Team:Slovenia/ModelingMutualRepressorSwitch

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<h2>The model</h2>
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<p>
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We can describe the relations for the mutual repressor switch by the following equations. Fractional occupancies of promoters are:
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<p><img src="https://static.igem.org/mediawiki/2012/7/71/Svn12_mrs_det_f1.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/d/d3/Svn12_mrs_det_f2.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/a/a3/Svn12_mrs_det_f3.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/3/3d/Svn12_mrs_det_f4.png"/></p>
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where:
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<ul style="margin-left:30px;">
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<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>
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<li>[TAL-A:KRAB], [TAL-B:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations at a given time;</li>
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<li>k<sub>1</sub>, k<sub>2</sub>, k<sub>3</sub> and k<sub>4</sub> are association constants;</li>
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<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>
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<li>K<sub>r</sub> is the amount of repressor required for 50% repression of constitutive promoter (equal to 1 in our simulations);</li>
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</ul>
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</p>
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<p>
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ODEs representing protein production are described by a set of equations:
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<p><img src="https://static.igem.org/mediawiki/2012/0/09/Svn12_mrs_det_d1_bfp.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/7/74/Svn12_mrs_det_d2_mcit.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/a/ae/Svn12_mrs_det_d4_talakrab.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/a/a6/Svn12_mrs_det_d3_talbkrab.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/b/bf/Svn12_mrs_det_dpip_mrs_new.png"/></p>
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<p><img src="https://static.igem.org/mediawiki/2012/6/65/Svn12_mrs_det_dekrab.png"/></p>
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</p>

Revision as of 20:21, 25 September 2012


Modeling - mutual repressor switch

  1. Deterministic model
  2. Stochastic model
  3. 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:
  • f1, f2, f3 and f4 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;
  • k1, k2, k3 and k4 are association constants;
  • n1, n2, n3 and n4 are exponents representing the degree of functional cooperativity;
  • Kr 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 >>

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