characterization of

               growth

Pablo Bravo

Topographic

biofilm

Quantitative Biosciences

PhD Defense

Outline

I. Biofilms and Interfaces

  • Why and how to study

II. Vertical growth dynamics

III.Biofilm topographies

  • How to measure vertical growth
  • Behavior and clues
  • Heuristic model
  • Characterization
  • Freezing
  • Modeling

Biofilms are                                                    3D structures

complex surface-attached

Surface

Interface

Cells

Extracellular matrix formed of polysaccharides, DNA, and proteins 

Extracellular matrix formed of polysaccharides, DNA, and proteins 

Surface

Interface

Cells

Biofilms are                                                    3D structures

complex surface-attached

                    in the biofilm surface

\(1 cm\)

\(1 cm\)

Dietrich, L., et al. Journal of Bacteriology (2013)

Structures

Colonies in a laboratory setting

Each circle is a colony

Starting inoculums also exhibit the coffee ring effect!

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

cycle

The (expanded) biofilm

Sauer, K., et al. Nature Reviews Microbiology (2019)

Inside the biofilms: confocal/light-sheet

Hartmann, R., et al. Nature Microbiology (2021)

Images by Dr. Gabi Steinbach

Unprocessed

Processed

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

Horizontal Growth

Growth

and accumulation

Morphologies and scaling of

advancing fronts

Matsuyama, T., et al. FEMS Microbiology Letters (1989)

Fujikawa, H. et al. JPSJ (1989)

Farrel, F.D.C., et al. Physical Review Letters (2013)

The same strain can exhibit different morphologies depending in the environment!

  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 interfaces?

Adkins, R., Kolvin, I., You, Z., et al. Science (2022)

Horizontal Growth

Vertical
Growth

Growth and accumulation

  • How do aggregates grow?
  • What are the underlying processes?
  • Simple quantitative model?
  • Multiple light sources in the instrument
  • Super-resolution measurements
  • Non-invasive
  • No preparation needed

\( 0.5 mm\)

0

2

4

6

8

10

\(\Delta z\) (\( \mu m\))

Central region of a vibrio cholerae biofilm

Surface topography + intensity!

White-light interferometry

Biofilm topographies & Yunkerlab

Kalziqi, A., et al. PRL (2018)

Kalziqi, A., et al. ArXiv preprint (2019)

  • Detect the amount of killing (T6SS)
  • Viscosity through topography
  • Rapid heteroresistance identification

Yan, J., et al. eLife (2019)

Outline

I. Biofilms and Interfaces

  • Why and how to study

II. Vertical growth dynamics

III.Biofilm topographies

  • How to measure vertical growth
  • Behavior and clues
  • Heuristic model
  • Characterization
  • Freezing
  • Modeling

Using                               to measure

interferometry

biofilm growth

Homeland

Agar

Coffee Ring

Interferometry at the single-cell level

Surface topography and intensity from Interferometry

S. cerevisiae, 48 hours of growth.
Bravo 2022

Things didn't go quite well the first ~10 attempts

Hours

0

48

                         during bioflim growth

Two regimes

Two regimes in which vertical growth depends

linearly with the height of the colony

                                      inside the colony

Nutrient dynamics

\(z\)

\frac{\partial c}{\partial t} = D \cdot \frac{\partial^2 c}{\partial z^2} - \lambda \cdot \frac{c}{k+c}
c(0, t) = c_0 \quad \quad \quad \dot{c}(h, t) = 0

Concentration in the substrate

No flux in the top

Region where cells can grow is finite

\int_0^h \frac{c(z)}{k+c(z)}dz \approx \text{min}(h, L)

Total growth of a colony saturates once they reach a critical length \(L\)

Diffusion constant

Consumption rate

Monod constant

                                      inside the colony

Nutrient dynamics

\(z\)

\frac{\partial c}{\partial t} = D \cdot \frac{\partial^2 c}{\partial z^2} - \lambda \cdot \frac{c}{k+c}
c(0, t) = c_0 \quad \quad \quad \dot{c}(h, t) = 0

Concentration in the substrate

No flux in the top

Region where cells can grow is finite

\int_0^h \frac{c(z)}{k+c(z)}dz \approx \text{min}(h, L)

Total growth of a colony saturates once they reach a critical length \(L\)

Consumption rate

Diffusion constant

Monod constant

2560

                                      in the agar?

Nutrient depletion

Agar is not running out of nutrients!

Colonies must be slowing down for a different reason

                                for vertical

biofilm growth

Heuristic model

Empirical data + biophysical insight:

  • Fits the dynamics across timescales
  • Captures two growth regimes
  • \(D, \lambda, k \rightarrow L\)
\frac{\partial h}{\partial t} = \alpha \cdot \text{min}(h, L) - \beta \cdot h\\

Diffusion length

Growth rate

Decay rate

Improving the \(\Delta h\) calculations

Clean set

Not-so clean set

Clean set

Not so clean set

Supplemental: pluses and minuses

\(\alpha h  \)

\(- \beta h \)

\( -\alpha \frac{h^2}{K_h} \)

\(- \beta h \)

\(\alpha h\)

\(\alpha G(h, h^*) \)

\(^{****}\)

Why is the prediction lower?

h_{\text{max}} = \frac{\alpha \cdot L}{\beta}

Growth

Decay

Small overestimation of \(\beta\) can lead to underestimating \(h_{\text{max}}\)

Measuring for 48h is going to dry the plate a bit more, even if we try to minimize it

High-tech containment chamber for timelapse measurements.

Even if the prediction gets corrected with time, residual changes very little!

Do the                        make sense?

parameters

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

\(800 \mu m^2 \cdot s^{-1}\)

\(38 \mu M\)

\(1.3\cdot10^3 \mu M \cdot s ^{-1}\)

E. coli growing in agar -> limited by L-serine

Using literature parameters we obtain

\(L = 14.8 \mu m\)

And using the interface model

\(L = 14.3 \pm 1 \mu m\)

2560

Do the                        make sense?

parameters

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

\(800 \mu  m^2 \cdot s^{-1}\)

\(38 \mu M\)

\(1.3\cdot10^3 \mu M \cdot s ^{-1}\)

E. coli growing in agar -> limited by L-serine

Using literature parameters we obtain

\(L = 14.8 \mu m\)

And using the interface model

\(L = 14.3 \pm 1 \mu m\)

1920

Bootstrapping growth curves

Get the best fit for each sampled dataset (1000x)

Original dataset

Why is the prediction lower?

\(h_{\text{max}}\) \( [\mu m]\)

Bootstrapping on the 48h data we get distributions

\(\alpha\) \( [\mu m /hr]\)

\(\beta\) \( [\mu m /hr]\)

\(L\) \( [\mu m]\)

Aeromonas

Yeast (aa)

E. coli

48h fit

All fit

                     behavior

Long-time

  • Measure colonies every 2 days
     
  • Equilibrium in maximum height
     

  • Model height prediction:

    \(h_{\text{max}} = \frac{\alpha L}{\beta}\)
     

  • Same behavior, different parameters
     

  • Good agreement even early!

Thinking about spatial dependence

Fit parameters \(\alpha, \beta, h^*\) to each trajectory

\( h_{\text{max}} = \frac{\alpha h^*}{\beta} \)

Merger initial conditions

Initial configuration is experimental (Gabi), except tweaking 0's and negative numbers.

                    in vertical growth

Universality

doi.org/10.1101/2022.08.11.503641

Experiments across a large cohort of microbes

  • Bacteria and fungi
  • Gram + and -
  • Different shapes
  • Different EPS production
  • Novel measurements of vertical growth.
  • Heuristic model that captures dynamics accurately

Summary

Modeling in 3D Yeast clusters

Shape of biofilms, and biofilm edge

Biofilm Topography

Outline

I. Biofilms and Interfaces

  • Why and how to study

II. Vertical growth dynamics

III.Biofilm topographies

  • How to measure vertical growth
  • Behavior and clues
  • Heuristic model
  • Characterization
  • Freezing
  • Modeling

What is                                    ?

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

\(500 \mu m\)

biofilm topography

Using white-light interferometry, we can capture the profiles of a growing colonies for extended periods of time

Subtracting from the homeland?

  • Width of perpendicular fluctuations in the height profile:

 

 

w_l(\mathbf{r}, t) = \langle (h (\mathbf{r}, t) - \langle h(\mathbf{r}, t) \rangle_l )^2 \rangle_l^{1/2}

\(\alpha\)

II. Quantifying fluctuations

Self similar systems link the fractal dimension \(FD\) and roughness \(\alpha\) with:

FD + \alpha = n + 1

Fractal Dimension FD

Measure of how  complexity  changes with scale

Surface roughness \(\alpha\)

                                           are different between strains

Staphylococcus aureus

Bacillus cereus

Eschericia coli

  • What is leading to the differences between profiles?
  • How do we characterize the dynamics?
  • Why does the topography freeze in later alligators?

\(2 mm\)

\(8 \mu m\)

Time since inoculation [hours]

\(0\)

\(24\)

\(48\)

Fluctuation dynamics

Fluctuations can 

Aeromonas veronii

Eschericia coli

or

relax

increase

Timelapses of fluctuations

For visualization purposes, is it okay to interpolate?

Measurement time is not constant

Biofilm topographies are

smooth

Magnitude of fluctuations goes from 10%, to 0.1-1%!

Stainless steel (UL)

B

A

Are fluctuations                   ?

\(10^4\)

\(10^3\)

\(10^2\)

\(10^1\)

scale-free

Wavelengths of \(\lambda = L/2\) were removed in each step

\(S(k, t) \sim k^{-\nu}\)

  • PSD exhibits \(1/f\) spectra
  • Self organized criticality
  • Observed in vacuum tubes, human hearts, brain activity, musical concertos.

         at 40 hours of growth

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

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

PSD

Testing                       again

self-affinity

We can test self-affinity using the fractal dimension \(D\)

\(D + H = 2\)

\(D + H = n +1\), where \(n\) is the base dimension of the system

Topography dynamics as a consequence of growth through a viscoelastic material:

  1. Reach SA while growth is fast
  2. Relax when the colony is tall, and fluctuations get damped
  • Width of perpendicular fluctuations in the height profile:

 

 

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

     
  • And a growth exponent \(\beta\):
w_{\ell}(\mathbf{r}, t) = \langle (h (\mathbf{r}, t) - \langle h(\mathbf{r}, t) \rangle_{\ell} )^2 \rangle_{\ell}^{1/2}

\(w_{\ell}(t) \propto \ell^{H} \)

                        fluctuations

Dervaux, et al. 2014

Martinez-Calvo and Bhattacharjee, et al. 2022

\(H\)

\({\ell}_{\text{sat}}\)

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

Quantifying

\( {\ell}\)

\( {\ell}\)

w_{\text{sat}}(t) \sim \begin{cases} t^{\beta} & \text{for } t < t_{\times}\\ \text{constant} & \text{for } t > t_{\times} \end{cases}

Filters, Fourier, and boundaries

  • Boundaries are tricky
  • Assumptions in Poly 2, or use more 'fancy' algorithms?

Butterworth \(\lambda = 500 \mu m\)

This worries me a little!

Spatial scaling:

Roughness stabilizes at \(H \sim 0.8\).

Biofilm interfaces, have been characterized at \(0.6-0.78\)

roughening

\(w_{\ell}(t) \propto \ell^{H} \)

\( {\ell}\)

\( {\ell}\)

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

\(N_x\)

\(N_y\)

On growth and form of Bacillus subtilis biofilms

 

  • Interpolated from fluorescence
  • 0-10 hours

Dervaux, et al. 2014

  • Local width
  • Surface roughening

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

Temporal scaling:

Saturation width decreases! 

 

Something different 

is happening after \(t_{\times}\)

saturation?

w_{\text{sat}}(t) \sim \begin{cases} t^{\beta} & \text{for } t < t_{\times},\\ \text{constant} & \text{for } t > t_{\times} \end{cases}

Scaling exponent varies between species and replicates

I
II

Topography

freezing

  • Two interface stages:
    1. Active
    2. Frozen
  • Qualitative behavior in all interfaces.
  • No traveling waves
  • Correlation length \(\xi\) increases slowly with time \(t\)

                   biofilm topographies

0

0.3

\(\Delta \vec{r}\)  \([\mu m]\)

-4

-0.5

\(\log\Delta \vec{r}\)  \([\mu m]\)

Modeling

1 perturbation

10 perturbations

  • 2D soft disks mechanically interacting
  • Bounded at the bottom
  • Periodic on the sides
  • Distribution of sizes around r =0.5µm
  • Let system relax before perturbation
  • Introduce a growth perturbation

In small colonies, displacements can reach the interface

In large colonies, displacements get dissipated before reaching the interface

Local disruptions change the topography

Displacement is homogeneous

Quantifying

topography change

  • Topography change decreases with relative perturbation distance
     
  • Variance also scales with \(d\)
     
  • Cell displacement decays  exponentially with distance to the perturbation.

\(d_0 \sim 13 \mu m\)

Interface dynamics and

growth

  • Fluctuations reach a maximum defined by \(w_{\text{sat}}\)
     
  • Growth saturates when colony reaches critical length \(L\)
     
  • Strong correlation between fluctuation and growth dynamics
     
  • Every additional layer, is a
    damping element for fluctuations.

Outline

I. Biofilms and Interfaces

  • Why and how to study

II. Vertical growth dynamics

III.Biofilm topographies

  • How to measure vertical growth
  • Behavior and clues
  • Heuristic model
  • Characterization
  • Freezing
  • Modeling

Vertical growth dynamics under

stress

What determines the antibiotic susceptibility of a biofilm?

  1. Antibiotic concentration
  2. Exposure time
  3. Biofilm size
  • Thresholds observed for bactericidal and bacteriostatic preliminary results!
  • Unexpected dynamics observed in
    large coloneis

Before - 24h

Before - 36h

After - Growth

After - Carb

Preliminary Results - Growth and stress in MH

  • \(h_0\) of 90 and 120 μm
  • Growth seems to saturate at ~220μm
  • Saturation height is consistent with and without transfer
  • Chloramphenicol seems to have little effect in growth
  • Carbenicillin is increasing height significantly

Awesome People

Yunker Lab

Dr. Peter Yunker

Dr. Gabi Steinbach

Dr. Alireza Zamani

Dr. Thomas Day

Dr. Miles Wetherington

Aawaz Pokhrel

Adam Krueger

Emma Bingham

Raymond Copeland

Maryam Hejri

Tremond Thomas

Lin Zhao

 

Committee Members

Dr. Brian Hammer

Dr. Sam Brown

Dr. Jennifer Curtis

Dr. Itamar Kolvin

Hammer Lab

Dr. Siu Lung Ng

Kathryn MacGillvray

Christopher Zhang

 

Ratcliff Lab

Dr. Will Ratcliff

Dr. Tony Burnetti

Dr. Rozenn Pineau

 

QBioS
Dr. Joshua Weitz

Dr. Andreea Magalie

Dr. Conan Zhao
 

CMDI
Dr. Ellinor Alseth
 

POLS

Topographic characterization of biofilm growth

  • Measured biofilm-air interfaces with high spatial and temporal resolution
     
  • Proposed a simple model for vertical growth dynamics
     
  • Link between growth and fluctuation dynamics through topography freezing

4x speed

10 \( \mu L \) inoculation

11 days

Playing it safe vs crazier research paths

Passive transport

Would grass follow the height dynamics?

NO!

Capillary action is passive transport!

1. Biofilms are not homoegenous

2. Could we make artificial channels?