Living organisms that have cells that do not have nuclei (no brain)are called

prokaryotic: Small cells in the domains Bacteria and Archaea that do not contain a membrane-bound nucleus or other membrane-bound organelles

The electrochemical proton gradient across the inner mitochondrial membrane is used to drive ATP synthesis in the critical process of oxidative phosphorylation. This is made possible by the membrane-bound enzyme ATP synthase, mentioned previously.