We explored the unique signal integration properties of the self-assembling 60-mer protein capsid of adeno-associated virus (AAV), a clinically proven human gene therapy vector, by engineering proteolytic regulation of virus–receptor interactions such that processing of the capsid by proteases is required for infection. We find the transfer function of our engineered protease-activatable viruses (PAVs), relating the degree of proteolysis (input) to PAV activity (output), is highly nonlinear, likely due to increased polyvalency. By exploiting this dynamic polyvalency, in combination with the self-assembly properties of the virus capsid, we show that mosaic PAVs can be constructed that operate under a digital AND gate regime, where two different protease inputs are required for virus activation. These results show viruses can be engineered as signal-integrating nanoscale nodes whose functional properties are regulated by multiple proteolytic signals with easily tunable and predictable response surfaces, a promising development toward advanced control of gene delivery.