Efforts to construct therapeutically useful models of biological systems require large and diverse sets of data on functional connections between their components. Here we show that cellular responses to combinations of chemicals reveal how their biological targets are connected. Simulations of pathways with pairs of inhibitors at varying doses predict distinct response surface shapes that are reproduced in a yeast experiment, with further support from a larger screen using human tumour cells. The response morphology yields detailed connectivity constraints between nearby targets, and synergy profiles across many combinations show relatedness between targets in the whole network. Constraints from chemical combinations complement genetic studies, because they probe different cellular components and can be applied to disease models that are not amenable to mutagenesis. Chemical probes also offer increased flexibility, as they can be continuously dosed, temporally controlled, and readily combined. After extending this initial study to cover a wider range of combination effects and pathway topologies, chemical combinations may be used to refine network models or to identify novel targets. This response surface methodology may even apply to non-biological systems where responses to targeted perturbations can be measured.