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The biophysical basis of bacterial colony growth


Bacteria often attach to surfaces and grow densely packed communities called biofilms. As biofilms grow, they expand across the surface, increasing their surface area and access to nutrients. Thus, the overall growth rate of a biofilm is directly dependent on its range expansion rate. A direct trade-off between horizontal and vertical growth impacts the range expansion rate and, crucially, the overall biofilm growth rate. The biophysical connection between horizontal and vertical growth remains poorly understood, in large part due to the difficulty in resolving the biofilm shape with sufficient spatial and temporal resolutions from small length scales to macroscopic sizes. Here we show that the horizontal expansion rate of bacterial colonies is strongly coupled to vertical expansion via the contact angle at the biofilm edge. Using white light interferometry, we measure the three-dimensional surface morphology of growing colonies, and find that small colonies are well described as spherical caps. At later times, nutrient diffusion and uptake prevent the tall colony centre from growing exponentially. We further show that a simple model connecting vertical and horizontal growth dynamics can reproduce the observed phenomena, suggesting that the spherical cap shape emerges due to the biophysical consequences of diffusion-limited growth.

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Fig. 1: Dependence of range expansion rate (Δat) on doubling time (τ) and contact angle (θ).
Fig. 2: Topographic images of bacterial colonies.
Fig. 3: Change in colony geometry over time.
Fig. 4: Definition and application of the SCNR geometry.
Fig. 5: Experiments agree with predictions from the SCNR model.
Fig. 6: A simple biophysical model replicates experimental observations.

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Data availability

Processed data used to generate the figures are available via GitHub at (ref. 44). All the raw interferometry and confocal images used to generate the data are archived in the Dropbox of Yunker Laboratories and are available from the corresponding author on request. Source data are provided with this paper.

Code availability

All codes used to process the raw interferometry images are available via GitHub at (ref. 44).


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P.J.Y. acknowledges funding from the NIH National Institute of General Medical Sciences (grant no. 1R35GM138354-01) and NSF Biomaterials (grant no. BMAT2003721). B.K.H. acknowledges funding from NSF Biomaterials (grant no. BMAT2003721).

Author information

Authors and Affiliations



A.R.P., G.S. and P.J.Y. conceived the project. A.R.P. and G.S. performed early experiments that inspired the direction of the project. A.R.P. and J.T. performed the experiments reported in the paper. S.L.N. and B.K.H. prepared the bacterial cultures. A.R.P., T.D., A.K. and P.J.Y. conceived and derived the geometrical SCNR framework. A.R.P. and P.B. developed the biophysical model. A.R.P., G.S. and P.J.Y. analysed the data. A.R.P. created the figures. A.R.P., G.S. and P.J.Y. wrote the first draft of the paper. All the authors contributed to the revision.

Corresponding author

Correspondence to Peter J. Yunker.

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The authors declare no competing interests.

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Nature Physics thanks Maxime Deforet, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Rugose colony’s edge retains a finite contact angle.

A) V.cholerae (EPS+) is grown from a single cell at 23C for approximately 170 hours. Over this period, the colony exhibits wrinkling and buckling at its center. Panel A displays an image of the entire colony captured using a Canon MP-E 65mm camera. B) Subsequently, we also measured the topography of the same colony via interferometry to quantiatively examine its edge.

Extended Data Fig. 2 Side by Side comparison of Experiment and Simulation result.

A side-by-side comparison of experimental and simulated results is presented. Experimentally generated topographies of V.cholerae (EPS-) (See Fig. 2h main text) appear visually similar to 3d simulated topographies (generated by rotating the two-dimensional height profiles through a full circle) (A and B, respectively). The simulated image is shown for a single time point with α = 1.113 (1/hr), D = 100 μm2/hr, L = 7, and β = 0.038 (1/hr). These are the experimentally measured values for same species measured in Bravo et. al. C, D) The time dependence of colony height and radius is shown for experiments and simulations (C and D, respectively). The central bands represent the LOESS-averaged mean, and the shaded region represents the standard derivation in three replicates. The model accurately captures the height saturation and constant range expansion rate seen in experiment.

Extended Data Fig. 3 Side by Side comparison of Experiment and Simulation result.

Using the same parameter values as in Extended Figure 2, we compared the time evolution of experimental topographies with those generated by the simulations. A, B) Similar to the findings reported in experiments (refer to Fig. 3b in the main text), height saturation in our simulated topographies eventually leads to a deviation from the spherical cap shape. C,D) Despite the height saturation and deviation from a perfect spherical cap shape, the constant contact angle is maintained in both experiments and simulated profiles (C and D, respectively). The central band represents the LOESS-averaged value and the shaded region represent the standard deviation in three replicates.

Extended Data Fig. 4 Side by Side comparison of Experiment and Simulation result.

Utilizing the same simulation parameters as those in Extended Figure 2, we examined the edges of the simulated topographies and compared the spherical cap napkin ring predictions to both experiments and simulations. A) The comparison between measured and predicted volumes of the napkin ring from our experiment in V.cholerae (WT) is presented, illustrating that the edge closely aligns with the geometry of a spherical cap napkin ring, as detailed in Fig. 4c of the main text. B) Similarly, this analysis was applied to our simulated topographies. Despite deviations from a perfect spherical cap shape, the edges are accurately described by the spherical cap napkin ring geometry, as seen in experiments. C) The range expansion rate is plotted against \(1/\tau \,\tan (\theta )\) as measured in experiments (this panel is the same as Main Text Fig. 5a. Data of range expansion rate is presented as mean values and standard deviation from three replicates. (See Methods and Supplementary Table 3 for details) D) The range expansion rateis plotted against \(1/\tau \,\tan (\theta )\) for a 400 unique simulations, covering a wide range of values of α and D while keeping L and β constant (L = 7um, and β = 0.038 (1/hr); this panel is the same as main text Fig. 6d. We observe that, similar to experimental results, our simulated colonies show excellent agreement with our spherical cap napkin ring prediction.

Supplementary information

Supplementary Information

Supplementary Sections 1–5, Figs. 1–26, Equations (1)–(50) and Tables 1–3.

Source data

Source Data Fig. 1–6

Statistical source data.

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Pokhrel, A.R., Steinbach, G., Krueger, A. et al. The biophysical basis of bacterial colony growth. Nat. Phys. (2024).

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