# Team:NTU-Taida/Modeling/Parameters

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+ - }} + + ==Single-Cell/ System analysis Model== + + +
Parameter Description  Value  Reference
+ + + + + + + + +
$$\alpha_{TetR}$$ TetR max. production rate $$0.8~\mu \text{M}\cdot\text{min}^{-1}$$ [5]
$$\alpha_{FadR}$$ FadR max. production rate $$100~\mu\text{M}\cdot\text{min}^{-1}$$ a.
$$\alpha_{GLP-1}$$ GLP-1 max. production rate $$1.23~\mu\text{M}\cdot\text{min}^{-1}$$ a.
$$\alpha_{LacI}$$ LacI max. production rate $$0.8~\mu\text{M}\cdot\text{min}^{-1}$$ [1]
$$k_{s1}$$ AHL i production rate $$0.01~\text{min}^{-1}$$ [2]
$$\rho_R$$ LuxR-AHL dimerization rate $$0.5~\mu\text{M}^{-3}\cdot \text{min}^{-1}$$ [1]
$$\beta_{TetR}$$ TetR repression coefficient $$0.13~\mu\text{M}$$ a.
$$\beta_{FA}$$ FA repression coefficient $$10~\mu\text{M}$$ [1]
$$\beta_{FadR}$$ FadR repression coefficient $$0.13~\mu\text{M}$$ [1]
$$\beta_{LacI}$$ LacI repression coefficient $$0.8~\mu\text{M}$$ [1]
$$\beta_R$$ LuxR-AHL repression coefficient $$0.01~\mu\text{M}$$ [1]
$$\gamma_{TetR}$$ TetR degradation rate $$0.0692~\text{min}^{-1}$$ a.
$$\gamma_{LacI}$$ LacI degradation rate $$0.0231~\text{min}^{-1}$$ [1]
$$\gamma_{GLP-1}$$ GLP-1 degradation rate $$0.0731~\text{min}^{-1}$$ [1]
$$\gamma_{LuxI}$$ LuxI degradation rate $$0.0167~\text{min}^{-1}$$ [3]
$$k_{s0}$$ AHLi degradation rate $$1~\text{min}^{-1}$$ [2]
$$k_{se}$$ AHLe degradation rate $$1~\text{min}^{-1}$$ [2]
$$\gamma_R$$ LuxR-AHL degradation rate $$0.0231~\text{min}^{-1}$$ [1]
$$\gamma_{RFP}$$ RFP degradation rate $$0.0041~\text{min}^{-1}$$ [4]
$$n_1$$ FadR cooperativity coefficient $$3$$ a.
$$n_2$$ FA cooperativity coefficient $$2$$ a.
$$n_3$$ LuxR-AHL cooperativity coefficient $$3$$ [1]
$$n_5$$ TetR cooperativity coefficient $$2$$ [2]
$$n_6$$ LacI cooperativity coefficient $$4$$ [1]
$$\eta$$ AHL Diffusion rate across the cell membrane $$2$$ [2]
$$\eta$$ext Average diffusion rate for all cells $$1$$ [2]
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ==Fatty Acid Reaction Absorption Model== + + + +
Parameter Description Value Reference
+ + + + + + + +
$$[E]_t$$ Total active enzyme $$50~\text{U}\text{mL}^{-1}$$ [8][10][11]
$$K_m$$ Reaction rate constant $$47.9$$ [6][7]
$$D_{FA}$$ FA Diffusion Constant $$6.46 \times 10^{-10}~\text{m}^2\text{s}^{-1}$$ [9]
$$d$$ Thickness of the unstirred water layer $$190~\mu\text{m}$$ [9]
$$K_{cat}$$ Catalytic Rate constant $$1.3\times10^{-5}\text{min}^{-1}$$ [6][7]
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ==Cell-Cell Communication Model== + + + +
Parameter Description Value Reference
+ + + + + + + +
$$cd$$ Relative E. coli Cell Density $$0.1$$
$$D_{FA}$$ FA Diffusion Constant $$6.46 \times 10^{-10}\text{m}^2\text{s}^{-1}$$ [9]
$$D_{AHL}$$ AHL Diffusion Constant $$4.9\times10^{-6}~\text{cm}^2\text{s}^{-1}$$ [9]
$$\gamma_{AHL,ext}$$ AHL cell-external degradation $$8.0225\times10^{6}~\text{s}^{-1}$$ Derived from 1 day half-life at pH 7 [7]
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ==Reference== + + + [1] Subhayu Basu, Yoram Gerchman, Cynthia H. Collins, Frances H. Arnold & Ron Weiss.A synthetic multicellular system for programmed pattern formation, Nature Vol. 434, 2005
+ [2] Garcia-Ojalvo, Michael B. Elowitz, and Steven H. Strogatz. Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, PNAS vol. 101 no. 30, 2004
+ [3] MIT igem 2010
+ [4] Michael Halter, Alex Tona, Kiran Bhadriraju, Anne L. Plant, John T. Elliott, Automated Live Cell Imaging of Green Fluorescent Protein Degradation in Individual Fibroblasts, Cytometry Part A, Volume 71A Issue 10, 2007
+ [5] Wilfried Weber, Markus Rimann, Manuela Spielmann, Bettina Keller, Marie Daoud-El Baba, Dominique Aubel, Cornelia C Weber & Martin Fussenegger, Gas-inducible transgene expression in mammalian cells and mice, Nature Biotechnology, volume 22, number 11, 2004
+ [6] Sulaiman Al-Zuhair, Masitah Hasan, K.B. Ramachandran, Kinetics of the enzymatic hydrolysis of palm oil by lipase, Process Biochemistry Volume 38, Issue 8, 2003
+ [7] Ho-Shing Wu, Ming-Ju Tsai, Kinetics of tributyrin hydrolysis by lipase, Enzyme and Microbial Technology, Volume 35, Issues 6–7, 2004
+ [8] Bengt Borgstrom, Luminal Digestion of Fats, Handbook of Physiology, The Gastrointestinal System, Intestinal Absorption and Secretion, 1991
+ [9] Sallee VL, Dietschy JM., Determinants of intestinal mucosal uptake of short- and medium-chain fatty acids and alcohols, Journal of Lipid Research, 1973
+ [10] J Keller, P Layer, Human pancreatic exocrine response to nutrients in health and disease, Gut, 2005
+ [11] M Lingumsky, E Granot, D Branski, H Stankiewicz, R Goldstein, Isolated lipase and colipase deficiency in two brothers, Gut, 1990
+ {{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Parameters}} {{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Parameters}}

# Parameters

## Single-Cell/ System analysis Model

 Parameter Description Value Reference $$\alpha_{TetR}$$ TetR max. production rate $$0.8~\mu \text{M}\cdot\text{min}^{-1}$$ [5] $$\alpha_{FadR}$$ FadR max. production rate $$100~\mu\text{M}\cdot\text{min}^{-1}$$ a. $$\alpha_{GLP-1}$$ GLP-1 max. production rate $$1.23~\mu\text{M}\cdot\text{min}^{-1}$$ a. $$\alpha_{LacI}$$ LacI max. production rate $$0.8~\mu\text{M}\cdot\text{min}^{-1}$$ [1] $$k_{s1}$$ AHL i production rate $$0.01~\text{min}^{-1}$$ [2] $$\rho_R$$ LuxR-AHL dimerization rate $$0.5~\mu\text{M}^{-3}\cdot \text{min}^{-1}$$ [1] $$\beta_{TetR}$$ TetR repression coefficient $$0.13~\mu\text{M}$$ a. $$\beta_{FA}$$ FA repression coefficient $$10~\mu\text{M}$$ [1] $$\beta_{FadR}$$ FadR repression coefficient $$0.13~\mu\text{M}$$ [1] $$\beta_{LacI}$$ LacI repression coefficient $$0.8~\mu\text{M}$$ [1] $$\beta_R$$ LuxR-AHL repression coefficient $$0.01~\mu\text{M}$$ [1] $$\gamma_{TetR}$$ TetR degradation rate $$0.0692~\text{min}^{-1}$$ a. $$\gamma_{LacI}$$ LacI degradation rate $$0.0231~\text{min}^{-1}$$ [1] $$\gamma_{GLP-1}$$ GLP-1 degradation rate $$0.0731~\text{min}^{-1}$$ [1] $$\gamma_{LuxI}$$ LuxI degradation rate $$0.0167~\text{min}^{-1}$$ [3] $$k_{s0}$$ AHLi degradation rate $$1~\text{min}^{-1}$$ [2] $$k_{se}$$ AHLe degradation rate $$1~\text{min}^{-1}$$ [2] $$\gamma_R$$ LuxR-AHL degradation rate $$0.0231~\text{min}^{-1}$$ [1] $$\gamma_{RFP}$$ RFP degradation rate $$0.0041~\text{min}^{-1}$$ [4] $$n_1$$ FadR cooperativity coefficient $$3$$ a. $$n_2$$ FA cooperativity coefficient $$2$$ a. $$n_3$$ LuxR-AHL cooperativity coefficient $$3$$ [1] $$n_5$$ TetR cooperativity coefficient $$2$$ [2] $$n_6$$ LacI cooperativity coefficient $$4$$ [1] $$\eta$$ AHL Diffusion rate across the cell membrane $$2$$ [2] $$\eta$$ext Average diffusion rate for all cells $$1$$ [2]

## Fatty Acid Reaction Absorption Model

 Parameter Description Value Reference $$[E]_t$$ Total active enzyme $$50~\text{U}\text{mL}^{-1}$$ [8][10][11] $$K_m$$ Reaction rate constant $$47.9$$ [6][7] $$D_{FA}$$ FA Diffusion Constant $$6.46 \times 10^{-10}~\text{m}^2\text{s}^{-1}$$ [9] $$d$$ Thickness of the unstirred water layer $$190~\mu\text{m}$$ [9] $$K_{cat}$$ Catalytic Rate constant $$1.3\times10^{-5}\text{min}^{-1}$$ [6][7]

## Cell-Cell Communication Model

 Parameter Description Value Reference $$cd$$ Relative E. coli Cell Density $$0.1$$ $$D_{FA}$$ FA Diffusion Constant $$6.46 \times 10^{-10}\text{m}^2\text{s}^{-1}$$ [9] $$D_{AHL}$$ AHL Diffusion Constant $$4.9\times10^{-6}~\text{cm}^2\text{s}^{-1}$$ [9] $$\gamma_{AHL,ext}$$ AHL cell-external degradation $$8.0225\times10^{6}~\text{s}^{-1}$$ Derived from 1 day half-life at pH 7 [7]

## Reference

[1] Subhayu Basu, Yoram Gerchman, Cynthia H. Collins, Frances H. Arnold & Ron Weiss.A synthetic multicellular system for programmed pattern formation, Nature Vol. 434, 2005
[2] Garcia-Ojalvo, Michael B. Elowitz, and Steven H. Strogatz. Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, PNAS vol. 101 no. 30, 2004
[3] MIT igem 2010
[4] Michael Halter, Alex Tona, Kiran Bhadriraju, Anne L. Plant, John T. Elliott, Automated Live Cell Imaging of Green Fluorescent Protein Degradation in Individual Fibroblasts, Cytometry Part A, Volume 71A Issue 10, 2007
[5] Wilfried Weber, Markus Rimann, Manuela Spielmann, Bettina Keller, Marie Daoud-El Baba, Dominique Aubel, Cornelia C Weber & Martin Fussenegger, Gas-inducible transgene expression in mammalian cells and mice, Nature Biotechnology, volume 22, number 11, 2004
[6] Sulaiman Al-Zuhair, Masitah Hasan, K.B. Ramachandran, Kinetics of the enzymatic hydrolysis of palm oil by lipase, Process Biochemistry Volume 38, Issue 8, 2003
[7] Ho-Shing Wu, Ming-Ju Tsai, Kinetics of tributyrin hydrolysis by lipase, Enzyme and Microbial Technology, Volume 35, Issues 6–7, 2004
[8] Bengt Borgstrom, Luminal Digestion of Fats, Handbook of Physiology, The Gastrointestinal System, Intestinal Absorption and Secretion, 1991
[9] Sallee VL, Dietschy JM., Determinants of intestinal mucosal uptake of short- and medium-chain fatty acids and alcohols, Journal of Lipid Research, 1973
[10] J Keller, P Layer, Human pancreatic exocrine response to nutrients in health and disease, Gut, 2005
[11] M Lingumsky, E Granot, D Branski, H Stankiewicz, R Goldstein, Isolated lipase and colipase deficiency in two brothers, Gut, 1990