(a) Two-layer protease-cascade function with a catalytically inactive split tobacco etch virus protease (TEVp*) domain fused to the autoinhibitory CC shows decreased leakage and higher fold activation (see also Supplementary Fig. 11). (b) Double inverter consisting of a split TEVp regulated by split plum pox virus protease (PPVp), where PPVp is regulated by the rapamycin-induced split soybean mosaic virus protease (SbMVp). (c) B nimply A logic function combining human immunodeficiency virus-1 (HIV-1p) and PPVp as input signals. “SQVSQNYPIVQNLQ” recognition sequence for HIV-1 protease was used. Transfection plasmid mixtures are listed in Supplementary Table 1, 4. Values are the mean of three (c) and four (a,b) cell cultures ± (s.d.) and are representative of at least two independent experiments, significance tested by 1-way ANOVA with Tukey’s comparison between the indicated ON and OFF states (CI=95%, df=11, F=72 (c)).