Parameters and Tools

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^-1min^-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^-1min^-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^-1min^-1	Dimerization rate of Bxb1	Fitted
k_-DBxb1	10^-6 min^-1	Dissociation rate of DBxb1	Fitted
k_SABxb1	1 nM^-1min^-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^-1min^-1	Dimerization rate of ϕc31	Fitted
k_-Dϕc31	10^-6 min^-1	Rate of dissociation of Dϕc31	Fitted
k_SAϕc31	1 nM^-1min^-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^-2min^-1	Rate of flipping of T_on,i to T_offBxb1	Assumed
k_-ToffBxb1	0.1 nM^-2min^-1	Rate of flipping of T_offBxb1 to T_on,f	Assumed
k_Toffϕc31	0.1 nM^-2min^-1	Rate of flipping of T_on,i to T_offϕc31	Assumed
k_-Toffϕc31	0.1 nM^-2min^-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 cm²/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
N₀	10⁷ cells	Initial number of cells per bead	Experimental setup
N_m	8 10⁸ 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]
DF	1e-5	Dilution factor	Assumed	} Tools We used the following tools for modelling and simulation: MATLAB version 8.3.0.532 (R2014a). Natick, Massachusetts: The MathWorks Inc., 2014. for deterministic model, curve fitting and parameter estimation. COMSOL Multiphysics software Version 4.4.0.248, COMSOL Ltd, 2014, for diffusion model and simulation. MEIGO Toolbox for parameter estimation.^[26] We thank our sponsors:

Team:ETH Zurich/modeling/parameters

From 2014.igem.org

Parameters

Tools