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<p> The next step in developing our simulation was to calculate our protein concentration at any given time when using CRISPRi. Discussion with wet-lab revealed our method would be using CRISPRi as a repressor, which works by inhibiting the expression of one or more genes by binding to the promoter region <sup> 1 </sup>. The expanded mRNA and Protein concentration models from the Constitutive Gene Expression Model <sup> 2 </sup> were modified to include the element of repression from the CRISPRi inhibition. </p> | <p> The next step in developing our simulation was to calculate our protein concentration at any given time when using CRISPRi. Discussion with wet-lab revealed our method would be using CRISPRi as a repressor, which works by inhibiting the expression of one or more genes by binding to the promoter region <sup> 1 </sup>. The expanded mRNA and Protein concentration models from the Constitutive Gene Expression Model <sup> 2 </sup> were modified to include the element of repression from the CRISPRi inhibition. </p> | ||
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− | $$ \color{white}{ | + | $$ \color{white}{ \frac{dgRNA,i}{dt} = k_{g,i} – δ_{dg} \cdot gRNA,i – k_{f} \cdot Cas9 \cdot gRNA,i} $$ |
+ | <p style="text-align: center;" > The above equation details the change in gRNA concentration extending along index i, i will account for us perhaps having multiple gRNAs which will compete with one another. At any given time, the concentration of gRNA,i will be increased by its production (kgi), and decreased by its association with cas9 at rate kf, relative to it's concentration, and it will also degrade and diffuse away at rate δdg, <sup> 3 </sup> : </p><br> | ||
− | $$ \color{white}{ | + | $$ \color{white}{ \frac{dCas9}{dt} = k_{c} – δ_{dc} \cdot Cas9 – k_{f} \cdot Cas9 \cdot \underset{i}{∑}gRNA,i} $$ |
+ | <p style="text-align: center;" > This equation details the change in Cas9 protein. It will <sup> 3 </sup> : </p><br> | ||
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+ | $$ \color{white}{ \frac{dCas9}{dt} = k_{c} – δ_{dc} \cdot Cas9 – k_{f} \cdot Cas9 \cdot \underset{i}{∑}gRNA,i} $$ | ||
+ | <p style="text-align: center;" > This change can be applied to the Law of Mass Action <sup> 3 </sup> : </p><br> | ||
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$$ \color{white}{ \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | $$ \color{white}{ \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | ||
+ | <p style="text-align: center;" > This change can be applied to the Law of Mass Action <sup> 3 </sup> : </p><br> | ||
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$$ \color{white}{ \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | $$ \color{white}{ \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | ||
+ | <p style="text-align: center;" > This change can be applied to the Law of Mass Action <sup> 3 </sup> : </p><br> | ||
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<p>Where...</p> | <p>Where...</p> |
Revision as of 00:25, 1 November 2017
MODELING