  Designing novel proteins with desired functions is crucial in biology and
chemistry. However, most existing work focus on protein sequence design,
leaving protein sequence and structure co-design underexplored. In this paper,
we propose GeoPro, a method to design protein backbone structure and sequence
jointly. Our motivation is that protein sequence and its backbone structure
constrain each other, and thus joint design of both can not only avoid
nonfolding and misfolding but also produce more diverse candidates with desired
functions. To this end, GeoPro is powered by an equivariant encoder for
three-dimensional (3D) backbone structure and a protein sequence decoder guided
by 3D geometry. Experimental results on two biologically significant
metalloprotein datasets, including $\beta$-lactamases and myoglobins, show that
our proposed GeoPro outperforms several strong baselines on most metrics.
Remarkably, our method discovers novel $\beta$-lactamases and myoglobins which
are not present in protein data bank (PDB) and UniProt. These proteins exhibit
stable folding and active site environments reminiscent of those of natural
proteins, demonstrating their excellent potential to be biologically
functional.
