  The design of \emph{de novo} functional proteins that bind specific ligand
molecules is paramount in therapeutics and bio-engineering. A critical yet
formidable task in this endeavor is the design of the protein pocket, which is
the cavity region of the protein where the ligand binds. Current methods are
plagued by inefficient generation, inadequate context modeling of the ligand
molecule, and the inability to generate side-chain atoms. Here, we present the
Full-Atom Iterative Refinement (FAIR) method, designed to address these
challenges by facilitating the co-design of protein pocket sequences,
specifically residue types, and their corresponding 3D structures. FAIR
operates in two steps, proceeding in a coarse-to-fine manner (transitioning
from protein backbone to atoms, including side chains) for a full-atom
generation. In each iteration, all residue types and structures are
simultaneously updated, a process termed full-shot refinement. In the initial
stage, the residue types and backbone coordinates are refined using a
hierarchical context encoder, complemented by two structure refinement modules
that capture both inter-residue and pocket-ligand interactions. The subsequent
stage delves deeper, modeling the side-chain atoms of the pockets and updating
residue types to ensure sequence-structure congruence. Concurrently, the
structure of the binding ligand is refined across iterations to accommodate its
inherent flexibility. Comprehensive experiments show that FAIR surpasses
existing methods in designing superior pocket sequences and structures,
producing average improvement exceeding 10\% in AAR and RMSD metrics. FAIR is
available at \url{https://github.com/zaixizhang/FAIR}.
