Table 1 Overview of state variables, variables, parameters and constants used in this paper

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_bin 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])