Vertical Biofilm Growth

Pablo Bravo

PoLS Lunch and Learn GT

A. veronii

E. coli

S. cerevisiae (wt)

S. cerevisiae (aa)

V. cholerae (wt)

V. cholerae (EPS-)

K. pneumoniae

B. cereus

S. aureus

Outline

I. Biofilms

II. Vertical growth dynamics

III.Biofilm topographies

  • What are they, and why we should care
  • How to measure vertical growth
  • Heuristic model
  • Why topographies
  • Characterization
  • Apples to oranges?

Biofilms in context

Hall-Stoodley, L., et al., Nat Rev Microbiol (2012)

Lacy, D. E., et al. Journal of Infection (1993).

McConoughey, S., et al. F. Microbiology (2014)

Enning, D., et al.  Appl. and env. microbiology (2014).

Biomedical

Industry

Ecological

Biofilms are complex surface-attached 3D structures

Extracellular matrix formed of polysaccharides, DNA, and proteins 

Surface

Interface

Cells

The (expanded) biofilm cycle

Growth and accumulation

  • How do aggregates grow?
  • What are the underlying processes?
  • Simple quantitative model?

Horizontal Growth

Vertical
Growth

Understanding vertical growth could provide insight in the developmental process

Visualizing Bacterial Colony Morphologies Using

Time-Lapse Imaging Chamber MOCHA
Peñil Cobo et al. 2017

Outline

I. Biofilms

II. Vertical growth dynamics

III.Biofilm topographies

  • What are they, and why we should care
  • How to measure vertical growth
  • Heuristic model
  • Why topographies
  • Characterization
  • Apples to oranges?

Using Interferometry to study biofilm growth

Two regimes during biofilm growth

The geometry of the colony is setting a limit in growth, not nutrient availability in the environment!

Interface model for vertical growth

\frac{\partial h}{\partial t} = \alpha \cdot \text{min}(h, L) - \beta \cdot h\\

Growth rate

Decay rate

Diffusion length

Describes the height \(h\) of a microbe colony

Tested against multiple microbes, and up to two weeks of growth!

In press at PNAS

Empirical basis for the interface model

Interface model

From nutrient dynamics:

\frac{\partial c}{\partial t} = D \cdot \frac{\partial^2 c}{\partial z^2} - \lambda \frac{c}{k+c}

We approximate the total amount of nutrients \(N\) inside a colony:

N(h, D, \lambda, k) = \int_0^h \frac{c}{k+c} dz \approx \text{min}(h, L)
\frac{\partial h}{\partial t} = \alpha \cdot \text{min}(h, L) - \beta \cdot h\\

Growth rate

Decay rate

Diffusion length

And build a heuristic model that  describes vertical growth dynamics

Long time accuracy

Additional measurements for 14 days. Showing that different growth dynamics in the 48h period, can lead to large changes in longer timescales

  • Height saturation correctly captured
  • Slower growth can lead to higher saturation heights
h_{\text{max}} = \frac{\alpha L}{\beta}

And long-time agreement does not mean lower accuracy in the shorter timescales!

Maximum height can be obtained from the model easily:

Outline

I. Biofilms

II. Vertical growth dynamics

III.Biofilm topographies

  • What are they, and why we should care
  • How to measure vertical growth
  • Heuristic model
  • Why topographies
  • Characterization
  • Apples to oranges?
  1. Inside/outside interactions
  2. It is what we can see/measure
  3. Statistics
  4. Spatial and temporal information
  5. Toolbox and theories!
  6. Subject to material properties and activity

Why study the interface?

Adkins, Kolvin, and You, et al. 2022

What is biofilm topography?

Profiles are flat. A few cells in amplitude, over thousands of micrometers!

\(500 \mu m\)

Fluctuation dynamics are different between strains

Staphylococcus aureus

Bacillus cereus

Eschericia coli

  • What is leading to the differences between profiles?
  • How do we characterize the dynamics?

\(2 mm\)

\(8 \mu m\)

Time since inoculation [hours]

\(0\)

\(24\)

\(48\)

A. veronii

E. coli

S. cerevisiae (aa)

S. cerevisiae (wt)

V. cholerae (wt)

V. cholerae (EPS-)

K. pnerumoniae

B. cereus

S. aureus

And very different between different microbes!

Fluctuations can relax

Aeromonas veronii

Eschericia coli

or increase

On growth and form of Bacillus subtilis biofilms

 

  • Interpolated from fluorescence
  • 0-10 hours

Dervaux, et al. 2014

  • Local width
  • Surface roughening

Fluctuations are not just noise!

Fluctuations in:

  • Between replicates
  • In replicates (forces, spatial structure)

Height differences

Different rates \( (\alpha, \beta, h^*) \)

Paper N_x N_y Roughness
On growth and form of Bacillus subtilis biofilms 2 1.5 0.5-0.7
Roughening instability of growing 3D bacterial colonies 1.2 1 0.67
Yunkerlab-Interferometry 3.2 3.6 0.74-0.84 

Morphological instability and roughening of growing 3D bacterial colonies

 

Martinez-Calvo and Bhattacharjee, et al. 2022

  • Grown in 3D
  • 0-97 hours
  • Power spectral density
  • 0-97 hours
  • Width of perpendicular fluctuations in the height profile:

 

 

  • With a roughness/Hurst scaling exponent \(H\):

     
  • The width saturates at \(l_\text{sat}\), and across the whole sample the width is \(w_\text{sat}\)
w_l(\mathbf{r}, t) = \langle (h (\mathbf{r}, t) - \langle h(\mathbf{r}, t) \rangle_l )^2 \rangle_l^{1/2}

\(w_l(t) \propto l^{H} \)

Quantifying fluctuations

Dervaux, et al. 2014

Martinez-Calvo and Bhattacharjee, et al. 2022

\(H\)

\(l_{\text{sat}}\)

\(w_{\text{sat}}\)

B

A

Roughening

Crystal growth

Biofilms

  • Temperature
  • Mechanical interactions
  • Birth and death
  • EPS production
  • Competition
  • Cooperation

 

of biofilms

Roughening across strains

Roughness \(H\), after a period of time, stabilizes at \(H_{\text{steady}} \sim 0.8\)

Paper Roughness
On growth and form of Bacillus subtilis biofilms ~2 ~1.5 0.5-0.7
Morphological instability and roughening of growing 3D bacterial colonies ~1.5 ~1 0.67
Yunkerlab-Interferometry ~3 ~2.5 0.74-0.84 

Sampling ranges in \(w_{loc}\) estimation

\(N_x\)

\(N_y\)

\(w_{sat}\) and vertical growth

There is high variability between microbes

And an apparent correlation between vertical growth dynamics and the topography!

Colonies reach nutrient depletion length \(L\)

Knowing the moment when the colony is growing the fastest, just by looking at                         

fluctuations

Are fluctuations scale-free?

\(S(k) [\mu m^4]\)

\(k [\mu m^{-1}]\)

\(10^4\)

\(10^3\)

\(10^2\)

\(10^1\)

Dynamic scaling, a test for self-similarity requires: 

 

\(\nu = 1+2H\)

We do not see observe dynamic scaling. 

It is close but not the same!

Power spectrum, noise, and dynamic scaling

Dynamic scaling
(Family-Vicsek)
\( \nu = 1 + 2\alpha\)

Two regimes:

  • Flat on small \(k\)
  • \(\sim k^{-\nu}\) large \(k\)

Traditional Interface Growth

Biofilm Interface Growth

  • Short timescales
  • Short lengthscales
  • Driven by interactions between the two phases
  • Constant activity in the interface
  • Long timescales (hours, days)
  • Long lengthscales ?
  • Driven by biofilm growth*
  • Pulse of activity from growth
  • Dampened by the material

*What about biofilm-liquid interface?

Future work

Biofilm composition and properties

Memory

  • Does an underlying pattern in the surface affect the topography?
  • How does the composition (%cells) affect the dynamics?
  • Quantify the forces driving the relaxation

Flat

Patterned

Wells, et al. 2014

Acknowledgements

NIH-NIMS

NSF BMAT

Biolocity

Dr. Peter Yunker

Dr. Brian Hammer

Dr. Siu Ling Ng

Dr. Thomas Day

Aawaz Pokhrel

Emma Bingham

Funding

Thanks!

Adam Krueger

Raymond Copeland

Maryam Hejri

Lin Zhao

Chris Zhang

 

Universal bulk vertical growth dynamics, but fluctuations do not appear to be!

Can we establish a link between topographies and biofilm development?

PoLS2023

By Pablo Bravo

PoLS2023

Presentation for PoLS Lunch and Learn at GT

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