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 | $nM^{-1} min^{-1}$ | - | 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
| 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 $k_{mNect}=0.1\cdot k_{GFP}$
Thanks to the sponsors that supported our project:
