Processes 2018, 6, 134
Appendix B. Parameter Estimation
¯
m r0 —Initial value of receptor mRNA: Rudling et al. (2002) [38] details copy numbers of mRNA found
in human liver cells under basal conditions. We take a value of 48 copies of receptor mRNA per cell,
i.e. per 10 −9 mL which gives 48 molecules/10 −9 mL = 4.8×10 10 molecules/ml. This value was then
refined using sensitivity analysis to give ¯
m r0 = 5.0 × 10 9 molecules/mL.
¯
μ mr —Rate of receptor mRNA transcription: As for ¯
μ mh , one human LDLR mRNA transcript is
5265 bases long [21]. To transcribe one molecule of LDLR mRNA, from one gene, at a rate of 12 bases
per second, takes
5265 bases
12 bases/s
= 438.75 s.
So per gene we have 1/438.75 s = 2.28 × 10 −3 molecules/s. There are two genes in a liver cell so
4.56 × 10 −3 LDLR mRNA molecules are synthesised per cell per second. With a cell volume equal to
10 −9 mL this gives 4.56×10 −3 molecules/s / 1×10 −9 mL giving ¯
μ mr = 4.56 × 10 6 molecules/mL/s.
¯
μ r —Rate of receptor translation: Soutar and Knight (1990) [19] tell us a human LDLR mRNA
transcript contains 839 amino acids. For one ribosome to transcribe one molecule of LDLR
protein, from one LDLR mRNA, at 6 amino acids per second, it takes 839 amino acids / 6 amino
acids/s = 139.83 s. Then per ribosome this gives
1 molecule
139.83 s
= 7.15 × 10
−3 molecules/s.
The coding region of LDLR mRNA is 839 amino acids × 3 = 2517 nucleotides long, and a
ribosome can attach every 35 nucleotides, so we have 71.91 ribosomes per mRNA molecule. Finally,
7.15×10 −3 molecules/s/ribosome × 71.91 ribosomes gives ¯
μ r = 0.51 molecules/s.
¯
δ mr —Rate of receptor mRNA degradation: In the absence of further details we assume the rate
of receptor mRNA degradation is equivalent to that HMGCR mRNA degradation and so take
¯
δ mr = 4.48 × 10 −5 /s.
¯
κ mr —Dissociation of SREBP-2 for receptor gene: Yang and Swartz (2011) [47] quantify DNA binding
affinities to other transcription factors at 54.2 nmol. We convert this value into units of molecules/mL
by the use of Avogadro’s constant, such that
100 × 10 −9 moles
1000 mL
× (6.022 × 10
23 molecules/mol)=3.26 × 10
13 molecules/mL,
as an estimate we took ¯
K 2 = O(10 13 ). This value was then refined using sensitivity analysis to give
¯
κ mr = 8.21 × 10 16 molecules/mL.
¯
ω—Rate of VLDL synthesis: We estimated a value for the rate of VLDL synthesis as
¯
ω = 6.00 × 10 7 particles/mL/s. This value was derived by a local sensitivity analysis such that model
reproduced known intracellular cholesterol concentrations.
x r —Number of binding sites on LDLR gene for SREBP-2: The number of binding sites on the
receptor gene available to SREBP-2 [12] is taken as being 1.
Appendix C. Sensitivity Analysis
Results of the local sensitivity analysis of Equations (36)–(48) showing the relative percentage
change from steady-state as each parameter was varied 100-fold below and above the values indicated
in Table 2. Here “mRNA H" is HMGCR mRNA, “LE" is extracellular LDL, “LRB" is receptor bound
LDL, “LI" is intenalised LDL, “VE" is extracellular VLDL, “VRB" is receptor bound VLDL, “VI" is
internalised VLDL, “RF" is free receptors and “RI" is internalised receptors. Green indicates a less than
102
Appendix B. Parameter Estimation
¯
m r0 —Initial value of receptor mRNA: Rudling et al. (2002) [38] details copy numbers of mRNA found
in human liver cells under basal conditions. We take a value of 48 copies of receptor mRNA per cell,
i.e. per 10 −9 mL which gives 48 molecules/10 −9 mL = 4.8×10 10 molecules/ml. This value was then
refined using sensitivity analysis to give ¯
m r0 = 5.0 × 10 9 molecules/mL.
¯
μ mr —Rate of receptor mRNA transcription: As for ¯
μ mh , one human LDLR mRNA transcript is
5265 bases long [21]. To transcribe one molecule of LDLR mRNA, from one gene, at a rate of 12 bases
per second, takes
5265 bases
12 bases/s
= 438.75 s.
So per gene we have 1/438.75 s = 2.28 × 10 −3 molecules/s. There are two genes in a liver cell so
4.56 × 10 −3 LDLR mRNA molecules are synthesised per cell per second. With a cell volume equal to
10 −9 mL this gives 4.56×10 −3 molecules/s / 1×10 −9 mL giving ¯
μ mr = 4.56 × 10 6 molecules/mL/s.
¯
μ r —Rate of receptor translation: Soutar and Knight (1990) [19] tell us a human LDLR mRNA
transcript contains 839 amino acids. For one ribosome to transcribe one molecule of LDLR
protein, from one LDLR mRNA, at 6 amino acids per second, it takes 839 amino acids / 6 amino
acids/s = 139.83 s. Then per ribosome this gives
1 molecule
139.83 s
= 7.15 × 10
−3 molecules/s.
The coding region of LDLR mRNA is 839 amino acids × 3 = 2517 nucleotides long, and a
ribosome can attach every 35 nucleotides, so we have 71.91 ribosomes per mRNA molecule. Finally,
7.15×10 −3 molecules/s/ribosome × 71.91 ribosomes gives ¯
μ r = 0.51 molecules/s.
¯
δ mr —Rate of receptor mRNA degradation: In the absence of further details we assume the rate
of receptor mRNA degradation is equivalent to that HMGCR mRNA degradation and so take
¯
δ mr = 4.48 × 10 −5 /s.
¯
κ mr —Dissociation of SREBP-2 for receptor gene: Yang and Swartz (2011) [47] quantify DNA binding
affinities to other transcription factors at 54.2 nmol. We convert this value into units of molecules/mL
by the use of Avogadro’s constant, such that
100 × 10 −9 moles
1000 mL
× (6.022 × 10
23 molecules/mol)=3.26 × 10
13 molecules/mL,
as an estimate we took ¯
K 2 = O(10 13 ). This value was then refined using sensitivity analysis to give
¯
κ mr = 8.21 × 10 16 molecules/mL.
¯
ω—Rate of VLDL synthesis: We estimated a value for the rate of VLDL synthesis as
¯
ω = 6.00 × 10 7 particles/mL/s. This value was derived by a local sensitivity analysis such that model
reproduced known intracellular cholesterol concentrations.
x r —Number of binding sites on LDLR gene for SREBP-2: The number of binding sites on the
receptor gene available to SREBP-2 [12] is taken as being 1.
Appendix C. Sensitivity Analysis
Results of the local sensitivity analysis of Equations (36)–(48) showing the relative percentage
change from steady-state as each parameter was varied 100-fold below and above the values indicated
in Table 2. Here “mRNA H" is HMGCR mRNA, “LE" is extracellular LDL, “LRB" is receptor bound
LDL, “LI" is intenalised LDL, “VE" is extracellular VLDL, “VRB" is receptor bound VLDL, “VI" is
internalised VLDL, “RF" is free receptors and “RI" is internalised receptors. Green indicates a less than
102