Q.57
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^th reaction flux in
g / (g dry mass · h).
Under pseudo-steady-state condition, the following reaction fluxes are available.

r₁ = 4,
r₃ = 1
and r₆ = 1.

The transport flux of B, r₄, is __________________
g / (g dry mass · h).

Compute Transport Flux r₄ Under Pseudo-Steady-State

Problem Overview

In this metabolic network, intracellular reactions convert substrate A to product B through intermediate metabolites.
Under pseudo-steady-state, metabolite accumulation is zero.

Given:

• r₁ = 4
• r₃ = 1
• r₆ = 1

The goal is to compute the transport flux of B, r₄.

Step-By-Step Solution

1. Mass Balance on Metabolite A_i

From the reaction diagram, r₁ produces intracellular A,
while r₂ and r₃ consume it.

Steady-state equation:

r1 = r2 + r3
4 = r2 + 1 → r2 = 3

2. Mass Balance on Metabolite B_i

B is formed from A at rate r₂ and leaves by
r₄ (transport) + r₆ (to metabolite D).

r2 = r4 + r6
3 = r4 + 1 → r4 = 2

Final Answer

r₄ = 2 g/(g dry mass·h)

Flux Role Summary

Flux	Meaning	Value	Role
r₁	Uptake of A	4	Supplies intracellular pool
r₃	A → C pathway	1	Diverts flux
r₂	A → B pathway	3 (derived)	Main formation route
r₆	B → D	1	Consumes B
r₄	B → Transported out	2	Product output

Conclusion

Applying pseudo-steady-state balances on intracellular intermediates yields
r₄ = 2 g/(g dry mass·h),
ensuring no metabolite buildup in the cell.