MattAFrench (Talk | contribs) |
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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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+ | <p> This system can be described as above. Where gRNA(i), Cas9, and mRNA are produced constitutively with their associated rates of production kc, kg, and k0 respectively. The Cas9 and gRNA(i) will undergo an inrreversible association to form Cas9:gRNA(i) at rate kf, which in turn inhibits the production of mRNA and reduce the production of Fluorescent protein (k1). All molecules spontaneously degrade and diffuse away at their own ssociated rate. (i) will account for us having multiple gRNAs and just as many fluorescent proteins i.e. i=3 with three fluorescent proteins and subsequent set of three gRNAs.</p> | ||
$$ \color{white}{(1) \frac{dgRNA,i}{dt} = k_{g,i} – δ_{dg} \cdot gRNA,i – k_{f} \cdot Cas9 \cdot gRNA,i} $$ | $$ \color{white}{(1) \frac{dgRNA,i}{dt} = k_{g,i} – δ_{dg} \cdot gRNA,i – k_{f} \cdot Cas9 \cdot gRNA,i} $$ | ||
<p style="text-align: center;" > | <p style="text-align: center;" > | ||
− | The above equation details the change in gRNA concentration per unit time, also extending along index i | + | The above equation details the change in gRNA concentration per unit time, also extending along index i. 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.</p><br><br> |
$$ \color{white}{(2) \frac{dCas9}{dt} = k_{c} – δ_{dc} \cdot Cas9 – k_{f} \cdot Cas9 \cdot \underset{i}{∑}gRNA,i} $$ | $$ \color{white}{(2) \frac{dCas9}{dt} = k_{c} – δ_{dc} \cdot Cas9 – k_{f} \cdot Cas9 \cdot \underset{i}{∑}gRNA,i} $$ | ||
− | <p style="text-align: center;" > This equation details the change in Cas9 protein per unit time. It will be increased by its production (kc) and reduced by its degradation (δdc), and again it's association to gRNA(s). This will be proportioal the sum of all the gRNA's along i, accounting for the competition for Cas9.</p><br> | + | <p style="text-align: center;" > This equation details the change in Cas9 protein per unit time. It will be increased by its production (kc) and reduced by its degradation (δdc), and again it's association to gRNA(s). This will be proportioal the sum of all the gRNA's along i, accounting for the competition for Cas9.</p><br><br> |
$$ \color{white}{(3) \frac{dCas9:gRNA,i}{dt} = k_{f} \cdot Cas9:gRNA,i – δ_{dcg} } $$ | $$ \color{white}{(3) \frac{dCas9:gRNA,i}{dt} = k_{f} \cdot Cas9:gRNA,i – δ_{dcg} } $$ | ||
− | <p style="text-align: center;" > This equation details the change in concentration of the Cas9 associated with gRNA(i). This is simply the rate of formation from before, minus its degredation. </p><br> | + | <p style="text-align: center;" > This equation details the change in concentration of the Cas9 associated with gRNA(i). This is simply the rate of formation from before, minus its degredation. </p><br><br> |
$$ \color{white}{(4) \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | $$ \color{white}{(4) \frac{dmRNA,i}{dt} = k_{0} \cdot \frac{1}{1+k{m} \cdot Cas9:gRNA,i} −δ_{dm} \cdot mRNA,i} $$ | ||
− | <p style="text-align: center;" > This equation details the change in mRNA(i), which is very similar to the equation seen earlier when describing transciption. This is produced at a rate k0, but it is also inhibited by Cas9:grna(i), so there is a standard inhibition function which will reduce rate k0 as Cas9:gRNA(i) increases. It is also simply reduced by it's degradation and diffusion rate δdm. </p><br> | + | <p style="text-align: center;" > This equation details the change in mRNA(i), which is very similar to the equation seen earlier when describing transciption. This is produced at a rate k0, but it is also inhibited by Cas9:grna(i), so there is a standard inhibition function which will reduce rate k0 as Cas9:gRNA(i) increases. It is also simply reduced by it's degradation and diffusion rate δdm. </p><br><br> |
$$ \color{white}{(5) {\frac{dFP,i}{dt} = k_{1} \cdot mRNA,i – δ_{dp} \cdot FP,i} $$ | $$ \color{white}{(5) {\frac{dFP,i}{dt} = k_{1} \cdot mRNA,i – δ_{dp} \cdot FP,i} $$ | ||
− | <p style="text-align: center;" > This details the rate of translation and is the same as before; only changes to protein translation are increased proportionally to mRNA(i) and reduced by it's degradation and diffusion δdp. <sup> 3 </sup> : </p><br> | + | <p style="text-align: center;" > This details the rate of translation and is the same as before; only changes to protein translation are increased proportionally to mRNA(i) and reduced by it's degradation and diffusion δdp. <sup> 3 </sup> : </p><br><br> |
Revision as of 01:15, 1 November 2017
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