Difference between revisions of "Team:Goettingen/Model"

Using B. subtilis as a glyphosate detector

As described in detail in our Background section glyphosate (N-(phospho­mono­methyl)glycine) specifically inhibits enol­pyruvyl-shikimate-3-phosphate (EPSP) synthase, an enzyme present in plants, fungi, bacteria and archea (2-5). It catalyses the conversion of shikimate-3-phosphate (S3P) and phosphoenolpyruvate (PEP) to EPSP an intermediate in the shikimate pathway, which eventually enables the synthesis of aromatic amino acids. Interaction of glyphosate with EPSP therefore leads to depletion of cellular levels of aromatic amino acids resulting in an inhibition of growth. (6).
As expected B. subtilis shows a strong sensitivity for glyphosate and a strongly stagnating growth rate (50% reduction of growth at 1 mM glyphosate, wild type). Exactly this sensitivity we aimed to abuse, but using only the wild type the maximum detection range promised to be around 2 mM. After our discovery of the first glyphosate transporters in a living system, we could use this knowledge to create a double mutant missing both of our identified transporters (ΔgltT and ΔgltP) as described in our Results leading to a strain with a much higher glyphosate resistance. A reduction of growth by 50% could be observed after addition of 8.0 mM! Working with this transporter mutant therefore made a much higher detection range possible, even at concentrations of 30 mM glyphosate and higher a change in growth behaviour could be observed.
To use B. subtilis as a detector system for glyphosate we had to quantify the reduction of growth, the growth rate seemed to be ideal for this application, being easily reproducible. It can be obtained by modelling our growth curves with the bacterial growth model:

The bacterial growth model

Under lab conditions, the right evironmental parameters and nutrients provided, bacterial growth can be observed in form of growth curves, plotting the bacterial mass as a function of time. A convenient way to observe those growth curves is provided by measuring the optical density also referred to as the turbidity.
During the growth of bacteria three distinct phases can be differentiated (Figure 1), all of which can be associated with physiological changes in the cell cultures: (1)

1. During lag phase the bacteria are suggested to adapt to physiological changes in the medium. Adaption can be achieved by e.g. changes in the Proteom of the Bacteria in order to meet the new culture requirements. Bacterial growth is strongly reduced
2. After adaption bacterial growth enters the log phase alternatively named exponential phase. During this phase the bacteria show exponential growth, the most rapid growth possible under given conditions. The actual double-timing of a certain strain is determined by the growth rate, the increase of cell mass per time.
3. In the stationary phase no net growth can be observed. Nutrients and carbon sources are used up and increase in cell mass is no longer possible. Dead cells can lyse and provide another source of nutrients, explaining a small increase in cell mass that sometimes still occurs.

To be scientifically correct a fourth phase can be observed in the bacterial growth curve namely the death phase. As we measured our bacterial mass in terms of optical density this phase couldn't be observed in our experiments and has no relevance for our modeling approaches.

Correlation between growth rate and glyphosate concentration

Obtaining the growth rate μ

During their growth bacteria reach a phase of exponential growth as described above. In this phase every bacteria in the culture divides at the fastest rate possible, therefore the growth of the colony is directly dependend on the amount of cells already grown. This is also true for the optical density as it's proportional to cell mass. To put this growth into a context that can be calculated, a constant of proportionality is needed. This constant can be described as the growth rate of the colony, it is specific to strains and also dependend on environmental influences like glyphosate. These dependencies can be described by the following formula:

This short differential equation describes the growth behaviour of the bacteria during the log phase. The equation can be solved by first separating the derivates:

Next the equation has to be integrated at both sides yielding to the following form:

Inserting the initial condition t=0 and OD_t=0 results in:

From this solution a very easy and convenient way to obtain the growth rate for every growth curve arrives. As it is probably known by everyone working in the field of microbiology plotting the logarithm of cell mass (or OD) against time leads to a linear section in the affiliated graph. This linear section is exactly what is described by the last formula, the logarithm of the exponential phase of bacterial growth with the growth rate as its slope. To reproducibly calculate the slope/growth rate we wrote a python script, that enables us to select the linear section of the graph by hand. After that a linear fit is calculated and the resulting growth rate is safed. In Figure X usage of the program is shown.

wildtype

double mutant (ΔgltT and ΔgltP)

Figure X. Usage of the python script to obtain the growth rate from the linear section of growth curves.

Describing the dependency of growth rate from glyphosate concentration

After assessing the growth rates by doing fits of the growth curves, we plotted them against the glyphosate concentration in the environment of every growth experiment respectively. The graphs can be observed in Figure X and X:

Figure 2. Dependency of growth rate to glyphosate concentration in the wild type strain.

Figure 3. Dependency of growth rate to glyphosate concentration in the double mutant strain (ΔgltT and ΔgltP).

As stated in the Results section of our project the growth rate is strongly on glyphosate concentration. While low concentrations of glyphosate (relative to the concentration of 50% growth reduction for every strain) doesn't impact the growth behaviour very strongly, increasing the concentration yields to very strong reduction, while higher doses of glyphosate doesn't change the growth rate very strongly anymore. While sadly our efforts to reveal the underlying mechanisms of this behaviour in a cooperation with iGEM Marburg failed (see characterization with EPSP synthesases) the graphs strongly resemble the well-known hill-equation suggesting cooperativity in either the transport of glyphosate or interaction with the EPSP synthase. We fitted the hill-equation to the data using a python script and the leastsq method of the scipy library, the fitted data are shown in figure X and X.

Figure X. Least square fit of the dependency between growth rate and glyphosate concentration for the wild type using the hill equation. In the right corner, the resulting function with determined parameters is shown.

Figure X. Least square fit of the dependency between growth rate and glyphosate concentration for the double mutant (ΔgltT and ΔgltP) using the hill equation. In the right corner, the resulting function with determined parameters is shown.

From the common form of the hill equation it can be transposed to show growth rate as dependency for glyphosate concentration:

With this transposition it is possible to determine the glyphosate concentration by evaluating the growth behaviour of the strains. With our modeled parameters for the double mutant and the wild type, a long A detection system for glyphosate therefore can be established with our model.
But there is one catch and this is why we tried to advance our modeling a little bit further: We can't be exactly sure, that no other environmental differences

References

1. Environmental Microbiology Second Edition, Maier Pepper Gerba, 2009
2. Amrhein et al. (1983) FEBS Lett. 157: 191-196.
3. Comai et al. (1983) Science 221: 370-371.
4. Schulz et al. (1984) Arch. Microbiol. 137: 121-123
5. Steinrücken & Amrhein (1980) Biochem. Biophys. Res. Commun. 94: 1207-1212.
6. Biochemical basis for glyphosate-tolerance in a bacterium and a plant tissue culture Nikolaus Amrhein, Detlef Joharming, Joachim Schab and Arno Schulz e
7. Fischer et al. (1986) J. Bacteriol. 168: 1147-1154