From: Diagnostic markers based on a computational model of lipoprotein metabolism
State Variables - determine the system state | ||
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d _{ i, j } | nm | Lipoprotein particle diameter in the i-th step of a lipolysis cascade, in the j-th subclass of the size range covered by that cascade step |
Q_{ ss }(d_{ i, j }) | Particles * dL^{-1} | Steady-state particle pool size in a pool with mean particle diameter d_{ i, j } |
Variables - specify processes and output | ||
${d}_{i,j}^{r}$ | nm | the radius of the subclass with average diameter d_{ i, j } |
J_{ l } (d_{ i, j }) |
Particles * dL^{-1} * day^{-1} | Particle flux into the pool with mean particle diameter d_{ i, j } due to extrahepatic lipolysis |
J_{ l, liver } (d_{ i, j }) |
Particles * dL^{-1} * day^{-1} | Particle flux into the pool with mean particle diameter d_{ i, j } due to hepatic lipolysis |
k_{ l }(d) | day^{-1} | Particle size dependent extrahepatic lipolysis rate |
k _{ a, liver } | day^{-1} |
Particle size dependent liver attachment rate (attachment is followed by either lipolysis or uptake) |
k_{ l, liver } (d) | day^{-1} | Particle size dependent liver lipolysis rate |
k_{ u, liver } (d) | day^{-1} | Particle size dependent liver uptake rate |
n_{ tg } (d_{ i, j }) | Molecules * particle^{-1} | Number of triglyceride molecules in a lipoprotein particle with diameter d_{ i, j } |
Q _{*} | Particles * dL^{-1} | Steady-state particle pool size in the size range called * |
$\overline{{k}_{u,liver}^{*}}$ | day^{-1} | Particle size dependent liver uptake rate, averaged per particle over the size range called * |
$\overline{{k}_{l}^{}}$ | day^{-1} | Particle size dependent extrahepatic lipolysis rate, averaged per particle over all particles in the model |
$\overline{{k}_{a,liver}^{}}$ | day^{-1} | Particle size dependent liver attachment rate, averaged per particle over all particles in the model |
J _{ p,* } | Particles * dL^{-1}*day^{-1} | Particle production flux into the size range called * |
J _{ in, * } |
Particles * dL^{-1} * day^{-1} | Particle production influx (production + lipolysis) into the size range called * |
Q_{ out } ([d_{ a } d_{ b }]) | Particles * dL^{-1} | Steady state particle pool size in interval from d_{ a } tod_{b}in the final particle concentration profile. |
Parameters - are optimized using data | ||
k _{ l, max } | day^{-1} | maximum rate at which extrahepatic lipolysis takes place |
k _{ a, apoEmax } | day^{-1} | maximum rate at which liver binding mediated by ApoE takes place |
k _{ a, apoB } | day^{-1} | rate at which liver binding mediated by ApoB takes place |
A | nm | shape parameter for liver binding mediated by ApoE |
B | - | shape parameter for liver binding mediated by ApoE |
σ _{ u, liver } | nm | shape parameter describing fraction of liver attachment which is taken up (instead of lipolyzed) - with changing particle size |
Model constants and derived variables - calibrated in this paper | ||
d _{ a, apoEmin } | 17 nm | minimum particle diameter at which liver binding mediated by ApoE takes place |
d_{hl, peak} | 31.33 nm | Hepatic lipase lipolysis peak size (see Eq. 5) |
s _{ u, liver } | 7.87 | Liver uptake shape constant (see Eq. 2) |
d _{ l, min } | 25.13 nm | minimum size at which extrahepatic lipolysis occurs (see Eq. 4 in [13]) |
σ _{ l } | 77.35 nm | shape constant for extrahepatic lipolysis (see Eq. 4 in [13]) |