B Tables of model species and parameters

B.1 Liquid culture model

Liquid culture model parameters3
Parameter Notation Value Units
Cell growth rate \(r_c\) \(2.6\times 10^{-4}\) second\(^{-1}\)
Density carrying capacity \(C_m\) 1 OD700
Synthase autodegradation \(\rho_s\) \(2\times 10^{-4}\) second\(^{-1}\)
Repressor autodegradation \(\rho_r\) \(8\times 10^{-6}\) second\(^{-1}\)
Synthase maximum expression \(x_S\) 389.2 \(\frac{a.u. }{\text{second OD700}}\)
Synthase AHL-activated Hill coefficient \(\lambda_S\) 2.3
Synthase AHL-activated IC50 \(K_S\) 126.4 nM
Synthase IPTG-activated Hill coefficient \(\lambda_I\) 1.4
Synthase IPTG-activated IC50 \(K_I\) 558 uM
Repressor maximum expression \(x_R\) 13.6 \(\frac{a.u. }{\text{second OD700}}\)
Repressor AHL-activated Hill coefficient \(\lambda_R\) 2.65
Repressor AHL-activated IC50 \(K_R\) 36.6 nM
Repressor-mediated inhibition Hill coefficient \(\lambda_C\) 2.3
Repressor-mediated inhibition IC50 \(K_C\) 11280 a.u. OD700\(^{-1}\)
AHL autodegradation \(\rho_A\) \(3\times 10^{-5}\) second\(^{-1}\)
Liquid culture model species
Species notation Units
Synthase \(S\) \(\frac{\text{a.u.}}{\text{OD700}}\)
Repressor \(R\) a.u. OD700\(^{-1}\)
Cell density \(c\) OD700
Intracellular AHL concentration \(A\) nM
Extracellular AHL concentration \(A_E\) nM
IPTG concentration \(I\) uM

B.2 Reaction-diffusion model

Table B.1: Model terms unique to the reaction-diffusion model4
Parameter Notation Value Units
Nutrient consumption rate \(\rho_n\) \(1.6\times10^{-2}\) second\(^{-1}\)
Nutrient Hill concentration \(K_n\) 68
Nutrient Hill coefficient \(\lambda_n\) 4
Sender cell synthase expression rate5 \(x_O\) 300 \(\frac{a.u. }{\text{second OD700}}\)
Sender cell synthase expression rate6 \(x_O\) 150 \(\frac{a.u. }{\text{second OD700}}\)
Amplifier cell synthase expression rate7 \(x_s\) 250 \(\frac{a.u. }{\text{second OD700}}\)
Synthase activity rate8 \(x_a\) \(2\times10^{-6}\) \(\frac{nM }{\text{second a.u.}}\)
Synthase activity rate9 \(x_a\) \(1\times10^{-7}\) \(\frac{nM}{\text{second a.u.}}\)
Nutrient diffusion rate \(D_n\) \(1.14\times 10^{-6}\) \(\frac{\text{mm}^2}{\text{second}}\)
AHL diffusion rate \(D_a\) \(2\times 10^{-4}\) \(\frac{\text{mm}^2}{\text{second}}\)

  1. Appendix A describes the parameter inference approach for the gene circuit parameters.↩︎

  2. Appendix C describes the parameter inference approach for the nutrient-based growth parameters.↩︎

  3. Out-of-plane diffusion model↩︎

  4. 2D model↩︎

  5. Calculated by applying agarose IPTG concentration, 1.5mM, to the IPTG-dependent Hill function from the liquid culture model↩︎

  6. Out-of-plane diffusion model↩︎

  7. 2D model↩︎