Modelling
We have developed models to detect the concentrations of and capture certain noxious gases and harmful chemicals (different models for different substrates like CO, oxides of Nitrogen, Xylene, Acetaldehyde, and phenolic compounds) through single cell modelling and stochastic cell modelling. The models use differential equations of chemical kinetics and thermodynamics with parameters such as chemical affinity, promoter strength, binding constants, and others. The model is written in Perl language and the graphical representations are in R. The genetic circuits are optimized to select the best genetic parts/BioBricks, to reduce leaky expression of proteins, reduce response time and to increase sensitivity and efficiency in capturing the gases. A colored output is given, quantification of which has been provided. The color is due to the expression of chromoproteins by synthetic bacteria which change color according to the concentration of the input chemical.
We present "gEco" as a graded colorimetric scale for differentiation between different concentrations of noxious gases and harmful chemicals. The color changes according to the concentration of the input chemical. To demonstrate, different simulation were done for two chromophores and single chromophore.
Single Cell modelling
To model the concentration of different chromophores and proteins and analyse the color produced by different concentration of pollutants, we simulated the single cell model using the parameters given below. The values used were taken from literatures and for the parts which do not have reported values, we used generic value. To simulate a realistic situation, the model initially predicted the concentration of different proteins in the absence of pollutant (Here salicylate was taken as an example, which activates the marR promoter):
Graph1: No salicylate: start everything 0
The yellow color chromophore will increase and stabilize due to the self inhibitory loop driven by TetR as shown in the latter part of the circuit 1, but the blue chromophore will not be expressed.
Then, various concentrations of salicylate were used to see the effect of pollutant concentration on the chromophore concentrations, given that the pollutant was present from the beginning:
Graphs for different concentrations from starting concentration 0
Salicylate = 0.1uM Starting Dynamics
Salicylate = 1uM Starting Dynamics
Salicylate = 10uM Starting Dynamics
Salicylate = 100uM Starting Dynamics
Salicylate = 1000uM Starting Dynamics
Salicylate = 10000uM Starting Dynamics
To simulate the real conditions, the final equilibrium concentrations from Graph 1 were used as the starting concentrations and different concentrations of salicylate were used to observe the effect on the concentration of both chromophores:
Graph for different concentrations of salicylate with starting equilibirium concentrations
Salicylate = 0uM Equilibirium Dynamics
Salicylate = 0.01uM Equilibirium Dynamics
Salicylate = 0.1uM Equilibirium Dynamics
Salicylate = 1uM Equilibirium Dynamics
Salicylate = 10uM Equilibirium Dynamics
Salicylate = 100uM Equilibirium Dynamics
Salicylate = 1000uM Equilibirium Dynamics
As seen from the above graphs, as the salicylate concentration increased, the concentration of blue chromophore increased whereas that of yellow chromophore decreased resulting in the final color combination.
We then carried on to find the relative concentrations of blue and yellow chromophores and converted them into CMYK percentages by giving blue chromophore percentages to cyan and yellow chromophore percentages to yellow while the remaining parameters were kept at 0. The color that we got transitioned from yellow to green to cyan depending upon the concentration of salicylate.
Stochastic Cell Modelling
One may argue that the yellow color is almost constant in the background, then why do we need 2 colors? We can simply do it with a single color. That is true for a single cell and simulations do show faster responses as shown in the following graphs for a single color.
Single promoter Graph
Salicylate = 0uM Equilibirium Dynamics single positive circuit
Salicylate = 0.01uM Equilibirium Dynamics single positive circuit
Salicylate = 0.1uM Equilibirium Dynamics single positive circuit
Salicylate = 1uM Equilibirium Dynamics single positive circuit
Salicylate = 10uM Equilibirium Dynamics single positive circuit
Salicylate = 100uM Equilibirium Dynamics single positive circuit
Salicylate = 1000uM Equilibirium Dynamics single positive circuit
But the advantage with the use of 2 colors comes up when multiple cells are taking part (while we are measuring the concentration of the pollutant). In case of single chromophore detection, the brightness of the chromophore is the only indicator, but that is unreliable if there is cell death. The brightness can also decrease due to the death of a few cells in the process. However, with a constant yellow color in the background, the yellow is an indicator of living cells and the proportion of 2 colors will result only from living cells.
Program photo
General Equations
Activator Equation
[Protein] += (([Activator] * α_Activator)/([Activator] + kon_Activator)) - (γ_Protein * [Protein])
Repressor Equation
[Protein] += (((α_Repressor) / (1 + (([Repressor])/(β_Repressor)))) - (γ_Protein * [Protein])
Equations for Salicylate
[T7_pol] += (((α_TetR) / (1 + (([TetR]*[TetR])/(β_tetR*β_tetR)))) - (γ_T7_pol * [T7_pol]));
[mRNA_chromo_II] += (([T7_pol] * α_T7_pol)/([T7_pol] + kon_T7_pol)) - (γ_chromo * [mRNA_chromo_II]);
[TetR] += (([T7_pol] * α_T7_pol)/([T7_pol] + kon_T7_pol)) - (γ_TetR * [TetR]) + (([ToxR] * α_CTx)/([ToxR] + kon_T7_pol));
[MarR] += cons + (((α_MarR * [MarR_Sali]) / (1 + (([MarR_dup])/(β_MarR)))) - (γ_MarR * [MarR]));
[MarR_dup] = ([MarR] * [MarR])/KI_MarR_MarR;
[MarR_Sali] = ([Sali] * [MarR_dup])/KI_Sali_MarR;
[Sali] = [Sali] - [MarR_Sali];
[MarR] = [MarR] - [MarR_Sali] - [MarR_dup];
[ToxR] += (((α_MarR * [MarR_Sali]) / (1 + (([MarR_dup])/(β_MarR)))) - (γ_ToxR * [ToxR]));
[mRNA_chromo_I] += (([ToxR] * α_CTx)/([ToxR + kon_CTx)) - (γ_chromo * [mRNA_chromo_I]);
The combination of negative and positive feedback loops confers explicit flexibility to biochemical switches.
Parameters
| alpha_TetR* | 1 |
| alpha_T7_pol* | 10 |
| alpha_CTx* | 10 |
| alpha_MarR* | 5 |
| alpha_ToxR* | 5 |
| beta_TetR | 0.1 |
| beta_MarR | 0.1 |
| Gamma_MarR | 0.4 |
| Gamma_T7_pol | 0.004 |
| Gamma_TetR | 0.069 |
| Gamma_ToxR | 0.05 |
| Gamma_chromo | 0.00039 |
| kon_T7_pol | 0.85 |
| kon_CTx | 0.8 |
| KI_MarR_MarR | 1.1 |
| KI_Sali_MarR | 0.05 |
