Although it is well known that highly expressed and highly interacting proteins evolve slowly across the tree of life, there is little consensus for why this is true. Here, I report that highly abundant and highly interacting proteins evolve slowly in the hypermutator populations of Lenski’s long-term evolution experiment with E. coli (LTEE). Specifically, the density of observed mutations per gene, as measured in metagenomic time series covering 60,000 generations of the LTEE, strongly anti-correlates with mRNA abundance, protein abundance, and degree of protein-protein interaction. Weaker positive correlations between protein thermostability and mutation density are observed in the hypermutator populations, counterbalanced by negative correlations between protein thermostability and mRNA and protein abundance. These results show that universal constraints on protein evolution are visible in data spanning three decades of experimental evolution. Therefore, it should be possible to design experiments to answer why highly expressed and highly interacting proteins evolve slowly.