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Optimising the function of a protein of length N amino acids by directed evolution involves navigating a 'search space' of possible sequences of some 20N. Optimising the expression levels of P proteins that materially affect host performance, each of which might also take 20 (logarithmically spaced) values, implies a similar search space of 20P. In this combinatorial sense, then, the problems of directed protein evolution and of host engineering are broadly equivalent. In practice, however,doi:10.1042/bcj20210535 pmid:34673920 pmcid:PMC8589332 fatcat:difpodhky5c3vcmmchymd6csl4