Maybe functional enzymes can be expressed in yeast, but efficient carbon fixation requires great amounts of reducing power (NADPH), which is mainly produced through photophosphorylation... so, you would also need to introduce a system for light absorption and energy transduction.

The alternative would be coupling these reactions to another process able to produce reducing power in yeast, such as Krebs cycle, but I don't think that would be efficient enough and probably would have a negative effect on yeast growth.

You could also look at how chemotrophs acquire energy to reduce chemical bonds. Either way energy will need to be supplied in some form.

From Wikipedia: Chemoautotrophs (or chemotrophic autotroph), (Gr: Chemo (χημία) = chemical, auto (αὐτός) = self, troph (τροφιά) = nourishment) in addition to deriving energy from chemical reactions, synthesize all necessary organic compounds from carbon dioxide. Chemoautotrophs use inorganic energy sources, such as hydrogen sulfide, elemental sulfur, ferrous iron, molecular hydrogen, and ammonia. Most are bacteria or archaea that live in hostile environments such as deep sea vents and are the primary producers in such ecosystems. Evolutionary scientists believe that the first organisms to inhabit Earth were chemoautotrophs that produced oxygen as a by-product and later evolved into both aerobic, animal-like organisms and photosynthetic, plant-like organisms.[citation needed] Chemoautotrophs generally fall into several groups: methanogens, halophiles, sulfur oxidizers and reducers, nitrifiers, anammox bacteria, and thermoacidophiles. Chemolithotrophic growth could be dramatically fast, such as Thiomicrospira crunogena with a doubling time around one hour.[1]

Why do you want your yeast to consume CO2?

Like mentioned by the others, fixing CO2 uses a large amount of energy that has to come from somewhere. Most CO2 fixation is done by photosynthesising organisms.

Depending on your application, you could have a photosynthetic organism, consuming CO2, which in turn produced the carbon source for your yeast.

So you are trying to make a new kind of algae from yeast by addition of light-gathering systems from cyanobacteria?

I am trying to obtain a new type of host that uses the most common carbon source while having the protein production complexity of yeast.

I thought of using the combination of two organisms but it will not be as useful for pharmaceutical production like the use of one.

If you put rubisco in yeast, and then just provide CO2 as a carbon source in the media, maybe you can get the yeast to grow, because of induction of other genes. I think I read that people tried to put RUBISCO in yeast, but it did not work. But you would also have to feed the yeast the sugar substrate besides CO2 that the RUBISCO uses. I would look for papers where RUBISCO was put in yeast.

I don't think you need the light gathering system. Can't fixing CO2 be uncoupled from photosynthesis?

There are some bacteria that can do chemoautotrophe production so the light gathering can be eliminated but only if the yeast would accept the bacterila genes. As for the RUBISCO use...what I am trying to do is to eliminate the use of any other carobn source other than CO2 in order to make the yest more cheaper to cultivate.

My idea would be to put the enzymes that make formate and formaldehyde to dihydroxyacetone under the control of some kind of inducible promoter, so that when glucose products are made, the products that are made from the CO2 could be used to induce the enzymes. and then select for the yeast molecules that grow. So formate dehydrogenase and formaldehyde dehydrogenase are the enzymes to express this way perhaps?

Do yeast even have carbonic anhydrase, formate and formaldehyde dehydrogenase genes? I have never used them before, but I would engineer them to have the enzymes, and then just grow them on CO2 as the sole carbon source. The ones that live, will multiply, and then save for starter cultures.

Maybe you can save the world! Good luck.

To covert the formaldehyde to dihydroxyacetone (phosphate), you need to use an engineered enzyme, that people have made. I don't believe there is a naturally occurring enzyme that does this. It is called Formolose. I imagine there are restrictions for using this enzyme.

Actually, formaldehyde can be converted to ethylene glycol in yeast, and then dihydroxyacetone synthase is used. So I retract my statement above. The yeast should be able to do all the reactions to make the units needed for glycolysis. But I would pick a strain that uses methanol, to begin with.

But perhaps knock out private decarboxylase so that the yeast don't make co2 and ethanol, and use the pyruvate to make amino acids, etc instead.

Not private, but pyruvate. I hate spellcheck.

What are the cells going to use for their energy source?

They use up 3 NADPH units to make methanol. Then thEy loose some if pyruvate decarboxylase is mutated. The pyruvate could be used as a energy source in the mitochondria by pyruvate dehydrogenase and to make amino acids, etc. Glycolysis still occurs. So what energy source were you thinking of? Can methanotrophs use MEOH as a sole carbon source? I don't know the answer to your question. It would seem that they would need an energy source since making meoH from CO2 would use a lot of energy. maybe you can just have CO2 as the major carbon source?

So I guess you want to put photosystem1 of Cyanobacteria into methanotrophic yeast?