)). As the filaments grew, no 'sharktooth' patterns in the advancement kinetics of the filamentous bacterial bridge were seen since no daughter cells were washed away ( figure 3(b), red lines and figure 3(a), top panel). For 20 µm spot-to-spot distances, filamentous E. coli bridged the non-adhesive regions three times faster than non-filamentous bacteria ( figure 3(b)).
For spot distances of 5 and 10 µm, fast bridging between the neighbouring adhesive spots was observed for filamentous and non-filamentous E. coli (figures 3(c) and (d)). For filamentous E. coli, the time to bridge the non-adhesive regions changed proportionally to the spot distance as no daughter cells are washed off ( figure 3(e)). For non-filamentous E. coli, the bridging time did not scale with the spot distance. Non-filamentous E. coli bridged the 5 µm distance non-proportionally faster than the 10 and 20 µm ( figure 3(e)). The bridging time, i.e. the time that filamentous and non-filamentous E. coli needed to fully bridge the distance between two adhesive spots, was statistically significantly different at all spot distances, however, at 10 and 20 µm spot distance the difference was highly significant ( p < 0.001) ( figure 3(e)).  . Filamentous E. coli bridged passivated areas between adhesive spots (dashed circles) reaching downstream spots to which they can adhere. Continued growth of a filament connecting adhesive spots resulted in its buckling and bending out of the focal plane. After gradually purging with cephalexin-free medium, cell division was resumed and the filaments fragmented. Only bacteria at the filament tip that were already in contact with adhesive spots were able to hold on and further divide.

Filament bridges disintegrate when removing cephalexin from the medium
To mimic the effect of fluctuating growth conditions, we asked how the removal of antibiotics from the cell medium might affect the further surface colonization. In the presence of cephalexin, E. coli filaments extended beyond the adhesive spot edge and once the non-adhesive region was bridged, the filament tip adhered to the adjacent downstream adhesive spot (figure 4(a) and supplementary movie S5 (available from stacks.iop.org/NJP/15/125016/mmedia)). Being fixed at both ends, further growth resulted in buckling of the filament as indicated by the filament being out of focus. Bacterial division resumed when cephalexin was reduced to sub-inhibitory concentrations (lower than 10 µg ml −1 [37]), which leads to a rapid fragmentation of the filaments.

A computational model of bacterial surface colonization predicts a kinetic advantage of filamentation when colonizing passivated surfaces that contain adhesive spots
The results obtained by time-lapse microscopy showed that bacterial filamentation accelerated the bridging of neighbouring adhesive spots ( figure 3). To evaluate if the kinetic advantage of bridging at early stages results in increased surface coverage at later times, a 2D computational model of bacterial growth was developed that accounted for filamentous and non-filamentous bacterial growth on micropatterned adhesive surfaces. Four basic model assumptions were made that were derived from our experimental data: (i) All bacteria grow with a constant doubling time T d of 26 min. This parameter was derived from our finding that the elongation rates did not differ significantly between filamentous and non-filamentous bacteria (supplementary figure S2). (ii) Filamentation of bacteria occurs with a probability P filament , while existing filaments can divide with a probability P divide . These two parameters were based on our experimental observation that cephalexin induced a homogeneously filamenting population which could be switched back to non-filamentous growth when cephalexin was diluted out (figure 4). (iii) Bacteria at the edge of the colony are washed off with a probability P wash-off that depends on the magnitude of flow and the orientation of the bacteria relative to the flow direction. The two parameters magnitude and orientation are represented by a flow factor F and an anisotropy factor (see supplementary information). (iv) Wash-off can only occur over non-adhesive regions. This model assumption is valid since bacteria firmly adhered to the adhesive RNaseB spots ( figure 3(b)).
We applied our model to adhesive spot distances of 5, 10 and 20 µm as probed experimentally. Three representative curves of filamenting (red) and non-filamenting (blue) conditions for a spot distance of 20 µm are shown ( figure 5(a)). Our model predicts a three times faster bridging for filamentous compared to non-filamentous conditions, which is in good agreement with our experimental observations ( figure 3(a)). Since the model reproduces the experimental results for 5, 10 and 20 µm distances, we applied it to larger distances of 40 and 80 µm ( figure 5(b)). The model predicts an increasing difference in bridging times between filamentous and non-filamentous bacteria for larger spot distances ( figure 5(b)). To gain insight into the effect of the flow factor F on the bridging time, we varied the flow factor from 30 to 300 ( figure 5(c)). Higher flow factors resulted in an increased bridging time of a 20 µm distance for non-filamentous bacteria ( figure 5(c), blue bars). Interestingly, for the chosen parameters the bridging time of filamentous bacteria was not influenced by an increase in the flow factor F ( figure 5(c), red bars). In our model, P filament defines the probability of a dividing bacterium to form a filament and was set to 0.5 for all simulations mimicking filamenting conditions. This probability reflects the amount of filaments in a bacterial population. To determine the influence of a  variation in the filamentation probability, the parameter P filament was set to 0.01, 0.03 and 0.1 and compared with non-filamenting conditions (P filament = 0) and the filamenting conditions used before (P filament = 0.5) ( figure 5(d)). The model predicts that a probability for filamentation of 0.03 is sufficient to reproduce the effect of filamentation on bridging times that we observed experimentally ( figure 3). Higher probability of filamentation did not decrease the bridging time any further ( figure 5(d)).
To investigate the effect of bridging time on surface colonization, we extended the simulations towards later time points and larger spot arrays. We modelled a 400 times 300 µm surface area with 10 µm adhesive spot diameter and 20 µm spot distances (figures 2(a) and 6(b)). Bacterial adhesion on five adhesive spots at the upstream side of the surface was defined as the initial condition (figure 6(a), 0 h). The model parameters were set to P filament = 0.5 (filamenting condition), P filament = 0 (non-filamenting conditions) and flow factor F = 100 ( figure 6(b)). As suggested from the previous comparison of filamentous and non-filamentous E. coli surface colonization (figure 3), the filamenting conditions accelerated the surface coverage ( figure 6(a)).
Finally, and analogous to the experimental setting where we removed cephalexin from the medium, the filament division in the model was resumed after the first five doubling periods by setting the parameters P filament to 0 and P divide to 0.5 (figure 6). The model again predicts a kinetic advantage of the filaments over non-filamentous bacteria. This kinetic advantage resulted from the ability of the filaments to bridge the distances to downstream adhesive spots that served as nucleation sites for further surface colonization. By lateral cell-cell contacts, nonfilamentous bacteria bridged the 20 µm distance between adhesive spots at later time points (figure 6(a)). Those differences in the early colonization kinetics are enhanced at later time points (figure 6(b)). We investigated the kinetic advantage of filamentation not only in terms of colonized surface area but also as a function of the number of adhesive spots that were colonized (figure 6(c)). Although the filamenting conditions were restricted to the first five doubling periods, this was sufficient to colonize twice as many spots than with non-filamenting conditions.

Discussion
Filamentation is a common trait of various bacteria, including E. coli, Pseudomonas aeruginosa and Salmonella enterica, and occurs in many natural and industrial habitats [17,21]. Here we have shown that filamentation of E. coli can accelerate the colonization of non-adhesive surfaces that expose microscale adhesive spots (figure 2), mimicking, for example, defects in a surface coating or heterogeneities within mucosal layers. Non-filamentous E. coli were typically washed off by the medium flow when they grew beyond the edge of the adhesive spots (figures 3(a) and (b)). In contrast, no offspring is washed away during filament growth. As a result, filamentous E. coli bridged non-adhesive distances that are greater than the length of an E. coli bacterium shortly before division (4-8 µm) significantly faster (figure 3) although the time needed to double in length is very similar for both phenotypes (25.4 ± 1.6 and 27.6 ± 3.4 min, respectively) (supplementary figure 2 (available from stacks.iop.org/NJP/15/ 125016/mmedia)).
As the microcolonies grew, we observed that non-filamentous E. coli were also able to bridge large non-adhesive distances (figures 2(a) and (b)). Since the PLL-g-PEG chemistry used here to passivate the inter-spot areas completely suppressed bacterial binding under low and high flow for at least 9 h (supplementary figure 1) [9,10,31], the bridging of the non-adhesive regions might only be possible by lateral cell-cell interactions. This interpretation is in agreement with the observation that bacteria growing on adhesive surfaces arrange to maximize lateral cell-cell contacts [17]. In the presence of adjacent neighbours within a microcolony, bacteria reached into the non-adhesive area ( figure 3(a), bottom panel and 3(b), blue lines). Stabilized by sufficient cell-cell interactions ( figure 3(b), 2 h), bridging of the non-adhesive regions can occur gradually.
We implemented a 2D Monte Carlo simulation based on four rules derived from our experimental data. We found good agreement of bridging rates between simulations (figure 5) and experimental data (figure 3). The model furthermore allowed us to predict the impact of filamentation on the surface colonization speed and bridging times for conditions not addressed experimentally. Even for adhesive spot distances of 40 and 80 µm, filamentation continued to accelerate the surface colonization (figure 5(b)). A higher flow factor F prolonged the bridging time for the non-filamenting system which reflects the influence of increased flow rates and wall shear stresses. Interestingly, changing the flow factor F had no effect under filamenting conditions ( figure 5(c)). This implies that the prevention of offspring wash-off is the mechanism leading to the observed accelerated bridging between adhesive spots by filaments. Our data suggests that short periods of filament-promoting conditions are sufficient to create a kinetic advantage over non-filamenting bacterial populations (figures 6(b) and (c)). We further varied the probability for filamentation in the model. This reflects the fraction of bacteria in a population that grow into filaments. Our model predicts a threshold probability of 0.03 at which the full kinetic advantage of filamentation is reached ( figure 5(d)). This suggests that it is sufficient if only a fraction of a bacterial population grows in filaments to have a colonization advantage over non-filamenting bacteria. An increase of the fraction of filamenting bacteria beyond this threshold does not further accelerate the surface colonization.
During the treatment of infections with antibiotics, little attention has been given to the fact that antibiotic doses that are too small to instantaneously kill bacteria might induce their filamentation. Previously, we showed that filamentation of E. coli slows their uptake by macrophages [18]. Macrophages have to reach the terminal ends of the filaments before they can form a phagocytic cup and internalize them. Otherwise, they are often observed to contact filaments, even pull on them, but the filamentation in those cases prevents phagocytosis thus impairing an immune response. Here we illustrate a second mechanism where filamentation might have an adverse effect in the fight against biofilms. We show that the antibiotic cephalexin can drastically accelerate the bridging of non-adhesive areas (figure 3). Our results imply that antibiotics that induce filamentation can lead to an accelerated colonization of a heterogeneously adhesive surface, which was not considered in the literature so far and should be taken into account to tailor the dosage of antibiotics. We show that environmental changes that promote a switch in the bacterial phenotype towards filamentation can accelerate bridging of non-adhesive areas ( figure 3). We demonstrated that filaments can attach to downstream adhesive regions leaving offspring there, which itself divide and grow into a colony, if the surrounding conditions allow division ( figure 4(a)). This may also suggest that heterogeneous surfaces in body tissues like Peyer's patches in the intestine or implant surfaces can be colonized faster if an infection is treated with a filament inducing antibiotic which thus might be detrimental for the host organism.

Conclusion
Using E. coli as bacterial model organism, our study highlights the profound kinetic advantage of bacterial filamentation to accelerate the colonization of heterogeneously adhesive surfaces. Our combined experimental and computational approaches show for early and late time points that filamentation can accelerate the surface colonization. Filamentation increased the rate of bridging non-adhesive areas and can thereby accelerate biofouling of passivated surfaces. While great awareness exists that the build-up of antibiotic resistance serves as an intrinsic survival strategy, the local underdosing of antibiotics can switch bacteria into a filamentous state which can accelerate the formation of difficult-to-treat biofilms on heterogeneously adhesive surfaces.