Project of Lead Biosensor
- Circuit Design
Project of Lead Biosensor
The brilliant advances in genetic engineering technologies based on proteins and non-coding small RNAs are enabling the systematic biological functions for both prokaryote and eukaryote. In this study, we utilize the mean field theory and the 4th Runge-Kutta method to mimic the engineering synthetic genetic circuits in Escherichia coli (E. coli), including the small RNA (sRNA) regulations and autoregulation circuits. For sRNA level in E. coli, the near simultaneously regulations that decrease (or increase) the target mRNA disable (enable) the target protein function. Therefore, the phase space for induction-regulation plays a key role and should be thoroughly investigated by simulations. In comparison with the sRNA level, the simulations and experimental methods based on the autoregulation circuit (Ptet-tetR) are designed to quantitatively describe the reporter protein or fluorescence response. The Hill coefficient is also checked to disclose the intrinsic properties of the autoregulation circuits in E. coli.
The introduction for genetic circuits
Negative regulation —Protein (repressor) inhibits transcription (Ex. LacI, TetR protein). Inducer– binds to repressor, alters form, reduces affinity for target, allows expression of gene. Sometimes, small molecule required for repressor activity.
Positive regulation —Activator protein increases transcription rate. Generally bound to a smaller signal molecule. (Ex. XylR protein activates Pu promoter).
sRNA-mediated gene silencing -(sRNA) are small (50-250 nucleotide) non-coding RNA molecules produced by bacteria; they are highly structured and contain several stem-loops. sRNAs can either bind to protein targets, and modify the function of the bound protein, or bind to mRNA targets and regulate gene expression. (Ex. RyhB and sodB)
Fig 1. Negative regulation: The TetR protein/Tc
Fig 2. Positive regulation :The XylR protein/Pu promoter
Fig 3. sRNA-mediated regulation: The RhyB-sodB RNA
Fig 4. The Constitutive expression: The Pcon-tetR
Fig 5.The repression-induction switch: The Ptet-tetR
Fig 6.The sRNA-mediated regulation circuit
Fig 7.The famous sRNA in E. coli
Circuit Design of Lead Biosensor
The introduction for binding constant
The dissociation constant K
Fig 8. The cartoon picture illustrating the the dissociation constant K and original of Hill coefficient n where n = 2.
The Hill coefficient n
Equation 1: The Hill equation: [R] as the concentration of reporter protein, [I] as the concentration of inducer and KM as the concentration of inducer when [R] reaches to the half of [Rmax]
Fig 9. The cartoon picture illustrating the the Hill coefficient n
The sRNA based genetic circuits
Fig 10.The complex designed regulation: The RhyB-sodB : w/o sodB
Fig 11.The complex designed regulation: The RhyB-sodB : w/ sodB
Fig 12.The sRNA-mediated regulation circuit
Equation 2: The mean field theory is used to describe the sRNA-mediated regulation circuit.
Equation 3: The steady state analysis for sRNA-mediated regulation circuit.
Equation 4: The approximation approach based on the certain condition of transcription rate
Fig 13. The Constitutive circuit and the related rate equations
A regular constitutive circuit contains multiple inducers and repressors with unidirectional regulations.
Fig 14. The Autoregulation circuit and the related rate equations
Constitutive PbrR circuit
Fig 15. Constitutive PbrR is used to measure the background expression of PbrR in E. Coli without any inducer
Fig 16. Autoregulation PbrR generator circuit: the generation of PbrR measured by GFP expression downstream and is under the control of TetR and promoter PTet
Equation 5: The fold analysis of Constitutive Circuit
Equation 6: The fold analysis of Autoregulation Circuit
Equation 7: The fold analysis of Autoregulatory and Constitutive circuits When [I] goes to 0, solve numerically.
The usage of our phase diagram can assist researchers to detect change under solution of different concentration and regulate the concentration of inducer.
Fig 17. The 2-D phase space for sRNA meediated circuit
Fig 18. The 3-D phase space for sRNA meediated circuit
Fig 19. The parameter relationship for circuits
Fig 20. Fold relationship for Autoregulatory and Constitutive circuits
 E. Levine, Z. Zhang, T. Kuhlman, T. Hwa, Quantitative Characteristics of Gene Regulation Mediated by small RNA, PLoS Biol 5 (2007) 1998-2010.
 David Braun et al. Parameter estimation for two synthetic gene networks: A case study. ICASSP (2005) 769-772.
 Timothy S. Gardner Charles R. Cantor & James J. Collins, Construction of a genetic toggle switch in Escherichia coli, Nature 403 (2000) 339-342.
 O. Scholz, P. Schubert, M. Kintrup and W. Hillen, Tet repressor induction without Mg2+, Biochemistry 39 (2000) 10914–10920.
 Peter Orth et al., Conformational changes of the Tet repressor induced by tetracycline trapping, J. Mol. Biol. 279 (1998) 439-447.
 Thomas A Geissmann and Daniele Touati, Hfq, a new chaperoning role: binding tomessenger RNA determines access for small RNA regulator, The EMBO J. 23 (2004) 396–405.
 Nicolae RaduZabet, Negative feedback and physical limits of genes, J. of Theoretical Biology 284 (2011) 82–91.