Answer:
Explanation:
Given that:
The brain cell which uses glucose transporter GLUT3 Km = 1.5 mM
The liver cell which stores glucose GLUT2 Km = 15 mM
The objective is to calculate the rate (as % of Vmax) of glucose uptake in brain cells and liver cells under starvation conditions.
Using the M-M equation i.e Michaelis- Menten equation;
[tex]Rate = \dfrac{V_{max}* [S]}{[S]+K_m}[/tex]
By rearrangement
[tex]\dfrac{Rate}{V_{max}}= \dfrac{[S]}{[S]+K_m}[/tex]
where;
[tex]V_{max}[/tex] = maximum velocity of a reaction
Thus; the rate as a % of Vmax of glucose uptake in brain cells is calculated as:
[tex]\dfrac{Rate}{V_{max}}= \dfrac{[3 \ mM]}{[3 \ mM]+1.5 \ mM}[/tex]
[tex]\dfrac{Rate}{V_{max}}= \dfrac{3 \ mM}{4.5 \ mM}[/tex]
[tex]\dfrac{Rate}{V_{max}}=0.667[/tex]
[tex]\dfrac{Rate}{V_{max}}=66.7 \%[/tex]
the rate as a % of Vmax of glucose uptake in liver cells is calculated as:
[tex]\dfrac{Rate}{V_{max}}= \dfrac{[3 \ mM]}{[3 \ mM]+15 \ mM}[/tex]
[tex]\dfrac{Rate}{V_{max}}= \dfrac{3 \ mM}{18 \ mM}[/tex]
[tex]\dfrac{Rate}{V_{max}}=0.166[/tex]
[tex]\dfrac{Rate}{V_{max}}=17 \%[/tex]
Thus, the uptake is larger brain cells due to the fact that the brain cells GLUT3 have higher tendency to attract glucose.
