Team:UANL Mty-Mexico/Modeling/Biosensor

Biosensor

Our biosensor model is a continuation of the previously exposed transport and accumulation model with the addition of the production of luciferase as a function of ArsR|As concentration. In this way, we can relate the concentration of extracellular As to the production of luciferase.

ODEs

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The ODEs that describe the kinetics of the biosensor modules include all the assumptions presented in the core model and the equations presented for the accumulation and transport module, along with their corresponding parameters.

Taking into account the equations from the accumulation and transport module, we introduce a generator for Luciferase:

Luciferase mRNA

\begin{equation} \large \frac{d[mRNA_{Luc}]}{dt} = \alpha _{mLuc}\cdot (pro_{ars})\cdot(\frac{k_{D1}^{h_{1}}}{k_{D1}^{h_{1}}+[ArsR]^{h_{1}}})- \delta _{mRNA_{Luc}}[mRNA_{Luc}] \end{equation}

Luciferase protein

\begin{equation} \large \frac{d[Luc]}{dt} = \alpha _{pLuc}\cdot[mRNA_{Luc}]- \delta _{Luc}[Luc] \end{equation}

Parameters

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The parameters for the ODEs describing the production of luciferase mRNA and protein are shown in the next table.

Parameter table

Parameter	Description	Value	References
αmArsR	Maximal transcription rate of ArsR	3.74 nM/min	Assumptions
αmFluc	Maximal transcription rate of Fluc	1.40 nM/min	Assumptions
αpArsR	Maximal translation rate of ArsR	9.74 nM/min	Assumptions
αpFluc	Maximal translation rate of Fluc	2.06 nM/min	Assumptions
δmRNAArsR	Degradation rate of ArsR mRNA	2.16x10-1 min-1	Assumptions, Selinger, et al. (2003)
δmRNAFluc	Degradation rate of Fluc mRNA	3.37x10-2 min-1	Assumptions, Suter, et al. (2011), Karetnivok and Lehto (2006).
δArsR	Degradation rate of ArsR	2.31x10-2 min-1	Assumptions
δFluc	Degradation rate of Fluc	2.60x10-2 min-1	Assumptions, Auld, et al. (2008)
proars	Concentration of ars promoter	aprox. 1*plasmid copy (nM)	Assumptions

Simulations

Figure 1. Time vs Luciferase production (nM)