Intra-colony channel morphology in Escherichia coli biofilms is governed by nutrient availability and substrate stiffness

Nutrient-transporting channels have been recently discovered in mature Escherichia coli biofilms, however the relationship between intra-colony channel structure and the surrounding environmental conditions is poorly understood. Using a combination of fluorescence mesoscopy and a purpose-designed open-source quantitative image analysis pipeline, we show that growth substrate composition and nutrient availability have a profound effect on the morphology of intra-colony channels in mature E. coli biofilms. Under all nutrient conditions, intra-colony channel width was observed to increase non-linearly with radial distance from the centre of the biofilm. Notably, the channels were around 25% wider at the centre of carbon-limited biofilms compared to nitrogen-limited biofilms. Channel density also differed in colonies grown on rich and minimal media, with the former creating a network of tightly packed channels and the latter leading to well-separated, wider channels with defined edges. Our approach paves the way for measurement of internal patterns in a wide range of biofilms, offering the potential for new insights into infection and pathogenicity.


Introduction
Biofilms are biological structures formed by microorganisms in a variety of environments, and they consist of cells embedded in a selfsecreted extracellular matrix [1]. Biofilm-forming organisms have evolved numerous mechanisms to protect their constituent cells from external biological and physiochemical stresses, resulting in populations of cells that exhibit increased resistance to a wide range of deleterious agents when compared to planktonic cells [2].
The structure of biofilms is integral to their role in infection, with mechanical deformation of soft substrates and epithelial cell monolayers being a major contributor to pathogenicity [3]. Pattern formation within biofilms is known to be affected by a change in the bulk carbon or nitrogen concentration of growth media [4,5], as well as by nonuniform growth due to frictional forces and nutrient depletion [6]. Environmental and surface properties also affect growth parameters, leading to biofilms being a major burden to public health and industry [7]. It has been shown that varying substrate stiffness can alter cell attachment [8,9], motility [10], growth dynamics [11] and expansion of constituent cells within biofilms [12], all of which are linked to infection.
It has long been known that bacterial growth rate and biomass formation depend on the type and concentration of nutrients available, and that altering the nature and availability of growth substrates can influence the growth of planktonic bacteria [13][14][15]. This has also been demonstrated for sessile biofilms, where growth substrates can have profound effects on biofilm morphology, growth dynamics, and mechanical properties [16][17][18][19]. Recent studies on single-species biofilms have identified crossfeeding mechanisms for acetate, alanine and other nutrients influencing biofilm viability and morphology [20][21][22]. Emergent biofilm properties have also been found to give rise to water and nutrient transport mechanisms [23][24][25], yet the factors governing how they form and how environmental cues govern their structure are currently unknown.
Complex channel networks were recently discovered in Escherichia coli by Rooney et al. [26] using the Mesolens, an optical mesoscope enabling sub-micron resolution across multi-millimeter size live biofilms [27]. These channels were found to transport small fluorescent microspheres, and their interior showed a higher accumulation of nutrients with respect to the rest of the biofilm. However, the large size of Mesolens datasets meant that only approximate measurements of intra-colony channel width could be made.
We hypothised that nutrient availability and agar concentration (a proxy for substrate stiffness) play an important role in channel morphology in mature E. coli biofilms, and we have developed a new open-source image analysis pipeline to test this conjecture. Our work shows that channel structure and distribution are strongly affected by both nutrient availability and substrate stiffness, and that the relative position of channels inside the biofilm determines their width for a given nutritional profile. The combination of Mesolens imaging and our image analysis pipeline provides precise and absolute measurements of intracolony channel widths in response to specific environmental conditions and gives new insights into the role of nutrient availability in biofilm growth and sustenance.

Nutrient availability affects biofilm morphology at the mesoscale
To test how biofilm morphology is affected by nutrient availability, specific carbon and nitrogen limiting conditions were determined for E. coli JM105-mini-Tn7-gfp ( Supplementary Fig. 1). Carbon and nitrogen were limited by controlling the nutrient concentrations of the growth media (glucose and ammonium chloride, respectively). The limiting carbon concentration was 15 ± 5 mM (C:N ratio of 1:1.25) and the limiting nitrogen concentration was 2.5 ± 1.5 mM (C:N ratio 27:1). These are broadly comparable with previous E. coli growth experiments in minimal medium [28].
We investigated the impact of nutrient concentration on biofilm morphology by measuring the global biofilm property of base area as a proxy for colony size and spreading ( Supplementary Fig. 2). Biofilms grown on glucose-limited substrates and those grown on ammoniumlimited substrates were similar in size, whereas glucose excess led to larger biofilms (p = 8.152⨯10 − 5 ) than ammoinium excess. As expected, biofilms grown on glucose-rich media were larger than those grown under glucose limitation (p = 1.968⨯10 − 5 ). These data show that glucose availability is the limiting factor governing biofilm base area during growth on minimal medium.
Biofilm maximum intensity projection images ( Fig. 1) which are colour-coded by depth also indicate that not all biofilms have the uniform dome-shaped structure typical of E. coli biofilms [29,30]. Instead, in Fig. 1c we observe that the thickest region of the biofilm is located at an intermediate radius, between the centre and the edge of the biofilm. A phenomenon similar to colony sectoring is observed on glucose-limited substrates (Fig. 1a), where radial sections of the biofilm have a considerably lower fluorescence signal than the rest of the biofilm. The pattern of intra-colony channels is also distributed Fig. 1. E. coli JM105-mini-Tn7-gfp biofilms grown on M9 minimal medium substrates with 15 mM carbon (a), 200 mM carbon (b), 2.5 mM nitrogen (c) and 10 mM nitrogen (d) concentrations. Intra-colony channel patterns appear radially expanding from the centre on nutrient-limited substrates (a,c), whereas they have a fractal structure with sharp turns on nutrient-sufficient substrates (b,d). The figure includes maximum intensity projections of confocal z-stacks made of images separated by 3 μm in the z-direction. Images are colour-coded in the axial direction, with purple corresponding to the base of the biofilm and white corresponding to the top. Scale bars: 500 μm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) heterogeneously inside the biofilm depending on the nutrient availability. Channels grown on nutrient-limited substrates appear to expand radially outwards from the centre in approximately straight lines, whereas on nutrient-rich substrates the channels often change direction sharply and do not follow a straight line. These observations confirm that the morphology of E. coli biofilms is strongly determined by nutrient availability.

Intra-colony channel width increases non-linearly with radial distance from the centre of the biofilm
Channel width was measured along whole circumferences in E. coli JM105-mini-Tn7-gfp biofilms grown on M9 minimal medium substrates with limitation and excess of both glucose and ammonium chloride. The average channel width was plotted against radial distance from the centre of the biofilm, revealing a nonlinear increase in width with radius. Representative plots of n = 3 repeats for each nutrient condition are shown in Fig. 2. The minimum observed channel width was approximately 10 μm, and corresponded to the innermost region of the biofilm (at 200 μm radius). This value was not limited by the resolution of the image datasets, but rather by the smallest radial distance at which channel width could be accurately measured by our pipeline.
The modality of increase in intra-colony channel width was explored by applying linear and exponential fits to each dataset, and R-squared values were calculated for each fit. Average R-squared values for linear fits were 0.816 for 15 mM carbon, 0.855 for 200 mM carbon, 0.825 for 2.5 mM nitrogen and 0.813 for 10 mM nitrogen. Average R-squared values for exponential fits were 0.845 for 15 mM carbon, 0.880 for 200 mM carbon, 0.882 for 2.5 mM nitrogen and 0.892 for 10 mM nitrogen. By verifying that the increase in channel width along the biofilm radius was non-linear, we ensured that the change was not just a result of polar geometry.

Glucose-limited biofilms possess wider channels than ammoniumlimited biofilms
To investigate the effect of nutrient availability on intra-colony channel width, colonial biofilms were grown on substrates with a range of nutrient concentrations: 15 mM carbon (n = 8 colonies), 200 mM carbon (n = 7 colonies), 2.5 mM nitrogen (n = 9 colonies) and 10 mM nitrogen (n = 4 colonies). Intra-colony channel width was compared across nutrient conditions at three normalised radial positions (Supplementary Fig. 4), revealing that channels were approximately 25% wider on glucose-limited substrates than on ammonium-limited substrates inside the biofilm. This increase was most significant at the midradius region of each biofilm, where channel widths measured on average 13.78 μm under glucose limitation and 11.27 μm under ammonium limitation.These data suggest that carbon-and nitrogenbased nutrients mechanistically affect channel morphology in different manners. The density of channels detected inside the biofilm also varied differently depending on the nutrient source, and was largest at midradius.

Substrate stiffness affects channel density and biofilm base area
The effect of substrate stiffness (determined by agar concentration) on internal biofilm morphology was investigated by imaging biofilms grown on soft and hard agar substrates, in both rich and minimal medium (Fig. 3). We observed an increase in out-of-focus fluorescence for biofilms grown on rich medium substrates compared to biofilms grown on minimal medium substrates. On minimal medium, channel borders were better resolved due to the higher contrast relative to the rest of the biofilm. On rich medium, the density of intra-colony channels increased with decreasing substrate stiffness. On 0.5% agar LB substrates (Fig. 3a) channels were densely packed in the whole biofilm, while some widelyseparated channels progressively appeared on portions of biofilms grown on stiffer substrates (1% and 2% agar concentration, Fig. 3b and c respectively).
Varying agar concentration was also associated with a change in biofilm base area for both rich and minimal medium substrates (Supplementary Fig. 3). On rich LB medium substrates, decreasing agar concentration resulted in an increase in biofilm base area, whereas the effect was opposite on M9 minimal medium substrates. Mann-Whitney U rank tests were performed between the 0.5% and the 2% agar concentration data for both rich and minimal medium, and revealed that agar stiffness had similar effects on biofilm base area for minimal medium (p = 0.0221) and rich medium (p = 0.0180). The difference in base area between biofilms grown on rich and minimal medium substrates was most significant at 0.5% agar concentration (p = 0.0092).

Discussion
This study constitutes the first quantitative analysis of intra-colony channels in mature E. coli biofilms. Using a simple custom image analysis pipeline based on the open-source software FIJI and the Python programming language, it was possible to quantify intra-colony channel width subject to various environmental conditions. We discovered that channel morphology was affected by both the type of substrate (rich or minimal medium agar) and by substrate properties (nutrient and agar concentration).
Environmental conditions altered the distribution of intra-colony channels inside biofilms. Channels formed on substrates with limiting carbon or nitrogen concentrations expanded radially outwards, in approximately straight lines. This could be because bacteria growing on nutrient-depleted substrates adhere less strongly on the surface of attachment, and expand more rapidly [31], or may be indicative of nutrient foraging behaviour. Conversely, channels formed on nutrient-rich substrates exhibited complex fractal patterns. It is hypothesised that this type of structure emerges due to rapid cell growth and larger cell dimensions, thereby resulting in a tighter network of channels. This in turn enables a greater proportion of cells to access the nutrients that are transported within the biofilm. A recent study by Fei et al. [6] highlighted two distinct types of patterns forming on the surface of V. cholerae biofilms, namely radial stripes and zigzag herringbone patterns. Conversely, the biofilms in our study only involved the same type of fractal patterns: intra-colony channel structures had homogeneous morphology, with only width and spacing varying depending on environmental conditions. Furthermore, we found that agar concentration in the substrate affected intra-colony channel density on rich medium substrates: channels were tightly packed and had a uniform, narrow width on semi-solid substrates, but as the agar concentration increased, wider channels appeared in portions of the biofilm. This observation appears to be in contrast with previous work on V. cholerae biofilms, where homogeneity in radial feature distribution and spacing at the edge of mature biofilms increased with agar stiffness [32].
An increase in out-of-focus fluorescence was also observed in widefield epi-fluorescence images of biofilms grown on rich medium compared to those grown on minimal medium. The fluorescence signal inside channels was likely due to bacterial cells being present inside Fig. 3. ROIs showing intra-colony channel morphologies of E. coli JM105-mini-Tn7-gfp biofilms grown on solid LB rich medium (top half) and solid M9 minimal medium (bottom half). The agar concentrations of the substrates were 0.5% (a,d), 1% (b,e) and 2% (c,f). All images were acquired using the Mesolens in widefield epi-fluorescence mode to capture the biofilms at the midpoint along biofilm thickness. The images were acquired with LB or M9 mounting medium and the Mesolens in water immersion, except for panel d, which was acquired in air with no mounting liquid to prevent the biofilm from detaching from the substrate. All images were deconvolved using Huygens proprietary software. Scale bars: 500 μm.
them, as a result of movement inside the biofilm, collective reorientation [33] or shedding of cells from the inner walls of the channels. Previous studies on V. cholerae [34] confirmed that expansion in the depth direction is dependent on friction between the substrate and the expanding cells, with softer substrates leading to flatter biofilms than stiff substrates. This could explain the reduction in contrast between channel border and constituent cells observed on stiff rich medium substrates. A variation in internal biofilm architecture along the depth direction has also previously been reported for E. coli growing on agar substrates [35] and was attributed to differences in extracellular matrix components assembly and organisation inside the biofilm volume.
The variation in channel width inside mature biofilms was discovered to increase non-linearly along the radial direction from the centre of the biofilm under all nutrient conditions. Remarkably, channels were on average 25% wider at the centre of glucose-limited media than inside ammoinium-limited media, which suggests that they are more important for the transport of carbon-based nutrients. We speculate that the increase in channel width at the edge of the biofilm is due to rapid cell growth in nutrient-rich conditions [36]. This would result in non-uniform radial expansion, as previously observed for B. subtilis [31] and V. cholerae [6], suggesting that variations in channel width are an emergent property of E. coli biofilm growth.
We speculate that the channels may become increasingly narrow in the centre of the biofilm because of fundamental fluid dynamics behaviour. We can consider a simplified model of the nutrients transported by the channels in an E. coli biofilm as fluid flow in a pipe. The continuity equation states that in the case of steady flow the mass flow rate remains constant: as fluid flows along a pipe of decreasing width, the velocity of the fluid increases proportionally [37]. Approximating our channels as pipes, the smaller width of the channels at the centre of the biofilm compared to the edge will result in a faster provision of nutrients where the demand is greatest to sustain the biofilm. In addition, narrow channels may also help to transport nutrients into the biofilm centre via capillary action. The distance over which fluid can be spontaneously transported through capillary action is inversely proportional to the width of a pipe [38]: the smaller channel width towards the centre of the biofilm would then support increased capillary action and hence provide an additional nutrient transport mechanism.
The mesoscopic effects of nutrient limitation were studied by calculating biofilm substrate area. Nutrient abundance in the substrate, achieved by increasing the amounts of either glucose or ammonia, led to larger biofilms than nutrient limitation. Biofilm base area was most significantly affected by the glucose concentration in the growth substrate and was 2.7 times larger for biofilms grown on glucose excess than on glucose limitation. On the other hand, increasing the ammonium concentration on a substrate with sufficient glucose availability did not significantly affect biofilm base area. These findings agree with the reported increase of biofilm formation with glucose concentration in Staphylococcus species [39] and the increase in colony size with glucose concentration for E. coli [40] and yeast [41]. While it is known that growth rate limitations and carrying capacity limitations differ due to the change in growth condition (homogeneous mixed environment or growth on a solid surface) [42], our data show a similar response to both conditions ( Supplementary Figs. 1 and 2).
The effect of agar concentration on biofilm base area varied based on the nutritional profile of the substrate. An increase in agar concentration in rich medium was associated with a reduction in biofilm base area, due to slower radial expansion of biofilms on the surface brought by stronger frictional forces [29]. An increase in agar concentration could also affect biofilm base area by decreasing the level of swarming motility [43]. The trend of increased base area with decreased agar stiffness has previously been observed in V. cholerae biofilms grown on LB medium with different agar concentrations [6]. However in our work, the opposite trend was observed on minimal medium: biofilms grown on stiff substrates had a base area on average 1.6 times larger than those grown on semi-solid substrates. This could be due to faster assimilation of nutrients occurring on semi-solid minimal media with respect to stiff minimal media, causing a halt to radial expansion. Finally, biofilm base area was on average almost 2.5 times larger on semi-solid rich medium substrates than on semi-solid minimal medium substrates. The slower growth of E. coli in minimal medium with respect to rich medium (with average doubling times of 18 ± 0.5 min in LB and 38 ± 1.1 min in M9-glucose [44]) can explain this difference in biofilm base area only in part, since we observed no significant difference in base area between rich and minimal medium substrates at higher agar concentrations of 1% and 2%.
Studying biofilm internal patterns at the cellular level is a task mostly relegated to theoretical modelling and computer simulations [29,[45][46][47][48]. Experimental approaches in imaging biofilms at single-cell resolution [49][50][51] have been limited in the total biofilm size that can be imaged at once (under 100 μm 2 ). The combination of mesoscale imaging and open-source image analysis tools has proven to be an essential platform technology to identify and quantify internal structure in larger biofilms than an ordinary microscope can accommodate. It can also be used without adaptation to validate existing numerical simulations of mature colony biofilm structure, or it can be readily applied for the quantification of any internal patterns and structures in a wide range of biofilms.

Imaging chamber design and 3D-printing
The imaging chamber to be used with the Mesolens was designed on AutoCAD (Autodesk, USA) by modifying the original design of Rooney et al. [26]. The chamber was designed to mimic a Petri dish, and consisted of a 120 mm × 100 mm × 12 mm plate with a 60 mm diameter, 10 mm deep well at its centre to hold the agar substrate ( Supplementary  Fig. 4). After 3D printing the chamber in black ABS plastic (FlashForge, Hong Kong) using a FlashForge Dreamer 3D printer (FlashForge, Hong Kong), the corners were smoothed out using a scalpel. This reduced the movement of the imaging chamber inside the square plate. The chamber was sterilised with a 70% (v/v) ethanol solution, and then under UV light for 20 min immediately before the addition of sterile solid growth medium.

E. coli biofilm specimen preparation
Liquid cultures of E. coli JM105-mini-Tn7-gfp were prepared in LB medium supplemented with 25 μg/mL gentamicin and incubated overnight at 37 • C. Overnight cultures were diluted (1:100) into fresh LB medium and incubated at 37 • C until they reached an optical density of 0.5 (mid-exponential growth phase).
To grow biofilms on rich medium, 100 μL of a liquid culture with density 1 × 10 4 colony-forming units (CFUs) per mL was inoculated on the 10 mm-thick LB agar substrate inside the imaging chamber. The specimen was incubated at 37 • C for 24 h in darkened condition prior to imaging. For minimal medium with varying nutrient concentration, mid-exponential phase liquid cultures were washed three times with 1× M9 salts. They were then resuspended in M9 medium with appropriate amounts of glucose and ammonium chloride (for carbon and nitrogen variation, respectively). M9 agar substrates cast into the 3D-printed imaging chambers were inoculated at a concentration of 1 × 10 4 /mL. Based on the dimensions of the imaging chamber ( Supplementary  Fig. 5), this corresponds to a seeding density of 1 cell per mm 2 , which ensured biofilms were sufficiently spaced out and did not have to compete for nutrients with others in their proximity. It was also ensured that only one biofilm was visible in the field of view of the Mesolens at once, which prevented background signal from nearby biofilms from reaching the detectors.

E. coli growth characterisation under different nutrient conditions
Mid-exponential growth phase liquid cultures of E. coli JM105-mini-Tn7-gfp were prepared as described above, then washed and resuspended in 1× M9 salts. The cultures were diluted to an OD 600 of 0.04, split in individual tubes and supplemented with appropriate amounts of the nutrient of interest. For carbon growth curves, the concentration of nitrogen was kept constant at 18.7 mM, and for nitrogen growth curves the concentration of carbon was kept constant at 66.7 mM. The nutrient concentrations were chosen to be between 0 mM and 80 mM -for comparison, the carbon and nitrogen concentrations in nominal M9 salts are 66.6 mM and 18.7 mM, respectively. Aliquots (200 μL) of liquid culture of each investigated concentration was added in triplicate to a black Nunc MicroWell 96-well optical-bottom plate with polymer base (ThermoFisher Scientific, US). Absorbance (OD 600 ) measurements were performed every 15 min for 24 h, with the plate being held at 37 • C and shaken continuously.
Growth curves were produced for each nutrient concentration thanks to the Gen5 microplate software (BioTek, USA), and exported to MATLAB (MathWorks, USA) for analysis. The average of the first absorbance value for each concentration was used as a baseline and subtracted from each growth curve. The y axis was displayed in logarithmic scale, in order to identify the exponential growth phase (the linear portion of the plot). A linear fit to this region was applied using MATLAB's Curve Fitting Toolbox by selecting an exponential function of the form y = a exp(bx), with the specific growth rate corresponding to the coefficient b. While error analysis was produced internally in MATLAB as R-squared, SSE and RMSE values, the error bars on the specific growth rate plots were calculated as the standard deviations across biological repeats for the same nutrient concentration. Note that the duration of the exponential growth condition varied depending on the nutrient concentration, and lasted between 6 and 18 h, hence the data points corresponding to exponential growth were selected manually. Growth curves and specific growth rates were plotted in Python using matplotlib.

Widefield epi-fluorescence and confocal laser scanning Mesolens imaging
All the data in this work was acquired using the Mesolens, a custommade optical microscope combining high numerical aperture (0.47) with low magnification (4×). These characteristics allow simultaneous imaging over a field of view of 6 mm × 6 mm with sub-cellular lateral resolution throughout (700 nm). Images can be acquired over a total thickness of 3 mm with an axial resolution of 7 μm. For widefield epifluorescence Mesolens imaging, GFP fluorescence was excited by a 490 nm pE-4000 LED (CoolLED, UK), and emitted fluorescent light was made to pass through a 540 ± 10 nm bandpass filter before being detected by a VNP-29MC sensor-shifting CCD camera (Vieworks, South Korea). The camera uses sensor shifting to acquire 9 images for each pixel (each shifted by 1/3 of a pixel width from the other, forming a square grid), effectively increasing the resolution to 259.5 MP [54]. In confocal laser scanning mode, GFP fluorescence was excited using a 488 nm laser (Multiline Laserbank, Cairn) at 5 mW power. Fluorescence emission was filtered through a 525/39 nm bandpass filter (MF525-39, Thorlabs, USA) before being detected using a PMT (PMM02, Thorlabs, USA). The emission path also included a 505 nm longpass dichroic mirror (DMLP505R, Thorlabs, USA). Both widefield and confocal laser scanning microscopy were performed with the lens in water immersion, to match the refractive index of the mounting media (LB and M9), except the 0.5% M9 agar datasets which were acquired in air, with no immersion or mounting liquid. This was needed to preserve biofilm structure, as biofilms grown 0.5% M9 agar were less adherent to the substrate and detached from it after addition of liquid mounting medium. The intra-colony channels formed by these biofilms remain evident even though the lower refractive index resulted in poorer spatial resolution (Fig. 3d). The Mesolens collars were adjusted to minimise spherical aberrations.

Image analysis
Confocal z-stacks were displayed as a maximum intensity projection, colour coded by depth across the z-direction using the "Fire" lookup table from FIJI (ImageJ version 1.53c). Where necessary, medianfiltered widefield epi-fluorescence Mesolens images (filter radius: 2 pixels) were deconvoluted using the proprietary Huygens Professional version 19.04 software (Scientific Volume Imaging, Netherlands). Deconvolution was performed after an in-built manual background subtraction and a theoretical point spread function estimation on Huygens, using the Classic Maximum Likelihood Estimation method with 50 iterations, a signal-to-noise ratio of 40 and a quality threshold of 0.01.
To calculate biofilm base area, widefield Mesolens images were opened in FIJI, and thresholded using the "adjust threshold" tool, using the mean of gray levels as the threshold value. The "Wand (tracing) tool" was then used to select the biofilm mask, and the area was calculated using the "Measure" function. The base area measurements were systematically underestimated due to the thresholding method used by FIJI to create the binary mask. Nonetheless, by using the same thresholding method on all images we ensured that this limitation had comparable effects on all datasets. Biofilm thickness was calculated by plotting z-axis profiles of confocal z-stacks in FIJI and calculating the distance between the two minima on each profile. Mesolens images were brightness-and contrast-adjusted using FIJI for presentation purposes [55].

Intra-colony channel width calculation
Intra-colony channel width was calculated using the image analysis workflow outlined in Fig. 4. The pipeline made use of the FIJI plugin "Polar transformer" [56], which performed an image transformation from polar to cartesian coordinates, as well as of two custom Python scripts. Initially, the coordinates of the centre of the biofilm were calculated using the "Measure" function on FIJI applied on an oval selection of the whole biofilm. The Polar Transformer plugin was then launched, and the origin of transformation was manually entered as the coordinates of the biofilm's centre. The number of pixels for each degree in angular coordinates was set to 7200 (corresponding to 20 pixels for each degree). The polar-transformed image was contrast-adjusted using the "CLAHE" (Contrast Limited Adaptive Histogram Equalization) feature on FIJI with block size 60, maximum slope 3 and 256 histogram bins to facilitate channel identification. The image was then despeckled using the "Despeckle" function on FIJI in order to remove noise. The image was also inverted, making intra-colony channels appear light and cells dark, which facilitated the rest of the analysis. Vertical line selections were taken at different x positions on the polar-transformed image, corresponding to circumferences around the biofilm taken at different radial distances from its centre. Signal profiles were obtained for each line selection using the "Plot profile" feature on FIJI, and were exported to Python, where signal peaks were located thanks to a custom script using the "find peaks()" function. For each dataset, peak thresholding was performed in order to exclude noise: peak prominence was chosen as 20% of the difference between maximum and minimum signal, and a minimum distance between adjacent peaks was selected as 9 pixels, which corresponds to the average length of an E. coli cell (2 μm) on a Mesolens widefield epi-fluorescence image. Intra-colony channel widths were then calculated as the full-width at half-maximum of each peak. The actual width of the channels in μm was converted according to the radial distance from the centre, using polar coordinate geometry.

Variation of intra-colony channel width along the radial dimension
Intra-colony channel width was measured along whole circumferences at radius intervals of 50 μm, starting from an initial radius of 200 μm. This initial radius value was chosen because at lower values, polar transformed images were distorted and signal analysis was not reliable. Because of the ellipticity of the biofilms, polar-transformed images appeared as rectangles with a non-straight right side (Fig. 4), corresponding to the biofilm perimeter. Regions beyond which a full circumference could not be obtained for the biofilm were excluded from the analysis.
Channel widths were measured for biofilms grown on the four nutrient conditions described in the Results section. Three biological replicates were used for each condition, giving a total sample size of 12 biofilms. Linear and exponential fits were applied to each plot of average channel width against radius, and R-squared values for the fits were computed for each dataset using Excel. The number of channels identified by the script varied between radial positions, and was highest for the intermediate radii. This is likely due to the fractal nature of intracolony channels, which have sharp changes in direction and fold on themselves inside the colony.
To compare channel widths across different nutrient concentrations of the substrate, intra-colony channel width was calculated at three normalised radial positions (full radius, 50% radius and 20% radius) to investigate the effect of nutrient concentration. Datasets were acquired for each of the following nutrient concentrations: 15 mM carbon (8 biofilms, giving 1062 channels), 200 mM carbon (7 biofilms, giving 1424 channels), 2.5 mM nitrogen (9 biofilms, giving 1524 channels) and 10 mM nitrogen (4 biofilms, giving 507 channels).

Statistical analysis
The comparison of biofilm base areas and channel widths under different nutrient availabilities and agar concentration was performed by means of a Mann-Whitney U rank test, chosen as datasets were not normally distributed and had unequal sample sizes. The testswere performed using thescipy.stats.mannwhitneyu() function in Python. Pvalues smaller than 0.05 were considered statistically significant.
Biofilm base area and intra-colony channel measurements were displayed using Python's seaborn.boxplot() and seaborn.stripplot() plotting tools, where the first and third quartile of the data (Q1 and Q3) are enclosed by a box which contains 50% of the data (the interquartile range, or IQR). The median is shown as a horizontal line inside each box, whereas the capped bars are the "minimum" and maximum" values, which are found a distance of 1.5×IQR above and below the Q3 and Q1 respectively. Average values for each measurement are shown as white diamonds.
Large areas of low fluorescence, mainly observed at the edge of the biofilms, were erroneously detected as channels by our measurement method. We removed these outliers by excluding data points which had a modified z-score greater than 3. The modified z-score was calculated using the median absolute deviation as described in Ref. [57] for non-normally distributed data.

Data and code availability
The Python script used to calculate intra-colony channel width was written on Python version 3.7, and is deposited on GitHub (https://gith ub.com/beatricebottura/biofilm_channel_width, https://doi.org/10. 5281/zenodo.5786305). An example dataset to be analysed with the Fig. 4. Image analysis workflow. A widefield Mesolens image is opened on FIJI, where an oval selection is used to obtain the coordinates of the centre of the biofilm. The coordinates are the input into the Polar Transformer FIJI plugin, which performs a transformation from polar to cartesian coordinates. The resulting image is locally contrast-enhanced, despeckled and inverted on FIJI. Signal profiles of vertical line selections are exported to Python, where the signal is analysed with a custom script in order to locate the peaks (orange crosses) and calculate the full-width at half-maximum (green horizontal lines) of each peak. The latter quantity corresponds to intra-colony channel width, converted from pixel units to μm using polar geometry. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) script is also available in the same repository. The remaining data used to generate channel width results is available upon reasonable request.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.