processes
Article
An Integrated Mathematical Model of
Cellular Cholesterol Biosynthesis and
Lipoprotein Metabolism
Frances Pool 1 , Peter K. Sweby 2 and Marcus J. Tindall 2,3, * ,†
1
Institute of Ophthalmology, University College London, Gower Street, London WC1E 6BT, UK;
fran_pool@hotmail.co.uk
2
Department of Mathematics and Statistics, University of Reading, Whiteknights, Reading RG6 6AX, UK;
p.k.sweby@reading.ac.uk
3
Institute of Cardiovascular and Metabolic Research, University of Reading, Whiteknights,
Reading RG6 6AA, UK
* Correspondence: m.tindall@reading.ac.uk; Tel.: +44-118-378-8989
† Current address: Department of Mathematics and Statistics, University of Reading, Whiteknights,
Reading RG6 6AX, UK.
Received: 29 June 2018; Accepted: 10 August 2018; Published: 18 August 2018
Abstract: Cholesterol regulation is an important aspect of human health. In this work we bring
together and extend two recent mathematical models describing cholesterol biosynthesis and
lipoprotein endocytosis to create an integrated model of lipoprotein metabolism in the context
of a single hepatocyte. The integrated model includes a description of low density lipoprotein (LDL)
receptor and cholesterol synthesis, delipidation of very low density lipoproteins (VLDLs) to LDLs and
subsequent lipoprotein endocytosis. Model analysis shows that cholesterol biosynthesis produces
the majority of intracellular cholesterol. The availability of free receptors does not greatly effect
the concentration of intracellular cholesterol, but has a detrimental effect on extracellular VLDL
and LDL levels. We test our model by considering its ability to reproduce the known biology of
Familial Hypercholesterolaemia and statin therapy. In each case the model reproduces the known
biological behaviour. Quantitative differences in response to statin therapy are discussed in the
context of the need to extend the work to a more in vivo setting via the incorporation of more dietary
lipoprotein related processes and the need for further testing and parameterisation of in silico models
of lipoprotein metabolism.
Keywords: ordinary differential equation; SREBP-2
1. Introduction
Cholesterol is an intrinsic part of living cells. Every cell in the human body requires cholesterol in
order to produce and maintain a healthy cell membrane. The formation of hormones and of bile acids
that assist in the digestion of food, depend on cholesterol. Myelin, which covers nerve axioms to assist
the conduction of electrical impulses, facilitating movement, vision, taste and the processing of sensory
input is 20%, by weight, cholesterol [1]. This makes cholesterol vital for our nervous system and for
memory and learning to take place. All cells have the ability to produce and regulate cholesterol,
but the liver is primarily responsible for the metabolism of dietary cholesterol and is the only organ
that can remove it from the body via the formation of bile.
Despite being such an important part of cellular health, irregular control of cholesterol homeostasis
in hepatocytes (liver cells) can cause the liver to poorly process dietary cholesterol. This in turn can
lead to high levels of circulating plasma cholesterol, which is widely known to be a major risk factor
Processes 2018, 6, 134; doi:10.3390/pr6080134
www.mdpi.com/journal/processes
80
Article
An Integrated Mathematical Model of
Cellular Cholesterol Biosynthesis and
Lipoprotein Metabolism
Frances Pool 1 , Peter K. Sweby 2 and Marcus J. Tindall 2,3, * ,†
1
Institute of Ophthalmology, University College London, Gower Street, London WC1E 6BT, UK;
fran_pool@hotmail.co.uk
2
Department of Mathematics and Statistics, University of Reading, Whiteknights, Reading RG6 6AX, UK;
p.k.sweby@reading.ac.uk
3
Institute of Cardiovascular and Metabolic Research, University of Reading, Whiteknights,
Reading RG6 6AA, UK
* Correspondence: m.tindall@reading.ac.uk; Tel.: +44-118-378-8989
† Current address: Department of Mathematics and Statistics, University of Reading, Whiteknights,
Reading RG6 6AX, UK.
Received: 29 June 2018; Accepted: 10 August 2018; Published: 18 August 2018
Abstract: Cholesterol regulation is an important aspect of human health. In this work we bring
together and extend two recent mathematical models describing cholesterol biosynthesis and
lipoprotein endocytosis to create an integrated model of lipoprotein metabolism in the context
of a single hepatocyte. The integrated model includes a description of low density lipoprotein (LDL)
receptor and cholesterol synthesis, delipidation of very low density lipoproteins (VLDLs) to LDLs and
subsequent lipoprotein endocytosis. Model analysis shows that cholesterol biosynthesis produces
the majority of intracellular cholesterol. The availability of free receptors does not greatly effect
the concentration of intracellular cholesterol, but has a detrimental effect on extracellular VLDL
and LDL levels. We test our model by considering its ability to reproduce the known biology of
Familial Hypercholesterolaemia and statin therapy. In each case the model reproduces the known
biological behaviour. Quantitative differences in response to statin therapy are discussed in the
context of the need to extend the work to a more in vivo setting via the incorporation of more dietary
lipoprotein related processes and the need for further testing and parameterisation of in silico models
of lipoprotein metabolism.
Keywords: ordinary differential equation; SREBP-2
1. Introduction
Cholesterol is an intrinsic part of living cells. Every cell in the human body requires cholesterol in
order to produce and maintain a healthy cell membrane. The formation of hormones and of bile acids
that assist in the digestion of food, depend on cholesterol. Myelin, which covers nerve axioms to assist
the conduction of electrical impulses, facilitating movement, vision, taste and the processing of sensory
input is 20%, by weight, cholesterol [1]. This makes cholesterol vital for our nervous system and for
memory and learning to take place. All cells have the ability to produce and regulate cholesterol,
but the liver is primarily responsible for the metabolism of dietary cholesterol and is the only organ
that can remove it from the body via the formation of bile.
Despite being such an important part of cellular health, irregular control of cholesterol homeostasis
in hepatocytes (liver cells) can cause the liver to poorly process dietary cholesterol. This in turn can
lead to high levels of circulating plasma cholesterol, which is widely known to be a major risk factor
Processes 2018, 6, 134; doi:10.3390/pr6080134
www.mdpi.com/journal/processes
80