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

$\frac{d[protein]}{dt}=k_{T}[mRNA]-d_{p}[protein]$

$\lambda=$ 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

$mRNA\xrightarrow[]{deg_{nonspec}}degmRNA$

$\frac{d[degmRNA]}{dt}=deg_{mRNA}[mRNA]$

$\frac{d[mRNA-siRNA^{*}]}{dt}=0$

Assuming that RISC* complex is replenished rapidly given ATP.

$siRNA^{*}+mRNA\xrightarrow[]{\lambda}mRNA-siRNA^{*}$

$\frac{d[mRNA]}{dt}=-\lambda[siRNA^{*}[mRNA]-\frac{d[degmRNA]}{dt}]$

$mRNA-siRNA^{*}\xrightarrow[]{\kappa}cleavedmRNA+siRNA^{*}$

$\frac{d[cleavedmRNA]}{dt}=\kappa[mRNA-siRNA^{*}]=\kappa[siRNA^{*}_{bound}]$

$mRNA-siRNA^{*}\xrightarrow[]{\kappa}cleavedmRNA+siRNA^{*}$

$\frac{d[cleavedmRNA]}{dt}=\kappa[mRNA-siRNA^{*}]=\kappa[siRNA^{*}_{bound}]$