Team:INSA-UPS France/Model/Predictive

Croc'n Cholera
iGEM UPS-INSA Toulouse 2017

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Model

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Model simulation

Modeling to simulate our system

At the beginning of the project, we needed to know if our microbial synthetic consortium would work and if the information transmission was possible. So we used our system of ODEs and our solver to have a first estimation of the functioning of our synthetic system. We already had some experimental data from microbial growth assays, and we used them to have more realistic predictions.

Design parameters, such as Vibrio harveyi and Pichia pastoris initial concentration and the device volume, were set to biologically plausible values.

• [Vh]_0,D = 10¹² cell/L (OD_600nm ≈ 1.5 (1))
• [Pp]_0,D = 10¹² cell/L (OD_600nm ≈ 1.5 (1))
• V_D = 20.10^-3 L

Simulation results

Simulation of Vibrio cholerae concentration

Response time: 53.6 min

Simulation

Blablabla

Sensitivity and robustness using an extension of MCA

Metabolic Control Analysis (MCA) is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them with respect to a metric of interest.(2)

Usually used to describe systems at steady state, we had extended the concept of MCA for our dynamic system to analyze the sensitivity and robustness of the response time of the system to each parameter. The response time given by our solver, which is the time before reaching a non-pathogenic Vibrio cholerae concentration, was thus defined as our metric of interest (τ). For each parameter (p), the control coefficient (C) was calculated.

\begin{equation*} C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p} \end{equation*}

This coefficient quantifies the relative change in the response time τ which results from a relative change δ of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. If the response time is reduced by an increase of the parameter p, the coefficient C will be negative. Finally, if the response time is enhanced by an increase of the parameter, the coefficient C will be positive. The variation δ was fixed at 0.01. This sensitivity analysis was performed for a wide range of initial concentration of Vibrio cholerae. Results are presented as a heatmap.

• Red: parameters favouring a short response time
• Green: parameters favouring a long response time
• White: parameters with no significant influence

Important conclusions can be reached from this analysis. First, we notice that the initial concentration in Vibrio harveyi and all the strain intrinsic parameters have no influence on the response time. V. harveyi works as a simple inducer: a small amount of it is enough to sense CAI-1 and produce enough diacetyl to activate Pichia pastoris. Then, on the contrary, Pichia pastoris concentration (and its intrinsic parameters) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill V. cholerae. Efforts to optimize the system to accelerate its response could thus consist in engineering P. pastoris to increase the expression of AMPs. Interestingly, the device volume also appears to be a key parameters for our system. We will have to consider this point when designing the device.

Global analysis

Min. :45.46 Median :53.70 Mean :53.87 Max. :65.05 stdev : 3.329391

References

• (2): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447884/