Model 4. Heterogeneous unbound and bound VLDL

RESULTS AND MODEL DEVELOPMENT

3.4. Model development

3.4.4. Model 4. Heterogeneous unbound and bound VLDL

population

of

particles

with

respect

to

^metabolic

and

^{probably physical and} compositional properties.

In this

regard there are several earlier studies. Thus, Nestel

et al

⁽¹⁹⁸³⁾

and

Huff

and

relford

⁽¹⁹⁸⁴⁾ observed different apo Elapo

C

ratios between the

unbound

and

bound fractions,

the ratio

being

higher in the

bound fraction.

Nestel

et al

(1983) noted that

this

relationship was consistent

with

the unbound

particles being the

precursor

of a more

remnant-like

bound particle,

a

relationship

that was also

supported

by the kinetic data. More

^recently

however

Hui et al

(1984) and Wilcox and Heinberg (1987) have observed that

recent

VLDL

may

be

removed

from the

circulation shortly after secretion, ^and that the transfer

of

apo

C3 to

^these particles, presumably

from HDL,

diminishes

this early

uptake. According

to this

concept nascent-like particles

could

^be found

in

either

the

bound

or

unbound fraction depending

on the

^ratios

of

^apo

Elapo

C in

the particle.

UR

Hou¡¡

Figure 30.

Disappearance curves

of

heparin-Sepharose

following the ^injection into

^minature

^pigs of

^labelled

bound

(R) VLDL

fractions

(Huff

and Telford, 1984).

fractionated apo

unbound ^(UR)

1m i

É0

!6

.:

^r0

È

!q cÀ .ãr€

ê

s

t 10 0

B, and

A

new model (Figure

31)

was proposed

to

incorporate these observations

with all of the

assumptions previously stated.

This

model assumed

that

within

the

bound

fraction, as in the

unbound

fraction, there aÍe

^{particles which} turnover

rapidly and that, in

addition

to

being

the

product

of the

unbound

fraction

newly

synthesized

VLDL?

apo

B

and triglyceride enter

directly

^into

the

bound fraction.

As

shown below

this

assumption relating

to direct

^input

into

the bound VLDL? fraction was ^necessary

in

order

to fit

the bound YLDL2

triglyceride kinetic behaviour. The model also allows for

remnant-like particles

to

appear,

after

delipidation

of the

more-nascent particles,

in

both

the

unbound and bound fractions.

Data from subjects

K

and

H is

used

to

show how this ^new model

fits

the

observed apo

B

and triglyceride specific radioactivity data.

In

addition

to

the

figures described below Figures

7 to l7

show

the

^{observed data and the}

fit

of this model, and the integrated model (Figure

5l), to

the ^{observed data.}

In this model the unbound fraction was ^modelled using

^three

compartments,

as in

^Figures

26

and

28. It

was hypothesised

that

because the

triglyceride specific radioactivity curve

of the

bound fraction increased

at

^a

rate equal to that of the

^unbound

fraction there must, within the

^bound

fraction, be particles with similar kinetic

characteristics

to those in

the

unbound

fraction.

Therefore,

in the

^{above model,}

it was

assumed

that

^the

turnover rate

of

such particles was

the

same as

that of the

unbound ^fraction.

In

addition

to the

turnover rates

of

these compartments being

the

same

it

^was

assumed

that the

triglycerid

elapo B ratios of ^unbound and

^bound

compartments

on the

^same

level

were

the

equal.

It

was also assumed that, for each

VLDL fraction

^{(unbound and bound),} triglyceride was derived

from

the same pools.

Glycerol System

Heparin-Unbound Heparin-Bound

Liver Tflglyceride Production

Nl -

N2-

R

Apo B

Figure 31.

Proposed

new VLDL

apo

B

and triglyceride model.

This

model

deþicts two ^parallel

delipidation ^pathways,

one for each of the

^fraction,

unbound and bound.

Nl, N2,

and

R

^represent the different stages

of

^metabolism

of VLDL

particles. From

a

modelling perspective

it

was assumed that both apo B

and triglyceride enter

into

both

the

unbound and bound fractions.

No

loss of apo

B

occurs prior

to

level

R

although delipidation

of

triglyceride occurs

at

^the

N and R level

compartments.

The

arrows

out of the R level

compartments

represent

the

sum

of

material

which is

converted

to the next

density level,

lost directly from the

plasma compartment

and for

triglyceride

what is

^lost

through

the

process

of

hydrolysis.

This new

model

can

therefore

be

simply described

as two

delipidation pathways,

one for

each

of the

fractions ^(unbound

and

bound),

which

^are

connected

via the slowly

turning

over

compartments, and which was ^required

to fit the

bound apo

B

specific radioactivity data. This connection accounts for

the net

conversion

of

^unbound

to

bound particles.

As in the

previous models

the

turnover rates

for

apo

B

and triglyceride

in a

^given compartmont are the

coupled, such that,

@

@

TG

L(18,17) = ^L(16,15)

=

L(0,10)+L(11'10) = L(0,3)+L(6,3) L(19,18)

=

^L(20,16)

=

L(0,11)*L(12'11)

=

L(0,6)+L(7,6) L(0,19)+L(20,19) = ^L(0,20) = L(0,12)+L(7,12) = ^L(0,7)

In this VLDL

model there are three levels

of

compartments. Levels Nt and

N2, for

which these compartments have

the

same rate constants, and the compartments

on level R,

these compartments turnover more

slowly.

^Although

not

apparently

the

same

the

turnover rates

of the

unbound and bound

R

^level

compartments

may be the

same

when the

^precursor

^product

relationship between these

two

fractions

is

taken

into

consideration. Input

of

apo

B

into the

model is via

compartments

17 and 15, on level Nl,

and loss

via level

^R compartments.

In the triglyceride section of the model

however

loss

of

triglyceride occurs at all levels while input of triglyceride is

into compartments

l0

and

3 on level N1. The fraction of

triglyceride ^hydrolysed from compartments on

the

^{same level was the same} and, was also the same for the N1 and N2

level

compartments, i.e.,

L(0,3) = ^L(0,10) = ^L(0,6) = ^L(0,11)

By imposing such

constraints

on the

compartments

in the

^bound

fraction it was

assumed

that within the

bound fraction there were ^particles

with

similar

kinetic

and triglyceridelapo

B

properties

to

^those

of the

unbound

fraction. Figures

32

and

33

show

the VLDL?

triglyceride specific radioactivity curves

for the

^unbound

and

bound fractions respectively

in

subject

K.

^In

addition, these figures

describe

the

simulated

kinetics of the

^individual

compartments hypothesised

to be found within each fraction. It is

^the

summation

of

these simulated functions which produces

the

observed ^specific radioactivity function.

The

specific radioactivity curves

of the

rapidly turning

over

N level

compartments

rise

without delay and appear

to

reach

a

maximum