mcauley1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000434) Biomodels notes: Figure 1b of the reference publication has been reproduced here. The figure in the paper has been generated using MathSBML. The author has generated the SBML file using Copasi, and finds that with the same intial conditions and parameter sets, LDLC enters a slightly higher steady statem, when running the simulation using Copasi. This is reflected in this curation figure, generated using SBML odeSolver. The model was simulated using SBML odeSolver and the plot was generated using Gnuplot. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. A global parameter 'multiplier' was added, and added to reaction 1. To reproduce Fig 1B the values for 'multiplier' needs to be set to 0.6667, 1, 1.3333, 1.6667, 2 and 2.3333 for DC values of 200, 300, 400, 500, 600 and 700 mg/day respectively.

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A whole-body mathematical model of cholesterol metabolism and its age-associated dysregulation.

  • Mark T Mc Auley
  • Darren J Wilkinson
  • Janette J L Jones
  • Thomas B L Kirkwood
BMC Syst Biol 2012; 6 : 130
Abstract
BACKGROUND: Global demographic changes have stimulated marked interest in the process of aging. There has been, and will continue to be, an unrelenting rise in the number of the oldest old ( >85 years of age). Together with an ageing population there comes an increase in the prevalence of age related disease. Of the diseases of ageing, cardiovascular disease (CVD) has by far the highest prevalence. It is regarded that a finely tuned lipid profile may help to prevent CVD as there is a long established relationship between alterations to lipid metabolism and CVD risk. In fact elevated plasma cholesterol, particularly Low Density Lipoprotein Cholesterol (LDL-C) has consistently stood out as a risk factor for having a cardiovascular event. Moreover it is widely acknowledged that LDL-C may rise with age in both sexes in a wide variety of groups. The aim of this work was to use a whole-body mathematical model to investigate why LDL-C rises with age, and to test the hypothesis that mechanistic changes to cholesterol absorption and LDL-C removal from the plasma are responsible for the rise. The whole-body mechanistic nature of the model differs from previous models of cholesterol metabolism which have either focused on intracellular cholesterol homeostasis or have concentrated on an isolated area of lipoprotein dynamics. The model integrates both current and previously published data relating to molecular biology, physiology, ageing and nutrition in an integrated fashion.
RESULTS: The model was used to test the hypothesis that alterations to the rate of cholesterol absorption and changes to the rate of removal of LDL-C from the plasma are integral to understanding why LDL-C rises with age. The model demonstrates that increasing the rate of intestinal cholesterol absorption from 50% to 80% by age 65 years can result in an increase of LDL-C by as much as 34 mg/dL in a hypothetical male subject. The model also shows that decreasing the rate of hepatic clearance of LDL-C gradually to 50% by age 65 years can result in an increase of LDL-C by as much as 116 mg/dL.
CONCLUSIONS: Our model clearly demonstrates that of the two putative mechanisms that have been implicated in the dysregulation of cholesterol metabolism with age, alterations to the removal rate of plasma LDL-C has the most significant impact on cholesterol metabolism and small changes to the number of hepatic LDL receptors can result in a significant rise in LDL-C. This first whole-body systems based model of cholesterol balance could potentially be used as a tool to further improve our understanding of whole-body cholesterol metabolism and its dysregulation with age. Furthermore, given further fine tuning the model may help to investigate potential dietary and lifestyle regimes that have the potential to mitigate the effects aging has on cholesterol metabolism.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1.0 dimensionless
86400.0 second
1.0 dimensionless
Id Name Spatial dimensions Size
Excreted Excreted 3.0 1.0 volume
HepaticTissue HepaticTissue 3.0 1.0 volume
Intake Intake 3.0 1.0 volume
Intestine Intestine 3.0 1.0 volume
PeripheralTissue PeripheralTissue 3.0 1.0 volume
Plasma Plasma 3.0 1.0 volume
Id Name Initial quantity Compartment Fixed
species_1 DC 304.0 <substance_units>/volume Intake (Intake)
species_10 NHDL 100.0 <substance_units>/volume Plasma (Plasma)
species_11 PFC 57516.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_12 HCS 0.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_13 HCE 10000.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_14 ACAT 100.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_15 CEH 100.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_16 HNHDLS 0.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_17 VLDLC 20.0 <substance_units>/volume Plasma (Plasma)
species_18 HLDLRs 100.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_19 HLDLRsS 600.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_2 IC 3150.0 <substance_units>/volume Intestine (Intestine)
species_20 HLDLRD 0.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_21 IDLC 20.0 <substance_units>/volume Plasma (Plasma)
species_22 LPL 100.0 <substance_units>/volume Plasma (Plasma)
species_23 LDLC 100.0 <substance_units>/volume Plasma (Plasma)
species_24 HSL 100.0 <substance_units>/volume Plasma (Plasma)
species_25 PLDLRs 100.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_26 PLDLRsS 575.16 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_27 PLDLRD 0.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_28 PCE 9363.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_29 PSS 0.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_3 ICS 0.0 <substance_units>/volume Intestine (Intestine)
species_30 HDLC 45.0 <substance_units>/volume Plasma (Plasma)
species_31 LCAT 100.0 <substance_units>/volume Plasma (Plasma)
species_32 PCS 0.0 <substance_units>/volume PeripheralTissue (PeripheralTissue)
species_33 CETP 100.0 <substance_units>/volume Plasma (Plasma)
species_34 SRB1 100.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_4 HBS 400.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_5 IBS 467.0 <substance_units>/volume Intestine (Intestine)
species_6 EBS 0.0 <substance_units>/volume Excreted (Excreted)
species_7 HFC 60000.0 <substance_units>/volume HepaticTissue (HepaticTissue)
species_8 EC 0.0 <substance_units>/volume Excreted (Excreted)
species_9 INHDLS 0.0 <substance_units>/volume Plasma (Plasma)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
reaction_1 Ingestion species_1 > species_2

k1 * species_1 * multiplier
reaction_10 Billary Cholesterol Release species_7 > species_2

function_6(BCRmax, BCRt, species_7, BS)
reaction_11 Hepatic Cholesterol Synthesis species_12 > species_7

function_7(HCSmax, species_7, HCSt, HS)
reaction_12 Hepatic Cholesterol Storage species_7 > species_13

function_8(k9, species_14, species_7)
reaction_13 Release of Stored Cholesterol species_13 > species_7

function_9(k10, species_15, species_13)
reaction_14 Hepatic Nascent HDL Synthesis species_16 > species_10

function_10(k11, species_11)
reaction_15 VLDL Cholesterol Formation species_7 > species_17

k1 * species_7
reaction_16 Hepatic LDLR Synthesis species_19 > species_18

function_11(khrs, species_19, species_7)
reaction_17 Hepatic LDL Receptor Degradation species_18 > species_20

k1 * species_18
reaction_18 VLDL Cholesterol ReUptake species_17 > species_7

k1 * species_17
reaction_19 IDL Cholesterol Formation species_17 > species_21

function_12(k15, species_17, species_22)
reaction_2 Intestinal Cholesterol Synthesis species_3 > species_2

function_1(ICSmax, species_2, ICt, IS)
reaction_20 IDL Cholesterol ReUptake species_21 > species_7

k1 * species_21
reaction_21 LDL Cholesterol Formation species_21 > species_23

function_13(k17, species_21, species_24)
reaction_22 Receptor Dependent Hepatic Uptake species_23 > species_7

function_14(k18, species_23, species_18)
reaction_23 Receptor Independent Hepatic Uptake species_23 > species_7

k1 * species_23
reaction_24 Receptor Dependent Peripheral Uptake species_23 > species_11

function_15(k20, species_25, species_23)
reaction_25 Receptor Independent Peripheral Uptake species_23 > species_11

k1 * species_23
reaction_26 Peripheral LDLR Synthesis species_26 > species_25

function_16(kprs, species_26, species_11)
reaction_27 Peripheral LDL Receptor Degradation species_25 > species_27

k1 * species_25
reaction_28 Peripheral Cholesterol Storage species_11 > species_28

function_17(k23, species_14, species_11)
reaction_29 Release of Stored Peripheral Cholesterol species_28 > species_11

function_18(k24, species_15, species_28)
reaction_3 Bile Salt Release species_4 > species_5

k1 * species_4
reaction_30 Peripheral Steroid Production species_11 > species_29

k1 * species_11
reaction_31 HDL Cholesterol Formation species_11 + species_10 > species_30

function_19(k26, species_11, species_10, species_31)
reaction_32 Peripheral Cholesterol Synthesis species_32 > species_11

function_20(PCSmax, species_11, PPCt, PCSS)
reaction_33 CETP Mediated Transfer To VLDL species_30 > species_17

function_21(k27, species_30, species_33)
reaction_34 CETP Mediated TransferTo LDL species_30 > species_23

function_22(k28, species_30, species_33)
reaction_35 Reverse Cholesterol Transport species_30 > species_7

function_23(k29, species_30, species_34)
reaction_4 Bile Salt Return species_5 > species_4

k1 * species_5
reaction_5 Bile Salt Excretion species_5 > species_6

k1 * species_5
reaction_6 Bile Salt Synthesis species_7 > species_4

function_2(k5, species_7, species_4)
reaction_7 Cholesterol Absorption species_2 > species_7

function_3(k6, species_2, species_5)
reaction_8 Cholesterol Excretion species_2 > species_8

function_4(k7, species_2, species_5)
reaction_9 Intestinal Nascent HDL Synthesis species_9 > species_10

function_5(k8, species_11)

Global parameters

Id Value
multiplier 1.0

Local parameters

Id Value Reaction
BCRmax 2000.0 reaction_10 (Billary Cholesterol Release)
k1 1.0 reaction_1 (Ingestion)
ICSmax 100.0 reaction_2 (Intestinal Cholesterol Synthesis)
ICt 3120.0 reaction_2 (Intestinal Cholesterol Synthesis)
IS 5.0 reaction_2 (Intestinal Cholesterol Synthesis)
k1 6.0 reaction_3 (Bile Salt Release)
k1 4.29 reaction_4 (Bile Salt Return)
k1 0.856 reaction_5 (Bile Salt Excretion)
k5 2.66 reaction_6 (Bile Salt Synthesis)
k6 0.0005286 reaction_7 (Cholesterol Absorption)
k7 0.0005286 reaction_8 (Cholesterol Excretion)
k8 0.0005 reaction_9 (Intestinal Nascent HDL Synthesis)
BCRt 55326.0 reaction_10 (Billary Cholesterol Release)
BS 5.0 reaction_10 (Billary Cholesterol Release)
HCSmax 500.0 reaction_11 (Hepatic Cholesterol Synthesis)
HCSt 93925.0 reaction_11 (Hepatic Cholesterol Synthesis)
HS 5.0 reaction_11 (Hepatic Cholesterol Synthesis)
k9 1.0 reaction_12 (Hepatic Cholesterol Storage)
k10 5.998 reaction_13 (Release of Stored Cholesterol)
k11 0.005 reaction_14 (Hepatic Nascent HDL Synthesis)
k1 0.016 reaction_15 (VLDL Cholesterol Formation)
khrs 100.0 reaction_16 (Hepatic LDLR Synthesis)
k1 0.01 reaction_17 (Hepatic LDL Receptor Degradation)
k1 0.0496 reaction_18 (VLDL Cholesterol ReUptake)
k15 0.43 reaction_19 (IDL Cholesterol Formation)
k1 0.054 reaction_20 (IDL Cholesterol ReUptake)
k17 0.38 reaction_21 (LDL Cholesterol Formation)
k18 0.068 reaction_22 (Receptor Dependent Hepatic Uptake)
k1 0.005 reaction_23 (Receptor Independent Hepatic Uptake)
k20 0.00675 reaction_24 (Receptor Dependent Peripheral Uptake)
k1 0.000005 reaction_25 (Receptor Independent Peripheral Uptake)
kprs 100.0 reaction_26 (Peripheral LDLR Synthesis)
k1 0.01 reaction_27 (Peripheral LDL Receptor Degradation)
k23 0.017386 reaction_28 (Peripheral Cholesterol Storage)
k24 0.1068 reaction_29 (Release of Stored Peripheral Cholesterol)
k1 0.0005 reaction_30 (Peripheral Steroid Production)
k26 0.000015 reaction_31 (HDL Cholesterol Formation)
PCSmax 500.0 reaction_32 (Peripheral Cholesterol Synthesis)
PPCt 80342.0 reaction_32 (Peripheral Cholesterol Synthesis)
PCSS 5.0 reaction_32 (Peripheral Cholesterol Synthesis)
k27 0.01 reaction_33 (CETP Mediated Transfer To VLDL)
k28 0.001 reaction_34 (CETP Mediated TransferTo LDL)
k29 0.05 reaction_35 (Reverse Cholesterol Transport)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
function_4(k7, IC, IBS) = k7 * IC * IBS
function_5(k8, PFC) = k8 * PFC
function_6(BCRmax, BCRt, HFC, BS) = BCRmax / (1 + pow(BCRt / HFC, BS))
function_10(k11, PFC) = k11 * PFC
function_8(k9, ACAT, HFC) = k9 * ACAT * HFC
function_16(kprs, PLDLRsS, PFC) = kprs * PLDLRsS / PFC
function_15(k20, PLDLRs, LDLC) = k20 * PLDLRs * LDLC
function_14(k18, LDLC, HLDLRs) = k18 * LDLC * HLDLRs
function_13(k17, IDLC, HSL) = k17 * IDLC * HSL
function_12(k15, VLDLC, LPL) = k15 * VLDLC * LPL
function_11(khrs, HLDLRsS, HFC) = khrs * HLDLRsS / HFC
function_1(ICSmax, IC, ICt, IS) = ICSmax / (1 + pow(IC / ICt, IS))
function_2(k5, HFC, HBS) = k5 * HFC / HBS
function_3(k6, IC, IBS) = k6 * IC * IBS
function_7(HCSmax, HFC, HCSt, HS) = HCSmax / (1 + pow(HFC / HCSt, HS))
function_9(k10, CEH, HCE) = k10 * CEH * HCE
function_23(k29, HDLC, SRB1) = k29 * HDLC * SRB1
function_22(k28, HDLC, CETP) = k28 * HDLC * CETP
function_21(k27, HDLC, CETP) = k27 * HDLC * CETP
function_20(PCSmax, PFC, PPCt, PCSS) = PCSmax / (1 + pow(PFC / PPCt, PCSS))
function_19(k26, PFC, NHDL, LCAT) = k26 * PFC * NHDL * LCAT
function_18(k24, CEH, PCE) = k24 * CEH * PCE
function_17(k23, ACAT, PFC) = k23 * ACAT * PFC
Trigger Assignments