In order to obtain our bioluminescent bacteria, we needed to introduce our tool, FIAT LUX, in our bacteria. We used two different vectors: pSEVA521 and pSEVA531, two mobilisable vectors with RK2 and pBBR1 origin of replication respectively. Our modeling work aimed at characterizing the effect of fiatlux on bacterial growth. Indeed, we wanted our engineered bacteria to behave as natural phytopathogens on the plants, to perfectly mimic infections.
We focused on four aspects:
- The comparison of the bacterial growth of bacteria containing the empty vectors, and bacteria containing vectors with our FIAT LUX tool, in order to verify whether or not our tool had a significant effect on bacterial growth.
- The study of the impact of several antibiotic concentrations (tetracycline 0, 3, 5, 7 and 10 µg/mL) on growth and luminescence. The purpose of the antibiotic is to select the bacteria that have the plasmid, so we were expecting more luminescence with a higher concentration of antibiotic.
- The study of the luminescence of our bacteria, in order to understand the ratio between luminescence and optical density (O.D.) (normalization).
- The comparison of the bacterial growth of bacteria containing both vectors, pSEVA521 and pSEVA531, in order to find the more suitable one for the use of our tool in D.solani.
In order to collect our data, we used a microplate reader, which allowed us to measure the OD600 (optical density) and the luminescence of our cultures for 48h.
The microplate is composed of a matrix with 96 wells, allowing us to measure the data for many different conditions at the same time. We produced 4 to 8 replicates for each antibiotic and plasmid condition.
If you want to find more about the protocol we used, it is described on the experiments page.
Prior to modeling the growths, we had to check and organize our data, by following the steps below:
-Remove outsider values: for instance contaminated wells.
-For the OD values, we subtracted the mean value of the control wells (containing Lysogeny Broth, LB, only) from other wells, in order to get rid of the background noise.
-Computed the luminescence/OD ratio, to study the luminescence normalized according to the number of bacteria. Indeed, if the OD is higher, the luminescence would obviously be higher.
-We also kept the variable luminescence alone, in case the bacterial growth would drastically change with the plasmid. In fact, if this would have been the case, we would have compared the luminescence between plasmids and not only the ratio luminescence/OD because it is better to have more luminescence with less bacteria than the opposite.
The growth of a bacterial population can be modeled thanks to a mathematical model. Several mathematical models can be used to do this (H. ZWIETERING et al. 1990), which are described below.
A bacterial growth usually has 4 phases: the lag phase, where the bacteria does not proliferate at all, the exponential phase, where the bacteria proliferate exponentially, the stationary phase, where the amount of bacteria stay at a high level without increasing or decreasing, and the death phase, where the amount of bacteria decreases. The mathematical models used to describe the bacterial growth only focus on the first three parts of the curves, without taking into account the death phase.
The theoretical curve of the bacterial growth is represented on the image below:
All of our work has been done with the development environment Rstudio, dedicated to open source statistical software R.
We plotted the OD as a function of time for each condition, in order to compare the bacterial growth. Here is an example of the curves we obtained for all the plasmids at the same antibiotic concentration.
We can see that the bacterial growth seems slightly different with pSEVA531-fiatlux than with the other plasmids. Indeed, the stationary phase shows an OD of around 0.58 for the other plasmids, and around 0.68 for pSEVA531-fiatlux. Before drawing a conclusion, we decided to perform a further statistical analysis, in order to take into account all the parameters in our study. More specifically, we wanted to test the effect of the measurement machine (microplate reader) before drawing conclusions from this graph, since the values obtained with pSEVA531-fiatlux were taken with a different machine than for the other plasmids. However, at first we had to determine the best model that fitted our growth curves, and collect the parameters for each case, to therefore perform the statistical analysis.
For each curve, we fitted 3 different bacterial growth models: Gompertz, Verhulst and Baranyi. Based on reports in the literature, those three models are the most widely used to model bacterial growth. (María-Leonor Pla et al. 2015).
Description of the models we tried:
- Verhulst: Also called the logistics model. Verhulst developed this model in response to the Malthus model that was growing continuously as an exponential growth. Verhulst added a new parameter K, representing the carrying capacity. (Nicolas Bacaër, 2020)
Equation of the model:
In this equation, N0 corresponds to the initial population of bacteria, r0 to the growth rate, K to the carrying capacity, that is to say the maximum population of the bacteria, and t to the time.
- Gompertz: Benjamin Gompertz proposed a braking term to the Malthus model, supposing that the mortality rate grew exponentially. The model was then improved by other scientists, but is still called the Gompertz model (Kathleen et al. 2017). The one we used is defined by the following equation:
In the Gompertz equation, the parameters 𝛼, k, 𝛽 and t correspond respectively to the carrying capacity, the growth rate, a constant and the time.
- Baranyi: The Baranyi model is particularly known to fit models with a lag phase at the beginning. Even if there is not necessarily a lag phase in the bacterial growth, The Baranyi model is well known to be a good fitting model (RXiong et al.1998).
with N0, Nmax, µ, lag and t corresponding respectively to the initial population, the carrying capacity (maximum population), the growth rate, the lag time, that is to say the time before the exponential growth of the bacteria starts, and the time.
In order to fit our model, we used the nlstools package of R. This package produces confidence intervals for the parameters in a nonlinear regression model fit.
This allowed us to compare the Aitken Indice Criterion (AIC) of each model adjusted to our curve and choose the appropriate model: in other words the one that best fit the obtained curve. This criterion provides a score for the fitting of the model, also taking into account the number of parameters (Aho, K. et al. 2014).
We observed that almost all of the curves fit a Baranyi model. We based this conclusion both visually and with the AIC. For example, when we plotted the evolution in time of the OD for the bacteria containing pSEVA521 with 5 µg/mL of Tetracycline, we obtained the following AIC: with the Baranyi model, we obtained an AIC of -1703.647; with Gompertz, -1445.594, and with Verhulst, -1252.391.
As the best AIC corresponds to the lowest value, we decided to use a Baranyi model as a reference. Although this model has a more complex writing, it seemed important for us to use it compared to the two other models we tried, as Baranyi is the only model taking the lag time into account. We observed during our experiments that there was a possible effect of the antibiotic concentration during the lag phase of the bacterial growth phase. Indeed, we hypothesized that a high concentration of tetracycline could delay the onset of growth. That is why the Baranyi model is the most appropriate one. Here is an example of the Baranyi model adjusted to our bacterial growth with pSEVA521 and 5 µg/mL of Tetracycline.
After collecting the values of the Baranyi model parameters for each condition, we performed a statistical analysis on these parameters, to see if the bacterial growth was significantly different with or without our tool FIAT LUX. We present this analysis below.
As a reminder, the bacterial growth model is written as follows:
The aim of this statistical analysis is to focus on the effect of our plasmids on two parameters:
- The growth rate: µ
- The load capacity: Nmax
Here is the representation of the Baranyi model and its parameters:
We performed a statistical analysis on the growth rate parameter µ and on the load capacity Nmax. As we were limited with time, we decided to focus on these two parameters rather than the lag time, which was less relevant for our study.
For both parameters, we first started by plotting boxplots to get an insight on the situation. We also plotted interaction plots to get an insight of the interaction between our fixed factors, and coplots to observe the effect of the random factor when we had one. We then used statistical models to determine if the observed differences were significant. Prior to perform the tests and looking at the p-values, we checked the following hypotheses of the models:
- The variance is homogenous.
- There are no outliers.
- The residuals follow a normal distribution.
- The measurements are independant.
-The linear model is not biased.
Description of the experimental plan:
To do this statistical analysis, we collected the parameters of the Baranyi model adjusted to our curve in a table, for each plasmid and each antibiotic concentration. We collected 8 values per condition (plasmid and antibiotic concentration) and took care of removing outliers prior to starting the analysis. We then ended up with a different number of replicates per condition. The table below represents the distribution of our replicates:
Table 1: Number of replicates per plasmid and Tetracycline (TET) concentration| Plasmid | ||||
|---|---|---|---|---|
| Antibiotic concentration (µg/mL) | pSEVA521 | pSEVA521-fiatlux | pSEVA531 | pSEVA531-fiatlux |
| medium without TET | 5 | 4 | 7 | 4 |
| medium with TET3 | 8 | 8 | 8 | 4 |
| medium with TET5 | 8 | 7 | 8 | 4 |
| medium with TET7 | 4 | 8 | 7 | 4 |
| medium with TET10 | 8 | 8 | 8 | 4 |
Moreover, we measured the optical density and the luminescence with two different machines, so we also took care of taking this into account during the study. The experimental plan taking into account the machine, and after removing the outliers was as follows:
Table 2: Number of replicates per plasmid, Tetracycline concentration and machine
| Machine | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| INSA | INSA | INSA | INSA | INSA | Lyon1 | Lyon1 | Lyon1 | Lyon1 | Lyon1 | |
| Tetracycline concentration (µg/mL) | 0 | 3 | 5 | 7 | 10 | 0 | 3 | 5 | 7 | 10 |
| pSEVA521 | 2 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 0 | 4 |
| pSEVA521-fiatlux | 0 | 0 | 0 | 0 | 0 | 4 | 8 | 7 | 8 | 8 |
| pSEVA531 | 4 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 3 | 4 |
| pSEVA531-fiatlux | 4 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | 0 | 0 |
Preliminary observation:
First of all, we drew boxplots of the growth rate according to the plasmid used for each antibiotic concentration. The 5 resulting boxplots are shown below:
The apparent heteroscedasticity of the variance on the boxplots is mainly due to the fact that we do not have the same amount of replicates for each plasmid.
For the concentrations TET3, TET5, and TET7, bacteria seem to have a higher growth rate when they contain the plasmids with fiatlux rather than when they contain the empty vectors, with a difference of around 3 or 4 s-1. Of course, we must be cautious when interpreting these graphs because we did not include the effect of the machine.
Thanks to an interaction plot, we noticed that the growth rate of bacteria containing a plasmid with fiatlux seemed to be different depending on the presence of antibiotics.
Without antibiotics (TET0), bacterial strains seem to have a lower growth rate than with a positive concentration. At this stage we cannot conclude on the effect of the antibiotic concentration without performing the statistical analysis. This effect of the antibiotic concentration on the growth rate is less visible for the bacteria containing an empty plasmid. This is why the curves corresponding to plasmids with fiatlux have a different shape than the ones corresponding to empty plasmids. As a result, we supposed a significant interaction between the antibiotic variable and the plasmid one, that we took into account when implementing our model.
We also performed a coplot to get an insight on the effect of the machine, but could not conclude since our experimental plan lacked some data, for example pSEVA521-fiatlux on the INSA machine.
To implement our model, we used a lmer model, known to fit linear mixed-effects models via restricted maximum likelihood (REML) or maximum likelihood (R library lme4). A mixed-effects model is a model containing both fixed factors and random ones. The fixed factors are the ones that we need to test and the random ones are factors that do not interest us in the study itself, but that we need to take into account to verify the hypothesis of independence of the data. We determined 2 fixed factors (plasmid and antibiotic) taking into account their interaction, and 1 random (machine). The mathematical model can be written as follows:
yijkp = µ + 𝜑i + 𝛾j + 𝛽k + 𝛿ij + 𝛳ik + 𝜎jk + 𝜀ijkp , with: yijkp = the theoretical OD value
Using this graph, we can see that the homogeneity of the variance has been verified, as all the points are proportionally scattered around the abscissa. Moreover, we confirmed that all the measurements were independant and that the model was not biased, so that we could use this model for our analysis.
Testing of the significance of random and fixed factors:We performed a ranova study to test the random machine effect, which resulted to be significant. In fact, the p-value, that is to say the probability to obtain a result at least as much aberant as the one we had, was equal to 3.734E-05. For all of our results, we determined a threshold at 0.05 for the p-value, to conclude of a significant result. With this ranova study, we thus considered a significant effect of the machine factor on our values and took it into account for the rest of the analysis.
Then, an anova study on our model allowed us to conclude that both the plasmid and the antibiotic concentration affected the growth rate significantly. An anova study consists of an analysis of the variance. The principle is to verify that the means of a group come from the same population by comparing the intra-group residuals to the inter-group residuals. In other words, when using a lmer model, the anova study aimed at determining the significant effects of the fixed factors, and the ranova study at determining the significant effects of the random ones.
In-depth analysis of the significance of fixed factors: We decided to perform another test to have a better insight on the situation, with the emmeans library.The emmeans library aims at making multiple tests, which enables simultaneous statistical tests. Here we performed a Tukey test: a single-step multiple comparison procedure and statistical test which compares all possible pairs of means. We obtained the following graph, showing the estimated marginal means for each condition:
Without antibiotics, the growth rate of the bacteria appears to be quite similar with all plasmids, except with pSEVA531-fiatlux which is a little lower. With this graph resulting from the Tukey test, we have a better point of view on the effect of the antibiotic than with the interaction plot. We will perform the statistical analysis to confirm or not the effect of fiatlux on each antibiotic concentration. For a concentration of 3, 5 or 7 µg/mL of antibiotics, we had a lower growth rate with empty plasmids (pSEVA521 and pSEVA531) than with fiatlux ones. Overall, pSEVA531-fiatlux and pSEVA521-fiatlux seem to have the same positive effect on the growth rate.
To conclude on the significance of the presence of fiatlux on the growth rate, we performed an MCP test by antibiotic concentration. Here are the conclusions we drew:
- For TET0, we concluded that there was no significant effect. Indeed, the p-value was equal to 0.4801 for the comparison between pSEVA521 and pSEVA521-fiatlux and 0.1781 for the comparison between pSEVA531 and pSEVA531-fiatlux.
- For TET3 and TET5, the presence of fiatlux in the plasmid had an effect: it accelerated the growth. For TET3, the p-values were equal to 0.0001 and 0.0003 for the comparisons between pSEVA521 and pSEVA521-fiatlux and between pSEVA531 and pSEVA531-fiatlux respectively, and to 0.0147 and 0.0001 for TET5.
- For TET7 and TET10, the presence of fiatlux in the plasmid has a significant positive effect on the growth rate with pSEVA521 but not with pSEVA531. Indeed, for a concentration of 7 µg/mL, with pSEVA521, the p-value was equal to 0.0224, which is less than our threshold 0.005, but with pSEVA531, it was equal to 0.1390. Likewise, for 10 µg/mL, the p-values were equal to 0.0001 and 0.2636 respectively.
We must be careful when interpreting a result as non-significative because the test loses power because of the high number of cases to compare (each plasmid compared with another). More studies, described below, are to be carried out to confirm these conclusions.
To conclude this global analysis: the presence of fiatlux in the plasmids significantly increased the growth rate for concentrations of 3 and 5 µg/mL of Tetracycline. For 7 and 10 µg/mL of Tetracycline, the growth rate of the bacteria with pSEVA521 increased in the presence of fiatlux, but the growth rate of the bacteria with pSEVA531 did not increase significantly with fiatlux.
As we intend to use our tool in situ to infect plants, where no pressure of selection can be applied, we focused on the growth curves of the bacteria containing the plasmids but grown in absence of antibiotics. The objective was to find what is the best backbone for our tool, between pSEVA531-fiatlux and pSEVA521-fiatlux.
To do so, we performed the same statistical analysis without considering the “antibiotic” factor. Thus, we used a lmer model with the plasmid factor as the fixed factor and the machine as the random one. According to the anova and ranova studies, the plasmid effect and the machine effect are both significant. On the boxplot representing the bacterial growth rate according to each plasmid without antibiotics, the growth rate seems much lower for both pSEVA531 plasmids (5E-05s-1) than for the pSEVA521 plasmids (1E-05s-1).
According to the MCP test, we can say that the growth rate of Dickeya containing pSEVA521-fiatlux is significantly higher than that of Dickeya containing pSEVA531-fiatlux, since we obtained a p-value of 0.0145. It accelerates the growth by 2.46E-05 s-1.
In order to analyze the effect of fiatlux on bacterial growth, we compared pSEVA531 and pSEVA531-fiatlux, and in a second time pSEVA521 and pSEVA521-fiatlux. This enabled us to use only data taken on one machine at a time. As the machine effect is significant on our data, we performed the same analysis for a single machine, to get rid of the random effect in our model.
Comparison of bacterial growth between pSEVA531 and pSEVA531-fiatlux: For the study of pSEVA531 and pSEVA531-fiatlux, we had the following balanced experimental plan: Table 3: Number of replicates per plasmid and Tetracycline concentration| Antibiotic concentration (µg/mL) | pSEVA531 | pSEVA531-fiatlux |
|---|---|---|
| medium without TET | 4 | 4 |
| medium with TET3 | 4 | 4 |
| medium with TET5 | 4 | 4 |
| medium with TET7 | 4 | 4 |
| medium with TET10 | 4 | 4 |
The growth rate of Dickeya with pSEVA531-fiatlux seems a little bit higher than without fiatlux but the difference appears to be approximately 1E-05 s-1, which is very low. This means that the OD with pSEVA531-fiatlux increases by 1E-05 units more than with pSEVA531 per second. For example, if the OD with pSEVA531 increases by 4E-05 units per second, the one with pSEVA531-fiatlux increases by 5E-05 units per second.
According to the interaction plot below, we can suppose that there is an interaction between the presence of fiatlux in the plasmid and the amount of antibiotics, as the curves don’t follow the same variations.
We therefore built a fixed linear model taking into account our antibiotics and plasmids parameters. The mathematical model is described as follows:
yijkp = µ + 𝜑i + 𝛾j + 𝛿ij 𝜀ijp , with: yijkp = the theoretical OD value
On these graphs, we checked the normality of residuals, and that we did not have any funnel effect or any outliers (Cook’s distances). Moreover, the measurements remain independent and the model unbiased. Thus, all the hypotheses were verified.
The anova study showed us that the antibiotic factor modified the growth rate significantly (p-value = 5.926E-05). However, neither the plasmid nor the interaction significantly modified the growth. Indeed, the p-value for the plasmid effect was 0.1444, and that of the interaction was 0.0588. To confirm this result, we performed a Tukey test with an aov model to compute the adjusted p-value for multiple tests, considering the parameter µ as a function of the plasmid. This test confirmed that the difference in the growth rate between pSEVA531 and pSEVA531-fiatlux was not significant (p-value = 0.29852).
Comparison of bacterial growth between pSEVA521 and pSEVA521-fiatlux: For the study of pSEVA521 and pSEVA521-fiatlux, we had the following experimental plan: Table 4: Number of replicates per plasmid and Tetracycline concentration| Antibiotic concentration (µg/mL) | pSEVA531 | pSEVA531-fiatlux |
|---|---|---|
| medium without TET | 3 | 4 |
| medium with TET3 | 4 | 8 |
| medium with TET5 | 4 | 7 |
| medium with TET7 | 0 | 8 |
| medium with TET10 | 4 | 8 |
As for the study on pSEVA531, the growth rate seems to be higher with fiatlux than without it. However, the difference between pSEVA521 and pSEVA521-fiatlux seems higher (around 3E-05 s-1) than the difference between pSEVA531 and pSEVA531-fiatlux (1E-05 s-1).
The interaction plot also suggests an interaction between the presence of fiatlux in the plasmid and the amount of antibiotics.
With the same model, the anova study revealed a significant effect of the plasmid (p-value = 3.092E-08), the antibiotic concentration (8.720E-06) and the interaction (1.721E-09) on the growth rate. The Tukey test confirmed the significance of the plasmid effect on the growth rate, regardless of the antibiotics concentration (p-value = 2.16E-05). We also performed a Tukey test on the significance of the plasmid effect on the growth rate without antibiotics and we obtained a p-value of 0.0396427, confirming that the plasmid has a significance effect on the growth rate even without antibiotics. This conclusion is different from the one we drew when comparing all the plasmids without antibiotics, with different machines, in part a). This conclusion is more valuable than the previous one, as this study was done on a single machine.
To conclude on the statistical study, when we focus on the effect of the plasmid without antibiotics, which is the more interesting case for our study, we can conclude that:
- part 2: the bacterial growth rate is significantly higher with pSEVA521-fiatlux than with pSEVA531-fiatlux.
- part 3: However, fiatlux has a significant effect on the growth rate in pSEVA521 and not in pSEVA531.
As a result, we would prefer pSEVA531-fiatlux as a backbone for our study, because the most important feature we value for our tool is that the presence of fiatlux does not have an impact on the growth, so as to perfectly mimic an infection with the wild-type strain.
| medium without TET | medium with TET3 | medium with TET5 | medium with TET7 | medium with TET10 |
|---|---|---|---|---|
| fiatlux has a significant positive effect on the growth rate, for pSEVA521 (2.67E-05 s-1, which is 9.61E-02 h-1), but not for pSEVA531 (2.32E-06, which is 8.35E-03 h-1). (part 3). pSEVA521-fiatlux provides a significantly higher growth rate than pSEVA531-fiatlux. The growth increases by 2.46E-05 s-1. | fiatlux has a significant effect on the growth rate, for both plasmids. The growth increases by 3.88E-05 s-1 (1.40E-1 h-1) with fiatlux in pSEVA521, and by 3.93E-05 s-1 (1.41E-1 h-1) in pSEVA531 (part 1). | fiatlux has a significant effect on the growth rate, for both plasmids. The growth increases by 2.28E-05 s-1 (8.21E-02 h-1) with fiatlux in pSEVA521, and by 4.52E-05 s-1 (1.63E-1 h-1) in pSEVA531 (part 1). | fiatlux has a significant effect on the growth rate, for pSEVA521, but not for pSEVA531. The growth increases by 2.64E-05 s-1 (9.50E-02 h-1) with fiatlux in pSEVA521, and by 1.65E-05 s-1 (5.94E-02 h-1) in pSEVA531 (part 1). | fiatlux has a significant effect on the growth rate, for pSEVA521, but not for pSEVA531. The growth increases by 6.78E-05 s-1 (2.44E-1 h-1) with fiatlux in pSEVA521, and decreases by 1.22E-05 s-1(4.44E-02 h-1) in pSEVA531 (part 1). |
| Comparison | Comments |
|---|---|
| Backbone effect without antibiotic: pSEVA521-fiatlux and pSEVA531-fiatlux |
Bacteria with pSEVA521-fiatlux grow significantly faster than with pSEVA531-fiatlux (part 2). The growth rate with pSEVA531-fiatlux increases by 2.46E-05 units more than with pSEVA521-fiatlux per second, which is 8.86E-02 units per hour. |
| fiatlux effect for all antibiotic concentrations: pSEVA521 and pSEVA521-fiatlux |
Bacteria with pSEVA521-fiatlux grow significantly faster than with pSEVA521 (part 3). The growth rate with pSEVA521-fiatlux increases by 2.83E-05 units more than with pSEVA521 per second, which is 1.02E-1 units per hour. |
| fiatlux effect for all antibiotic concentrations: pSEVA531 and pSEVA531-fiatlux |
There is no significant difference in the growth rate (part 3). The growth rate with pSEVA531-fiatlux increases by 8.53E-06 units more than with pSEVA531 per second, which is 3.07E-02 units per hour. |
For this parameter, we conducted exactly the same study as for the growth rate parameter. We summarized the results and conclusions that we obtained, without detailing the methods used. Of course, all the hypotheses of the models have been tested in this study, as for the growth rate study.
As we collected all the parameters at the same time, we had exactly the same experiment plan, with the same amount of replicates for each condition.
Here are the boxplots representing the Nmax parameter according to the plasmid, for each antibiotic concentration:
Regarding the MCP test, we obtained the following conclusions:
- In all the media with antibiotics, fiatlux did not have any significant effect on the load capacity (p-values > 0.4 for all cases).
- In the media without antibiotics, the p-value resulting from the comparison between pSEVA521 and pSEVA521-fiatlux was 0.5854, which is not significant, but the p-value for pSEVA531 and pSEVA531-fiatlux was inferior than 0.0001, which is significant. Therefore, the load capacity is significantly different between bacteria carrying pSEVA531 and pSEVA531-fiatlux. Specifically, fiatlux increased the load capacity by 1.30 in pSEVA531 in the medium without antibiotics.
When comparing our data without antibiotics, the MCP test revealed that the differences between pSEVA531-fiatlux and pSEVA521-fiatlux were significant (p-value = 0.0020). pSEVA531-fiatlux increases the load capacity of our bacteria by 1.59 compared to pSEVA521-fiatlux. On the other hand, we could not see any significant differences between the load capacity of our bacteria containing empty plasmids pSEVA531 and pSEVA521 (p-value = 0.5352).
For the comparison of the plasmids on a single machine, we obtained the following graphs:
The conclusions of the anova tests for these comparisons were that the Nmax parameter does not change significantly between pSEVA531 and pSEVA531-fiatlux (p-value = 0.08321) and between pSEVA521 and pSEVA521-fiatlux (p-value = 0.1475). The Tukey tests also confirmed these conclusions (p-values: 0.2777061 and 0.2700767 respectively), for all antibiotic concentrations, but especially for the medium without antibiotics (p-values: 0.1413542 and 0.1372849 respectively).
To conclude on this statistical study, when we focus on the effect of the plasmid without antibiotics, which is the more appropriate case for our study, we can conclude that:
- part 2: The load capacity is significantly higher with pSEVA531-fiatlux than with pSEVA521-fiatlux.
- part 3: The study to compare both pSEVA521-fiatlux with pSEVA521, and pSEVA531-fiatlux with pSEVA531 revealed that the difference in the load capacity was not significant between either pSEVA531-fiatlux and pSEVA531 or between pSEVA521-fiatlux and pSEVA521. This proves that the carrying capacity is not affected by our tool fiatlux.
| medium without TET | medium with TET3 | medium with TET5 | medium with TET7 | medium with TET10 |
|---|---|---|---|---|
| fiatlux has no significant effect on the carrying capacity, for either plasmid (part 3). pSEVA531-fiatlux provides a significantly higher load capacity than pSEVA521-fiatlux (OD max increased by 1.5882 (part 2)). | fiatlux has no significant effect on the carrying capacity, for either plasmid (part 1). | fiatlux has no significant effect on the carrying capacity, for either plasmid (part 1). | fiatlux has no significant effect on the carrying capacity, for either plasmid (part 1). | fiatlux has no significant effect on the carrying capacity, for either plasmid (part 1). |
| Comparison | Comments |
|---|---|
| Backbone effect without antibiotic: pSEVA521-fiatlux and pSEVA531-fiatlux |
pSEVA531-fiatlux increases the load capacity of our bacteria by 1.5882 compared to pSEVA521-fiatlux (part 2). |
| fiatlux effect for all antibiotic concentrations: pSEVA521 and pSEVA521-fiatlux |
There is no significant difference in the load capacity (part 3). |
| fiatlux effect for all antibiotic concentrations: pSEVA531 and pSEVA531-fiatlux |
There is no significant difference in the load capacity (part 3). |
After modeling the optical density to characterize the bacterial growth, we focused on the luminescence. According to our statistical analysis, the difference of the growth between pSEVA531-fiatlux and pSEVA531 is not significant (STATISTICAL ANALYSIS - Analysis of the growth rate parameter µ - part 3). Therefore, we could analyze the luminescence/OD ratio as a function of time, instead of the luminescence as a function of time. Moreover, since there is not necessarily the same amount of bacteria, at a given time, for each condition, it is better to analyze the luminescence/OD ratio than the luminescence. Finally, by plotting the ratio luminescence/OD, we could check the effect of the antibiotic concentration. As a reminder, the purpose of the antibiotic is to select the bacteria that contains the plasmid, and inhibit the growth of the others. The antibiotic can also have an effect on the copy number of a plasmid in bacteria.
The aim of this study is to determine the necessary amount of time after infection to provide the best luminescence/OD ratio, and to compare the luminescence emitted by bacteria containing pSEVA521-fiatlux, and bacteria containing pSEVA531-fiatlux. As for the OD modeling, we used the software R thanks to R studio for this task.
As expected, only the bacteria with plasmids containing fiatlux produced luminescence. Indeed, the values of luminescence collected by the machines for pSEVA521 and pSEVA531 were negligible compared to the ones with fiatlux. We had values from 0 to 50 RLU for plasmids without fiatlux, and from 1,000 to 60,000 for fiatlux containing ones.
Below is the graph of the luminescence/OD ratio of Dickeya with pSEVA521-fiatlux plotted against time, for different antibiotic concentrations.
On this graph we can see that the curves have the same shape for all antibiotic concentrations. However, the peak of light intensity and the time after which it is reached vary according to the concentration of antibiotic. We observe that the more antibiotics we add, the higher the peak of intensity is. This is due to the fact that the antibiotic properly selected the bacteria with the plasmid. Moreover, we observe on the graph that the higher the antibiotic concentration, the later the peak of intensity can be found. Below, we plot the OD as a function of time for exactly the same plasmid and concentrations. On the above graph, we added vertical lines where the peak was reached, and we will add them on the graph with the OD as well to check that the peak of luminescence is indeed reached during the exponential phase of the bacterial growth.
We notice that the higher the antibiotic concentration, the longer the lag time, thus the later the exponential phase. Thanks to the vertical lines, we confirm that the peak of intensity is reached during the exponential phase of the bacterial growth, whatever the antibiotic concentration. Moreover, the bacteria grow slower when the concentration of antibiotics increases. This explains why the peak of intensity is reached later with 10 µg/mL of Tetracycline than with lower concentrations.
Now, we plot the graph of the luminescence/OD as a function of time for pSEVA531-fiatlux.
The curves on this graph have a peak at the beginning like the other graph, but these peaks are less visible because the basal luminescence is higher than the one in the other graph. However, we see 2 peaks of luminescence for an antibiotic concentration of 10 µg/mL. Since we were afraid that the luminescence did not work properly for this replicate, we plotted its OD as a function of time and added the 2 vertical lines corresponding to the luminescence peak to check that one of the 2 was during the exponential phase of the growth.
Then, we wanted to study the link between the luminescence and the bacterial concentration for pSEVA531-fiatlux. To do so, we plotted the luminescence against the OD to check if there was any relation. We obtained the following graph:
We realized that the first part of the curves were linear, starting at 0, which suggests that there is a linear relation between the luminescence and the OD. One of our next goals after iGEM is to characterize this relation between the strength of the luminescence emitted, and the number of bacteria. To do so, we need to perform further experiments to collect more data.
This part of the curves corresponds to the exponential phase of the bacterial growth. At higher values of OD, the luminescence does not appear to be proportional to the OD anymore. In the stationary phase, the luminescence values are decreasing. We can conclude that during the exponential growth phase, the emission of luminescence increases proportionally with the number of bacteria. Then, when the stationary phase is reached, the luminescence starts to decrease, even though the number of bacteria remains constant. This phenomenon may be explained by the fact that the reaction consumes a lot of energy, so when there is not enough energy anymore, the metabolism slows down and then stops. Those results are in line with the observations on solid medium, explained in the experiments page. Even though the results on both liquid and solid media are coherent, in order to have an insight on how the level of luminescence is impacted by the quantity of bacteria to characterize our tool, we need to perform more tests in situ, where growth conditions are different.
The aim of the study was to verify that the operon did not alter bacterial growth. We also wanted to study the effect of antibiotic concentration on bacterial growth, and the emitted luminescence. Finally, we wanted to determine the ideal backbone for our operon, between pSEVA521 and pSEVA531.
To do so, we needed to find the model that best fit our data. We concluded on the Baranyi model and studied two parameters of this model: the growth rate mu and the load capacity Nmax.
After modeling our bacterial growths for each plasmid and antibiotic concentration, and the luminescence, we are able to draw the following conclusions:
-The fiatlux operon did not alter the growth of Dickeya in terms of growth rate, and load capacity in the pSEVA531 backbone, in an antibiotic-free medium (STATISTICAL ANALYSIS - Analysis of the growth rate parameter µ - part 4 and Analysis of the load capacity parameter Nmax - part 4). We can assume fiatlux does not use too much of the bacteria’s energy, when grown in liquid medium.
-The antibiotic concentration has an effect on the bacterial growth and luminescence. As for the luminescence, we noticed that the more antibiotics we added, the higher and longer the luminescence was, which confirms that the antibiotic properly selects and maintains the bacteria containing the luminescent plasmid (LUMINESCENCE MODELING - Results) However, as no antibiotic can be used in situ, we thought of another way to force the bacteria to keep the plasmid. For that purpose we intend to add a toxin/antitoxin system on the engineered fiatlux plasmids. We succeeded in the cloning of toxin/antitoxin genes but missed time to add them on fiatlux plasmids.
-The luminescence is higher and lasts longer with pSEVA531-fiatlux than with pSEVA521-fiatlux (LUMINESCENCE MODELING - Results). Moreover, for the exponential phase of the growth, the luminescence is proportional to the OD.
- pSEVA531-fiatlux is the best plasmid to use for our tool. According to the above results, the difference in the growth rate was not significant between pSEVA531-fiatlux and pSEVA531, but was significant between pSEVA521-fiatlux and pSEVA521 (STATISTICAL ANALYSIS - Analysis of the growth rate parameter µ - part 4). This leads us to think that the effect of fiatlux on bacterial growth is stronger when used in pSEVA521. Moreover, the load capacity of our Dickeya population is higher with pSEVA531-fiatlux than with pSEVA521-fiatlux, and the luminescence stays much longer, and is more intense. As a result, we concluded that pSEVA531-fiatlux was the best plasmid to use with the bacteria Dickeya that we used in our study. This conclusion has to be linked to the result we obtained for the characterization on solid media on the Experiments page, which also presents pSEVA531 as the most suitable vector for our tool.
The results obtained in this part led us to adapt our work in the wet lab: at some point, we started to work only on pSEVA531. We must keep in mind that those results are only valid for D.solani, and could vary depending on the host.
To further improve this study, it would be possible to do the same analysis on E coli, for example, but also perform other tests in order to evaluate the effect of fiatlux on D.solani’s growth in situ. Moreover, the next step of our statistical work will be to analyze another parameter of the Baranyi model: the lag time.
If you need more information on the R code we used for this modeling page, you can read our R markdown page.
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