Inputs, outputs, and balancing the system
To make a cell-free enzyme system (or cell-free system, or CFS) useful, the goal is to make it completely regenerative and balanced with respect to co-factors and chemical energy so that the system needs minimal input. For instance, arguably the most famous carbon-fixation system is the Calvin Cycle, in which a cycle of reactions fixes a CO2 molecule to a growing sugar molecule and in the process consumes 3 ATP molecules to ADP and 2 NADPH molecules to NADP. As such, for the cycle to continue, ADP has to be converted back to ATP and NADP has to be converted back to NADPH. Plant cells handle this by using photosynthesis to generate the energy necessary to replenish these co-factors that are necessary for the Calvin Cycle. Similarly, any necessary co-factors for a carbon-fixation pathway utilized in a CFS would need to be replenished by auxiliary pathways or subsequent reactions in the carbon-fixation pathway. Ultimately, the system would ideally be designed to be completely balanced.
The simplest system would require no starting material, but could utilize CO2 and water to make a hydrocarbon and oxygen gas. This would likely require a fair bit of energy, typically converted from chemical, solar, electric and/or other energy sources into chemical energy stored in the form of ATP in the biological world. Theoretically, one could try to build a simplified version of this in a CFS, although cells typically use membranes and chemical gradients as tools to master these energy conversions, so there would be some engineering challenges to go that route.
+– Definitions and Units
Alkalinity - Constituents of a solution or water body, which are chemical bases that can neutralize acids. Alkaline rocks produce alkalinity when they dissolve.
BECCS – energy production via combustion of plant biomass with the capture and storage of the resulting carbon dioxide; a form of negative-emissions energy production.
Bicarbonate – a chemical compound composed of hydrogen, carbon and oxygen, with the formula - HCO3. This is very a common dissolved, ionic constituent of the Earth's hydrosphere/ocean and is the most abundant form of carbon on the Earth’s surface. Certain types of bicarbonate have important uses, e.g. sodium bicarbonate, NaHCO3, or baking soda.
CO2 - carbon dioxide; a colorless, odorless gas given off by the combustion of fossil fuels and other industrial processes, by the metabolism of biota and by volcanic and geothermal processes.
DAC – the capture and concentration of atmospheric CO2 by engineered chemical and/or physical means whose end product is concentrated CO2 that can be stored or used.
Gt – 1 billion metric tons, or tonnes, e.g., 1 Gt CO2 is equivalent to about 70 days of US CO2 emissions. 1 Gt CO2 would fill about 180,000 Goodyear blimps (which would not fly since CO2 is heavier than air).
H2 – hydrogen gas; typically formed by the splitting of water or methane.
IPCC – Intergovernmental Panel on Climate Change, under auspice of the United Nations
kWh – 1,000 watt hours of energy.
NE – negative CO2 emissions or carbon dioxide removal from the atmosphere, as caused by various natural and engineered processes.
OTEC – Ocean Thermal Energy Conversion; a method of converting the vertical thermal energy potential in the ocean to electrical energy.
Tonne – 1 metric ton = 1.1 US tons = 2204.6 lbs.
TWh – 1 trillion watt hours of energy; 1 Wh is the energy required to light a 60 watt bulb for 1 minute. 1 TWh = about 2 hours of energy consumption by the US. World energy consumption = 160,000 TWh per year.
Alternatively, one could design a system that fixes a carbon to another molecule (an input) and then uses the resulting product in further reactions, driving toward a productive output. The advantage of this is that the input would in essence provide a head start for the system and would likely make the system itself less complex. The disadvantage of course is that the input would have to be regenerated, much like the CO2 acceptor ribulose 1,5-bisphosphate is continually regenerated in the Calvin Cycle. Or alternatively it would be consumed, requiring the CFS to be "fed" input continually. As such, the input would need to be cheap and readily available in massive quantities.
One possible input that could be available in massive quantities would be a mineral, such as calcium or magnesium or alkaline rocks that could nucleate a precipitate of a solid carbonate, such as calcium carbonate, which has several extremely useful applications like as construction material. The advantage of an solid output such as calcium carbonate is that the CO2 is stable and can be disposed of or put to use without re-releasing the CO2 back into the atmosphere (at least not right away).
Controlling the system
Once a pathway (or pathways) have been designed, another massive challenge is figuring out where to put these enzymes and how do they gain access to atmospheric CO2? The most basic idea is a bioreactor full of salty water and enzymes. This reactor could potentially be controlled for temperature and pressure if necessary. In one scenario, the bioreactors are massive and in a large industrial facility, such as Chr. Hansen's ~300,000L fermenter facility in Denmark. The advantage of large centralized bioreactors is that power, systems, and maintenance would all be streamlined. The disadvantage is that it would require a large amount of up-front capital to build and would likely have high power and energy demands that in themselves could create CO2 emissions.
How could we get atmospheric CO2 into the bioreactor? The most straightforward approach is to bubble air into a closed system and then use back-pressure to increase the amount of CO2 dissolved in the solution. Alkaline solutions will also dissolve CO2 better, and since there are no living organisms in a CFS, we have the advantage of being able to raise the pH without having to worry about the viability of cells. Granted, we'd have to have enzymes that could function at higher pH, but that is far easier to engineer than an entire organism that functions at high pH.
Another way to get CO2 into the bioreactor would be to install these bioreactors next to facilities that generate a lot of CO2-rich exhaust, and funnel that exhaust into the bioreactor. This has the advantage of using the energy already expended by the target facility as the power source to bubble the CO2-rich air through the bioreactor. It also targets the richest sources of CO2 pollution. Companies like NovoNutrients and Blue Planet are already tackling these rich sources of CO2 and have demonstrated that it's possible to convert this into useful material.
If we wanted to avoid the massive up-front capital required to build and maintain huge bioreactor facilities, an alternative solution could be to make millions or billions of smaller bioreactors that could be sold commercially and installed in homes, farms, businesses, etc. For this to be reasonable and viable, the bioreactors would have to be relatively simple and require minimal maintenance, and they'd have to do something that gave a benefit to the consumer. The most obvious benefit would be that the output of the CFS was something common and useful to an individual, such as a daily consumable like food or soap or energy (e.g. ethanol). Of course, these individual bioreactors would break and need new enzymes and upgrades and the like continually, which would be a logistical nightmare, although it could spawn a new industry, with private businesses emerging that specialize in servicing and maintaining these bioreactors for the consumer.
If we really want to dream big, and we want to avoid the whole bioreactor challenge altogether, we could potentially put the enzymes in membrane "bubbles" and drop them in the ocean. The membranes would be permeable to water, air, dissolved ions, and small molecules (e.g. the output of the system) but would keep out larger molecules like proteases (proteins that destroy other proteins) and living organisms. The advantage here is that the enzymes would have access to CO2 via passive diffusion from the air and dissolved bicarbonate in the ocean water. This would limit the energy requirements of the system. The disadvantage is that these membranes would inevitably tear or otherwise be destroyed and new CFS "bubbles" would have to be continually manufactured and dropped into the ocean. In addition, since the membranes would be in the ocean, ideally they would not be harmful to sea life or damaging to the ecosystem. The material would have to be simultaneously resilient and strong enough to survive in the ocean, but also able to break down if eaten by a sea creature. I imagine such a material would be very difficult to develop!