Model
We have created a complete model of our system involving 22 chemical species participating in 32 biochemical reactions. Our model consists of a toggle switch which is controled by either two ligand-receptor pathways or more directly by the addition of guide RNA, like in our liposome fusion experiments.
ON and OFF and ON and OFF and ON again...
This simulation of our model shows that the toggle switch can be switched between two stable states of gene expression ("ON" and "OFF") endlessly by temporarly increasing only a single chemical species as a trigger.
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<img class="d-block w-100" src="/images/model/model-1.jpg" alt="First slide">
<p>This is a complete representation of the model with all reactions and species involved. It further includes important constants and gives hints at the type of interactions. At first sight this might look rather complex, but it can be broken down into smaller pieces. Our model is divided into 4 Independent sections:</p>
- two receptor pathways, which produce a transcription activator,
- the reporter pathway, which produces a reporter protein (here Ubiquitin-GFP) that indicates whether the toggle switch is in an ON or OFF position, and,
- the toggle switch itself
<img class="d-block w-100" src="/images/model/model-2.jpg" alt="Second slide">
<p>Let's assume our toggle switch is currently in the OFF position, which means there is a lot of repressor OFF (red) in the system. This trimeric repressor reduces the production of gON, short for guide RNA ON, and UGFP mRNA to a minimum, which means we won't see any fluorescence signal.</p>
<p>Repression is expressed by the repression function (1). Where the product P is produced over time t dependent on the concentration of the repressor [R] in the system. k represents the strength of the promoter, which we choose to be 0.05 in the case of gON and 0.1 for UGFP mRNA. Furthermore, ka and kb stand for the efficiency of the repression.</p>
<img class="w-100" src="/images/model/eq1.png" alt="Equation One" />
<img class="d-block w-100" src="/images/model/model-3.jpg" alt="Third slide">
<img class="w-100" src="/images/model/eq2.png" alt="Equation Two" />
<p>Now that we know what our current state is, let's see what happens if we add ligand ON to our system (indicated by a green arrow). First of all the ligand ON will bind to his receptor ON thereby forming an activator ON.</p>
<p>Since this step is reversible, even though favoring the activator: k25 > k-25, it is indicated by a forward and backward arrow respectively.</p>
<p>For a similar reaction A + B ⥂ C the formation of the complex C over time t will follow the rules of simple mass action (2). Where ki and k-i are the rate constants for the forward and backward reaction.</p>
<img class="d-block w-100" src="/images/model/model-4.jpg" alt="Fourth slide">
<p>After our activator ON was formed it will bind to its target DNA sequence and will live up to his name, activating (green) the expression of gON. Since we know that our repressor OFF is constantly trying to shutdown gONs production, we need enough activator ON to compete against. This is a critical point of our system. However in reality repressor and activator do not act on the same gene, so gON should always be expressed in the presence of activator ON.</p>
<p>The activation is formulated in the activation function (3). Where the product P is produced over time t dependent on the concentration of the activator [A] in the system. Just like in the repression function kc and kd stand for the efficiency of the activation.</p>
<img class="d-block w-100" src="/images/model/model-5.jpg" alt="Third slide">
<p>Now that we have gON in the system it can bind to dCas9 and form an initial collision complex dCas9.gONcc, which more slowly then undergoes a transition to the active dCas9.gON complex, like described by Raper et al. (2018). Both reactions are reversible and follow the mass action law. The dCas) in the active complex can then be guided by gON to its DNA target site gtON, which will lead to the trimeric repressor ON complex. Repressor ON is a rather stable complex indicated by k7 >> k-7</p>
<img class="d-block w-100" src="/images/model/model-6.jpg" alt="Third slide">
<p>Since the target site lies in the promoter region of a gene coding for gOFF. The repressor ON will hinder the production of gOFF, just like the repressor OFF did to gON.</p>
<p>The crucial point here is that if gOFF is not being expressed anymore, then new repressor OFF can not form. Over time repressor OFF will degrade until it reaches its minimal concentration. This allows for both the production of gON, which accelerates the toggling event, and UGFP mRNA, showing us that it actually switched by the translation of UGFP.</p>
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A simulation of our model shows that the toggle switch can be switched between two stable states of gene expression ("ON" and "OFF") endlessly by temporarly increasing only a single chemical species as a trigger. We have shown that this behaviour is observable over a wide range of different parameters. We have taken results and hints from our model and used them in our design process, such as for selecting promoters for our genes, designing our synthetic regulatory regions and using certain ligand-receptor pathways. Furthermore, we have compared data of the simulation to actual results obtained in the wet lab.
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Reference
Raper, Austin T.; Stephenson, Anthony A.; Suo, Zucai (2018): Functional Insights Revealed by the Kinetic Mechanism of CRISPR/Cas9. In: Journal of the American Chemical Society 140 (8), S. 2971–2984. DOI: 10.1021/jacs.7b13047
