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Eukaryotic cells transmit information by signaling through complex networksof interacting proteins. Here we develop a theoretical and computationalframework that relates the biophysics of protein-protein interactions (PPIs)within a signaling network to its information processing properties. To do so,we generalize statistical physics-inspired models for protein binding toaccount for interactions that depend on post-translational state (e.g.phosphorylation). By combining these models with information-theoretic methods,we find that PPIs are a key determinant of information transmission within asignaling network, with weak interactions giving rise to "noise" thatdiminishes information transmission. While noise can be mitigated by increasinginteraction strength, the accompanying increase in transmission comes at theexpense of a slower dynamical response. This suggests that the biophysics ofsignaling protein interactions give rise to a fundamental "speed-information"trade-off. Surprisingly, we find that cross-talk between pathways in complexsignaling networks do not significantly alter information capacity--anobservation that may partially explain the promiscuity and ubiquity of weakPPIs in heavily interconnected networks. We conclude by showing how ourframework can be used to design synthetic biochemical networks that maximizeinformation transmission, a procedure we dub "InfoMax" design.

The strength of protein-protein interactions controls the information capacity and dynamical response of signaling networks