Problem 1: Basic Stoichiometry

Question: How many ATP and NADPH molecules are needed to fix 3 molecules of $CO_{2}$ in the Calvin cycle, and how many G3P molecules are produced?

Step-by-Step Solution:

Step 1: Identify the number of turns. 3 $CO_{2}$ fixed = 3 turns of the Calvin cycle (1 $CO_{2}$ per turn).

Step 2: Calculate G3P produced. Each turn: $CO_{2}$ + RuBP → 2 × 3-PGA → 2 G3P. 3 turns → 3 × 2 = 6 G3P produced.

Step 3: Calculate ATP for reduction (Stage 2). Each PGA → G3P requires 1 ATP + 1 NADPH. 6 PGA (from 3 turns × 2 PGA/turn) → 6 G3P. ATP for reduction = 6 ATP; NADPH = 6 NADPH.

Step 4: Calculate ATP for regeneration (Stage 3). 3 turns = 3 RuBP to regenerate. 3 RuBP regeneration requires 3 ATP (1 ATP per RuBP).

Step 5: Total. Total ATP = 6 (reduction) + 3 (regeneration) = 9 ATP Total NADPH = 6 NADPH G3P available for biosynthesis = 6 − 5 (regeneration, for 3 RuBP) = 1 G3P

Answer: 9 ATP, 6 NADPH, 6 G3P produced, 1 G3P net for biosynthesis.

Problem 2: Extending to Glucose

Question: To make 1 glucose (6C), how many G3P must leave the cycle, and how many turns are required?

Solution: 1 glucose (6C) requires 2 G3P (3C each, 2 × 3C = 6C). Each turn produces 2 G3P but only a fraction exits. To have 2 G3P exit, you need 6 turns (12 G3P produced; 2 exit; 10 regenerate 6 RuBP). 6 turns → 6 $CO_{2}$ fixed → 18 ATP + 12 NADPH total.

Answer: 6 turns, 2 G3P exit cycle, 18 ATP, 12 NADPH.