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Matrix composition determines the dimensions of Bacillus subtilis NCIB 3610 biofilm colonies grown on LB agar

The production of biomolecules can provide new functionalities to the synthesizing organism. One important example is the secretion of extracellular polymeric substances (EPS) by biofilm forming bacteria. This biofilm matrix protects the individual bacteria within the biofilm from external stressors such as antibiotics, chemicals and shear flow. Previous studies have determined several main matrix components of biofilms formed by Bacillus subtilis. However, how these matrix components influence the growth behavior and final dimensions of B. subtilis biofilms has not yet been determined. Here, we combine different experimental techniques with theoretical modeling to assess this relation. In particular, we quantify the area covered by the biofilm and the biofilm height by performing time-lapse microscopy and light profilometry, respectively. We study the development of biofilms formed by two wild-type strains (B-1 and NCIB 3610) differing in their matrix composition and NCIB 3610 mutant strains lacking the ability to produce specific EPS. Based on the experimentally obtained growth dynamics, we develop a mathematical model that allows us to quantify the influence of three key biofilm matrix components on the final NCIB 3610 biofilm colony dimensions. In detail, we show that two matrix components, the exopolysaccharide produced by the epsA-O operon and the surface layer protein BslA control the area covered by the biofilm colony. The height of these mature biofilm colonies is mostly affected by BslA. Together, our results emphasize the importance of the biofilm matrix composition for biofilm growth and the final dimensions of mature B. subtilis NCIB 3610 biofilm colonies.


Introduction
Biolms are spatially structured surface-attached communities of microbes where the individual cells are surrounded by a matrix of secreted macromolecules. 1,2 This biolm matrix can be composed of various extracellular polymeric substances (EPS) such as proteins, exopolysaccharides, lipids or nucleic acids. [3][4][5] The EPS promotes biolm adhesion to surfaces, provides the mechanical stability of the biolm, and protects cells within the biolm from chemical stresses and invasion of foreign bacteria. 3,6 Although biolm formation can be benecial for industrial applications 7 such as waste water treatment, 8 biolms growing on medical implants can cause serious infections and device failure. 1,9 Bio-lm formation comprises four phases: the attachment of single cells to surfaces, followed by two-dimensional cell growth and the formation of microcolonies (microcolony growth), followed by three-dimensional growth of the entire biolm colony and bio-lm maturation (macrocolony growth), and nally biolm dispersal. 10 The process of biolm formation oen involves division of labor, such as the differentiation into distinct cell types within an isogenic population seen in the bacterial species Myxococcus xanthus, Bacillus subtilis and Pseudomonas aeruginosa. 11 In the case of B. subtilis, biolm formation also includes the production of communal goods that form the biolm matrix. 2,12 In the past years, the main matrix composition has been resolved for many bacterial biolms. 2,4,[13][14][15][16] Improvements in computational analyses allowed quantication of biolm structure for biolms grown in liquid conditions [17][18][19][20] and recent technical advances in high-resolution optical microscopy enabled the investigation of the extracellular matrix structure, 21,22 even at the single cell level. 23 Together, those studies provided crucial information that is urgently needed to prevent or control biolm formation, 9,24 such as the fundamental role of the biolm matrix in establishing emergent biolm properties. 25 While many bacteria produce biolms on surfaces under water-saturated conditions (in liquid), 17,20,23 B. subtilis forms biolms on solid nutrient surfaces in air, or at liquid-air interfaces. 10,12,26 For these types of biolm formation, quantitative aspects of biolm formation have been addressed theoretically, [27][28][29][30] but studies investigating how EPS production inuences biolm dimensions are just emerging. 28,31,32 For example, it has been suggested that the physical mechanism responsible for the spreading of biomass in B. subtilis biolms is the pressure generated by bacterial division. 33 Two growth parameters that are typically used to describe the dimensions of a biolm are the area covered by the biolm and the biolm height. 34 However, it remains unclear how the different molecular components of the biolm matrix quantitatively modulate B. subtilis biolm growth. Deletion mutants which are unable to produce selected biolm components can be a helpful tool to unravel the contribution of specic biomolecules on the macroscopic biolm properties. The use of deletion mutants of B. subtilis has enabled to demonstrate that the protein BslA contributes to the strong wetting resistance 35 as well as the surface stiffness and roughness of B. subtilis biolms. 36 Here, we employ a similar approach and quantify the formation of biolm colonies grown on solid agar surfaces of two B. subtilis wild type strains (B-1 and NCIB 3610) that differ in their biolm matrix composition, 35,[37][38][39] and a biolm defective B. subtilis strain (BD630) which is unable to produce a biolm on solid LB agar surfaces. Using a combination of time-lapse microscopy and light prolometry, we show that for the wellstudied B. subtilis strain NCIB 3610, for which the main components of the biolm matrix are known, 35,38,39 specic matrix components control the dimensions of mature biolm colonies. Furthermore, by tting a logistic growth model to our experimentally obtained data for the wild-type NCIB 3610 and selected mutant strains, and separating the composed parameters into their constituting factors using a multiplicative model, we quantify the impact of these matrix elements on biolm area coverage and biolm height.

Strains and growth conditions
The B. subtilis strains used in this study are BD630, B-1, NCIB 3610, CA017, ZK3660, N24, and bslA/tasA, as described in Table 1. LB Medium (Luria/Miller; Carl Roth GmbH, Karlsruhe, Germany) served as complex medium for all B. subtilis strains and contained the corresponding antibiotic (Table 1). Bacteria were cultivated overnight in 5 ml medium at 37 C and 300 rpm agitation. The cultures were then diluted to an OD 600 of 0.05 and grown until an OD 600 of 0.1 was reached, representing the beginning of the exponential growth phase. The cultures were again diluted to an OD 600 of 0.05 and 18 droplets of 0.5 mL per bacterial strain were applied to an LB-agar plate (1.5% agar, 1.5 g per 100 ml w/v). This allowed for investigating biolm colony growth starting from single cells distributed across the agar plate. Biolm colony growth was then investigated over a time-course of 17 h. Longer growth times were not studied as no considerable change in area or increase in height was obtained for the biolm forming wild-type strains used in this study thereaer.
For motility measurements (Fig. S1 †) the cultures of NCIB 3610 and the epsA-O mutant were prepared as described above. Then, 5 droplets of 0.5 mL each were applied to LB-agar plates with varying agar concentrations (1.25% (1.25 g per 100 ml w/v), 1.50% (1.5 g per 100 ml w/v), 1.75% (1.75 g per 100 ml w/v) and 2.00% (2 g per 100 ml w/v)) and grown for 21 h in an incubator at 37 C. Pictures of the area covered by the colonies were taken with a Nikon SMZ 25 stereoscopic microscope (Nikon, Germany).
To test if growth conditions such as medium composition and growth temperature affect the size of biolm colonies, the tasA mutant and NCIB 3610 wild type strain were grown and plated similarly to expansion measurements, but on different plate compositions. LB agar and MSgg agar plates (minimal medium containing 5 mM potassium phosphate, 100 mM Mops, 2 mM MgCl 2 , 700 mM CaCl 2 , 50 mM MnCl 2 , 50 mM FeCl 3 , 1 mM ZnCl 2 , 2 mM thiamine, 0.5% glycerol, 0.5% glutamate, 50 mg ml À1 tryptophan, 50 mg ml À1 phenylalanine, and 50 mg ml À1 threonine) were used and both types of plates were incubated at 30 C and 37 C for different time-spans (Fig. S2 †).

Construction of the bslA/tasA double deletion mutant
For the construction of the bslA/tasA double deletion mutant, genomic DNA of the CA017 mutant (Table 1) was puried using the MasterPure™ Gram positive DNA Purication Kit (Epicentre). Then, 1 mg ml À1 of the genomic DNA was transformed  61 B. subtilis 168 is not able to produce a proper biolm matrix compared to NCIB 3610 due to several mutations and the lack of a plasmid required for biolm formation. 61 Hence, this strain is not able to form a biolm and can therefore serve as a biolm-growth negative control. + These strains are non-isogenic derivatives of strain NCIB 3610. # We conrmed deletion of the TasA protein in strain CAO17 by PCR analysis and sequencing (Fig. S7).
into the N24 strain (Table 1). Transformants were selected on LB agar plates containing kanamycin (50 mg ml À1 ) and chloramphenicol (5 mg ml À1 ). Successful transformation was conrmed by sequencing.

Analysis of area coverage
The area covered by a bacterial colony of a strain unable to form a biolm (BD630, Table 1) or a strain able to form a bio-lm (biolm colony, all other strains) was recorded using an upright microscope (90i, Nikon, Düsseldorf, Germany). Bright eld images were taken with a DS-Qi1MC digital camera (Nikon). For the rst 90 min, an image was obtained for each droplet every 15 min using a 50Â objective. Aer 90 min, the bacteria had covered the initial area, and the following images were taken every hour with a 1Â objective for a total time span of 17 h. To prevent dehydration of the agar plates and to ensure a constant temperature of 37 C over the whole timecourse of the experiment, the agar plates were kept in a custom made climate chamber (Pecon GmbH, Erbach, Germany) on the microscope. Experiments were conducted on three different days resulting in $36 data curves for each strain. Image analysis was performed using a self-written script in MatLab (Version 2013b). Microscopy images presented in Fig. 1A were obtained with a Nikon SMZ 25 stereoscopic microscope. Images of biolm colony morphology ( Fig. 2A and 3A) were obtained with a stereomicroscope (Nikon SMZ1000) and the colonies were grown in an incubator (INNOVA 4200, New Brunswick) for 17 h. Consequently, their nal biolm colony size differs slightly from biolm colonies grown directly on the microscope. However, the biolm colony morphology is comparable to biolm colonies grown on the upright microscope used for the quantitative analysis of area coverage.

Analysis of biolm colony height and biolm colony roughness
To investigate the height and roughness development of growing biolm colonies, light prolometry images of these colonies were obtained for a period of 17 h. The measurements were performed on two different days, resulting in 14 data curves per strain. The images were acquired at an edge of the biolm colonies, such that a corner of the image would not contain biolm (Fig. S3 †). Prolometry surface images were taken every two hours with a NanoFocus msurf prolometer (NanoFocus AG, Oberhausen Germany) using a 20Â objective, resulting in surface images with an area of 800 Â 772 mm. The data was evaluated with the soware mso (Version 6.0, Nano-Focus AG, Oberhausen, Germany) to obtain two metrological surface parameters: the root mean squared surface roughness , and the maximum height S z , which represents the distance between the highest peak and the deepest valley of a given image. For the calculation of both parameters, a correction method was applied to early stage biolms so that the agar structure below the biolm colonies does not contribute to the calculated parameters. This agar layer was subtracted using a linear correction method which removes the tilt of the surface (see Fig. S3a-c †). The resulting image shows a surface prole corresponding to the biolm colony only (Fig. S3c †). At later stages (growth times > 5 h), the biolm colonies form a continuous layer on the agar surface. For these images, it is not possible to perform the same correction anymore as it is very difficult to distinguish the tilted agar layer from a (potentially also tilted) continuous biolm layer. Therefore, at these growth times, values for S z were calculated from the uncorrected prolometry images (Fig. S3a †). For the calculation of S q at growth times later than 5 h (when a continuous biolm layer had formed), only data from the image quadrant (a region of 400 Â 382 mm) opposite to the agar border was analyzed (Fig. S3e †). This procedure ensured that the edge of the biolm colony itself did not contribute to the calculated S q values. Data presentation was partly performed using Igor Pro 6.37.

Bacterial population growth
Bacterial population growth (Fig. S4 †) was analyzed with a plate reader (POLARstar OPTIMA, BMG Labtech). Overnight cultures were generated as described above, and diluted to an OD 600 of 0.05 in 0.5 ml LB medium. Bacterial population growth was followed for $6 h while the cultures were maintained at constant shaking at 37 C. Optical density was measured at 600 nm every 15 min. The resulting population growth curves represent a mean of at least eleven wells. From this data, aer blank correction, the population growth rate (GR) was obtained as follows: population growth curves as represented by OD 600 were tted using the linear t function (fL ¼ a + b Â x, with a the y-intercept and b the slope of the function) of the IGOR PRO 6.36 soware to t the natural logarithm of the population growth curves. Then, population growth rate (GR) was calculated according to: 40 Mathematical tting of the growth parameters area coverage and biolm height Each matrix component can affect the nal dimensions of the biolm colony (area covered by the biolm and biolm height) in three different ways: (a) by simply adding biomass, (b) by changing the growth rate of the respective strain in the macroscopic growth rate regime, as it has been shown that the tness of non-matrix producing cells increases under planktonic conditions, 41 and (c) by crosslinking the individual cells within the biolm. As these different mechanisms are closely interconnected and cannot clearly be disentangled, we chose to t the experimentally obtained data, to retrieve the carrying capacity as a measure of the nal dimension of the biolm colony in the absence or presence of a particular matrix component. Hence, the carrying capacity quanties how the dimensions of the biolm colony are affected by a particular matrix component, as a sum of all of the above described mechanisms. The tting of the experimental data is described in the following. How the carrying capacity is used in the subsequent mathematical model to calculate the inuence of each matrix component on the nal biolm colony dimensions is described in the next main paragraph.
In the experiments, we observed sigmoidal data curves in the macrocolony regime for the development of the area covered by the biolm colony and for biolm colony height. From a variety of different sigmoidal functions, 42 we chose the solution of the logistic differential equation (eqn (1)) for modeling our data. The advantage of this model is its simplicity, as it only requires three free tting parameters. Moreover, since its introduction in the 19 th century 43 it became textbook knowledge for the modeling of population dynamics. 44 In this model, a population with P individuals grows with rate r until it reaches the carrying capacity k. The sigmoidal solution has the following form (eqn (2)): We assumed that, within a given strain, there are always forces that act in favor or against the development of a biolm colony's characteristic dimensions, such as area covered by the biolm colony and the biolm colony height. Furthermore, we assumed, that those forces inuence both the rate of development (r) and the nal level (k) of these dimensions. This reasoning motivated us to apply the logistic growth model to the two growth parameters of interest (area covered by the biolm colony and biolm colony height) (eqn (3)). As the biolm roughness also increased sigmoidally with time, the same tting procedure was applied to the surface roughness data (Fig. S5 †).
Here, P i (t) describes the temporal development of the dimension of interest P (biolm colony area coverage or biolm colony height) for a strain i. The tted parameters k P,i , P 0,i , and r P,i describe the carrying capacity (saturation value of the respective growth parameter corresponding to the nal dimension of the biolm colony), the level at t ¼ 0, and the rate of increase of the two growth parameters, respectively. P 0 is not a tting parameter but describes the average initial value for the considered strains.
With this model, we performed nonlinear least square regression using the Levenberg-Marquardt algorithm 45 as implemented in the Matlab Curve tting toolbox. Initial values of k P,i and P 0,i for the optimization procedure were taken from the nal and rst value of the considered time trace of the two growth parameters, respectively.
To determine the inection points of the biolm colony area growth curves, we calculated the maximum difference between subsequent values of the sigmoidal t curves numerically. This is equivalent to calculating the maximum of the rst derivative, that is the inection point.
In order to calculate the uncertainty of the tting parameters (tting parameter vector q ¼ (k, P 0 , r)), the weighted Jacobian matrix X i;j ¼ 1 s i vPðt i ; qÞ vq j was explicitly calculated in the vicinity of the optimal tting parameters. Here, s i is the standard deviation of the experimentally observed data measured at time t i . Then, we used the following formula to estimate the variance of the tting parameters Dq j 2 ¼ var(q j ) ¼ ([X T X] À1 ) j,j as described in ref. 46.

Mathematical model of biolm matrix composition affecting biolm colony growth
In the sigmoidal model (eqn (3)), the nal saturation value of the biolm colony dimensions P (biolm area coverage and biolm height) is given by the carrying capacity k P,i for each strain i. For clarity, we restricted ourselves to show the reasoning for just one biolm colony dimension and omit the index P in the following. We assumed that the carrying capacities of biolm colony dimensions are primarily determined by growth through cell division of the individual bacterial cells within the biolm colony and are independent of the biolm matrix elements. Then, this biolm colony growth due to bacterial cell division contributes a basal level b 0 to the carrying capacity. However, the embedding of cells in the extracellular matrix can increase or decrease the strain's ability to develop the considered biolm colony dimension (biolm area coverage and biolm height) compared with the basal level b 0 . This effective phenomenological alteration can be modeled through multiplication by a factor b i for a biolm matrix element i. This motivates the following multiplicative ansatz for the carrying capacity of a given mutant strain Here, the contribution indicator Kobayashi and Iwano, 2012 35 have shown that the production of the surface layer protein BslA depends on the expression of the epsA-O operon, which is responsible for the production of the exopolysaccharide. Hence, d EpsA-O,i is set to zero for both biolm matrix components (BslA and the exopolysaccharide) in the epsA-O mutant. Ostrowski et al., 2011 47 showed that BslA is not involved in the synthesis, export, or polymerization of the TasA amyloid bers or the exopolysaccharide. Therefore, a feedback effect of BslA on the expression of TasA or the exopolysaccharide is not incorporated into our model. In addition, further feedback mechanisms or unknown factors that might contribute to the biolm matrix are not considered.
More explicitly, this leads to the following system of equations for the carrying capacities of the NCIB 3610 and the three single deletion mutants bslA, tasA and epsA-O: For the wild-type strain, the carrying capacity includes all factors; the basal rate b 0 and the contributions of all matrix elements: b BslA , b EpsA-O , and b TasA . For the single deletion strains of the proteins TasA or BslA, the contributions of the lacking matrix components are absent. The carrying capacity of the epsA-O mutant does not have contributions from both the exopolysaccharide and BslA because the production of the exopolysaccharide is necessary for BslA production. 35 This system of four equations with four unknowns (eqn (5)) can be easily solved to obtain values for the individual factor b j of each of the matrix elements (Table S3 †). Note that b EpsA-O only contains contributions due to its own activity and not due to its coupling to BslA production. Uncertainties of the factors Db j are calculated from the uncertainties of the carrying capacities Dk i by uncertainty propagation. Please note, that the same set of equations (eqn (5)) have also been used to model the development of the biolm colony surface roughness (Table S3 †). Based on the model described above, we can calculate the carrying capacity of the bslA/tasA double deletion mutant using the following equation: This predicted value of the double deletion mutant is then compared to the value of the carrying capacity calculated by tting the experimentally obtained growth parameters: biolm area coverage and biolm height. This procedure allows us to investigate possible feedback effects between the BslA and the TasA protein (Table S2 †).

Biolm colony growth of B. subtilis wild type strains
The dimensions of a mature bacterial biolm colony can be described by two growth parameters: the area covered by the biolm and the biolm height. We investigated biolm colony growth (biolm colony development over time) starting from single cells distributed across the agar plate ( Fig. 1A and B, Section a), and followed this growth over a time-course of 17 h to allow the analysis of micro and macrocolony biolm growth (Fig. 1A). To determine the area increase for growing Bacillus subtilis biolm colonies, we performed time-lapse microscopy (Methods), and investigated the area coverage for both the micro and macrocolony biolm growth phases (Fig. 1A). During the microcolony growth phase, single cells dividing in the initially spotted zone rst ll up this area and then start to grow into the third dimension approximately 60-90 min aer inoculation. This phase is followed by the macrocolony growth phase; here, the whole three-dimensional biolm colony expands in range. During this expansion, the biolm colony is not only expected to increase its thickness but also to develop a rough surface. 36 Hence, a parallel analysis of the biolm colony surface roughness can serve as an indicator for accurate biolm colony formation. To quantify biolm height development and alterations in biolm surface roughness, we performed light prolometry (Fig. 1B). As the biolm height of all studied strains did not increase within the rst three hours (microcolony growth phase) (Table 1), we did not distinguish micro and macrocolony growth in our prolometer studies. The S z value was calculated, as it is a parameter that describes the absolute height of the biolm surface, and the parameter S q was chosen to quantify the biolm surface roughness (see Methods and Fig. S3 †).
In the rst experiment, we analyzed the two biolm colony growth-parameters: area coverage and biolm height, for two biolm forming Bacillus subtilis wild type strains (B-1 37 and NCIB 3610 48 ) that differ in their biolm matrix composition (Table 1). Whereas the biolm matrix of NCIB 3610 is described to be mainly composed of two proteins (BslA and TasA) and an exopolysaccharide; 35,38,39 the biolm matrix of strain B-1 is described to be mainly composed of g-polyglutamate. 37 The results obtained for these biolm forming strains was compared to data obtained for a B. subtilis strain (BD630, 49 Table 1) that is unable to form a biolm ( Fig. 2A). We observed that the strains NCIB 3610 and BD630 exhibit a similar microcolony growth behavior, whereas strain B-1 grew considerably slower (Fig. 2B). The previous nding was unexpected as these three strains grow similarly in a well-mixed liquid environment ( Fig. S4 and Table S1 †) and possess a similar cell size when grown on LB agar plates ( Fig. S6a and b †). A possible explanation for the observed slower microcolony area growth of strain B-1 in comparison to strain NCIB 3610 could be that B-1 initiates growth into the third dimension at earlier time points and thus invests less biomass into lateral expansion. However, this was not the case (Fig. S6c †), which led us to the hypothesis that the slower microcolony growth observed for B. subtilis B-1 on LB agar plates might be attributed to the presence of g-polyglutamate (g-PGA). 37 Basal expression of this matrix element, which is absent in NCIB 3610 biolms, could interconnect single bacterial cells, resulting in a reduced lateral-expansionrate during microcolony growth. In contrast, it was shown that biolm matrix gene expression is induced at later timepoints in strain NCIB 3610, i.e., when a critical colony thickness (growth into the third dimension ¼ macrocolony growth) is reached. 28 Furthermore, EPS expression at the single cell level can only be triggered by reducing nutrient concentration. 28 Such nutrient limiting conditions are, however, absent in the microcolony growth phase when cells are grown on nutrientrich LB medium as done in this study.
During macrocolony growth, the area growth curves of the two biolm forming wild-type strains possess a sigmoidal shape with a clear saturation. In contrast, the area growth-curve obtained for the non-biolm forming strain BD630 is almost linear and does not saturate within the time-course of the experiment (Fig. 2C). When applying a sigmoidal t to this data (Methods, Fig. S5a †), we observed that for both biolm forming strains the inection point of the sigmoidal t lies below or close to 6 h. For the strain unable to form a biolm, however, this inection point occurs signicantly later, i.e., somewhat aer 9 h (Fig. S5a and e †).
Together, the data obtained for microcolony and macrocolony biolm growth indicate that it is not the individual growth rates of the different strains, but other factors such as the composition of the biolm matrix, that determine the lateral expansion of biolm macrocolonies. During the macrocolony growth phase, the biolm matrix could serve either as a structural element interconnecting individual cells within the biolm colony, or simply as additional biomass allowing for faster biolm spreading.
We next assessed the development of the biolm height over time for the three strains NCIB 3610, B-1 and BD630 using light prolometry. At the edge of the biolm colony, we observed that the two biolm formers develop more height over time than the non-biolm forming strain (Fig. 2D). Furthermore, the height increase of strain B-1 biolm colonies is by a factor of 2.3 larger than that of biolm colonies formed by strain NCIB 3610. This can be explained by the larger amount of biomass produced by B-1 biolms. 36 We next speculated that a higher amount of produced biomass should also result in an increased surface roughness. To verify this hypothesis, we also analyzed the surface roughness of biolm colonies formed by the three B. subtilis strains over time. Indeed, B-1 biolm colonies exhibit the strongest increase in surface roughness, followed by strain NCIB 3610 (Fig. 2E). In contrast, BD630 exhibited a smooth colony surface ( Fig. 2A and E). The nal surface roughness values at 17 h obtained for biolm colonies formed by strains B-1 and NCIB 3610 agree with previous investigations 36 and correlate well with the rough biolm colony morphology seen in microscopy images (Fig. 2A).
Interestingly, strain B-1 exhibited a reduction in both biolm colony height and surface roughness at later time-points. We believe, that the strong formation of wrinkles observed for strain B-1 ( Fig. 2A) (a feature that is less pronounced for biolm colonies generated by strain NCIB 3610 and fully absent for colonies generated by strain BD630) leads to an increase in the experimental error for data obtained with the prolometer at time-points later than 12 h. Aer 12 h the local area that is imaged with the prolometer to obtain the S z and S q values (Methods) differs at each time-point. Hence, for biolm colonies generated by strain B-1, the prolometric images might be obtained either on top of a wrinkle or within a valley, which increases the error at later time-points.

Matrix composition determines the dimensions of mature NCIB 3610 B. subtilis biolm colonies
Up to now, we have investigated the temporal development of two biolm colony growth parameters, area coverage and height increase, for two biolm forming and one non-biolm forming strains. We detected compelling differences in both growth parameters for the biolm formers in comparison to the non-biolm forming strain. This indicated that the matrix produced by the biolm forming strains could affect these growth parameters. To further investigate the inuence of the matrix composition on the dimensions of mature biolm colonies, we focused on the well-studied strain NCIB 3610, for which the main components of the biolm matrix are known. The matrix of B. subtilis strain NCIB 3610 biolms is mainly composed of an exopolysaccharide produced by the gene products of the epsA-O operon 38 and an amyloid ber-forming protein, TasA. 39,50 A second biolm matrix protein, BslA, is a self-assembling hydrophobin which is primarily found on the surface of B. subtilis NCIB 3610 biolms. 35,51 To quantify the inuence of those three matrix biomolecules, we next analyzed the temporal evolution of the two biolm colony growth parameters for three different mutants of strain NCIB 3610. Each of these mutant strains lacks the ability to produce a particular matrix component. The data obtained for biolm colonies formed by these mutant strains was then compared to the data obtained for the NCIB 3610 wild type strain (Fig. 3A). We noted similar development in biolm area coverage for all studied NCIB 3610 strains during microcolony biolm growth (Fig. 3B), which underscores that the individual strain growth rate (Fig. S4 and Table S1 †) does not affect micro and macrocolony growth behavior.
During macrocolony growth, the lateral expansion of biolm colonies formed by the mutant strain unable to produce the TasA ber forming protein does not considerably differ from the lateral expansion obtained for the wild-type NCIB 3610 strain (Fig. 3C). This nding was unexpected, as the tasA mutant forms notably smaller biolm colonies than the NCIB 3610 wild-type when grown on MSgg medium. 39 We attributed this observation to the different growth conditions used in this study (Fig. S2 †). Whereas the absence of TasA (Fig. S7 †) does not affect the lateral biolm expansion of biolm colonies grown on LB agar, the absence of the surface layer protein BslA leads to a delay in macrocolony growth (Fig. 3C), but results in a larger nal biolm area coverage compared to the wild-type strain. A third mutant, one that is unable to produce the exopolysaccharide, showed an even longer delay in macrocolony growth but reached a similar biolm area coverage as the wild-type strain at the end of the experiment (Fig. 3C). This shows that both the surface layer protein BslA and the exopolysaccharide affect the area covered by the biolm colony.
When investigating the height increase for biolm colonies formed by these mutant strains, we obtained a different picture. Absence of the TasA ber forming protein resulted in an increase of the nal biolm height by $30% compared to the wild-type strain (Fig. 3D). Again, this nding was unexpected as tasA biolm pellicles formed on MSgg medium are considerable decreased in biolm height compared to pellicles generated by the wild-type strain. 52 Whereas the absence of the TasA protein leads to an increased biolm height for biolm colonies grown on LB agar plates, the absence of the BslA protein led to a decrease of the nal biolm height by $30%. A similar result was obtained for biolm colonies formed by the epsA-O mutant strain. As the production of the exopolysaccharide is required for the production of the BslA protein, 35 we can mostly attribute the decrease of the nal biolm height observed in biolm colonies formed by the epsA-O mutant to the absence of BlsA in these biolms. In summary, two main matrix components: the surface layer protein BslA and the TasA ber forming protein, contribute to controlling the height of biolm colonies formed by the strain NCIB 3610.
In a next step, we analyzed the increase in biolm colony surface roughness by calculating the S q value (see Methods) at different time points of biolm formation. We observed that the biolm colony formed by the mutant unable to produce the TasA protein has the roughest nal biolm surface, followed by the surface of NCIB 3610 wild-type biolms. In contrast, biolm colonies formed by the epsA-O mutant and the bslA mutant show smooth surfaces (Fig. 3E). This nding, together with the small height increase observed for these two mutant strains, indicates that biolm formation by these strains is heavily impaired. This conclusion also agrees with the colony morphology seen in microscopy images (Fig. 3A).
The kinetics of the lateral biolm colony expansion data also showed differences for the three mutant strains (Fig. S5 †). Here, the macrocolony growth curves of both the tasA mutant and the NCIB 3610 wild type strain have an inection point at $6 h, whereas in the data obtained for the bslA mutant and the epsA-O mutant, the inection points occurred considerably later, at $11 and 13 h, respectively (Fig. S5 †). Hence, we conclude that the quality of biolm formation by bacteria of the genera B. subtilis can be estimated by the inection point of the sigmoidal t applied to the biolm area coverage data, where an early inection point indicates efficient three-dimensional biolm colony formation.

Quantifying the contribution of matrix biomolecules on NCIB 3610 B. subtilis biolm colony dimensions
Our experimental analysis demonstrated that specic matrix components control the dimensions of mature B. subtilis NCIB 3610 biolm colonies when grown on LB agar plates. Next, we aimed at quantifying the inuence of these main matrix components on the dimensions of mature NCIB 3610 biolm colonies. To do so, we set up a mathematical model to analyze the saturation values calculated by tting the experimental data curves obtained for the two growth parameters: biolm area coverage and biolm height (Methods). We assumed that the saturation values of mature biolm colony dimensions are primarily determined by growth through cell division of the individual bacterial cells within the biolm colony, and that this basal biolm growth rate is independent of the presence or absence of specic biolm matrix elements. However, in the presence of biolm matrix elements, the bacterial cells embed themselves in an extracellular matrix. Compared with the basal biolm growth rate (cell division occurring at all phases of biolm formation), this embedding process may increase or decrease the strain's ability to expand laterally or grow in height. We translated this assumption into a multiplicative model (Methods) where the inuence of each of the main bio-lm matrix elements (TasA, BslA and the exopolysaccharide) on the growth parameters (biolm area coverage and biolm height) are considered in terms of a simple factor which can either boost or retard basal biolm growth. In this model, we also accounted for the fact that BslA biosynthesis depends on the expression of the epsA-O operon responsible for the production of the exopolysaccharide 35 (Methods). The quantitative results obtained from applying this model to the investigated biolm colony growth are given in the inset of Fig. 4A. Values equal to one indicate no inuence, values above 1 indicate that this matrix component leads to an increase in the respective biolm growth parameter, and values below 1 indicate that this matrix component retards biolm colony growth. Our results suggest that the surface layer protein BslA decreases lateral expansion of the biolm during macrocolony growth, whereas TasA and the exopolysaccharide stimulate it. In contrast, TasA reduces the nal height of mature biolm colonies grown on LB agar, whereas the exopolysaccharide and primarily BslA increase biolm height. Hence, our mathematical model underscores our previous conclusions and quanties the impact of the NCIB 3610 main matrix components on the nal dimensions of mature biolm colonies formed by this strain.
Furthermore, our data indicate that one role of the BslA protein could be to counteract the inuence of TasA. To test this  (Table S3 †). The error is given as the standard deviation. (B) Schematic of the proposed major influences of the specific matrix elements on biofilm colony structure. The BslA protein coats the entire B. subtilis biofilm, 12 thereby restricting both lateral and vertical biofilm colony growth. The TasA protein primarily reduces biofilm height, possibly by vertically interconnecting the individual bacteria within the biofilm colony via amyloid fibers. 50,58 The exopolysaccharide slightly increases the area covered by the biofilm colony, possibly by serving as a gliding material 55 or simply by increasing biomass. hypothesis, we constructed a bslA/tasA double deletion mutant ( Table 1, Methods). For such a bslA/tasA deletion mutant, our model predicts a carrying capacity for area coverage of 17.72 mm 2 , and for biolm height of 134.60 mm (Table S2 †). Whereas this prediction agrees well with the experimentally determined biolm height of 131.88 mm (Fig. 3), tting the experimentally obtained data for area growth returns a value of 13.85 mm 2 , which differs from the model prediction by 20%. As our model does not include any coupling effects between these two biolm matrix components (BslA and TasA), this result may indicate that a coupling between BslA and TasA might be relevant for modelling the lateral expansion of the biolm colony in detail. However, with regard to the biolm height, BslA seems to counteract the action of TasA. Whereas we obtained a decreased and increased biolm height for the bslA and tasA mutant, respectively; the nal biolm height of the bslA/tasA double deletion mutant is comparable to that of the wild-type strain.
When the same model was applied to the surface roughness data (Table S3 †), we found that BslA is the main player affecting the surface roughness of NCIB 3610 biolm colonies. This agrees with previous results where it was shown that the surface layer protein BslA is mainly responsible for the surface properties of mature NCIB 3610 biolms. 36

Discussion
In this study, we present a quantitative, time-resolved analysis of two biolm growth parameters to describe the dimensions of mature Bacillus subtilis biolm colonies: the area covered by the biolm and biolm height. We nd that the macrocolony growth of B. subtilis biolm formers can be quantitatively distinguished from that of strains impaired in biolm formation by determining the position of the corresponding inection points in the time-resolved biolm area growth data. This quantitative approach could serve as a quality control measure to validate the accurate formation of B. subtilis biolm colonies, but might also be transferable to the process of biolm formation of other bacterial species. 53,54 In the past years, mathematical efforts have been made to address B. subtilis biolm formation theoretically. Focusing on B. subtilis biolm formation on solid substrates as in the case of this study, many of these mathematical and experimental investigations 27,28,32,33 analyzed how nutrient availability affects biolm growth 27,28,32 or how bacterial division generates pressure that leads to the spreading of biomass in B. subtilis bio-lms. 33 Other mathematical models describe B. subtilis biolm formation at the air-liquid interface. 29 28,32 For B. subtilis strain NCIB 3610 biolms, for which the main components of the biolm matrix are known (the proteins BslA, TasA and an exopolysaccharide), we here provide a detailed experimental and mathematical analysis of how these three different biolm matrix components determine the nal dimensions of mature biolm colonies grown on solid LB agar surfaces. Our experimental ndings, in combination with the quantitative results of our mathematical analysis suggest the following model (Fig. 4B): the lateral expansion during NCIB 3610 biolm colony growth is restricted by the surface layer protein BslA encapsulating the biolm, 51 and the area covered by the biolm is slightly increased in the presence of the exopolysaccharide. In the case of the exopolysaccharide, it might simply increase the biomass and thus the total covered area of the biolm, or it may serve as a gliding material 55 leading to an increased distance between the individual cells on the agar surface aer cell division. Exopolysaccharides have also been described to facilitate the colonization of surfaces and the long-term attachment of biolms, 56 and both effects may contribute to an increased lateral expansion of a biolm. A further important factor that might inuence the lateral biolm expansion is bacterial motility, although this is inhibited during B. subtilis NCIB 3610 biolm formation. Regulation by SinI/SinR leads to the repression of the a/che operon transcript abundance inhibiting de novo agellar gene expression. 57 However, as agella are numerous and stable, preventing the production of the a/che operon transcript is insufficient to inhibit motility. Here, a second mechanism comes into play: the short term inhibition of agellar rotation by EpsE, which is produced by the epsA-O operon. 57 In the case of the epsA-O mutant, the whole epsA-O operon has been deleted; therefore, this strain is not able to produce EpsE and lacks the short term inhibition of agellar rotation. In theory, if motile cells are present in bio-lms formed by the epsA-O mutant, this should lead to an enhanced lateral expansion as compared to the wild-type strain. However, we observed that the lateral expansion is delayed in this mutant strain, (Fig. 3) and its biolm colony nal area is constant for a broad range of agar concentrations and does not exceed area coverage values obtained for the NCIB 3610 wild type strain (Fig. S1 †). Hence, we concluded, that motility does not play a major role in our investigations. The height of mature NCIB 3610 biolm colonies is primarily controlled by two matrix components: the surface layer protein BlsA and the amyloid ber forming protein TasA. The TasA protein reduces the biolm height possibly by vertically interconnecting the individual bacteria within the biolm via amyloid bers. 50,58 The importance of interconnecting amyloid bers has already been shown for biolms formed by Staphyolococcus aureus, 2 where PSM (phenol soluble modulins) amyloid bers are involved in the formation of channels within the biolm. BslA, the surface layer protein, shows the strongest contribution in controlling the height of mature NCIB 3610 biolm colonies. By encasing the entire biolm, BslA might stabilize the biolm and allow for an increased nal biolm height, counteracting the action of the TasA protein.
In this study, we show that the production of specic matrix components of B. subtilis NCIB 3610 biolms inuence biolm colony growth in different ways. In particular, our ndings indicate that the two proteins BslA and TasA act in concert to tune wild-type biolm height. An intricate interplay of multiple matrix components has already been shown for many biolm forming bacteria with regard to biolm structure. 2 For instance, bacterial cells within biolms formed by Escherichia coli are encased by curli bers, while cellulose serves as an architectural element. 21,22 In Vibrio cholerae biolms, cell-cell adhesion is mediated by the protein RbmA and the proteins Bap1 and RbmC, whereas the Vibrio polysaccharide encases bacterial cell clusters. 13 With regard to Pseudomonas aeruginosa, quantitative studies demonstrated that the Psl polysaccharide is required for bacterial attachment to surfaces and intercellular adhesion affecting biolm structure. 59,60 However, much more quantitative research is needed to unravel the function of each biolm matrix component, and to relate a particular biolm property to the biolm matrix composition.