Step 1: Understand Calvin Cycle Stoichiometry for 6 CO\textsubscript{2}
The Calvin cycle must run 6 times to produce one molecule of glucose. Each turn fixes one CO\textsubscript{2}.
For 6 CO\textsubscript{2} molecules to enter the cycle:
1. Carboxylation: 6 molecules of Ribulose-1,5-bisphosphate (RuBP, a 5-carbon sugar) combine with 6 molecules of CO\textsubscript{2} to form 12 molecules of 3-Phosphoglycerate (PGA, a 3-carbon compound).
2. Reduction: The 12 molecules of PGA are then reduced to 12 molecules of Glyceraldehyde-3-phosphate (G3P or triose phosphate, a 3-carbon sugar).
3. Regeneration: Out of the 12 G3P molecules, 2 G3P molecules leave the cycle to synthesize glucose or other carbohydrates. The remaining 10 G3P molecules (10 x 3 carbons = 30 carbons) are used to regenerate 6 molecules of RuBP (6 x 5 carbons = 30 carbons) to continue the cycle.
Step 2: Focus on the Regeneration Phase Intermediates
The regeneration phase involves a complex series of reactions that interconvert various sugar phosphates. For the regeneration of 6 RuBP from 10 G3P, the key 5-carbon (pentose) sugar phosphate intermediates that are formed and then ultimately converted to Ribulose-5-phosphate (which is then phosphorylated to RuBP) are:
\begin{itemize}
\item Xylulose-5-phosphate (Xylulose 5P): Approximately 4 molecules are formed as intermediates.
\item Ribose-5-phosphate (Ribose 5P): Approximately 2 molecules are formed as intermediates.
\item Ribulose-5-phosphate (Ribulose 5P): All 6 molecules of RuBP are regenerated via the phosphorylation of 6 molecules of Ribulose-5-phosphate. This is the final 5-carbon sugar before it becomes RuBP.
\end{itemize}
So, for 6 turns of the Calvin cycle, the number of molecules of these key 5-carbon intermediates formed during regeneration are: 4 Xylulose 5P, 2 Ribose 5P, and 6 Ribulose 5P.
Step 3: Compare with Options
Let's check the given options against our derived sequence (4 Xylulose 5P, 2 Ribose 5P, 6 Ribulose 5P):
% Option
(1) 4 xylulose 5P, 6 Ribulose 5P (Missing Ribose 5P)
% Option
(2) 4 xylulose 5P, 2 Ribose 5P, 6 Ribulose 5P (Matches our sequence and numbers)
% Option
(3) 2 Ribose 5P, 4 xylulose 5P, 6 Ribulose 5P (Numbers are correct but the order is different, though the question asks for a "sequence" implying the constituents)
% Option
(4) 4 xylulose 5P, 2 Ribulose 5P, 2 Ribose 5P (Incorrect numbers for Ribulose 5P and Ribose 5P)
Option (2) provides the correct types and quantities of the 5-carbon molecules involved in the regeneration phase for 6 CO\textsubscript{2} inputs.