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The cycle of chemical reactions during photosynthesis which releases oxygen and reduces carbon dioxide to glucose (carbon fixation). Named after its principal discoverer, Melvin Calvin.

The cycle works like this:

CO2 -> ribulose bisphosphate -> 3-phosphoroglycic acid (PGA) -> 1,3-bisphosphoroglycic acid (DPGA) -> 3-phosphoroglyceraldehyde (PGAL) -> fructose, glucose, and ribulose phosphate -> ribulose bisphosphate, which is now ready to take on some more CO2.

Source: John W. Kimball's Biology Pages, which note that "All the reactions of carbon fixation occur in the stroma of the chloroplast".

This cycle is also known as light independent, non-light requiring, or dark reactions, since the energy is provided by ATP or NADPH molecules which are created by the light reactions. "Thus the Calvin cycle is inseparable from the light reactions...they only occur in the light! This is why "dark reactions" is a poor name for the Calvin cycle", (L. Taiz and E. Zeiger, Plant Physiology, 2nd ed., 1998)

Melvin Calvin and Andrew Benson worked this out by studying the green algae Chlorella at UCB.

The Calvin Cycle is one of the most important biosynthetic pathways because it is responsible for the fixation of carbon dioxide into organic compounds. The pathway consists of the so called Dark Reactions of photosynthesis, which use the energy of ATP and NADPH (produced by the Light Reactions of photosynthesis) to synthesize glucose or other compunds from carbon dioxide. In plants the cycle takes place in the stroma of the chloroplasts.

The Three Stages of the Calvin Cycle
1. CO2 fixation to ribulose 1,5-bisphosphate, and the formation of three carbon compounds.
2. Conversion of the three carbon compounds to hexoses.
3. Regeneration of ribulose 1,5-bisphosphate.

The Pathway
The net reaction of the calvin cycle is:
6 CO2 + 18 ATP + 12 NADPH + 12 H+ + 12 H2O --> C6H12O6 + 18 ADP + 18 Pi + 12 NADP+

Enzymes
1. Ribulose Bisphosphate Carboxylase (Rubisco)
2. Phosphoglycerate Kinase
3. Glyceraldehyde-3-Phosphate Dehydrogenase
4. Triose Phosphate Isomerase
5. Aldolase
6. Fructose Bisphosphatase
7. Phosphoglucoisomerase
8. Glucose-6-phosphatase
9. Transketolase
10. Aldolase
11. Sedoheptulose Bisphosphatase
12. Transketolase
13. Phosphopentose Epimerase
14. Phosphopentose Isomerase
15. Phosphoribulose Kinase

Reactions
1. 6 Ribulose 1,5-bisphosphate + 6 CO2 --> 12 3-Phosphoglycerate
2. 12 3-Phosphoglycerate + 12 ATP --> 12 1,3-Bisphosphoglycerate (1,3-BPG) + 12 ADP
3. 12 1,3-BPG + 12 NADPH --> 12 Glyceraldehyde-3-Phosphate (GAP) + 12 NADP+ + 12 Pi
4. 5 GAP --> Dihydroxyacetone phosphate (DHAP)
5. 3 GAP + 3 DHAP --> 3 Fructose-1,6-bisphosphate (FBP)
6. 3 FBP --> 3 Fructose-6-Phosphate (F6P) + 3 Pi
7. F6P --> Glucose-6-Phosphate (G6P)
8. G6P --> Glucose + Pi
9. 2 GAP + 2 F6P --> 2 Erythrose-4-Phosphate (E4P) + 2 Xylulose-5-Phosphate (Xu5P)
10. 2 DHAP + 2 E4P --> 2 Sedoheptulose-1,7-bisphosphate (SBP)
11. 2 SBP --> 2 Sedoheptulose-7-Phosphate (S7P) + 2 Pi
12. 2 S7P + 2 GAP --> 2 Xu5P + 2 Ribose-5-Phosphate (R5P)
13. 4 Xu5P --> 4 Ribulose-5-Phosphate (Ru5P)
14. 2 R5P --> 2 Ru5P
15. 6 Ru5P + 6ATP --> 6 Ribulose 1,5-bisphosphate + 6 ADP

This list of reactions may be somewhat difficult to wade through, but pay attention to the stoichiometry of each reaction and you'll see that they balance out to the net equation listed above.

Regulation of The Calvin Cycle
The Calvin Cycle is indirectly regulated by light. Despite being called Dark Reactions the reactions of the cycle only occur in light. Their nomenclature simply refers to the fact that the do not directly use light.

When a chloroplast is exposed to light three changes occur in the stroma as a result of the activity of the photosynthetic apparatus ('why' explanations would be better suited for a photosynthesis writeup):
pH Increase: The increse in pH shifts equilibrum towards the carbamylation of the Lysine 201 residue of Rubisco, an event needed for activation of the enzyme. The increase in pH also increases the activities of other Calvin Cycle enzymes.
Mg2+ Concentration Increase: Rubisco requires a magnesium ion for catalytic activity. The ion is coordinated by the carbamylated lysine residue.
Increase in NADPH and Reduced Ferredoxin: Several Calvin Cycle enzymes are activated by reduction of disulfide linkages. This activity is mediated by an enzyme called thioredoxin, which has a disulfide bond. This linkage is reduced by ferredoxin forming two free cysteine residues. Thioredoxin can then activate other enzymes by reducing their disulfide linkages. NADPH works by binding to and separating the inactive complex of Phosphoribulose Kinase and Glyceraldehyde-3-Phosphate Dehydrogenase


The pathway may vary from text to text. This stoichiometry was selected to show production of one glucose molecule, although in reality GAP may go on to form other products.
Sources:
Fundamentals of Biochemistry Upgrade Edition by Voet, Voet & Pratt.

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