Model 3. Heterogeneous unbound YLDL

RESULTS AND MODEL DEVELOPMENT

3.4. Model development

3.4.3. Model 3. Heterogeneous unbound YLDL

for apo B and

triglyceride

in the

same compartments

while

accounting for different residence times

for

these moieties

in the

unbound fraction overall.

1.26 0.089

0.089

M(3)=14.83 mg M(6)=14.83 mg M(7)=206.1rng M(10)=386.7 mg IC(3)=1.5058+05 cpm

IC(6)=1505E+05 cpm lC(7)=2.9068+06 cpm [C(10)=3.7¿AE+06 cpm U(3)=18.490 mg/h U(10)=16.19ó mg/h

Figure

26. Four compartment model used

to

describe the kinetics

of

apo

B

in unbound (comp

3,6

and

7)

and bound (comp

l0)

VLDL2 fractions

in

subject K.

Although

not

observed

in the

unbound decay curve

it

was assumed

that

^the

unbound fraction contained particles which turned over rapidly.

^The

turnover rate of

these compartments

being

determined

by the rise of

^the

triglyceride specific radioactivity curve.

The

turnover

rate of

compartment ⁷ was equal

to

the slope

of

the unbound apo

B

decay curve.

It

was also assumed

that the turnover rate

of

the bound apo

B

fraction was the same as that

of

^the

compartment

7.

This model allowed

for

the direct input

of

apo

B

into the bound

fraction.

L(i,j)

¡- ^1.

To

construct

this

model

it was

assumed

that apo B

radioactivity was

distributed uniformly throughout the

unbound

fraction. This

assumption,

together with the relationship which exists

between

mass and the

^rate

constants

of

connecting compartments enabled

the following

relationships to

be

defined relating radioactivity amd rate constants.

For

example,

where, and,

I C ( 6 )=IC ⁽ 3)*L(6,3) lL(7,6) IC(7)=IC( 6)*L(7,6) lL( ^{I 0, 7} )

L(6,3)=L(7,6)

IC(3)+IC(6)+IC(7)=¡.2068+06 cpm

1.246

The

fit of

this model to rhe 131¡

y¡¡¡2

_apo

_{B of}

_subject

_{K is}

shown

in

Figure 27.

The

fit to

^{both the unbound} and bound fractions was better than that obtained

by

using

the

simpler precursor product model (Figure 18).

1C

10 40 50

Hours

Figure 27. Fit of four

compartment model (Figure

26) to

unbound

(n)

and

bound

(^) VLDL2

apo

B

data

of

^subject

K,

where the kinetics

of

^{the unbound}

fraction were

described

by the sum of three

compartments,

two of

^which

tumed over

at a

^rafe

of

^1.246

h-1.

The rapid turnover rate was defined

by

the

rise

of the

YLDL2 triglyceride specific radioactivity ^data.

A

three compartment model was

fit to the

unbound fraction despite the absence

of any kinetic

evidence

to

^suggest

the

^presence

of

^more

than

^one compartment.

The inclusion of rapidly turning over

compartments

in

the

model was based upon

the

need

to

account

for the rapid rise of the

VLDL

triglyceride specific

radioactivity

curve;

assuming

that the live¡

triglyceride compartments turnover more slowly that

of VLDL. It is

important

to

^remember

that during the

development these models apo

B

and triglyceride data ^were

4

6

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30 c 2C

modelled simultaneously.

As a

consequence

of this the

^turnover

^rates

^of

compartments

3

and

6 in

Figure

26

were defined

by the

function describing

the rapid rise

of

the unbound VLDL2 triglyceride ^data.

Examination

of the

unbound and bound

VLDL2

apo

B

decay curves ⁱⁿ subjects

H

and

K

^revealed

that the

unbound fraction decayed

at a

^{faster rate}

and mono-exponentially and as shown

in

^Figure 18

the

data could

be

^modelled

in

such

a way.

Closer examination

of

these curves may however suggest that

they

decay

at the

^{same rate and that}

the

differences observed

in

these curves

may be a function of the

^precursor product relationship

existing

^between these fractions. The model

in

Figure

26

incorporated

this

idea and as shown in

Figure

27 the fit to the

data was better than

that in Figure 19

where the

simpler model was used. Note

the

change

in the

turnover

rate of the

^bound

compartment between

this

and the simpler model (0.089

vs.0.059 h-l).

Figure

28

depicts

the

model used

to fit

the unbound VLDL? triglyceride kinetics

of

subject

K.

This model which

is

coupled

to

that

of

Figure 26, the apo B

model,

incorporates

two rapidly turning over

compartments

within

^the

unbound fraction and one unbound

VLDL2

triglyceride compartment (comp. 7)

which turns over

at

the same rate as that

of

the bound fraction (comp. ^10).

The

following basic relationships between rate constants

that

define the

coupled models (apo

B

and triglyceride) were ^assumed.

L(0,3)rC ⁺ L(6,3þ6 ₌ L(6,3)¿ps 3 L(0,6)rC ⁺ L(7,6þ6 ₌ L(7,6)¿psg

L(10,7)16 ₌ L(1O,7)apoB

lE.167 ^5.100 15.600

M(3)=1852.6 mg M(6)=372.2ms M(7)=1039.2 mg M(10)=3264 mg IC(4)=6.6E+08 dpm

0.089

0.089

Figure

28. VLDL2 triglyceride model

for

subject

K. In

this model two unbound

compartments (comp

3 and 6)

^{turnover more}

rapidly than that of the

liver compartment (comp

2)

illustrating

that the liver

triglyceride compartment ^is

the rate limiting

step.

The

turnover rate

of the

^{bound fraction (comp.}

10)

^is equal

to that of the

^more slowly turning over unbound compartment (comp 7).

The

turnover

rate of

compartments

7

was determined

by the

kinetics

of

^the

unbound

VLDL} apo B data. L(0,3) and L(0,6)

^represent hydrolysis of triglyceride

from

compartments

3

and

6

respectively.

It

was assumed

in

^this

model

that all

triglyceride

in

compartment

7 was

transported

to the

bound

fraction.

L(ij)

^{¡- 1.}

In

the earlier model which was used

to fit

this data (Figure 20) one

of

the liver triglyceride compartments (comp.

2)

turned over more rapidly than

that of

the

unbound fraction. In this model however the turnover rate of

^this

compartment was

a

magnitude slower than

that of the first two

compartments

(comps.

3 and 6)

describing

the

unbound

fraction. It is

important

to

^note

however that the ^turnover

^f

ate of

compartment

7 (slow

unbound) ^is comparable

to that of the liver

triglyceride compartment.

This

observation ^is

of

great significance and

will ^be

^{addressed later.}

The

fit of

this model

to

^the data

is

shown

in

Figure 29. The

fit of

this model

to

the unbound data was good, as

it

was

in

the other earlier models.

0.250

tr

40 50

Hours

Figure 29. Fit of VLDL

triglyceride model (Figure

28) to

unbound

(^)

and

bound

(¡)

data

of

subject

K.

^{The dashed line} represents the

fit of

^{the model to}

the

^{bound data}

Again it is clear that the use of a

^precursor

product

relationship

between

the

unbound

and bound triglyceride fractions will not fit

^the

observed data (Figure 29>. The

fit to the

bound fraction was worse when the

more

complex

rather than

when

the

simpler

model (Figure 24) was

used'

Apparently

the rate

constant between

the last of the

unbound and

the

^bound

compartment as defined

by

the apo

B

data

is

too slow

to

permit

a

^good

fit fot

^he bound

VLDL

triglyceride fraction.

In

order

to fit the

bound triglyceride data

there must

be

either

a

^much more rapid transport

into this

fraction

from

^the unbound

than is

^predicted

or like the

unbound

fraction the

bound fraction

must

represent

a

heterogeneous

population of particles, some of

^which

turnover

rapidly.

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