. 2022 Nov 24;14(23):4992. doi: 10.3390/nu14234992

Table 2.

List of hepatic lipid metabolism model balances proposed by Pratt et al. [35].

Variable	Balance	Initial Conditions
plasma insulin	$\frac{d I}{d t} = k_{11} + k_{22} \cdot \erf (\frac{G_{B} - v}{c c}) - k_{d} \cdot I$	60 pmol/L
liver glucose	$α_{L} \cdot \frac{d G_{L}}{d t} = S_{G} (t) - k_{g l} \cdot G_{L} + k_{g l 2} \cdot G_{B} - \frac{v_{L G} \cdot G_{L}}{k_{L G} + G_{L}} - \frac{v_{L H} \cdot G_{L}}{k_{L H} + G_{L}} \cdot (\frac{1}{1 + k_{r e p} \cdot P_{L}}) \cdot k_{61} \cdot P_{L}$	8 mmol/L
liver glucose-6-phospahte	$α_{L} \cdot \frac{d P_{L}}{d t} = - \frac{1}{2} \cdot k_{y l} \cdot I \cdot P_{L} \cdot (1 + t a n h \cdot (\frac{l_{m a x} - Y_{L}}{c_{0}})) + \frac{β_{L}}{1 + k_{p 6} \cdot I} \cdot (\frac{Y_{L}}{Y_{L} + y_{0}}) - k_{p} \cdot I \cdot P_{L} + k_{g p} \cdot L_{A} + \frac{β_{6} \cdot R_{L}}{1 + k_{p 6} \cdot I} + \frac{v_{L G} \cdot G_{L}}{k_{L G} + G_{L}} + \frac{v_{L H} \cdot G_{L}}{k_{L H} + G_{L}} \cdot (\frac{1}{1 + k_{r e p} \cdot P_{L}}) - k_{61} \cdot P_{L}$	2.06 mmol/L
liver glycogen	$α_{L} \cdot \frac{d Y_{L}}{d t} = \frac{1}{2} \cdot k_{y l} \cdot I \cdot P_{L} \cdot (1 + t a n h \cdot (\frac{l_{m a x} - Y_{L}}{c_{0}})) - \frac{β_{L}}{1 + k_{d l} \cdot I} \cdot (\frac{Y_{L}}{Y_{L} + y_{0}})$	50 mmol/L
liver pyruvate	$α_{L} \cdot \frac{R_{L}}{d t} = k_{p p} \cdot R_{M} + μ_{B} + k_{p} \cdot I \cdot P_{L} - \frac{β_{6}}{1 + k_{p 6} \cdot I} \cdot R_{L} - k_{a l} \cdot I \cdot R_{L} + μ_{B}$	0.37 mmol/L
free fatty acids in liver	$α_{L} \cdot \frac{d A_{L}}{d t} = 3 \cdot k_{c l} \cdot T_{C B} + k_{b l} \cdot A_{B} + 3 \cdot k_{r} \cdot T_{L B} + k_{a l} \cdot I \cdot R_{L} - \frac{3 \cdot v_{6} \cdot A_{L}}{k_{6} + A_{L}} + \frac{3 \cdot v_{10} \cdot T_{L}}{k_{10} + T_{L}} - \frac{3 \cdot v_{8} \cdot A_{L}}{1 + k_{5} \cdot I} - \frac{k_{7} \cdot A_{L}}{1 + k_{5} \cdot I}$	0.57 mmol/L
triacylglycerides secretory pool in liver	$α_{L} \cdot \frac{d S_{L}}{d t} = \frac{v_{6} \cdot A_{L}}{k_{6} + A_{L}} - k_{9 a} \cdot S_{L}$	0.0149 mmol/L
triacylglycerol storage pool in liver	$α_{L} \cdot \frac{d T_{L}}{d t} = \frac{v_{8} \cdot A_{L}}{k_{8} + A_{L}} - (k_{12} \cdot t a n h (\frac{v_{12} - I}{k_{13}}) + k_{14}) \cdot \frac{v_{9} \cdot T_{L}}{k_{9} + T_{L}} - \frac{v_{10} \cdot T_{L}}{k_{10} + T_{L}}$	40 mmol/L
glucose in muscles	$α_{L} \cdot \frac{d G_{M}}{d t} = (1 + k_{g i} \cdot I) \cdot (k_{g m} \cdot G_{B} - k_{g m 2} \cdot G_{M}) - \frac{v_{M H} \cdot G_{M}}{k_{M H} + G_{M}} \cdot (\frac{1}{1 + k_{r e p} \cdot P_{M}})$	0.5 mmol/L
glycogen in muscle	$α_{L} \cdot \frac{d Y_{M}}{d t} = \frac{1}{2} \cdot k_{y m} \cdot I \cdot P_{M} \cdot (1 + t a n h \cdot (\frac{m_{m a x} - Y_{M}}{c_{0}})) - \frac{β_{M}}{1 + k_{d y} \cdot I} \cdot (\frac{Y_{M}}{Y_{M} + y_{0}})$	20 mmol/L
glucose-6-posphate in muscle	$α_{L} \cdot \frac{d P_{M}}{d t} = \frac{v_{M H} \cdot G_{M}}{k_{M H} + G_{M}} \cdot (\frac{1}{1 + k_{r e p} \cdot P_{M}}) - \frac{1}{2} \cdot k_{y m} \cdot I \cdot P_{M} \cdot (1 + t a n h (\frac{m_{m a x} - Y_{M}}{c_{0}})) + \frac{β_{M}}{1 + k_{d y} \cdot I} \cdot (\frac{Y_{M}}{Y_{M} + y_{0}}) - k_{6 p} \cdot I \cdot P_{M}$	0.133 mmol/L
pyruvate in muscle	$α_{L} \cdot \frac{R_{M}}{d t} = k_{6 p} \cdot I \cdot P_{M} - k_{p p} \cdot R_{M} - μ_{3} \cdot R_{M} \cdot I \cdot P$	0.009 mmol/L
free fatty acids in muscle	$α_{L} \cdot \frac{A_{M}}{d t} = - 3 m_{s} \cdot I \cdot A_{M} + 3 m_{e} + 3 k_{c m} \cdot T_{C B} + k_{b m} \cdot A_{B} + 3 k_{t} \cdot T_{L B} - μ_{4} \cdot A_{M} \cdot P$	0.53 mmol/L
triacylglycerides in muscle	$α_{L} \cdot \frac{d T_{M}}{d t} = m_{s} \cdot I \cdot A_{m} - m_{e}$	14.8 mmol/L
AMP in muscles	$\frac{d P}{d t} = μ_{a m p} - μ_{4} \cdot A_{M} \cdot P - μ_{3} \cdot R_{M} \cdot I \cdot P$	0 mmol/L
adipose triacylglycerides	$α_{L} \cdot \frac{d T_{A}}{d t} = k_{a a} \cdot I \cdot A_{A} \cdot G_{A} - \frac{β_{f}}{1 + k_{f t} \cdot I^{2}}$	500 mmol/L
adipose free fatty acids	$α_{L} \cdot \frac{d A_{A}}{d t} = - 3 \cdot k_{a a} \cdot I \cdot A_{A} \cdot G_{A} + 3 \cdot k_{a} \cdot (1 + k_{a i} \cdot I) \cdot T_{C B} + 3 \cdot k_{b a} \cdot T_{L B} + k_{n a} \cdot A_{B}$	0.57 mmol/L
adipose glycerol	$α_{L} \cdot \frac{d L_{A}}{d t} = \frac{β_{f}}{1 + k_{f t} \cdot I^{2}} - k_{g p} \cdot L_{A}$	0.17 mmol/L
adipose glucose	$α_{L} \cdot \frac{d G_{A}}{d t} = d_{b a} \cdot (1 + k_{g a} \cdot I) \cdot (G_{B} \cdot G_{A}) - k_{a a} \cdot I \cdot A_{A} \cdot G_{A}$	2.53 mmol/L
exogenous plasma triacylglycerides	$\frac{d T_{C B}}{d t} = S_{F} (t) - k_{c m} \cdot T_{C B} - k_{c l} \cdot T_{C B} - k_{a} \cdot (1 + k_{a i} \cdot I) \cdot T_{C B}$	0 mmol/L
plasma free fatty acids	$\frac{A_{B}}{d t} = - k_{b m} \cdot A_{B} - k_{b l} \cdot A_{B} - k_{n a} \cdot A_{B} + \frac{3 \cdot β_{f}}{1 + k_{f t} \cdot I} + 3 \cdot k_{a}$	0.5 mmol/L
endogenous plasma triacylglycerides	$\frac{d T_{L B}}{d t} = F (I) \cdot \frac{v_{9} \cdot T_{L}}{k_{9} + T_{L}} + k_{9 a} \cdot S_{L} - k_{r} \cdot T_{L B} - k_{t} \cdot T_{L B} - k_{b a} \cdot T_{L B}$	Table 4
plasma glucose	$\frac{d G_{B}}{d t} = k_{g l} \cdot G_{L} - k_{g l 2} \cdot G_{B} - (1 + k_{g i} \cdot I) \cdot (k_{g m} \cdot G_{B} - k_{g m 2} \cdot G_{M}) - d_{b a} \cdot (1 + k_{g a} \cdot I) \cdot (G_{B} - G_{A}) - μ_{1}$	Table 4