Modelling
At the start of the project we set out several goals so our eventual protocol would be easy to use,
robust, reproducible and safe.
Goals:
- Use a mathematical model to predict optimal growth conditions for V. natriegens.
- Determine optimal media for V. natriegens based on the mathematical model we
developed
Findings:
- We found that high NaCl concentrations delay the stationary phase and increase the
carrying capacity of the organism of interest.
- We confirm that v2 salts (204 mM NaCl, 4.2 mM KCl, and 23.14 mM MgCl2) increase the
growth rate of V. natriegens
1. Introduction
The main focus of our project is to grow
Escherichia coli and
Vibrio natriegens in the
shape of
the QR code. The growth of
E. coli in various types of media has been very well
characterized.
For our project it is important to know what media compositions are ideal for growth and
sustainability of
V. natriegens. However, only a few articles report the growth of
V.
natriegens
under different media compositions. This prompted us to model the growth dynamics of this
microorganism to investigate which media is optimal for its growth.
V. natriegens is a halophile marine bacterium that is found in salty environments. We
modelled
the growth of
V. natriegens based on Lysogeny broth (LB), brain heart-infusion (BHI)
media basis
with varying NaCl concentrations and v2 and v3 ocean salts.To model the growth of the bacterial
population over time, we considered the logistic differential equation:
where:
- r - growth rate of the population (1/min)
- K - carrying capacity (OD units)
- y - population of bacteria (OD units)
- t - time (min)
This mathematical model deals with the growth characteristics of a bacterial population
(Figure 1). We can use this equation to model growth for
V. natriegens.
The fastest exponential growth combined with a delayed deceleration phase would be ideal
conditions for the growth of
V. natriegens. Our goal was to find optimal growth media to
optimize bio-ink production by increasing the responsiveness of the vibrio cultures. We
do so by comparing growth curves for
V. natriegens in different media with different
salts and salt concentrations.
2. Experiments with LB media
2.1 Media Components
The experiments were conducted with the following variations of LB:
- LB with NaCl concentrations of 0.5 g/L, 5 g/L, 10 g/L, 15 g/L, 20 g/L, 22.5 g/L,
25 g/L, 27.5 g/L, 30 g/L, 32.5 g/L, 35 g/L, 37.5 g/L, 40 g/L, 45 g/L
- LBv2
- LBv3
The recipes involved were:
- For LB with varied salt concentration: LB broth: 10.0 g/L Tryptone, 5.0 g/L
Yeast Extract, 0.5 g/L NaCl.
- For LBv2: LB broth supplemented with additional salts (204 mM NaCl, 4.2 mM KCl,
and 23.14 mM MgCl2)
- For LBv3: LB broth + v3 salts: LB broth supplemented with additional salts (475
mM NaCl, 9.7 mM KCl, and 54 mM MgCl2)
The experiment was carried out in triplicates for a period of 6h30min. The graph below
(Figure 2) is a representation of the results of the OD measurements.
2.2 Results & discussion:
We observe from Figure 2 that every media composition leads to a different exponential
growth. As we can see in the graph, the steepness (exponential phase) and the
deceleration phase of the growth curve with increase in salt (NaCl) concentration. After
a certain concentration (20 g/L) of NaCl in LB, we observe that increasing the
concentration has no positive effect on the growth of
V. natriegens. As concentration of
NaCl increases stagnation of growth occurs. It is important to note that the growth
curve of
V. natriegens is most favorable for LBv2. This satisfied our need for the
steepest curve and tallest exponential phase to increase the responsiveness of the
bacteria. In conclusion, for LB media, it is optimal to use 20 g/L of NaCl concentration
or v2 salts (204 mM NaCl, 4.2 mM KCl and 23.14 mM MgCl
2) concentration.
To further verify our conclusions we plot carrying capacity against salt
concentrations (Fig 3). It is not a good idea to plot growth rate against salt
concentrations unless the growth rate for every concentration curve is measured at
the exact time interval.
The plot above shows that the maximum population size is achieved at 15 g/L and 20
g/L of NaCl concentration (Kmax=1.4 OD600) . But as seen previously (Fig2), the 20
g/L curve is more optimal than 15 g/L curve. This indeed reinforces our claim that
for LB based media the use of 20 g/L of NaCl concentration is indeed optimal for
efficiently growing and transforming V. natriegens. Although the use of LBv2
is more
effective practically, the use of NaCl is preferred considering cost effectiveness.
3. Experiments with BHI media
3.1 BHI media components
We performed similar experiments with BHI based media by varying the salts and their
concentrations as follows:
- BHI with NaCl concentrations of 0.5 g/L, 5 g/L, 10 g/L, 15 g/L, 20 g/L, 22.5
g/L, 25 g/L, 27.5 g/L, 30 g/L, 32.5 g/L, 35 g/L, 37.5 g/L, 40 g/L, 45 g/L
- BHIv2
- BHIv3
The recipes for this media involved:
- For BHI with varied salt concentration: Brain Heart Infusion Broth. 37 g/L
Teknova Brain Heart Infusion Broth Dry Media (Cat. No. B9500) + 20 g/L NaCl
- For BHIv2: 37 g/L Teknova Brain Heart Infusion Broth Dry Media (Cat. No.
B9500) supplemented with additional salts (204 mM NaCl, 4.2 mM KCl, and
23.14 mM MgCl2)
- For BHIv3: 37 g/L Teknova Brain Heart Infusion Broth Dry Media (Cat. No.
B9500) supplemented with additional salts (475 mM NaCl, 9.7 mM KCl, and 54
mM MgCl2)
The data was collected in triplicates over a period of 6h30min. The graph below
(Fig. 4) is a representation of the results of the OD measurements.
3.2 Results & discussion
In this case, LBv2 has the steepest exponential phase but a shorter deceleration
phase as compared to NaCl concentrations. This suggests that even though the
carrying capacity of
V. natriegens is less in LBv2, the responsiveness of
the
culture is high. In case of NaCl concentrations, even though 35 g/L has a delayed
exponential phase, we observe a prolonged deceleration phase. This translates to
delayed yet better responsiveness than other NaCl concentrations. Also, the carrying
capacity for this curve is the highest. In conclusion we can say that, for BHI based
media it is optimal to use 35 g/L of NaCl concentration or v2 salts (204 mM NaCl,
4.2 mM KCl, and 23.14 mM MgCl
2) concentration.
We observe that the 35 g/L NaCl concentration curve yields the highest value of
carrying
capacity (Kmax=1.4 OD
600). This confirms our claim that for BHI media, the use of 35
g/L NaCl
solution is optimal for growth of
V. natriegens. In this case the 35 g/L NaCl
concentration
works better than the v2 salts.
4. Conclusion
Using modelling we evaluated several BHI and LB formulations as estimations for an
optimal media for growth of
V. natriegens. For our bio-ink it is important that
bacteria stay responsive. It is also interesting to know what medium supports the
fastest growth with effective responsiveness. The experimental data collected on
LBv2 is in agreement with our estimations given by the model when compared with
BHIv2 (KBHIv2= 1.29OD
600). For media based on NaCl concentrations, LB with 20 g/L of
NaCl (KLBNacl= 1.402OD
600) is a better option than BHI with 35 g/L NaCl
(KLBNacl=1.404OD
600) since BHI media would require more amount of NaCl for the same
results.The cost of BHI is about 11 euro per liter (Sigma Aldrich) and LB is about 2
euro per liter (Sigma Aldrich), hence LB is the optimal choice. According to our
data we conclude that LB with 20 g/L of NaCl concentration is the optimal choice as
the media for growing
V. natriegens.