Biomod/2014/UCR/Breaking RNA/Results
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Results
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^*_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
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. All experiments are incubated at 30°C in both the spectrofluorometer and thermocycler.
Aptamer-RNA Polymerase Interactions
Purpose
Enzyme Inhibition with RNA Aptamers for the RNA Switch
The topologies of our RNA clocks and switches rely on the idea that inhibition of a module is possible, whether it is self-mediated or caused by another module. A fluorescent RNA aptamer genelets, Malachite Green and Spinach, are used to characterize and quantify our system. This reporting system will be our visual determining guide for whether the enzyme's transcriptional funciton is altered, specifically inhibition. A spectrofluorometer is used to characterize the inhibition of T7 RNA Polymerase and SP6 RNA Polymerase by measuring fluorescence in the system.
These experiments successfully demonstrated three important concepts that are necessary to achieve oscillations and bistablity behaviors for our systems:
1) The proper binding of specific enzymes to the inhibiting aptamer sequences.
2) The production of RNA aptamer strands through transcription of DNA to RNA.
3) Inhibitor aptamer RNA product successfully suppresses the transcriptional function of their specific target enzyme.
Gel electrophoresis is another useful tool in determining the functionality of enzymes prior and post interaction of the inhibiting aptamer RNA products.
Aptamer-Kleptamer Interactions
Bound Aptamer-Kleptamer Interactions
Inhibition of the modules is not sufficient for RNA clocks and switches. It must also be possible for the enzymes to regain transcriptional activity after the addition of the kleptamer. The following experiments show unequivocally that the kleptamers can successfully undermine inhibition. In the gel experiment, R1 and SP6 RNAP were mixed together and incubated for 20 minutes at 30°C. Next, K1 was added to the mixture and the solution was incubated for another 10 minutes at 30°C. Unfortunately, lane 3 has both versions of K1 when it was originally intended just for the 23 base pair K1. However, this does not skew the control data since both strands are clearly distinguishable. In lane 5, no K1 is in solution. For lanes 6 and 7, K1 were added. The enzyme band near the top for both lanes 6 and 7 are smaller than for lane 5, indicating less R1 aptamer is bound. Thus, a majority of the aptamer must have been properly removed through the use of K1, as expected.
Unbound Aptamer-Kleptamer Interaction
An important factor in the oscillatory system is to ensure the R1 and K1 strands are not strongly interacting before the inhibition of SP6 RNAP. In this gel, the R1 and K1 aptamers were mixed into solution together at the same concentration and incubated at 30°C for 10 minutes. For both variations of the K1 strand (23&38 bp), there are two distinct bands in lanes 4 and 6. This indicates that there are little interactions occurring between these two strands before R1 binds to the enzyme. This can be explained by a difference in secondary structure between the bound and unbound forms of R1.
Bistable Mechanisms Verification
Oscillatory Mechanisms Verification
Inhibition of T7 RNA Polymerase with Genelets By transcribing G3, T7 RNAP will become inhibited by the transcribed RNA aptamer. This can be seen using fluorometry by measuring the transcription rate of Malachite Green. The blue trace represents our negative control in which there is no G3. The orange trace represent the solution with G3 added. The gene was added around 1 hour into the experiment at 500 nM. It’s evident that the activity has been completely inhibited.
Reactivation of T7 RNA Polymerase with Genelets
In this case, the genes- G3 and G2 –were used instead of the aptamers. There is obvious inhibition of the enzyme with the addition of varying concentrations of G3. After a few hours, G2 (750 nM) was added to the mixture to be transcribed into the reactivator, R2. Unfortunately, there was no reactivation of the enzyme. It’s possible this may be because the transcription of G3 is outcompeting the transcription of G2. This would prevent any reactivation since T7 RNAP would immediately re-inhibit itself.
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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