Parameters
No model is complete without parameters. Our exhaustive list of parameters are summarised in the table below.
Parameter | Value | Description | Reference |
---|---|---|---|
α_{LuxR} | 0.005 μMmin^{-1} | Production rate of LuxR | Literature ^{[20]} |
k_{RLux} | 0.1 nM^{-1}min^{-1} | Rate of formation of RLux from LuxAHL and LuxR | Literature ^{[19]} |
k_{-RLux} | 10 min^{-1} | Dissociation rate of RLux | Literature ^{[19]} |
K_{mLux} | 10 nM | Lumped parameter for the Lux system | Fitted to experimental data |
d_{LuxAHL} | 0.004 min^{-1} | External degradation rate of LuxAHL (30C6HSL) | Fitted |
d_{LuxR} | 0.0231 min^{-1} | Degradation rate of LuxR | Literature ^{[21]} |
d_{RLux} | 0.0231 min^{-1} | Degradation rate of RLux | Literature ^{[20]} |
d_{mRNABxb1} | 0.2773 min^{-1} | Degradation rate of mRNA_{Bxb1} | Literature ^{[22]} |
d_{Bxb1} | 0.01 min^{-1} | Degradation rate of Bxb1 | Assumed |
L_{PLux} | 0.01463 nMmin^{-1} | Leakiness after using riboswitch for P_{lux} | Fitted to experimental data |
K_{mRNABxb1} | 5 nMmin^{-1} | Rate of transcription of Bxb1 | Estimated |
k_{Bxb1} | 0.1 min^{-1} | Rate of formation of Bxb1 | Assumed |
α_{LasR} | 0.005 μMmin^{-1} | Production rate of LasR | Literature ^{[20]}(Assumed to be the same as Lux system) |
k_{RLas} | 0.1 nM^{-1}min^{-1} | Rate of formation of RLas from LasAHL and LasR | Literature ^{[19]}(Assumed to be the same as Lux system) |
k_{-RLas} | 10 min^{-1} | Dissociation rate of RLas | Literature ^{[19]}(Assumed to be the same as Lux system) |
K_{mLas} | 0.45 nM | Lumped parameter for the Las system | Fitted to experimental data |
d_{LasAHL} | 0.004 min^{-1} | Degradation rate of LasAHL (30C12HSL) | Fitted to experimental data |
d_{LasR} | 0.0231 min^{-1} | Degradation rate of LasR | Literature ^{[21]} (Assumed to be the same as Lux system) |
d_{RLas} | 0.0231 min^{-1} | Degradation rate of RLas | Literature ^{[20]} (Assumed to be the same as
Lux system) |
d_{mRNAϕc31} | 0.2773 min^{-1} | Degradation rate of mRNA_{ϕc31} | Literature ^{[22]} |
d_{ϕc31} | 0.01 min^{-1} | Degradation rate of ϕC31 | Assumed |
L_{PLas} | 0.02461 nMmin^{-1} | Leakiness after using riboswitch for P_{las} | Fitted to experimental data |
K_{mRNAϕc31} | 5 nMmin^{-1} | Rate of transcription of ϕc31 | Estimated |
k_{ϕc31} | 0.1 min^{-1} | Rate of formation of ϕc31 | Assumed |
k_{DBxb1} | 1 nM^{-1}min^{-1} | Dimerization rate of Bxb1 | Fitted |
k_{-DBxb1} | 10^{-6} min^{-1} | Dissociation rate of DBxb1 | Fitted |
k_{SABxb1} | 1 nM^{-1}min^{-1} | Rate of formation of SA_{Bxb1} from DBxb1 and SI_{Bxb1} | Fitted |
k_{-SABxb1} | 10^{-6} min^{-1} | Dissociation rate of SA_{Bxb1} | Fitted |
d_{DBxb1} | 0.02 min^{-1} | Degradation rate of DBxb1 | Assumed |
k_{Dϕc31} | 1 nM^{-1}min^{-1} | Dimerization rate of ϕc31 | Fitted |
k_{-Dϕc31} | 10^{-6} min^{-1} | Rate of dissociation of Dϕc31 | Fitted |
k_{SAϕc31} | 1 nM^{-1}min^{-1} | Rate of formation of SA_{ϕc31} from Dϕc31 and SI_{ϕc31} | Fitted |
k_{-SAϕc31} | 10^{-6} min^{-1} | Rate of dissociation of SA_{ϕc31} | Fitted |
d_{Dϕc31} | 0.02 min^{-1} | Degradation rate of Dϕc31 | Assumed |
k_{ToffBxb1} | 0.1 nM^{-2}min^{-1} | Rate of flipping of T_{on,i} to T_{offBxb1} | Assumed |
k_{-ToffBxb1} | 0.1 nM^{-2}min^{-1} | Rate of flipping of T_{offBxb1} to T_{on,f} | Assumed |
k_{Toffϕc31} | 0.1 nM^{-2}min^{-1} | Rate of flipping of T_{on,i} to T_{offϕc31} | Assumed |
k_{-Toffϕc31} | 0.1 nM^{-2}min^{-1} | Rate of flipping of T_{offϕc31} to T_{on,f} | Assumed |
k_{mRNAGFP} | 5 nMmin^{-1} | Production rate of mRNA_{GFP} | Estimated |
k_{GFP} | 1 min^{-1} | Rate of formation of folded GFP | Estimated |
d_{mRNAGFP} | 0.2773 min^{-1} | Degradation rate of mRNA_{GFP} | Literature ^{[22]} |
d_{GFP} | 0.0049 min^{-1} | Degradation rate of GFP | Fitted to experimental data |
k_{mRNALasI} | 5 nMmin^{-1} | Production rate of mRNA_{LasI} | Estimated |
k_{LasI} | 20 min^{-1} | Rate of formation of LasI | Estimated |
d_{mRNALasI} | 0.2773 min^{-1} | Degradation rate of mRNA_{LasI} | Literature ^{[22]} |
d_{LasI} | 0.0167 min^{-1} | Degradation rate of LasI | Literature ^{[21]} |
k_{LasAHL} | 0.04 min^{-1} | Production rate of LasAHL (30C12HSL) from the LasI | Literature ^{[19]} |
θ | 0.01 μM | K_{m} value for the production of mRNA_{GFP} and mRNA_{LasI} | Literature ^{[20]} (approximation) |
D_{AHLext} | 4.9 10^{-6} cm^{2}/s | Diffusion coefficient of extracellular AHL in liquid | Literature ^{[27]} |
D_{m} | 100 min^{-1} | Diffusion rate of AHL through the membrane | Estimated from literature ^{[27]} |
r | 0.006 min^{-1} | Growth rate of E. coli in our alginate beads | |
α | 100 min^{-1} | Ratio of E. coli volume to the volume of one bead | V_{ E. coli} from literature ^{[28]}, bead volume from experimental setup |
N_{0} | 10^{7} cells | Initial number of cells per bead | Experimental setup |
N_{m} | 8 10^{7} cells | Maximum number of cells per bead | Estimated from literature ^{ [29]} |
C_{beads} | 1 | Correction factor (a priori) for diffusion of LuxAHL in alginate beads | Estimated from literature ^{ [30]} |