"

From 2013hs.igem.org

Parameters and variables

Our gene circuit is made of six different variables: the concentrations of three proteins (cI, VIP and GFP) and their respective mRNA inside a cell. In table 1, the symbols for each variable are shown. Proteins are represented by a single letter and their mRNAs are represented by that same letter with a lowercase "m" before it.

Table 1.- Variables

Symbol	Definition	Gene size in bp	Source
mC, C	Transcription factor cI (mRNA and protein)	775	<a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051">http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051</a>
mV, V	Insecticide protein VIP (mRNA and protein)	2412	<a href="http://www.ncbi.nlm.nih.gov/nuccore/HQ876489">http://www.ncbi.nlm.nih.gov/nuccore/HQ876489</a>
mG, G	Reporter protein GFP (mRNA and protein)	876	<a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240">http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240</a>

To parameterize our model, we chose to follow the approach of team Beijing 2009; they propose a relationship between the gene length in base pairs and the maximum transcription rate and, similarly, between the protein length in amino acid numbers and the maximum translation rate. Assuming that the number of polymerases and ribosomes are the average values determined for E. coli, the following equations are used:

Parameters

Symbol	Definition	Values	Formula	Source
α1	Transcription rate of cI	5.6	4200/Gene Length (nM/min)	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
α2	Translation rate of cI	9.6	2400RBS/Protein Length	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
α3	Transcription rate of VIP	1.74129353	4200/Gene Length (nM/min)	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
α4	Translation rate of VIP	2.985075	2400RBS/Protein Length	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
α5	Transcription rate of GFP	5.53359684	4200/Gene Length (nM/min)	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
α6	Translation rate of GFP	9.486166	2400RBS/Protein Length	<a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>

For all the variables the degradation rate is expressed by the formula (ln(2)/half life)+(ln(2)/division time), with the same division time of e. coli (30 min), because all the process occurs within it. The only thing that change is the half time; for cI, VIP and GFP (mRNA) is 6.8 minutes and for cI (Selinger, GW, et al., 2003), VIP and GFP protein is more than 10 hours (Varshavsky, (1997) and Tobias et al., 1991).

Degradation

Symbol	Definition	Values	Formula	Source
μ1μ3,μ5,	Degradation rate of cI (mRNA	0.18063836	Half life = 6.8 min, Division time = 30 min	(Selinger, GW, et al., 2003)
μ2,μ4,μ6	Degradation rate of cI (protein)	0.03885825	Half life > 10 h; division time = 30 min	(Varshavsky, (1997) and Tobias et al., 1991)