Biomod/2014/UCR/Breaking RNA/Results

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Results


EDIT

ODE Models

Reaction Design: Oscillator
The overall list of reactions are:
[math]\displaystyle{ E_1 + g_1 -\gt E_1 + g_1 + R_1 }[/math] (RNA production)
[math]\displaystyle{ E_2 + g_2 -\gt E_2 + g_2 + R_2 }[/math] (RNA production)
[math]\displaystyle{ E_1 + g_3 -\gt E_1 + g_3 + R_3 }[/math] (RNA production)
[math]\displaystyle{ E_2 + g_4 -\gt E_2 + g_4 + R_4 }[/math] (RNA production)
[math]\displaystyle{ R_1 + R_4 -\gt O }[/math] (Titration)
[math]\displaystyle{ R_2 + R_3 -\gt O }[/math] (Titration)
[math]\displaystyle{ E^\ast_1 + R_2 -\gt E_1 }[/math] (Activation )
[math]\displaystyle{ E_2 + R_1 -\gt E^*_2 }[/math] (Inhibition )
[math]\displaystyle{ E_1 + R_3 -\gt E^*_1 }[/math] (Self Inhibition )
[math]\displaystyle{ E^*_2 + R_4 -\gt E_2 }[/math] ( Self Activation)
[math]\displaystyle{ R_1 + D_1 -\gt R_1.D_1 }[/math] (Inhibition)
[math]\displaystyle{ R_1.D_1 -\gt D_1 }[/math] (Titration)
[math]\displaystyle{ D_1 + E^*_2 -\gt E_2 + R_1.D_1 }[/math] (Titration)
where [math]\displaystyle{ E_i }[/math] are active enzymes, [math]\displaystyle{ E^*_i }[/math] are inactive enzymes, [math]\displaystyle{ R_i }[/math] are RNA species, [math]\displaystyle{ g_i }[/math] are genes.
Applying the law of mass action, the dynamics of the system can be derived in the following ordinary differential equations (ODEs).

[math]\displaystyle{ \dot{[R_1]} = k_1[E_1][g_1]-\delta_1 [R_1][R4] - \gamma_2 [E_2][R_1] - \gamma_3 [R_1][D_1] }[/math]
[math]\displaystyle{ \dot{[R_2]} = k_2[E_2][g_2]-\delta_2 [R_2][R3] - \gamma_1 ([E_1^{tot}] - [E_1])[R_2] }[/math]
[math]\displaystyle{ \dot{[R_3]} = k_3[E_1][g_3]-\delta_2 [R_2][R3] - \beta_1 [E_1][R_3] }[/math]
[math]\displaystyle{ \dot{[R_4]} = k_4[E_2][g_4]-\delta_1 [R_1][R4] - \beta_2 ([E_2^{tot}]-[E_2])[R_4] }[/math]
[math]\displaystyle{ \dot{[E_1]} = - \beta_1 [E_1][R_3] +\gamma_1 ([E_1^{tot}] - [E_1])[R_2] }[/math]
[math]\displaystyle{ \dot{[E_2]} = \beta_2 ([E_2^{tot}]-[E_2])[R_4]- \gamma_2 [E_2][R_1] + \beta_3([E_2^{tot}]-[E_2])[D_1] }[/math]
[math]\displaystyle{ \dot{[D_1]} = \theta_1 ([D^{tot}_1]-[D_1]) - \gamma_3 [R_1][D_1] - \beta_3([E_2^{tot}]-[E_2])[D_1] }[/math]

Reaction Design: Bistable
The overall list of reactions are:

[math]\displaystyle{ E_1 + g_1 -\gt E_1 + g_1 + R_1 }[/math] (RNA production)
[math]\displaystyle{ E_2 + g_2 -\gt E_2 + g_2 + R_2 }[/math] (RNA production)
[math]\displaystyle{ E_1 + R_2 -\gt E^*_1 }[/math] (Inhibition )
[math]\displaystyle{ E_2 + R_1 -\gt E^*_2 }[/math] (Inhibition )
[math]\displaystyle{ E^*_1 + D_2 -\gt E_1 }[/math] (Self Activation )
[math]\displaystyle{ E^*_2 + D_1 -\gt E_2 }[/math] ( Self Activation)
[math]\displaystyle{ R_1 + D_1 -\gt R_1.D_1 }[/math]
[math]\displaystyle{ R_1.D_1 -\gt D_1 }[/math]
[math]\displaystyle{ R_2 + D_2 -\gt R_2.D_2 }[/math]
[math]\displaystyle{ R_2.D_2 -\gt D_2 }[/math]
where [math]\displaystyle{ E_i }[/math] are active enzymes, [math]\displaystyle{ E^*_i }[/math] are inactive enzymes, [math]\displaystyle{ R_i }[/math] are RNA species, [math]\displaystyle{ g_i,D_i }[/math] are genes.
Applying the law of mass action, the dynamics of the system can be derived in the following ordinary differential equations (ODEs).

[math]\displaystyle{ \dot{[R_1]} = k_1[E_1][g_1]-\delta_1 [R_1][D_1] - \gamma_2 [E_2][R_1] }[/math]
[math]\displaystyle{ \dot{[R_2]} = k_2[E_2][g_2]-\delta_2 [R_2][D_2] - \gamma_1 [E_1][R_2] }[/math]
[math]\displaystyle{ \dot{[E_1]} = \beta_1 ([E_1^{tot}]-[E_1])[D_2] -\gamma_1 [E_1][R_2] }[/math]
[math]\displaystyle{ \dot{[E_2]} = \beta_2 ([E_2^{tot}]-[E_2])[D_1]- \gamma_2 [E_2][R_1] }[/math]
[math]\displaystyle{ \dot{[D_1]} = \theta_1([D^T_1 - D_1]) - \delta_1 [R_1][D_1] - \beta_2 ([E_2^{tot}]-[E_2])[D_1] }[/math]
[math]\displaystyle{ \dot{[D_2]} = \theta_2([D^T_2 - D_2]) - \delta_2 [R_2][D_2] - \beta_1 ([E_1^{tot}]-[E_1])[D_2] }[/math]
Parameter Fitting

Experimental Characterization

The oligonucleotide sequences are specified in the Supplementary section. Once the necessary genelets and strands for our RNA clocks and switches systems are designed, it is important to characterize and verify that our DNA sequences are designed correctly.



Assembling the Circuits




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  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA'><span>Home</span></a></li>
  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA/Project'><span>Motivation & Objectives</span></a></li>
  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA/Methods'><span>Results</span></a></li>
  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA/Results'><span>Methods</span></a></li>
  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA/Members'><span>Supplement</span></a></li>
  <li><a href='http://openwetware.org/wiki/Biomod/2014/UCR/Breaking_RNA/Achievements'><span>Team</span></a></li>

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