Covalent modification cycles through the spatial prism.

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.