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Biological carbon fixation
Biological carbon fixation, or сarbon assimilation, is the process by which living organisms convert inorganic carbon (particularly in the form of carbon dioxide) to organic compounds that are then used to store energy and as structures for other biomolecules. Carbon is primarily fixed through photosynthesis, but some organisms use the process called chemosynthesis in the absence of sunlight.

Organisms that grow by fixing carbon are called autotrophs, which include photoautotrophs (which use sunlight) and lithoautotrophs (which use inorganic oxidation). Heterotrophs are not themselves capable of carbon fixation but are able to grow by consuming the carbon fixed by autotrophs or other heterotrophs. "Fixed carbon," "reduced carbon," and "organic carbon" may all be used interchangeably to refer to various organic compounds. Chemosynthesis is carbon fixation driven by chemical energy rather than from sunlight. Sulfur- and hydrogen-oxidizing bacteria often use the Calvin cycle or the reductive citric acid cycle.

Net vs. gross CO2 fixation
The primary form of fixed inorganic carbon that is fixed is carbon dioxide (CO2). It is estimated that approximately 250 billion tons of carbon dioxide are converted by photosynthesis annually. The majority of the fixation occurs in terrestrial environments, especially the tropics. The gross amount of carbon dioxide fixed is much larger since approximately 40% is consumed by respiration following photosynthesis. Historically, it is estimated that approximately 2×1011 billion tons of carbon has been fixed since the origin of life.

[Note Add] terrestrial, marine, and microorganisms divide the percentage.

Overview of pathways
Seven autotrophic carbon fixation pathways are known. The Calvin cycle fixes carbon in the chloroplasts of plants and algae, and in the cyanobacteria. It also fixes carbon in the [https://bio.libretexts.org/Bookshelves/Microbiology/Microbiology_(Boundless)/08%3A_Microbial_Evolution_Phylogeny_and_Diversity/8.09%3A_Nonproteobacteria_Gram-Negative_Bacteria/8.9B%3A_Anoxygenic_Photosynthetic_Bacteria#:~:text=Anoxygenic%20photosynthesis%20is%20the%20phototrophic,used%20as%20an%20electron%20donor. anoxygenic photosynthesis] in one type of Pseudomonadota called purple bacteria and in some non-phototrophic Pseudomonadota.

Of the five other autotrophic pathways, two are known only in bacteria (the reductive citric acid cycle and the 3-hydroxypropionate cycle), two are known only in archaea (two variants of the 3-hydroxypropionate cycle), and one is known in both bacteria and archaea (the reductive acetyl CoA pathway).

Calvin cycle
The Calvin cycle accounts for 90% of biological carbon fixation (note citation needed). Consuming adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH), the Calvin cycle in plants accounts for the preponderance of carbon fixation on land. In algae and cyanobacteria, it accounts for the preponderance of carbon fixation in the oceans. The Calvin cycle converts carbon dioxide into sugar (Note: glucose check and specific sugar) as triose phosphate (TP), which is glyceraldehyde 3-phosphate (GAP) together with dihydroxyacetone phosphate (DHAP):


 * 3 CO2 +  12 e−  +  12 H+  +  Pi   →   TP   +   4 H2O

An alternative perspective accounts for NADPH (source of e−) and ATP:


 * 3 CO2 +  6 NADPH  +  6 H+  +  9 ATP  +  5 H2O   →   TP  +  6 NADP+  +  9 ADP  +  8 Pi

The formula for inorganic phosphate (Pi) is HOPO32− + 2H+. Formulas for triose and TP are C2H3O2-CH2OH and C2H3O2-CH2OPO32− + 2H+<!--===Evolutionary considerations=== Somewhere between 3.8 and 2.3 billion years ago, the ancestors of cyanobacteria evolved oxygenic photosynthesis, enabling the use of the abundant yet relatively oxidized molecule H2O as an electron donor to the electron transport chain of light-catalyzed proton-pumping responsible for efficient ATP synthesis. When this evolutionary breakthrough occurred, autotrophy (growth using inorganic carbon as the sole carbon source) is believed to have already been developed. However, the proliferation of cyanobacteria, due to their novel ability to exploit water as a source of electrons, radically altered the global environment by oxygenating the atmosphere and by achieving large fluxes of CO2 consumption.

CO2 concentrating mechanisms
Many photosynthetic organisms have not acquired CO2 concentrating mechanisms (CCMs), which involve a reversible (not net) fixation of CO2. They operate by PEP carboxylase (PEPC), to carboxylate phosphoenolpyruvate (PEP) to oxaloacetate (OAA) which is a C4 dicarboxylic acid. CCM's ultimately contribute to the Calvin cycle. Their benefits include increased tolerance to low external concentrations of inorganic carbon, and reduced losses to photorespiration. CCMs can make plants more tolerant of heat and water stress. CCMs use the enzyme carbonic anhydrase (CA), which catalyze both the dehydration of bicarbonate to CO2 and the hydration of CO2 to bicarbonate
 * HCO3− + H+ CO2 + H2O--> <!--Lipid membranes are much less permeable to bicarbonate than to CO2. To capture inorganic carbon more effectively, some plants have adapted the anaplerotic reactions


 * HCO3− + H+ + PEP → OAA + Pi

catalyzed

CAM plants
CAM plants that use Crassulacean acid metabolism as an adaptation for arid conditions. CO2 enters through the stomata during the night and is converted into the 4-carbon compound, malic acid, which releases CO2 for use in the Calvin cycle during the day, when the stomata are closed. The dung jade plant (Crassula ovata) and cacti are typical of CAM plants. Sixteen thousand species of plants use CAM. These plants have a carbon isotope signature of −20 to −10 ‰.

C4 plants
C4 plants preface the Calvin cycle with reactions that incorporate CO2 into one of the 4-carbon compounds, malic acid or aspartic acid. C4 plants have a distinctive internal leaf anatomy. Tropical grasses, such as sugar cane and maize are C4 plants, but there are many broadleaf plants that are C4. Overall, 7600 species of terrestrial plants use C4 carbon fixation, representing around 3% of all species. These plants have a carbon isotope signature of −16 to −10 ‰.

C3 plants
The large majority of plants are C3 plants. They are so-called to distinguish them from the CAM and C4 plants, and because the carboxylation products of the Calvin cycle are 3-carbon compounds. They lack C4 dicarboxylic acid cycles, and therefore have higher CO2 compensation points than CAM or C4 plants. C3 plants have a carbon isotope signature of −24 to −33‰.

Bacteria and cyanobacteria
Almost all cyanobacteria and some bacteria utilize carboxysomes to concentrate carbon dioxide. Carboxysomes are protein shells filled with the enzyme RuBisCO and a carbonic anhydrase. The carbonic anhydrase produces CO2 from the bicarbonate that diffuses into the carboxysome. The surrounding shell provides a barrier to carbon dioxide loss, helping to increase its concentration around RuBisCO.

Eukaryotic algae
In eukaryotic algae, various bicarbonate transporters and carbonic anhydrases serve to increase the CO2 flux balance toward the pyrenoid, a low CO2-permeable subcellular compartment in the chloroplast containing most of the RuBisCO.

Other autotrophic pathways
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Reverse Krebs cycle
The reverse Krebs cycle, also known as the reverse TCA cycle (rTCA) or the reductive citric acid cycle, is an alternative to the standard Calvin-Benson cycle for carbon fixation. It has been found in strict anaerobic or microaerobic bacteria (as Aquificales) and anaerobic archea. It was discovered by Evans, Buchanan and Arnon in 1966 working with the photosynthetic green sulfur bacterium Chlorobium limicola. In particular, it is one of the most used pathways in hydrothermal vents by the Campylobacterota. This feature is very important in oceans. Without it, there would be no primary production in aphotic environments, which would lead to habitats without life. This feature allows primary production in the ocean's aphotic environments., or "dark primary production." So this kind of primary production is called "dark primary production".

The cycle involves the biosynthesis of acetyl-CoA from two molecules of CO2. The key steps of the reverse Krebs cycle are:


 * Oxaloacetate to malate, using NADH + H+
 * Fumarate to succinate, catalyzed by an oxidoreductase, Fumarate reductase
 * Succinate to succinyl-CoA, an ATP dependent step
 * Succinyl-CoA to alpha-ketoglutarate, using one molecule of CO2
 * Alpha-ketoglutarate to isocitrate, using NADPH + H+ and another molecule of CO2
 * Citrate converted into oxaloacetate and acetyl-CoA, this is an ATP dependent step and the key enzyme is the ATP citrate lyase
 * Succinyl-CoA to alpha-ketoglutarate, using one molecule of CO2
 * Alpha-ketoglutarate to isocitrate, using NADPH + H+ and another molecule of CO2
 * Citrate converted into oxaloacetate and acetyl-CoA, this is an ATP dependent step and the key enzyme is the ATP citrate lyase
 * Citrate converted into oxaloacetate and acetyl-CoA, this is an ATP dependent step and the key enzyme is the ATP citrate lyase
 * Citrate converted into oxaloacetate and acetyl-CoA, this is an ATP dependent step and the key enzyme is the ATP citrate lyase

This pathway is cyclic due to the regeneration of the oxaloacetate.

The bacteria Gammaproteobacteria and Riftia pachyptila switch from the Calvin-Benson cycle to the rTCA cycle in response to concentrations of H2S.

Reductive acetyl CoA pathway
The reductive acetyl CoA pathway (CoA) pathway, also known as the Wood-Ljungdahl pathway uses CO2 as electron acceptor and carbon source, and H2 as an electron donor to form acetic acid. This metabolism is wide spread within the phylum Bacillota, especially in the Clostridia.

The pathway is also used by methanogens, which are mainly Euryarchaeota, and several anaerobic chemolithoautotrophs, such as sulfate-reducing bacteria and archaea. It is probably performed also by the Brocadiales, an order of Planctomycetota that oxidize ammonia in anaerobic condition. Hydrogenotrophic methanogenesis, which is only found in certain archaea and accounts for 80% of global methanogenesis, is also based on the reductive acetyl CoA pathway.

The Carbon Monoxide Dehydrogenase/Acetyl-CoA Synthase is the oxygen-sensitive enzyme that permits the reduction of CO2 to CO and the synthesis of acetyl-CoA in several reactions.

One branch of this pathway, the methyl branch, is similar but non-homologous between bacteria and archaea. In this branch happens the reduction of CO2 to a methyl residue bound to a cofactor. The intermediates are formate for bacteria and formyl-methanofuran for archaea, and also the carriers, tetrahydrofolate and tetrahydropterins respectively in bacteria and archaea, are different, such as the enzymes forming the cofactor-bound methyl group.

Otherwise, the carbonyl branch is homologous between the two domains and consists of the reduction of another molecule of CO2 to a carbonyl residue bound to an enzyme, catalyzed by the CO dehydrogenase/acetyl-CoA synthase. This key enzyme is also the catalyst for the formation of acetyl-CoA starting from the products of the previous reactions, the methyl and the carbonyl residues.

This carbon fixation pathway requires only one molecule of ATP for the production of one molecule of pyruvate, which makes this process one of the main choice for chemolithoautotrophs limited in energy and living in anaerobic conditions.

3-Hydroxypropionate bicycle
The 3-Hydroxypropionate bicycle, also known as 3-HP/malyl-CoA cycle, discovered only in 1989, is utilized by green non-sulfur phototrophs of Chloroflexaceae family, including the maximum exponent of this family Chloroflexus auranticus by which this way was discovered and demonstrated. The 3-Hydroxipropionate bicycle is composed of two cycles and the name of this way comes from the 3-Hydroxyporopionate which corresponds to an intermediate characteristic of it.

The first cycle is a way of synthesis of glyoxylate. During this cycle, two equivalents of bicarbonate are fixed by the action of two enzymes: the Acetyl-CoA carboxylase catalyzes the carboxylation of the Acetyl-CoA to Malonyl-CoA and Propionyl-CoA carboxylase catalyses the carboxylation of propionyl-CoA to methylamalonyl-CoA. From this point a series of reactions lead to the formation of glyoxylate which will thus become part of the second cycle.

In the second cycle, glyoxylate is approximately one equivalent of propionyl-CoA forming methylamalonyl-CoA. This, in turn, is then converted through a series of reactions into citramalyl-CoA. The citramalyl-CoA is split into pyruvate and Acetyl-CoA thanks to the enzyme MMC lyase. At this point the pyruvate is released, while the Acetyl-CoA is reused and carboxylated again at Malonyl-CoA thus reconstituting the cycle.

A total of 19 reactions are involved in 3-hydroxypropionate bicycle and 13 multifunctional enzymes are used. The multifunctionality of these enzymes is an important feature of this pathway which thus allows the fixation of three bicarbonate molecules.

It is a very expensive pathway: 7 ATP molecules are used for the synthesis of the new pyruvate and 3 ATP for the phosphate triose.

An important characteristic of this cycle is that it allows the co-assimilation of numerous compounds making it suitable for the mixotrophic organisms.

Cycles related to the 3-hydroxypropionate cycle
A variant of the 3-hydroxypropionate cycle was found to operate in the aerobic extreme thermoacidophile archaeon Metallosphaera sedula. This pathway is called the 3-hydroxypropionate/4-hydroxybutyrate cycle.

Yet another variant of the 3-hydroxypropionate cycle is the dicarboxylate/4-hydroxybutyrate cycle. It was discovered in anaerobic archaea. It was proposed in 2008 for the hyperthermophile archeon Ignicoccus hospitalis.

enoyl-CoA carboxylases/reductases
fixation is catalyzed by enoyl-CoA carboxylases/reductases.

Non-autotrophic pathways
Although no heterotrophs use carbon dioxide in biosynthesis, some carbon dioxide is incorporated in their metabolism. Notably pyruvate carboxylase consumes carbon dioxide (as bicarbonate ions) as part of gluconeogenesis, and carbon dioxide is consumed in various anaplerotic reactions.

6-phosphogluconate dehydrogenase catalyzes the reductive carboxylation of ribulose 5-phosphate to 6-phosphogluconate in E. coli under elevated CO2 concentrations.

Carbon isotope discrimination
Some carboxylases, particularly RuBisCO, preferentially bind the lighter carbon stable isotope carbon-12 over the heavier carbon-13. This is known as carbon isotope discrimination and results in carbon-12 to carbon-13 ratios in the plant that are higher than in the free air. Measurement of this ratio is important in the evaluation of water use efficiency in plants,  and also in assessing the possible or likely sources of carbon in global carbon cycle studies.