ESTIMATION METHODS

We used two different approaches for parameter estimation from experimental data:

MEIGO

MEIGO is an open source global optimization toolbox that provides several solvers for different applications. In our project we used the Cooperative enhanced Scatter Solver (CeSS) from the MATLAB version of the toolbox. Parameters were estimated by fitting ODE simulations to the experimental data using a least-square error function.

INSIGHT

INSIGHT is a parameter estimation method based on stochastic simulations and Approximate Bayesian computation (ABC). Parameters are estimated by minimizing the Kolmogorov distance between simulated and measured (through flow cytometry) distributions. This distance is defined as the tolerance of the fit, and is progressively reduced using Sequential Monte Carlo (SMC). The result is a posterior distribution of parameters that fit the data within a specific tolerance. As final value of the parameters we select the Maximum A Posteriori (MAP) estimates.

The estimations have been performed using the INSIGHTv3 implementation developed by Jan Mikelson. The tool is freely available online, but we highly encourage to check the website of our department, as a new improved version is expected to be published in the months after the Jamboree.

Parameter constant for the NO module

Name	Description	Unit	range values	value Estimation	method of Evaluation	Source
$knor_no$	NorR NOproduction rate	$nM^{-1} min^{-1}$	-	0,0011183	MEIGO from plate reader	Computed from parameter estimation
$k_{nor_no}$	NorR NOdissociation rate	$min^{-1}$	-	0,0363665	MEIGO from plate reader	Computed from parameter estimation
$knorV1$	DNorR NO2binding rate	$nM^{-1} min^{-1}$	-	0,0014788	MEIGO from plate reader	Computed from parameter estimation
$k_norV1$	DNorR NO2unbinding rate	$min^{-1}$	-	0,00081	MEIGO from plate reader	Computed from parameter estimation
$knorV2$	DNorR NO2binding rate	$nM^{-1} min^{-1}$	-	0,00185016	MEIGO from plate reader	Computed from parameter estimation
$k_norV2$	DNorR NO2unbinding rate	$min^{-1}$	-	7.1	MEIGO from plate reader	Computed from parameter estimation
$knorV3$	DNorR NO2binding rate	$nM^{-1} min^{-1}$	-	0,986026	MEIGO from plate reader	Computed from parameter estimation
$k_norV3$	DNorR NO2unbinding rate	$min^{-1}$	-	6.1	MEIGO from plate reader	Computed from parameter estimation
$knorprod$	NorR constitutive production rate	$nM min^{-1}$	-	0,958777	MEIGO from plate reader	Computed from parameter estimation
$dnor$	NorR degradation rate	$min^{-1}$	-	89,159	MEIGO from plate reader	Computed from parameter estimation
$d_{nor_no}$	NorR NOdegradation rate	$min^{-1}$	-	46,678	MEIGO from plate reader	Computed from parameter estimation
$kdnor$	DNorR dimerization constant	$nM^{-1} min^{-1}$	-	75698,5	MEIGO from plate reader	Computed from parameter estimation
$k_dnor$	DNorR dissociation rate	$min^{-1}$	-	1,91699	MEIGO from plate reader	Computed from parameter estimation
$kmrna$	mRNA production rate for pnorV promoter	$min^{-1}$	-	3438,47	MEIGO from plate reader	Computed from parameter estimation
$dmrna$	mRNA degradation rate	$min^{-1}$	-	0,0199458	MEIGO from plate reader	Computed from parameter estimation

Parameter constant for the AHL module

Name	Description	Unit	range values	value Estimation	method of Evaluation	Source
$kesarProd$	EsaR constitutive production rate	$nM min^{-1}$	-	3,24412	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$desar$	DEsaR degradation rate	$min^{-1}$	-	0,0152529	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$kl$	promoter leakiness	-	-	0,00242729	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k5$	DEsaR production rate	$nM^{-1} min^{-1}$	-	0,01	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k_5$	DEsaR dissociation rate	$min^{-1}$	-	0,65492	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k6$	DEsaR AHL production rate	$nM^{-1} min^{-1}$	-	0,0100102	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k_6$	DEsaR AHL dissociation rate	$min^{-1}$	-	0,719465	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k7$	AHL to Pesar promoter binding rate	$nM^{-1} min^{-1}$	-	0,4878	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$k_7$	AHL to Pesar promoter unbinding rate	$min^{-1}$	-	0,0383841	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$kmrna$	mRNA production rate for Pconst+esaboxes promoter	$min^{-1}$	-	0,0121775	Estimation from FACS Data using MEIGO	Computed from parameter estimation
$dmrna$	mRNA degradation rate	$min^{-1}$	-	0,0142082	Estimation from FACS Data using MEIGO	Computed from parameter estimation

Parameter constant for the AHL module

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Name	Description	Unit	range values	value Estimation	method of Evaluation	Source
$klac_{pyr}$	NorR NOpyruvate production rate from lactate	$min^{-1}$	-	1.2 e+05	Literature	click on this link to see the publication
$kdlldr$	LLdR dimerization rate	$nM^{-1} min^{-1}$	-	0.1	Estimated	-
$k_{dlldr}$	LLdR dissociation rate	$min^{-1}$	-	1	Estimated	-
$kgoff$	binding of LldR to the promoter (represion)	$nM^{-1} min^{-1}$	-	0.1	Estimated	-
$k_{goff}$	Unbinding of LldR from the promoter (activation)	$min^{-1}$	-	8.1	Estimated	-
$kdlldr_{lac}$	binding of 1 Lac protein to DLldR	$nM^{-1}min^{-1}$	-	0.1	Estimated	-
$k_{dlldr_lac}$	unbinding of 1 Lac protein from DLldR	$min^{-1}$	-	6.1	Estimated	-
$kgoff_{lac}$	binding of 1 Lac protein to the promoter + DLldR dimer	$nM^{-1} min^{-1}$	-	0.1	Estimated	-
$k_{goff_lac}$	ubinding of 1 Lac protein to the promoter + DLldR dimer	$min^{-1}$	-	6.1	Estimated	-
$dlld$	degradation rate of LldD	$min^{-1}$	-	0.1	Estimated	-
$kllddProd$	production rate of LldD	$nM min^{-1}$	-	1	Estimated	-
$klldrProd$	production rate of LldR	$nM min^{-1}$	-	100	Estimated	-
$kl$	leakiness of the promoter	-	-	0.1	Estimated	-

REPORTER MODULE PARAMETERS

Name	Description	Unit	Prior range	Value	Source
$k_{DBxb1}$	Bxb1 dimerization rate	$nM^{-1}min^{-1}$	-	1	Assumed
$k_{-DBxb1}$	DBxb1 dissociation rate	$min^{-1}$	-	10	Assumed
$k_{attBP}$	Affinity of DBxb1 to attB and attP binding sites	$nM^{-1}$	-	70	doi:10.1371/journal.pgen.1003490
$k_{attLR}$	Affinity of DBxb1 to attL and attR binding sites	$nM^{-1}$	-	15	doi:10.1371/journal.pgen.1003490
$k_{flip}$	Switch flipping rate	$min^{-1}$	-	0.04	doi:10.1046/j.1365-2958.2003.03723.x

REPORTER MODULE PARAMETERS

Name	Description	Unit	Prior range	Value	Source
$l_{pTet}$	Tet promoter leakiness	$-$	0.0 - 0.5	0.057	Estimated with INSIGHT
$n$	Sensitivity of the tet promoter	$-$	0.8 - 2.8	1.57	Estimated with INSIGHT
$K_m$	aTc concentration for half occupation	$nM$	10 - 15000	9853.6	Estimated with INSIGHT
$k_{mRNAgfp}$	sfGFP mRNA transcription rate	$min^{-1}$	0.001 - 10	0.382	Estimated with INSIGHT
$d_{mRNAgfp}$	sfGFP mRNA degradation rate	$min^{-1}$	0.05 - 20	8.93	Estimated with INSIGHT
$k_{GFP}$	sfGFP translation rate	$min^{-1}$	0.00005 - 0.5	0.012	Estimated with INSIGHT
$d_{GFP}$	sfGFP degradation rate	$min^{-1}$	0.0001 - 0.1	0.018	Estimated with INSIGHT

Parameters for mNectarine ($k_{mRNAmnect}$, $d_{mRNAmnect}$, $d_{mNect}$) are assumed to be on the same order of magnitude as the parameters for sfGFP. Since sfGFP is engineered for faster folding, we assume $k_{mNect}=0.1\cdot k_{GFP}$