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ODE Model


Table: Variables used to identify concentrations.
Variable concentration
$R$ LasR
$A$ 3-oxo-C12-HSL
$P$ LasR/3-oxo-C12-HSL
$L$ LasI
$S$ RsaL
$r$ lasR mRNA
$l$ lasI mRNA
$s$ rsaL mRNA

Equations describing these biochemical reactions are
$\displaystyle {\frac {dP}{dt}}$ $\textstyle =$ $\displaystyle k_{RA} R A -k_PP,$ (1)
$\displaystyle {\frac {dR}{dt}}$ $\textstyle =$ $\displaystyle -k_{RA} RA +k_PP- k_RR +
k_1r,$ (2)
$\displaystyle {\frac {dA}{dt}}$ $\textstyle =$ $\displaystyle -k_{RA}R A +k_PP +k_2L-
k_AA,$ (3)
$\displaystyle {\frac {dL}{dt}}$ $\textstyle =$ $\displaystyle k_{3}l - k_LL.$ (4)
$\displaystyle {\frac {dS}{dt}}$ $\textstyle =$ $\displaystyle k_4s-k_SS.,$ (5)
$\displaystyle {\frac {ds}{dt}}$ $\textstyle =$ $\displaystyle V_s\frac{P}{K_s+P}-k_ss,$ (6)
$\displaystyle {\frac
{dr}{dt}}$ $\textstyle =$ $\displaystyle V_r\frac{P}{K_r+P}-k_rr + r_0,$ (7)
$\displaystyle {\frac {dl}{dt}}$ $\textstyle =$ $\displaystyle V_l\frac{P}{K_l+P}\frac{1}{K_S+S}-k_ll + l_0$ (8)


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Jim Keener
2000-09-06