Supplementary Information includes Supplementary methods, 5 supplementary figures, 3 supplementary tables, and supplementary references. Supplementary MethodsΔΔG calculation. The ΔΔG of the 830 mutants in the quantitative dataset can be calculated in two ways: (1) by taking the difference between WT and mutant fitted ΔG(H 2 O) values given by the linear extrapolation method 1 (ΔΔG(H 2 O)), or (2) by taking the difference between WT and mutant C m values and multiplying by their mean m-value 2 (ΔΔG(m-avg)). The ΔΔG(m-avg) value avoids fitting issues near low denaturant values when estimating ΔG(H 2 O), but loses validity when variants greatly affect the m-value or the stability of the mutant protein 2,3 . As roughly 80% of the dataset has values ±1 kcal/mol away from WT, and the WT m-value is within 1 standard deviation of the mean m-value for the dataset, the m-avg method appears valid. After averaging repeat measurements, the two methods correlate extremely well (r = 0.99) with over 90% of the dataset differing by no more than 0.2 kcal/mol and none more than 1 kcal/mol ( Supplementary Fig. 2a). The only major difference between the methods is that the ΔΔG(H 2 O) method is less precise than the ΔΔG(m-avg) method ( Supplementary Fig. 2b), likely due to the uncertainties inherent in estimating ΔG(H 2 O) values. Thus, the mean of the ΔΔG(m-avg) values recorded for each variant (referred to as ΔΔG) were used for all further analysis.

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We present a combined computational and experimental method for the rapid optimization of proteins. Using ␤-lactamase as a test case, we redesigned the active site region using our Protein Design Automation technology as a computational screen to search the entire sequence space. By eliminating sequences incompatible with the protein fold, Protein Design Automation rapidly reduced the number of sequences to a size amenable to experimental screening, resulting in a library of Ϸ200,000 mutants. These were then constructed and experimentally screened to select for variants with improved resistance to the antibiotic cefotaxime. In a single round, we obtained variants exhibiting a 1,280-fold increase in resistance. To our knowledge, all of the mutations were novel, i.e., they have not been identified as beneficial by random mutagenesis or DNA shuffling or seen in any of the naturally occurring TEM ␤-lactamases, the most prevalent type of Gram-negative ␤-lactamases. This combined approach allows for the rapid improvement of any property that can be screened experimentally and provides a powerful broadly applicable tool for protein engineering.computational protein design ͉ protein engineering ͉ mutagenesis ͉ directed evolution ͉ ␤-lactamase