Difference between revisions of "Team:ColumbiaNYC/Model"
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| − | + | Therefore the relationship between total concentration of siRNA and rate of degradation of mRNA due to gene knockdown can | |
| + | be expressed in an enzymatic kinetic reaction (Michaelis-Menten) | ||
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<p>$\therefore deg_{siRNA \rightarrow mRNA}=\frac{\kappa\lambda[siRNA^{*}_{total}][mRNA]}{\kappa+\lambda[mRNA]}$</p> | <p>$\therefore deg_{siRNA \rightarrow mRNA}=\frac{\kappa\lambda[siRNA^{*}_{total}][mRNA]}{\kappa+\lambda[mRNA]}$</p> | ||
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<img src="https://static.igem.org/mediawiki/2017/8/86/Columbia_university_shrnaknockdown.png" alt=""> | <img src="https://static.igem.org/mediawiki/2017/8/86/Columbia_university_shrnaknockdown.png" alt=""> | ||
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<h2>A tetR decay model</h2> | <h2>A tetR decay model</h2> | ||
<h2>Bacterial growth curves</h2> | <h2>Bacterial growth curves</h2> | ||
Revision as of 21:18, 6 October 2017
Modelling
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Modelling the relationship between siRNA and protein translation
$k_{m}=$ transcription rate of mRNA
$\delta([mRNA],[siRNA])=$ rate of mRNA degraded by siRNA
$\frac{d[mRNA]}{dt}=k_{m}-\delta([mRNA],[siRNA])$
$k_{T}=$ rate of protein translation
$d_{p}=$ decay rate of protein
$\frac{d[protein]}{dt}=k_{T}[mRNA]-d_{p}[protein]$
Finding $\delta([mRNA],[siRNA])$
$\lambda=$ affinity of siRNA target site for siRNA guided RISC complex
$\kappa=$ mRNA cleave + dissociation rate of bound siRNA RISC
$siRNA^{*}=$ siRNA loaded (active) RISC complex
$siRNA^{*}_{bound}=$ mRNA bound siRNA^{*} complex
Rate of mRNA degradation/decay
$mRNA\xrightarrow[]{deg_{nonspec}}degmRNA$
$\frac{d[degmRNA]}{dt}=deg_{mRNA}[mRNA]$
Rate of formation of mRNA-siRNA* complexes (takes into account siRNA* recycling)
$\frac{d[mRNA-siRNA^{*}]}{dt}=0$
Assuming that RISC* complex is replenished rapidly given ATP.
Rate of formation of mRNA
$siRNA^{*}+mRNA\xrightarrow[]{\lambda}mRNA-siRNA^{*}$
$\frac{d[mRNA]}{dt}=-\lambda[siRNA^{*}[mRNA]-\frac{d[degmRNA]}{dt}]$
Rate of mRNA cleavage
$mRNA-siRNA^{*}\xrightarrow[]{\kappa}cleavedmRNA+siRNA^{*}$
$\frac{d[cleavedmRNA]}{dt}=\kappa[mRNA-siRNA^{*}]=\kappa[siRNA^{*}_{bound}]$
By Conservation of Rates
$0=\frac{d[mRNA]}{dt}+\frac{d[mRNA-siRNA^{*}]}{dt}+\frac{cleavedmRNA}{dt}+\frac{d[degmRNA]}{dt}-\frac{d[mRNA]}{dt}$
$=0+\frac{d[cleavedmRNA]}{dt}+\frac{d[mRNA]}{dt}$
$\lambda[siRNA^{*}][mRNA]+\frac{d[degmRNA]}{dt}=\frac{d[cleavedmRNA]}{dt}+\frac{d[degmRNA]}{dt}$
$\lambda[siRNA^{*}][mRNA]=\kappa[siRNA^{*}_{bound}]$
$[siRNA^{*}]=[siRNA^{*}_{total}]-[siRNA^{*}_{bound}]$
Substituting and solving for $[siRNA^{*}_{bound}]$
$[siRNA^{*}_{bound}]=\frac{\lambda[siRNA^{*}_{total}][mRNA]}{\kappa+\lambda[mRNA]}$
$\frac{d[cleavedmRNA]}{dt}=\kappa[siRNA^{*}_{bound}]=\frac{\kappa\lambda[siRNA^{*}_{total}][mRNA]}{\kappa+\lambda[mRNA]}$
Therefore the relationship between total concentration of siRNA and rate of degradation of mRNA due to gene knockdown can be expressed in an enzymatic kinetic reaction (Michaelis-Menten)
$\therefore deg_{siRNA \rightarrow mRNA}=\frac{\kappa\lambda[siRNA^{*}_{total}][mRNA]}{\kappa+\lambda[mRNA]}$
A tetR decay model
Bacterial growth curves
