Processes 2018, 6, 134
Dysregulated cholesterol biosynthesis and lipoprotein metabolism can lead to a number of health
conditions. Dyslipidemia, raised levels of LDL in blood plasma and/or reduced levels of high density
lipoprotein (HDL), is a major health issue throughout the world [5], which has been linked to increases
in dietary fat and sugar intake and sedimentary lifestyles. Hypercholesterolemia, elevated levels of
cholesterol in blood plasma, has been linked to cardiovascular and pulmonary inflammation [6] and
the overloading of macrophages with cholesterol in vitro has been shown to initiate immune responses.
In contrast, unduly lowering the biosynthetic production of cholesterol levels, such as more recently
shown via pathogenic infections which may lead to sepsis, can have dramatic adverse results [7,8].
There exists a growing literature on the mathematical modelling of lipoprotein metabolism as
recently reviewed in [9]. Such models have generally been formulated using the theory of linear and
nonlinear ordinary differential equations and parameterised and tested, to varying degrees, against
the experimental literature. The mathematical models reviewed in [9] were tested for their ability to
correctly predict the response of each to statin therapy. They found that only a small proportion of
models within the literature correctly predicted the well known effect of statins on increasing LDL
uptake from the circulation.
In contrast there are few mathematical models of cholesterol biosynthesis. Those that do exist
vary in the size of the mathematical models formulated (number of variables and parameters) and
complexity. In [10] the authors derived, parameterised and analysed a three variable nonlinear
ordinary differential equation (ODE) model of cholesterol biosynthesis via the HMGCR pathway.
They demonstrated that whilst the system only exhibited one steady-state, three types of behaviour
were possible; monotic, damped and oscillatory. A more recent ODE model of the mevalonate pathway
has been formulated and analysed in detail by [11]. This model describes cholesterol biosynthesis via
the HMGCR and squalene synthase pathways, demonstrates the effect of the cholesterol-SREBP-2
feedback on the network’s temporal responses, whilst more localised positive feedbacks within the
network ensure cholesterol levels remained tightly bound should any products within the pathway be
adversely increased or decreased.
Limited work has focused on integrating molecular scale cholesterol synthesis with lipoprotein
endocytosis and LDLR synthesis. One exception is that of the unpublished work of [12],
which integrated a description of LDL endocytosis [13] with that of cholesterol biosynthesis [10].
This was favourably evaluated by [9] in assessing how well the model reproduced the known cellular
response to statins, but no mathematical or computational analysis of the model was undertaken.
In this work we present a model of integrated cholesterol biosynthesis, which includes a
description of SREBP-2 regulation by cholesterol (as detailed in [14]), a full description of VLDL
and LDL uptake (as detailed in [15]) coupled with a description of receptor biosynthesis. The work
provides a full account of model formulation, analysis and testing thereof. We are motivated by
the following considerations. Firstly, we wish to develop a well-informed integrated mathematical
model of the core exogenous and endogenous cholesterol pathways within a hepatocyte. We wish
to evaluate whether a simplified model formulated in an in vitro context can capture the known in
vivo biological response of the system in respect of Familial Hypercholesterolaemia and statin therapy,
without having to complicate the model by accounting for other in vivo aspects (for instance HDL,
chylomicron remnants, VLDL hepatocyte recycling). Secondly, we wish to consider how rates of VLDL
to LDL delipidation coupled with competition between the two particles for cell membrane level
receptors may affect intracellular cholesterol levels. High levels of circulating LDL is an indicator of
risk in a number cardiovascular diseases and one of the main sources of circulating LDL is delipidation.
Because of this we have included VLDL to LDL delipidation in this model in order to explore it’s effects
without the complication of a full description of dietary lipoprotein metabolism. Finally, we wish to
evaluate any differences that the assumption of a continuum of receptors on the surface of a cell has
(as per [15]) versus that of discrete description of receptors bound by differing numbers of VLDL and
LDL particles (as per [13]).
82
Dysregulated cholesterol biosynthesis and lipoprotein metabolism can lead to a number of health
conditions. Dyslipidemia, raised levels of LDL in blood plasma and/or reduced levels of high density
lipoprotein (HDL), is a major health issue throughout the world [5], which has been linked to increases
in dietary fat and sugar intake and sedimentary lifestyles. Hypercholesterolemia, elevated levels of
cholesterol in blood plasma, has been linked to cardiovascular and pulmonary inflammation [6] and
the overloading of macrophages with cholesterol in vitro has been shown to initiate immune responses.
In contrast, unduly lowering the biosynthetic production of cholesterol levels, such as more recently
shown via pathogenic infections which may lead to sepsis, can have dramatic adverse results [7,8].
There exists a growing literature on the mathematical modelling of lipoprotein metabolism as
recently reviewed in [9]. Such models have generally been formulated using the theory of linear and
nonlinear ordinary differential equations and parameterised and tested, to varying degrees, against
the experimental literature. The mathematical models reviewed in [9] were tested for their ability to
correctly predict the response of each to statin therapy. They found that only a small proportion of
models within the literature correctly predicted the well known effect of statins on increasing LDL
uptake from the circulation.
In contrast there are few mathematical models of cholesterol biosynthesis. Those that do exist
vary in the size of the mathematical models formulated (number of variables and parameters) and
complexity. In [10] the authors derived, parameterised and analysed a three variable nonlinear
ordinary differential equation (ODE) model of cholesterol biosynthesis via the HMGCR pathway.
They demonstrated that whilst the system only exhibited one steady-state, three types of behaviour
were possible; monotic, damped and oscillatory. A more recent ODE model of the mevalonate pathway
has been formulated and analysed in detail by [11]. This model describes cholesterol biosynthesis via
the HMGCR and squalene synthase pathways, demonstrates the effect of the cholesterol-SREBP-2
feedback on the network’s temporal responses, whilst more localised positive feedbacks within the
network ensure cholesterol levels remained tightly bound should any products within the pathway be
adversely increased or decreased.
Limited work has focused on integrating molecular scale cholesterol synthesis with lipoprotein
endocytosis and LDLR synthesis. One exception is that of the unpublished work of [12],
which integrated a description of LDL endocytosis [13] with that of cholesterol biosynthesis [10].
This was favourably evaluated by [9] in assessing how well the model reproduced the known cellular
response to statins, but no mathematical or computational analysis of the model was undertaken.
In this work we present a model of integrated cholesterol biosynthesis, which includes a
description of SREBP-2 regulation by cholesterol (as detailed in [14]), a full description of VLDL
and LDL uptake (as detailed in [15]) coupled with a description of receptor biosynthesis. The work
provides a full account of model formulation, analysis and testing thereof. We are motivated by
the following considerations. Firstly, we wish to develop a well-informed integrated mathematical
model of the core exogenous and endogenous cholesterol pathways within a hepatocyte. We wish
to evaluate whether a simplified model formulated in an in vitro context can capture the known in
vivo biological response of the system in respect of Familial Hypercholesterolaemia and statin therapy,
without having to complicate the model by accounting for other in vivo aspects (for instance HDL,
chylomicron remnants, VLDL hepatocyte recycling). Secondly, we wish to consider how rates of VLDL
to LDL delipidation coupled with competition between the two particles for cell membrane level
receptors may affect intracellular cholesterol levels. High levels of circulating LDL is an indicator of
risk in a number cardiovascular diseases and one of the main sources of circulating LDL is delipidation.
Because of this we have included VLDL to LDL delipidation in this model in order to explore it’s effects
without the complication of a full description of dietary lipoprotein metabolism. Finally, we wish to
evaluate any differences that the assumption of a continuum of receptors on the surface of a cell has
(as per [15]) versus that of discrete description of receptors bound by differing numbers of VLDL and
LDL particles (as per [13]).
82