Processes 2018, 6, 134
3.3.1. Class I FH
Let us first consider Class I where LDL receptors are not synthesised. In this case the associated
parameter is μ mr , which we vary in order to investigate the model response. The results illustrated
in Figure A1 show how the inhibition of receptor synthesis prolongs uptake of extracellular LDL,
which would equate to higher circulating plasma LDL levels.
As expected, with μ mr = 0, receptor numbers deplete and lipoproteins are unable to be
internalised. Levels of extracellular VLDL increase because of continuous influx, as do LDL as
VLDL are broken down into LDL. This increase in extracellular LDL concentration biologically would
increase the risk of health problems. When varying μ mr successively we find that even a small increase
in the number of receptors synthesised decreases the levels of extracellular LDL and VLDL. For instance
increasing the value from 0 to 20% of normal function halves the concentration of circulating VLDL and
LDL. Increasing the value from 0 to 40% of normal function decreases the concentration of circulating
VLDL and LDL by 80–90%, respectively.
3.3.2. Class III FH
We now consider Class III where binding of LDL and receptors is ineffective. In this case the
associated parameter is α l (LDL receptor binding), which we vary in order to investigate the model
response. The results are illustrated in Figure A2 and show that the amount of extracellular LDL
is affected significantly by the inability of LDL to bind to LDLR on the cell surface. We can see
that increasing LDL-LDLR binding from 0 to just 20% of normal function decreases extracellular
LDL concentrations by 67%. Subsequently restoring normal function reduces extracellular LDL
concentrations by nearly 97%.
3.3.3. Class IV FH
Here LDL bound to receptors on the cell surface are not internalised properly. In this case we vary
the associated parameter, β l and investigate the model response. The results illustrated in Figure A3
demonstrate the concentration of extracellular LDL is significantly affected if β l = 0, but is only
marginally altered if β l is increased. There is also a significant difference between the amount of
bound LDL when β l = 0 and when β l is increased, however this does not appear to significantly affect
extracellular VLDL concentrations. Aside from when β l = 0, the system is fairly robust to changes in
the internalisation rate of bound LDL particles.
3.3.4. Class V FH
Finally we consider Class V where LDL receptors are not recycled effectively. To investigate
this case we vary the associated parameter f . The results in Figure A4 show the number of free and
internalised receptors declines significantly for reduced receptor recycling which causes an increase
in extracellular concentrations of LDL and VLDL. However the number of bound and internalised
VLDL is not affected as significantly as the number of bound and internalised LDL. This is because
VLDL have a greater binding affinity and so are more successful in binding competition. We also see a
reduction by more than half in both free and internalised receptor concentrations between the usual
value f = 0.7 and altered values f ≤ 0.7.
3.3.5. Individual Class FH Summary
Having explored the effects of different classes of FH, we have found that Class I has the greatest
effect on extracellular LDL and Class IV the least.
The lack of variation in intracellular cholesterol, HMGCR mRNA and HMGCR levels suggest
that despite the effects of FH, the cell is able to maintain intracellular cholesterol levels genetically.
This makes sense as without this control the concentration of cholesterol may decline to cytotoxic
95
3.3.1. Class I FH
Let us first consider Class I where LDL receptors are not synthesised. In this case the associated
parameter is μ mr , which we vary in order to investigate the model response. The results illustrated
in Figure A1 show how the inhibition of receptor synthesis prolongs uptake of extracellular LDL,
which would equate to higher circulating plasma LDL levels.
As expected, with μ mr = 0, receptor numbers deplete and lipoproteins are unable to be
internalised. Levels of extracellular VLDL increase because of continuous influx, as do LDL as
VLDL are broken down into LDL. This increase in extracellular LDL concentration biologically would
increase the risk of health problems. When varying μ mr successively we find that even a small increase
in the number of receptors synthesised decreases the levels of extracellular LDL and VLDL. For instance
increasing the value from 0 to 20% of normal function halves the concentration of circulating VLDL and
LDL. Increasing the value from 0 to 40% of normal function decreases the concentration of circulating
VLDL and LDL by 80–90%, respectively.
3.3.2. Class III FH
We now consider Class III where binding of LDL and receptors is ineffective. In this case the
associated parameter is α l (LDL receptor binding), which we vary in order to investigate the model
response. The results are illustrated in Figure A2 and show that the amount of extracellular LDL
is affected significantly by the inability of LDL to bind to LDLR on the cell surface. We can see
that increasing LDL-LDLR binding from 0 to just 20% of normal function decreases extracellular
LDL concentrations by 67%. Subsequently restoring normal function reduces extracellular LDL
concentrations by nearly 97%.
3.3.3. Class IV FH
Here LDL bound to receptors on the cell surface are not internalised properly. In this case we vary
the associated parameter, β l and investigate the model response. The results illustrated in Figure A3
demonstrate the concentration of extracellular LDL is significantly affected if β l = 0, but is only
marginally altered if β l is increased. There is also a significant difference between the amount of
bound LDL when β l = 0 and when β l is increased, however this does not appear to significantly affect
extracellular VLDL concentrations. Aside from when β l = 0, the system is fairly robust to changes in
the internalisation rate of bound LDL particles.
3.3.4. Class V FH
Finally we consider Class V where LDL receptors are not recycled effectively. To investigate
this case we vary the associated parameter f . The results in Figure A4 show the number of free and
internalised receptors declines significantly for reduced receptor recycling which causes an increase
in extracellular concentrations of LDL and VLDL. However the number of bound and internalised
VLDL is not affected as significantly as the number of bound and internalised LDL. This is because
VLDL have a greater binding affinity and so are more successful in binding competition. We also see a
reduction by more than half in both free and internalised receptor concentrations between the usual
value f = 0.7 and altered values f ≤ 0.7.
3.3.5. Individual Class FH Summary
Having explored the effects of different classes of FH, we have found that Class I has the greatest
effect on extracellular LDL and Class IV the least.
The lack of variation in intracellular cholesterol, HMGCR mRNA and HMGCR levels suggest
that despite the effects of FH, the cell is able to maintain intracellular cholesterol levels genetically.
This makes sense as without this control the concentration of cholesterol may decline to cytotoxic
95