Processes 2018, 6, 134
biosynthesis system [12] becomes damped as the signal dissipates from transcription in the cell nucleus
to translation in the cell cytoplasm.
Our work has highlighted that small changes in the rate of VLDL to LDL delipidation had
significant effects on extracellular LDL concentrations but not the rest of the system. Hence this process
could be a good candidate target for LDL reductive therapies. While modelling processes in this way
is helpful to identifying possible new methods of treatments, the enzymes responsible for this reaction
(lipoprotein lipase, hepatic lipase and cholesteryl ester transfer protein) have dual functions which are
not represented by our model, so it is hard to predict the full extent of including this change without
further work.
Our model demonstrates that cholesterol biosynthesis is the dominant source of cholesterol for the
cell. Thus any major disruption of this pathway is likely to have a detrimental effect on human health.
Thus whilst any therapy targeted at reducing intracellular cholesterol, such as statins, will favourably
decrease plasma levels of circulating lipoproteins in time, our model results suggest the counteracting
of any decrease in intracellular cholesterol is limited by the number of receptors available on the cell
surface (a function of the cell size and receptor internationalisation and recycling) and their rate of
internalisation. Hence in cases where cholesterol biosynthesis is compromised we speculate it will be
difficult to supplement intracellular cholesterol levels via increases in plasma cholesterol levels alone.
Although the mathematical formulation of lipoprotein endocytosis used here assumes the
surface of the cell is covered in a continuum of LDLR [15], the main outcome of the model
(total cholesterol content) does not greatly differ to that of [12] in respect of predicting each class
of Familial Hypercholesterolaemia and statin therapy. We, however, note the differences between each
of [13,15] at the lower level detail of receptor occupancy levels and rate of lipoprotein uptake require
further investigation.
We have been able to explore the effects of the genetic disease Familial Hypercholesterolaemia
and statins using our integrated model of cholesterol metabolism. We found that Case I FH has the
greatest effect on extracellular LDL concentrations and Case IV the least. The effects of combined
cases were shown to affect receptor mRNA, free and internalised receptor levels and the extracellular
concentrations of LDL and VLDL. We also found the model replicates the qualitative effects of statins
very closely.
Quantitatively the model produced a 25% reduction in extracellular LDL levels for repeated
statin dosing over a seven day period when the receptor mRNA transcription rate was decreased by
70%. Whilst our the model was able to reproduce the clinically reported lower bound of extracellular
LDL reductions following statin therapy, we believe improvement in this result could be made by
including a more thorough description of in vivo lipoprotein metabolism (e.g., chylomicrons, HDL)
and longer dosing periods. Thus we believe further model extensions coupled with clinically informed
parameterisation of this work are required to fully capture the quantitative regulation of lipoproteins
and their responses to statin therapy.
In conclusion, our work has demonstrated that mathematical modelling can provide a useful
tool for understanding the cellular (lipoprotein endocytosis) and subcellular (biosynthesis and genetic
regulation of cholesterol and receptors) processes that occur during lipoprotein metabolism. Whilst the
level of abstraction of our mathematical model is quite high, this work demonstrates that such
simplifications of a complex system can still reproduce the known biology of disease states and
therapeutic interventions. Future work and extensions to the model presented here is thus needed to
consider the effect of other aspects of the overall system, occurring at the subcellular and tissue level.
There thus remains scope for further testing and application of such models and their extension to
contexts that include a description of other dietary lipoproteins.
Author Contributions: F.P. undertook research and wrote the paper, P.K.S. and M.J.T. both supervised the research
and wrote the paper.
99
biosynthesis system [12] becomes damped as the signal dissipates from transcription in the cell nucleus
to translation in the cell cytoplasm.
Our work has highlighted that small changes in the rate of VLDL to LDL delipidation had
significant effects on extracellular LDL concentrations but not the rest of the system. Hence this process
could be a good candidate target for LDL reductive therapies. While modelling processes in this way
is helpful to identifying possible new methods of treatments, the enzymes responsible for this reaction
(lipoprotein lipase, hepatic lipase and cholesteryl ester transfer protein) have dual functions which are
not represented by our model, so it is hard to predict the full extent of including this change without
further work.
Our model demonstrates that cholesterol biosynthesis is the dominant source of cholesterol for the
cell. Thus any major disruption of this pathway is likely to have a detrimental effect on human health.
Thus whilst any therapy targeted at reducing intracellular cholesterol, such as statins, will favourably
decrease plasma levels of circulating lipoproteins in time, our model results suggest the counteracting
of any decrease in intracellular cholesterol is limited by the number of receptors available on the cell
surface (a function of the cell size and receptor internationalisation and recycling) and their rate of
internalisation. Hence in cases where cholesterol biosynthesis is compromised we speculate it will be
difficult to supplement intracellular cholesterol levels via increases in plasma cholesterol levels alone.
Although the mathematical formulation of lipoprotein endocytosis used here assumes the
surface of the cell is covered in a continuum of LDLR [15], the main outcome of the model
(total cholesterol content) does not greatly differ to that of [12] in respect of predicting each class
of Familial Hypercholesterolaemia and statin therapy. We, however, note the differences between each
of [13,15] at the lower level detail of receptor occupancy levels and rate of lipoprotein uptake require
further investigation.
We have been able to explore the effects of the genetic disease Familial Hypercholesterolaemia
and statins using our integrated model of cholesterol metabolism. We found that Case I FH has the
greatest effect on extracellular LDL concentrations and Case IV the least. The effects of combined
cases were shown to affect receptor mRNA, free and internalised receptor levels and the extracellular
concentrations of LDL and VLDL. We also found the model replicates the qualitative effects of statins
very closely.
Quantitatively the model produced a 25% reduction in extracellular LDL levels for repeated
statin dosing over a seven day period when the receptor mRNA transcription rate was decreased by
70%. Whilst our the model was able to reproduce the clinically reported lower bound of extracellular
LDL reductions following statin therapy, we believe improvement in this result could be made by
including a more thorough description of in vivo lipoprotein metabolism (e.g., chylomicrons, HDL)
and longer dosing periods. Thus we believe further model extensions coupled with clinically informed
parameterisation of this work are required to fully capture the quantitative regulation of lipoproteins
and their responses to statin therapy.
In conclusion, our work has demonstrated that mathematical modelling can provide a useful
tool for understanding the cellular (lipoprotein endocytosis) and subcellular (biosynthesis and genetic
regulation of cholesterol and receptors) processes that occur during lipoprotein metabolism. Whilst the
level of abstraction of our mathematical model is quite high, this work demonstrates that such
simplifications of a complex system can still reproduce the known biology of disease states and
therapeutic interventions. Future work and extensions to the model presented here is thus needed to
consider the effect of other aspects of the overall system, occurring at the subcellular and tissue level.
There thus remains scope for further testing and application of such models and their extension to
contexts that include a description of other dietary lipoproteins.
Author Contributions: F.P. undertook research and wrote the paper, P.K.S. and M.J.T. both supervised the research
and wrote the paper.
99