Multi-scale reactor designs extend the physical limits of fixation

$$ valorization is a promising strategy for climate adaptation and transitioning towards a circular carbon economy. Here, we present a multi-scale, integrated systems approach for designing biomanufacturing systems that can utilize $$ as a feedstock, focusing on the Wood-Ljungdahl and reductive glycine pathways. This approach relies on first principles, coupling the optimization of pathway and process variables. We examine the $$ -fixation capacity of both pathways in single- and multi-compartment reactor systems, demonstrating that the reductive glycine pathway has the potential to fix $$ at significantly higher rates than photosynthetic organisms. We show that small differences in the energy-dissipative and stoichiometric structures of carbon-fixation pathways could significantly impact optimal designs and feasible design spaces. Our first-principle, systems-level approach quantifies these differences and uncovers strategies to expand the design space and extend the physical limits of carbon fixation, offering insights into pathway selection and process configurations for efficient biomanufacturing.