Question

Figure below depicts simplified metabolic and transport reactions taking place in the production of B from A in a cell. The subscript ‘i’ refers to intracellular metabolites. $r_j$ is the $j^{\text{th}}$ reaction flux in $\frac{g}{(g\;dry\;mass)\;h}$. Under pseudo–steady–state condition, the following reaction fluxes are available: $r_1 = 4,\; r_3 = 1,\; r_6 = 1$. The transport flux of B, $r_4$, is _________ $\frac{g}{(g\;dry\;mass)\;h}$.

Hint:

In pseudo–steady–state metabolic flux analysis, write a mass balance for each intracellular metabolite and set accumulation to zero.

Answer 1

Correct Answer: 2

Under pseudo-steady-state, net accumulation of intracellular metabolite $B_i$ is zero:
\[ r_2 - r_4 - r_6 = 0 \]
But $B_i$ is generated from $A_i$ by $r_2$, and $A_i$ at steady state satisfies:
\[ r_1 - r_2 - r_3 = 0 \]
Substitute values:
\[ 4 - r_2 - 1 = 0 \]
\[ r_2 = 3 \]
Now substitute into the $B_i$ balance:
\[ 3 - r_4 - 1 = 0 \]
\[ r_4 = 2 \]
Thus, the transport flux of B is:
\[ \boxed{2} \]