Team:ETH Zurich/Parameters

PARAMETERS

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-1min-1 - 0,0011183 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$k_{nor_no}$ NorR NOdissociation rate min-1 - 0,0363665 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$knorV1$ DNorR NO2binding rate nM-1min-1 - 0,0014788 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$k_norV1$ DNorR NO2unbinding rate min-1 - 0,00081 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$knorV2$ DNorR NO2binding rate nM-1min-1 - 0,00185016 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$k_norV2$ DNorR NO2unbinding rate min-1 - 7.1 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$knorV3$ DNorR NO2binding rate nM-1min-1 - 0,986026 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$k_norV3$ DNorR NO2unbinding rate min-1 - 6.1 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$knorprod$ NorR constitutive production rate nM min-1 - 0,958777 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$dnor$ NorR degradation rate min-1 - 89,159 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$d_{nor_no}$ NorR NOdegradation rate min-1 - 46,678 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$kdnor$ DNorR dimerization constant nM-1min-1 - 75698,5 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$k_dnor$ DNorR dissociation rate min-1 - 1,91699 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$kmrna$ mRNA production rate for pnorV promoter min-1 - 3438,47 MEIGO metaheuristic evaluation from plate reader Computed from parameter estimation
$dmrna$ mRNA degradation rate min-1 - 0,0199458 MEIGO metaheuristic evaluation 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-1min-1 - 0,01 Estimation from FACS Data using MEIGO Computed from parameter estimation
$k_5$ DEsaR dissociation rate min-1 - 0 0,65492 Estimation from FACS Data using MEIGO Computed from parameter estimation
$k6$ DEsaR AHL production rate nM-1min-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-1min-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-1min-1 - 0.1 Estimated -
$k_{dlldr}$ LLdR dissociation rate min-1 - 1 Estimated -
$kgoff$ binding of LldR to the promoter (represion) nM-1min-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-1min-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-1min-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 -
$klldrProd$ DNorR dissociation 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 $k_{mNect}=0.1\cdot k_{GFP}$

Thanks to the sponsors that supported our project: