Team:TecMonterrey GDL/Model
The characterization of a promoter, which is Pompc with a fluorescent reporter that is green fluorescent protein (GFP) is presented. The growth kinetics of E. coli DH5-α with the Pompc promoter subject to different osmolarity concentrations is presented, furthermore, a model for describing the GFP promoter response maximization is proposed.
Modified E. coli DH5-𝜶 with the
Pompc promoter kinetic growth
model
The growth of the microorganism with the promoter Pompc osmolarity was analyzed when being subject to different salt (NaCl) concentrations (1, 5, 10, 20 and 40 g/L). A kinetic was performed by triplicate and the average was taken to elaborate different models to describe the behavior of Pompc. Several equations were used to model the growth, but it was found that a polynomial equation (linearly) best fitted the experimental data (R-squared ≥94%).
The promoter behavior can be described through a quadratic polynomial equation for 1, 5, 10, 20 and 40 g/L osmolarity concentrations. Each model presents a good fit for the experimental data, as shown in Figure 1. These models describe the behavior of E. coli DH5-α with the Pompc promoter subject to different osmolarities.
Figure 1.-
E. coli DH5-𝜶 kinetics at 1, 5 and 40 g/L salt concentration.
Additionally to find other important variables such as: μmax (specific growth rate) and σ (doubling time), the models were enhanced with the Gompertz non-linear approach for growth modelling (Figure 2). The Equation 1 denotes the Gompertz model. The E. coli DH5-α growth kinetics at different NaCl concentrations and the adjustment of the empirical data with Gompertz model are presented in Figures 3-5. It can be observed that Gompertz has a good adjustment for describing our empirical data (R-squared>94%), so we use it to obtain the specific growth rate and doubling time of E. coli DH5-𝜶.
Equation 1
Where:
Figure 2. Gompertz model.
Figure 3A. E. coli DH5-𝜶 at 1g/L salt concentration, adjusted data to Gompertz model.
The relation between
the
experimental response and the calculated model response is presented.
Figure 3B. E. coli DH5-𝜶 at 5g/L salt concentration, adjusted data to Gompertz model.
The relation between
the
experimental response and the calculated model response is presented.
Figure 3C. E. coli DH5-𝜶 at 40g/L salt concentration, adjusted data to Gompertz model.
The relation between
the
experimental response and the calculated model response is presented.
Figure 3D. E. coli DH5-𝜶 at 40g/L salt concentration, adjusted data to Gompertz model.
The relation between
the
experimental response and the calculated model response is presented.
Figure 3E. E. coli DH5-𝜶 at 40g/L salt concentration, adjusted data to Gompertz model.
The relation between
the
experimental response and the calculated model response is presented.
For each model the Gauss-Newton algorithm was used until finding (7-13 iterations) the constants suitable for each experimental condition:
Following Gompertz model, we can calculate important parameters for the growth of E. coli DH5-α, as described in Equations 2, 3. The obtained parameters for each growth model are shown in Table 1.
Equation 2
Equation 3
The obtained parameters for each growth model is shown in Table 1.
Table 1. μmax (specific growth rate) and σ (doubling time), obtained from the kinetics adjusted data Gompertz models.
GFP promoter characterization
subject to different osmolarities
The behavior of Pompc promoter expression subject to time (hours) was characterized at different salt (NaCl) concentrations (1, 5, 10, 20 and 40 g/L). Response surface methodology was performed to model the response from the promoter. The equation, adjustment of the proposed model and surface response for the GFP (green fluorescent protein) expression from Pompc is presented in Equation 4. This model showed a good fit for describing the Pompc GFP behavior (Table 2). The tridimensional (Figure 4) and bidimensional (Figure 5) representations of the model are also presented.
Equation 4:
Where:
Table 2. Obtained R-squared for the proposed model.
Figure 4. Pompc promoter response to different NaCl concentrations, using a GFP reporter. Results of the model
presented
tridimensional.
Figure 5. Pompc promoter response to different NaCl concentrations, using a GFP reporter. Results of the model
presented bidimensional.
It can be concluded that an over-increase of salt (NaCl) concentration decreases the growth of our genetically modified microorganism, increasing up to one hour the doubling time required when no salt is used, as well as exhibiting a lower specific growth rate. The best response for GFP happens at low and medium concentrations of NaCl and longer times, however, the interaction between NaCl and Time shows an important significant contribution to the model as shown in Figure 6 in order to maximize GFP response.
Figure 6. Pareto chart for standardized effects for the critical factors of the model.
Therefore, the interaction between salt (NaCl) and time are important factors to be considered for enhancing the Pompc expression. The previous model can be used to describe the Pompc behavior when being subject to different NaCl concentrations and contribute in the design of further experiments that can be used in simulations to find an optimization for the Pompc response. The mathematical model analysis highlights the importance of adding a knock-out in further research with our promoter, because our microorganism already possesses an intrinsic signal that can’t be ignored and influences the GFP response to the different osmolarities. In this way, it is important that further research is performed.
