# Team:Slovenia/ModelingMutualRepressorSwitch

### From 2012.igem.org

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+ | <h2>The model</h2> | ||

+ | <p> | ||

+ | We can describe the relations for the mutual repressor switch by the following equations. Fractional occupancies of promoters are: | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/7/71/Svn12_mrs_det_f1.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/d/d3/Svn12_mrs_det_f2.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/a/a3/Svn12_mrs_det_f3.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/3/3d/Svn12_mrs_det_f4.png"/></p> | ||

+ | |||

+ | where: | ||

+ | <ul style="margin-left:30px;"> | ||

+ | <li>f<sub>1</sub>, f<sub>2</sub>, f<sub>3</sub> and f<sub>4</sub> are probabilities of promoters 1 (construct 1), 2 (construct 2), 3 (construct 3) and 4 (construct 4), respectively, being in an active state, resulting in gene expression;</li> | ||

+ | <li>[TAL-A:KRAB], [TAL-B:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations at a given time;</li> | ||

+ | <li>k<sub>1</sub>, k<sub>2</sub>, k<sub>3</sub> and k<sub>4</sub> are association constants;</li> | ||

+ | <li>n<sub>1</sub>, n<sub>2</sub>, n<sub>3</sub> and n<sub>4</sub> are exponents representing the degree of functional cooperativity;</li> | ||

+ | <li>K<sub>r</sub> is the amount of repressor required for 50% repression of constitutive promoter (equal to 1 in our simulations);</li> | ||

+ | </ul> | ||

+ | |||

+ | </p> | ||

+ | |||

+ | |||

+ | <p> | ||

+ | ODEs representing protein production are described by a set of equations: | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/0/09/Svn12_mrs_det_d1_bfp.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/7/74/Svn12_mrs_det_d2_mcit.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/a/ae/Svn12_mrs_det_d4_talakrab.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/a/a6/Svn12_mrs_det_d3_talbkrab.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/b/bf/Svn12_mrs_det_dpip_mrs_new.png"/></p> | ||

+ | <p><img src="https://static.igem.org/mediawiki/2012/6/65/Svn12_mrs_det_dekrab.png"/></p> | ||

+ | </p> | ||

## Revision as of 20:21, 25 September 2012

# Modeling - mutual repressor switch

**Deterministic model**- Stochastic model
- C#Sim model

# Deterministic model of the mutual repressor switch

Deterministic analysis demonstrated that while theoretical conditions under which the mutual repressor switch would exhibit bistability exist, they are unlikely to occur in a realistic experimental setting. This was because: - high transcription factor cooperativity of value 2 or above was required for high-level bistability;
- even for high cooperativity values, the switch was highly intolerant to even very low leaky gene expression, which is always present to a certain extent in an actual cellular environment.
Increase in cooperativity lead to more robust behavior – higher expression levels of stable states were reached and higher – but still low - tolerance to leaky expression was observed. Experimental results confirmed that the mutual repressor switch did not exhibit bistability. |

## The model

We can describe the relations for the mutual repressor switch by the following equations. Fractional occupancies of promoters are:

where:- f
_{1}, f_{2}, f_{3}and f_{4}are probabilities of promoters 1 (construct 1), 2 (construct 2), 3 (construct 3) and 4 (construct 4), respectively, being in an active state, resulting in gene expression; - [TAL-A:KRAB], [TAL-B:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations at a given time;
- k
_{1}, k_{2}, k_{3}and k_{4}are association constants; - n
_{1}, n_{2}, n_{3}and n_{4}are exponents representing the degree of functional cooperativity; - K
_{r}is the amount of repressor required for 50% repression of constitutive promoter (equal to 1 in our simulations);

ODEs representing protein production are described by a set of equations:

**Next: Stochastic model of the mutual repressor switch >>**