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The assembly of proteins into functional complexes is critical to life's processes. While textbooks depict complex assembly as occurring between fully synthesized proteins, we know today that thousands of proteins in the human proteome assemble co-translationally during their synthesis. Why this process takes place, however, remains unknown. We show that co-translational assembly is governed by biophysical and structural characteristics of the protein complex, and involves mutually stabilized, intertwined subunits. Consequently, these subunits are also co-regulated across the central dogma, from transcription to protein degradation. Leveraging structural signatures with AlphaFold2-based predictions enables us to accurately predict co-translational assembly on a proteome-wide scale, which we validated by ribosome profiling, genetic perturbations, and smFISH experiments. Notably, the latter showed that co-translationally assembling subunits exhibit co-localized mRNAs. This work unveils a fundamental connection between protein structure and the translation process, highlighting the overarching impact of three-dimensional structure on gene expression, mRNA localization, and proteostasis.