Although artificial neural networks are powerful classifiers, their internal structures are hard to interpret. In the life sciences, extensive knowledge of cell biology provides an opportunity to design visible neural networks (VNNs) that couple the model's inner workings to those of real systems. Here we develop DCell, a VNN embedded in the hierarchical structure of 2,526 subsystems comprising a eukaryotic cell (http://d-cell.ucsd.edu/). Trained on several million genotypes, DCell simulates cellular growth nearly as accurately as laboratory observations. During simulation, genotypes induce patterns of subsystem activities, enabling in silico investigations of the molecular mechanisms underlying genotype-phenotype associations. These mechanisms can be validated, and many are unexpected; some are governed by Boolean logic. Cumulatively, 80% of the importance for growth prediction is captured by 484 subsystems (21%), reflecting the emergence of a complex phenotype. DCell provides a foundation for decoding the genetics of disease, drug resistance and synthetic life.