Modeling

Model

EnvZ Equations

Synthetic Sensor Equations

Model

EnvZ Model

Sensor Design

Currently our engineered cells rely on the sensory histidine kinase, EnvZ, which senses for environmental osmolarity. In high osmolarity, EnvZ phosphorylates a transcriptional regulatory protein, OmpR, which then binds to the ompC promoter to begin the transcription of our tripeptides.

Glucose Sensor Model

Description

Osmolarity of the blood is affected by many factors besides just sugar levels so in the future we want to implement a sensor specifically for glucose. The lac operon has the ability to sense cAMP, which has an inverse relationship to environmental glucose concentration. To use this system, we will knock out the lacI repressor and replace lacZ with a tetR repressor. Separate from the operon, the tripeptides will be located under the control of a constitutively expressing Ptet promoter. In the case of a glucose spike (or hyperglycemia), cAMP levels would fall and transcription of the tetR repressor would drop. The lack of TetR would allow the PTet promoter to transcribe the tripeptides and regulate blood sugar.

Variable Table

Name	Description
s	DescriptionSynthesis rate of QSP
δ	Degradation rate of QSP
R	Concentration of QSP
ξ	Amount of OmpC/OmpR that’s expressing peptides
Kon	Transcription factor activation coefficient
Koff	Dissociation rate of OmpR for the peptide DNA
φ	Concentration of the OmpC/OmpR complex
M	Concentration of peptide mRNA
Γ	Maximum transcription rate of mRNA
σ	Degradation rate of peptide mRNA
γ	Concentration of translated QSP
χ	Maximum translation rate of peptide
Ι	Concentration of incoming glucose
ζ	Concentration of outgoing glucose
Kin	Proportionality constant for the influx of glucose
EnvZAct	Concentration of Activated EnvZ
Kact	Proportionality constant for EnvZ phosphorylation
Z	Concentration of EnvZ-OmpR-P complex
OmpR	Concentration of OmpR
Kphosphorylated	Proportionality constant for the phosphorylation of OmpR
Koff	Proportionality constant for the dissociation of OmpR from EnvZ
ε	Concentration of cAMP bound to CRP
Con/Coff	Binding affinity of cAMP to CRP
v	Degradation rate of cAMP from CRP
P	Proportionality constant for glucose levels
ω	Concentration of TetR
Φ	Concentration of PTet
τ	Dissociation constant of TetR to Ptet
Y	Concentration of free TetR
cAMP-CRPdis	Concentration of unbound cAMP-CRP
cAMP-CRPbind	Concentration of bound cAMP-CRP
υ	Activation rate of TetR
T	Binding affinity of cAMP-CRPdis to the ABS
Ψ	Dissociation constant of cAMP-CRPdis to the ABS