Processes 2018, 6, 134
levels and the cell perish. However we know that humans are able to survive with FH indicating their
cells do not perish.
We now wish to simulate the effects of being afflicted with a combination of all four cases.
3.3.6. Combined FH
We used Latin Hypercube Sampling [43], to consider the possible outcomes for a range of
combined effects of FH Class types I, III, IV and V. Latin Hypercube Sampling generates a sample of
plausible collections of parameter values from a multidimensional distribution. The method takes
the midpoint of each quartile for parameters selected and randomly samples the combination of the
effects of the four FH class types. In this case this leads to the four hypothetical combined FH cases
detailed below.
FH Combined Case 1—(62.5% of μ mr , 12.5% of α L , 87.5% of β L , 87.5% of f ),
FH Combined Case 2—(87.5% of μ mr , 62.5% of α L , 37.5% of β L , 12.5% of f ),
FH Combined Case 3—(12.5% of μ mr , 37.5% of α L , 62.5% of β L , 37.5% of f ),
FH Combined Case 4—(37.5% of μ mr , 87.5% of α L , 12.5% of β L , 62.5% of f ).
Figure 4 provides a summary of the effects of each of the combined cases of FH on HMGCR mRNA,
HMGCR, LDLR mRNA, extracellular LDL and VLDL and cellular cholesterol levels. For completeness
full model results are provided in Appendix E . These lead to a disruption in receptor production,
free receptors, extracellular levels of VLDL and LDL and the binding and internalisation of VLDL and
LDL that we would expect to see as a result of the disease. Our model shows that despite lipoprotein
uptake being significantly reduced, the cell will keep intracellular cholesterol levels within a tightly
controlled range as a result of genetic regulation via the SREBP-2 cholesterol feedback. This feedback
ensures the cell responds to low levels of cholesterol by upregulating cholesterol biosynthesis, allowing
it to produce around 80% of the cholesterol the cell needs, in spite of disruptions to receptor function.
Whilst direct comparison with experimental values of intracellular cholesterol is not possible due to a
lack of reported values in the literature, we postulate here that this effect could be tested experimentally
via a series of VLDL and LDL uptake experiments. For populations of cells each affected by the different
FH classes, the relative difference in the uptake of the lipoproteins could be compared to that of a
control group of cells, in order to discern the differences detailed here.
From these model results we can infer the increased susceptibility to CVD events, as a result of
FH leading to increased plasma LDL levels concurs with the known biology. Furthermore, we can see
from the samplings taken, Case 3 leads to the greatest rise in plasma LDL levels, due to low receptor
synthesis and recycling combined with that of low LDL receptor binding affinity.
3.4. Modelling Statin Therapy
We can also consider if our model produces the known biological response to statins, globally the
most commonly used pharmaceutical treatment for lowering plasma cholesterol levels. These drugs
competitively bind to HMGCR preventing binding with HMGCoA and so inhibiting cholesterol
biosynthesis. This reduces intracellular cholesterol concentrations thereby up-regulating receptor
synthesis which clears more lipoproteins from the circulation. In this model, the effect of taking statins
can be modelled by modifying the transcription of HMGCR mRNA, μ mh . We here show the numerical
results for an idealised statin that instantaneously halts transcription of HMGCR mRNA, for 11 doses
over a period of 7 days such that
μ mh =
0,
for approx. 9 h 45 m + n × 14h45m≤ t ≤ 23 h + n × 14h45m,
1.406 × 10 −7 , otherwise,
where n is the number of dosage periods. Although this is a dramatic change in μ mh it is sufficient to
show that the model replicates the expected dynamical behaviour. We have run the model to steady
96
levels and the cell perish. However we know that humans are able to survive with FH indicating their
cells do not perish.
We now wish to simulate the effects of being afflicted with a combination of all four cases.
3.3.6. Combined FH
We used Latin Hypercube Sampling [43], to consider the possible outcomes for a range of
combined effects of FH Class types I, III, IV and V. Latin Hypercube Sampling generates a sample of
plausible collections of parameter values from a multidimensional distribution. The method takes
the midpoint of each quartile for parameters selected and randomly samples the combination of the
effects of the four FH class types. In this case this leads to the four hypothetical combined FH cases
detailed below.
FH Combined Case 1—(62.5% of μ mr , 12.5% of α L , 87.5% of β L , 87.5% of f ),
FH Combined Case 2—(87.5% of μ mr , 62.5% of α L , 37.5% of β L , 12.5% of f ),
FH Combined Case 3—(12.5% of μ mr , 37.5% of α L , 62.5% of β L , 37.5% of f ),
FH Combined Case 4—(37.5% of μ mr , 87.5% of α L , 12.5% of β L , 62.5% of f ).
Figure 4 provides a summary of the effects of each of the combined cases of FH on HMGCR mRNA,
HMGCR, LDLR mRNA, extracellular LDL and VLDL and cellular cholesterol levels. For completeness
full model results are provided in Appendix E . These lead to a disruption in receptor production,
free receptors, extracellular levels of VLDL and LDL and the binding and internalisation of VLDL and
LDL that we would expect to see as a result of the disease. Our model shows that despite lipoprotein
uptake being significantly reduced, the cell will keep intracellular cholesterol levels within a tightly
controlled range as a result of genetic regulation via the SREBP-2 cholesterol feedback. This feedback
ensures the cell responds to low levels of cholesterol by upregulating cholesterol biosynthesis, allowing
it to produce around 80% of the cholesterol the cell needs, in spite of disruptions to receptor function.
Whilst direct comparison with experimental values of intracellular cholesterol is not possible due to a
lack of reported values in the literature, we postulate here that this effect could be tested experimentally
via a series of VLDL and LDL uptake experiments. For populations of cells each affected by the different
FH classes, the relative difference in the uptake of the lipoproteins could be compared to that of a
control group of cells, in order to discern the differences detailed here.
From these model results we can infer the increased susceptibility to CVD events, as a result of
FH leading to increased plasma LDL levels concurs with the known biology. Furthermore, we can see
from the samplings taken, Case 3 leads to the greatest rise in plasma LDL levels, due to low receptor
synthesis and recycling combined with that of low LDL receptor binding affinity.
3.4. Modelling Statin Therapy
We can also consider if our model produces the known biological response to statins, globally the
most commonly used pharmaceutical treatment for lowering plasma cholesterol levels. These drugs
competitively bind to HMGCR preventing binding with HMGCoA and so inhibiting cholesterol
biosynthesis. This reduces intracellular cholesterol concentrations thereby up-regulating receptor
synthesis which clears more lipoproteins from the circulation. In this model, the effect of taking statins
can be modelled by modifying the transcription of HMGCR mRNA, μ mh . We here show the numerical
results for an idealised statin that instantaneously halts transcription of HMGCR mRNA, for 11 doses
over a period of 7 days such that
μ mh =
0,
for approx. 9 h 45 m + n × 14h45m≤ t ≤ 23 h + n × 14h45m,
1.406 × 10 −7 , otherwise,
where n is the number of dosage periods. Although this is a dramatic change in μ mh it is sufficient to
show that the model replicates the expected dynamical behaviour. We have run the model to steady
96